Python Tutorial.ipynb

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    "from IPython.display import display\n",
    "from IPython.core.display import HTML\n",
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   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Introduction-\" data-toc-modified-id=\"Introduction--1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Introduction <a class=\"anchor\" id=\"intro\" rel=\"nofollow\"></a></a></span></li><li><span><a href=\"#Python-\" data-toc-modified-id=\"Python--2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Python <a class=\"anchor\" id=\"pythonprimer\" rel=\"nofollow\"></a></a></span><ul class=\"toc-item\"><li><span><a href=\"#Containers\" data-toc-modified-id=\"Containers-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Containers</a></span></li><li><span><a href=\"#List-comprehension\" data-toc-modified-id=\"List-comprehension-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>List comprehension</a></span></li><li><span><a href=\"#Indexing\" data-toc-modified-id=\"Indexing-2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>Indexing</a></span></li><li><span><a href=\"#Printing\" data-toc-modified-id=\"Printing-2.4\"><span class=\"toc-item-num\">2.4&nbsp;&nbsp;</span>Printing</a></span></li></ul></li><li><span><a href=\"#NumPy-\" data-toc-modified-id=\"NumPy--3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>NumPy <a class=\"anchor\" id=\"numpy\" rel=\"nofollow\"></a></a></span><ul class=\"toc-item\"><li><span><a href=\"#Array-Creation\" data-toc-modified-id=\"Array-Creation-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Array Creation</a></span></li><li><span><a href=\"#In-place-operations\" data-toc-modified-id=\"In-place-operations-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>In-place operations</a></span></li><li><span><a href=\"#Broadcasting-(IMPORTANT!)\" data-toc-modified-id=\"Broadcasting-(IMPORTANT!)-3.3\"><span class=\"toc-item-num\">3.3&nbsp;&nbsp;</span>Broadcasting <strong>(IMPORTANT!)</strong></a></span></li><li><span><a href=\"#Indexing-and-Slicing\" data-toc-modified-id=\"Indexing-and-Slicing-3.4\"><span class=\"toc-item-num\">3.4&nbsp;&nbsp;</span>Indexing and Slicing</a></span></li><li><span><a href=\"#Stacking-and-Concatenation\" data-toc-modified-id=\"Stacking-and-Concatenation-3.5\"><span class=\"toc-item-num\">3.5&nbsp;&nbsp;</span>Stacking and Concatenation</a></span></li><li><span><a href=\"#Logic-operations\" data-toc-modified-id=\"Logic-operations-3.6\"><span class=\"toc-item-num\">3.6&nbsp;&nbsp;</span>Logic operations</a></span></li><li><span><a href=\"#np.array-vs.-np.matrix---whats-the-difference?\" data-toc-modified-id=\"np.array-vs.-np.matrix---whats-the-difference?-3.7\"><span class=\"toc-item-num\">3.7&nbsp;&nbsp;</span>np.array vs. np.matrix - whats the difference?</a></span></li><li><span><a href=\"#Views\" data-toc-modified-id=\"Views-3.8\"><span class=\"toc-item-num\">3.8&nbsp;&nbsp;</span>Views</a></span></li><li><span><a href=\"#Other-manipulations\" data-toc-modified-id=\"Other-manipulations-3.9\"><span class=\"toc-item-num\">3.9&nbsp;&nbsp;</span>Other manipulations</a></span></li><li><span><a href=\"#Aggregations\" data-toc-modified-id=\"Aggregations-3.10\"><span class=\"toc-item-num\">3.10&nbsp;&nbsp;</span>Aggregations</a></span></li><li><span><a href=\"#Basic-Mathematical-Operations\" data-toc-modified-id=\"Basic-Mathematical-Operations-3.11\"><span class=\"toc-item-num\">3.11&nbsp;&nbsp;</span>Basic Mathematical Operations</a></span><ul class=\"toc-item\"><li><span><a href=\"#np.dot,-np.multiply,-np.matmul\" data-toc-modified-id=\"np.dot,-np.multiply,-np.matmul-3.11.1\"><span class=\"toc-item-num\">3.11.1&nbsp;&nbsp;</span>np.dot, np.multiply, np.matmul</a></span></li><li><span><a href=\"#Linear-algebra\" data-toc-modified-id=\"Linear-algebra-3.11.2\"><span class=\"toc-item-num\">3.11.2&nbsp;&nbsp;</span>Linear algebra</a></span></li></ul></li><li><span><a href=\"#Filtering\" data-toc-modified-id=\"Filtering-3.12\"><span class=\"toc-item-num\">3.12&nbsp;&nbsp;</span>Filtering</a></span></li><li><span><a href=\"#Sampling\" data-toc-modified-id=\"Sampling-3.13\"><span class=\"toc-item-num\">3.13&nbsp;&nbsp;</span>Sampling</a></span></li><li><span><a href=\"#ufuncs\" data-toc-modified-id=\"ufuncs-3.14\"><span class=\"toc-item-num\">3.14&nbsp;&nbsp;</span>ufuncs</a></span></li><li><span><a href=\"#Accessing-array-attributes\" data-toc-modified-id=\"Accessing-array-attributes-3.15\"><span class=\"toc-item-num\">3.15&nbsp;&nbsp;</span>Accessing array attributes</a></span></li><li><span><a href=\"#Good-practices\" data-toc-modified-id=\"Good-practices-3.16\"><span class=\"toc-item-num\">3.16&nbsp;&nbsp;</span>Good practices</a></span></li></ul></li><li><span><a href=\"#Matplotlib\" data-toc-modified-id=\"Matplotlib-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Matplotlib</a></span><ul class=\"toc-item\"><li><span><a href=\"#Creating-a-plot\" data-toc-modified-id=\"Creating-a-plot-4.1\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>Creating a plot</a></span></li><li><span><a href=\"#Styling-a-plot\" data-toc-modified-id=\"Styling-a-plot-4.2\"><span class=\"toc-item-num\">4.2&nbsp;&nbsp;</span>Styling a plot</a></span><ul class=\"toc-item\"><li><span><a href=\"#Subplots\" data-toc-modified-id=\"Subplots-4.2.1\"><span class=\"toc-item-num\">4.2.1&nbsp;&nbsp;</span>Subplots</a></span></li></ul></li><li><span><a href=\"#Built-in-stylesheets\" data-toc-modified-id=\"Built-in-stylesheets-4.3\"><span class=\"toc-item-num\">4.3&nbsp;&nbsp;</span>Built in stylesheets</a></span></li></ul></li><li><span><a href=\"#SciPy\" data-toc-modified-id=\"SciPy-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>SciPy</a></span><ul class=\"toc-item\"><li><span><a href=\"#scipy.stats\" data-toc-modified-id=\"scipy.stats-5.1\"><span class=\"toc-item-num\">5.1&nbsp;&nbsp;</span>scipy.stats</a></span></li><li><span><a href=\"#scipy.fft\" data-toc-modified-id=\"scipy.fft-5.2\"><span class=\"toc-item-num\">5.2&nbsp;&nbsp;</span>scipy.fft</a></span></li><li><span><a href=\"#scipy.linalg\" data-toc-modified-id=\"scipy.linalg-5.3\"><span class=\"toc-item-num\">5.3&nbsp;&nbsp;</span>scipy.linalg</a></span></li><li><span><a href=\"#scipy.special\" data-toc-modified-id=\"scipy.special-5.4\"><span class=\"toc-item-num\">5.4&nbsp;&nbsp;</span>scipy.special</a></span></li></ul></li><li><span><a href=\"#Other-Native-Python-Libraries\" data-toc-modified-id=\"Other-Native-Python-Libraries-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Other Native Python Libraries</a></span></li><li><span><a href=\"#3rd-party-libraries\" data-toc-modified-id=\"3rd-party-libraries-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>3rd-party libraries</a></span></li><li><span><a href=\"#Optimizations\" data-toc-modified-id=\"Optimizations-8\"><span class=\"toc-item-num\">8&nbsp;&nbsp;</span>Optimizations</a></span><ul class=\"toc-item\"><li><span><a href=\"#JAX\" data-toc-modified-id=\"JAX-8.1\"><span class=\"toc-item-num\">8.1&nbsp;&nbsp;</span>JAX</a></span></li></ul></li><li><span><a href=\"#Exercises\" data-toc-modified-id=\"Exercises-9\"><span class=\"toc-item-num\">9&nbsp;&nbsp;</span>Exercises</a></span></li></ul></div>"
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   "source": [
    "# Introduction <a class=\"anchor\" id=\"intro\"></a>"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "This notebook is intended to give a crash course on how to effectively use common python packages for data science, scientific computing, and visualization. Good practices are too often neglected and lead to inefficient, slow-to-update and code chock full of bugs.\n",
    "\n",
    "We will first go over some fundamentals of Python as a refresher, as a prerequisite to some of the more efficient routines in NumPy. Next, we will go over the basics of the main data structures and manipulations in NumPy. We will then look at using Matplotlib for visualization, and finish off with some common functions and methods in SciPy as well as a couple of brief practical examples. At the end there is a optional section for those interested that covers some additional tips, tricks and good practices, with links to suggested reading material."
   ]
  },
  {
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   "metadata": {},
   "source": [
    "# Python <a class=\"anchor\" id=\"pythonprimer\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://docs.python.org/3/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Containers\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This section will quickly go over the most commonly used Python data structures."
   ]
  },
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      "Empty list using []:  []\n",
      "Empty list using list()  []\n",
      "Homogeneous list:  [3, 4, 1, 2]\n",
      "Heterogeneous list:  [3, 4, 1, 2]\n",
      "List of range of values:  [0, 1, 2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "# empty list\n",
    "a = []\n",
    "print('Empty list using []: ', a)\n",
    "a = list()\n",
    "print('Empty list using list() ', a)\n",
    "\n",
    "# list with homogeneous types\n",
    "a = [3, 4, 1, 2]\n",
    "print('Homogeneous list: ', a)\n",
    "\n",
    "# list with heterogeneous types\n",
    "b = [\"apple\", 3, True, \"meaning of life is 42\"]\n",
    "print('Heterogeneous list: ', a)\n",
    "\n",
    "# range of values\n",
    "a = list(range(5))\n",
    "print('List of range of values: ', a)\n",
    "\n"
   ]
  },
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      "Empty dict using dict():  {}\n",
      "Empty dict using  {}:  {}\n",
      "{'hello': 3, 'foo': 'bar'}\n",
      "{'tree': {'subtree': {'leaf': 5}}}\n"
     ]
    }
   ],
   "source": [
    "empty_dict1 = dict()\n",
    "empty_dict2 = {}\n",
    "dict_1 = {'hello': 3, 'foo': 'bar'}\n",
    "dict_2 = {'tree':{'subtree':{'leaf':5}}}\n",
    "print('Empty dict using dict(): ', empty_dict1)\n",
    "print('Empty dict using  {}: ', empty_dict2)\n",
    "print(dict_1)\n",
    "print(dict_2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
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     "name": "stdout",
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     "text": [
      "Third element of the tuple:  apple\n",
      "First element of the tuple:  3\n",
      "Second element of the tuple:  2\n"
     ]
    }
   ],
   "source": [
    "# Underscores signal that you don't care about the assignment of the corresponding elements\n",
    "x = (3,2,\"apple\")\n",
    "_, _, c = x\n",
    "\n",
    "print('Third element of the tuple: ', c)\n",
    "a, b, _ = x\n",
    "print('First element of the tuple: ', a)\n",
    "print('Second element of the tuple: ', b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## List comprehension"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rather than spreading nests of for loops over many lines, you can use list comprehension to simplify the readability of your code."
   ]
  },
  {
   "cell_type": "code",
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     "text": [
      "Using for loops:\n",
      "  [2, 4, 10, 24, 10]\n",
      "Using list comprehension:\n",
      "  [2, 4, 10, 24, 10]\n",
      "Using for loops:\n",
      "  [(1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3)]\n",
      "Using list comprehension:\n",
      "  [(1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3), (1, 2, 3)]\n"
     ]
    }
   ],
   "source": [
    "# Single for-loop\n",
    "a1 = [1,2,5,12,5]\n",
    "comb = []\n",
    "for i in a1:\n",
    "  comb.append(2*i)\n",
    "\n",
    "print('Using for loops:\\n ', comb)\n",
    "\n",
    "# list comprehension equivalent\n",
    "comb_lc = [2*i for i in a1]\n",
    "print('Using list comprehension:\\n ', comb_lc)\n",
    "\n",
    "# Nested for-loops\n",
    "b1 = [1,1,1]\n",
    "b2 = [2,2,2]\n",
    "b3 = [3,3,3]\n",
    "combined = []\n",
    "\n",
    "for i in b1:\n",
    "  for j in b2:\n",
    "    for k in b3:\n",
    "      combined.append((i, j, k))\n",
    "print('Using for loops:\\n ', combined)\n",
    "\n",
    "# list comprehension equivalent\n",
    "combined_lc = [(i,j,k) for i in b1 for j  in b2 for k in b3]\n",
    "print('Using list comprehension:\\n ', combined_lc)"
   ]
  },
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   "metadata": {},
   "source": [
    "## Indexing\n",
    "\n",
    "Indexing is generally exclusive (half-open interval, `[start, stop)`). Be careful of one off errors.\n",
    "\n",
    "You can index in a collection with positive indices (which correspond directly to the element index), or negative indices (which denotes the position relative to the end of the collection).\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Positive indexing:  3\n",
      "Negative indexing:  6\n"
     ]
    }
   ],
   "source": [
    "a = [1,2,3,4,5,6,7]\n",
    "print('Positive indexing: ', a[2])\n",
    "print('Negative indexing: ', a[-2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Printing"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can choose to format standard output in many different ways. Below are three of the most commonly used:\n",
    "1. Printing multiple strings by passing as separate arguments\n",
    "2. Using the `%` operator\n",
    "3. Using `.format()`\n",
    "4. f-strings\n",
    "\n",
    "The code below illustrates each with an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This string was printed using different arguments\n",
      "Number 1 is 31 while number 2 is 23\n",
      "Mean of x is 3.85 and pi is 3.1400 \n",
      "My response is foo bar.\n"
     ]
    }
   ],
   "source": [
    "print('This string was', 'printed using', 'different arguments')\n",
    "print('Number 1 is %d while number 2 is %d' % (31, 23))\n",
    "print('{0} is {1:.2f} and pi is {2:.4f} '.format(\"Mean of x\", (3.5 + 4.2)/2, 3.14))\n",
    "\n",
    "x = \"foo\"\n",
    "\n",
    "print(f\"My response is {x} bar.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also ignore escape characters by using r-strings (raw):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Characters not escaped \\n \\r \\t \\b\n"
     ]
    }
   ],
   "source": [
    "print(r'Characters not escaped \\n \\r \\t \\b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is useful especially when you want to format LaTeX in matplotlib charts later on, as we'll see in a later section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard printing has a lot to be desired in terms of ease of formatting and customizability. We can often use the `pprint` module to make our lives easier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of lists printed using print: \n",
      " [[[['mac n cheese'], 'one,', 'two', 'three']], [['mac n cheese'], 'one,', 'two', 'three']]\n",
      "List of lists printed using pprint: \n",
      " [[[['mac n cheese'], 'one,', 'two', 'three']], [['mac n cheese'], 'one,', 'two', 'three']]\n",
      "[  [[['mac n cheese'], 'one,', 'two', 'three']],\n",
      "   [['mac n cheese'], 'one,', 'two', 'three']]\n"
     ]
    }
   ],
   "source": [
    "import pprint\n",
    "\n",
    "a = [[['mac n cheese'], 'one,', 'two', 'three', ]]\n",
    "a.insert(0,a[:])\n",
    "\n",
    "# standard print\n",
    "print('List of lists printed using print: \\n', a)\n",
    "\n",
    "# pprint output\n",
    "print('List of lists printed using pprint: \\n', a)\n",
    "pp = pprint.PrettyPrinter(indent=3)\n",
    "pp.pprint(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy <a class=\"anchor\" id=\"numpy\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://numpy.org/doc/stable/reference/index.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NumPy has become the de-facto Python package for scientific computing. It enables fast and efficient computation and is broadly useful in machine learning and statistical methods. All manipulations are done on an essential data structure called an `NDArray`, which is a representation of a (multi)-dimensional array or matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array Creation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most common way to create a numpy array is to instantiate one with `np.zeros`. It takes as an argument the desired shape of the output array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0.]\n",
      "[[0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.zeros((2,)))\n",
    "print(np.zeros((3,5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to initialize your array with all ones, or with any other number, you can use either `np.ones` or `np.full`, respectively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      "[[3.7 3.7 3.7 3.7]\n",
      " [3.7 3.7 3.7 3.7]\n",
      " [3.7 3.7 3.7 3.7]\n",
      " [3.7 3.7 3.7 3.7]\n",
      " [3.7 3.7 3.7 3.7]]\n"
     ]
    }
   ],
   "source": [
    "print(np.ones((10,)))\n",
    "print(np.full((5,4), 3.7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arrays can also be created from existing Pythonic data structures like lists:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is a python list:  [[3, 5], [2, 4], [8, 6]]\n",
      "Converted to a NumPy array:\n",
      "  [[3 5]\n",
      " [2 4]\n",
      " [8 6]] \n",
      "\n",
      "This is a python dictionary:  {'foo': 3, 'bar': 8, 'apple': 2, 'orange': 4}\n",
      "Converted to a NumPy array:\n",
      "  [['foo' '3']\n",
      " ['bar' '8']\n",
      " ['apple' '2']\n",
      " ['orange' '4']]\n",
      "[['foo' '3']\n",
      " ['bar' '8']\n",
      " ['apple' '2']\n",
      " ['orange' '4']]\n"
     ]
    }
   ],
   "source": [
    "python_list = [[3,5],[2,4],[8,6]]\n",
    "print('This is a python list: ', python_list)\n",
    "arr = np.array(python_list)\n",
    "print('Converted to a NumPy array:\\n ', arr, '\\n')\n",
    "\n",
    "python_dict = {'foo': 3, 'bar': 8, 'apple': 2, 'orange': 4}\n",
    "print('This is a python dictionary: ', python_dict)\n",
    "arr = np.array(list(python_dict.items()))\n",
    "\n",
    "print('Converted to a NumPy array:\\n ', arr)\n",
    "\n",
    "\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create a grid of coordinates, `np.meshgrid` or `np.mgrid` come in handy. Both have the same functionality but slightly different syntax, and the syntax itself can be confusing. \n",
    "\n",
    "With `np.meshgrid`, the arguments are 1D arrays representing the desired ranges along each coordinate axes. \n",
    "\n",
    "With `np.mgrid`, you use indexing notation (see the Indexing section). Complex valued step lengths indicate the number of points to generate between the start and stop indices, rather than the step size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([[2, 3, 4, 5],\n",
      "       [2, 3, 4, 5],\n",
      "       [2, 3, 4, 5],\n",
      "       [2, 3, 4, 5],\n",
      "       [2, 3, 4, 5]]), array([[0, 0, 0, 0],\n",
      "       [1, 1, 1, 1],\n",
      "       [2, 2, 2, 2],\n",
      "       [3, 3, 3, 3],\n",
      "       [4, 4, 4, 4]])]\n"
     ]
    }
   ],
   "source": [
    "# Using np.meshgrid\n",
    "x = np.arange(2,6)\n",
    "y = np.arange(5)\n",
    "print(np.meshgrid(x, y))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[2 2 2 2]\n",
      "  [3 3 3 3]\n",
      "  [4 4 4 4]\n",
      "  [5 5 5 5]]\n",
      "\n",
      " [[0 1 2 3]\n",
      "  [0 1 2 3]\n",
      "  [0 1 2 3]\n",
      "  [0 1 2 3]]]\n",
      "\n",
      "\n",
      "[[[1.  1.  1.  1.  1.  1. ]\n",
      "  [2.  2.  2.  2.  2.  2. ]]\n",
      "\n",
      " [[0.  0.8 1.6 2.4 3.2 4. ]\n",
      "  [0.  0.8 1.6 2.4 3.2 4. ]]]\n"
     ]
    }
   ],
   "source": [
    "# Using np.mgrid\n",
    "print(np.mgrid[2:6,0:4])\n",
    "print('\\n')\n",
    "\n",
    "# Using np.mgrid, complex-valued step size\n",
    "print(np.mgrid[1:3,0:4:6j])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create an array of evenly spaced values between a range, we can use either `np.arange` or `np.linspace` functions. **These are not the same!** `np.arange` outputs values over a half open interval, from [start, end); values from `np.linspace`, on the other hand, are returned over a completely closed interval [start, end]. In addition, `np.arange` asks for a  *step size*, while np.linspace asks for a *number of steps*.\n",
    "\n",
    "Both functions take the arguments (start, stop, step).  Some of these are optional; you can refer to the documentation for more information. You can use integers as well as floating points values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "np.arange output:\n",
      "  [0 1 2 3 4 5 6 7 8 9]\n",
      "np.linspace output:\n",
      "  [ 0.          0.52631579  1.05263158  1.57894737  2.10526316  2.63157895\n",
      "  3.15789474  3.68421053  4.21052632  4.73684211  5.26315789  5.78947368\n",
      "  6.31578947  6.84210526  7.36842105  7.89473684  8.42105263  8.94736842\n",
      "  9.47368421 10.        ]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(0,10,1)\n",
    "x2 = np.linspace(0,10,20)\n",
    "\n",
    "print('np.arange output:\\n ', x)\n",
    "print('np.linspace output:\\n ', x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often times if you are working over a large dataset, you may want to creating the same large array over and over in memory, especially if you only need to modify one instance of it at a time. NumPy allows you to perform operations *in place* rather than needing to create a modified version of an array all the time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In-place operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is unmodified using np.sort: [2 3 5 1]\n",
      "y contains the new modified, sorted array [2 3 5 1]\n",
      "x is directly sorted using a.sort(): [1 2 3 5]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([2,3,5,1])\n",
    "y = np.sort(x)\n",
    "print('x is unmodified using np.sort:', x)\n",
    "print('y contains the new modified, sorted array', x)\n",
    "\n",
    "x.sort()\n",
    "print('x is directly sorted using a.sort():', x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pythonic infix operators already modify variables in-place, and the extended functionality NumPy provides on arrays is no different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addition:\n",
      "  [[2. 1. 1. 1. 1.]\n",
      " [1. 2. 1. 1. 1.]\n",
      " [1. 1. 2. 1. 1.]\n",
      " [1. 1. 1. 2. 1.]\n",
      " [1. 1. 1. 1. 2.]]\n",
      "Division:\n",
      "  [[5.  2.5 2.5 2.5 2.5]\n",
      " [2.5 5.  2.5 2.5 2.5]\n",
      " [2.5 2.5 5.  2.5 2.5]\n",
      " [2.5 2.5 2.5 5.  2.5]\n",
      " [2.5 2.5 2.5 2.5 5. ]]\n",
      "Multiplication:\n",
      "  [[30. 15. 15. 15. 15.]\n",
      " [15. 30. 15. 15. 15.]\n",
      " [15. 15. 30. 15. 15.]\n",
      " [15. 15. 15. 30. 15.]\n",
      " [15. 15. 15. 15. 30.]]\n",
      "Exponentiation:\n",
      "  [[900. 225. 225. 225. 225.]\n",
      " [225. 900. 225. 225. 225.]\n",
      " [225. 225. 900. 225. 225.]\n",
      " [225. 225. 225. 900. 225.]\n",
      " [225. 225. 225. 225. 900.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.ones((5,5))\n",
    "b = np.eye(5)\n",
    "\n",
    "a += b\n",
    "print('Addition:\\n ', a)\n",
    "\n",
    "a /= .4\n",
    "print('Division:\\n ', a)\n",
    "\n",
    "a *= 6\n",
    "print('Multiplication:\\n ', a)\n",
    "\n",
    "a **= 2\n",
    "print('Exponentiation:\\n ', a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In most cases, a library-level call corresponds to creation of a modified copy of an array, while the method-level call modifies in-place."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Broadcasting **(IMPORTANT!)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Broadcasting is by far one of the simplest yet most easily misunderstood rules in NumPy. It is *imperative* you understand how this works. NumPy has this functionality implemented to make your life easier, not harder, and knowing these rules by heart will help you avoid pesky shape errors.\n",
    "\n",
    "What is broadcasting? Let's say you had an array of shape `(1,2)` and another one of shape `(6,2)`, and you wanted to multiply the values in the second by the two values in the first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of arr1 is (1, 2), Shape of arr2 is (6, 2)\n",
      "[[1 2]] \n",
      "\n",
      "[[3 4]\n",
      " [8 2]\n",
      " [5 5]\n",
      " [3 1]\n",
      " [1 2]\n",
      " [1 2]]\n"
     ]
    }
   ],
   "source": [
    "arr1 = np.array([[1,2]])\n",
    "arr2 = np.array([[3,4],[8,2],[5,5],[3,1],[1,2],[1,2]])\n",
    "\n",
    "print('Shape of arr1 is {}, Shape of arr2 is {}'.format(arr1.shape, arr2.shape))\n",
    "\n",
    "print(arr1, '\\n')\n",
    "print(arr2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though the two arrays are of different shapes, NumPy has the ability to infer that this computation is exactly what you want to do. Broadcasting is a way to way to implicitly reshape and stretch arrays to make operations performed on two different shapes consistent.\n",
    "\n",
    "The three things to keep in mind:\n",
    "  1. Dimensions are considered from right to left and compared one by one.\n",
    "  2. Between a pair of dimensions, if one is of size 1 then the operation is allowed.\n",
    "  3. Between a pair of dimensions, if both are the same size then the operation is allowed.\n",
    "\n",
    "\n",
    "So if we have an array of shape `(1,2,3,1,5)` and another of shape `(2,3,1`), broadcasting does *not work*; if on the other hand due to the first point; if on the other hand, the second shape was `(2,3,1,5)`, broadcasting would be allowed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examples of how NOT understanding broadcasting will make your life harder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (2,2,2,2,3) (2,2,2,2) ",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-40-7e44364fb9a8>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mones\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,2,2,2,3) (2,2,2,2) "
     ]
    }
   ],
   "source": [
    "x = np.full((2,2,2,2,3), 2)\n",
    "y = np.ones((2,2,2,2))\n",
    "\n",
    "x + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (4,3) (4,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_28344/2813331315.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mb\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4.0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 8\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,3) (4,) "
     ]
    }
   ],
   "source": [
    "a = np.array([[ 1.0,  2.0,  3.0],\n",
    "           [5.0, 2.0, 4.0],\n",
    "           [1.0, 6.0, 5.0],\n",
    "           [3.0, 6.0, 3.0]])\n",
    "\n",
    "b = np.array([1.0, 2.0, 3.0, 4.0])\n",
    "\n",
    "print(a + b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing and Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([0, 1, 2, 3, 4]), array([0, 1, 2, 3, 4]))\n",
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "[1 3 5 7 9]\n"
     ]
    }
   ],
   "source": [
    "# Extract the indices of the diagonal of a square matrix\n",
    "print(np.diag_indices(5))\n",
    "\n",
    "# Every 2nd element from index 1 to 10\n",
    "a = np.arange(10)\n",
    "print(a)\n",
    "print(a[1:10:2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not all of these options need to be specified. You can tell NumPy to index from a start value and end implicitly at the end of the array, or start implicitly at the beginning of the array and end at a desired indeex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1]\n",
      "[3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "# from beginning up to index 2\n",
    "print(a[:2])\n",
    "\n",
    "# from index 3 up to end of array\n",
    "print(a[3:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also index relative to the *end* of the array -- just use negative indices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "[6 8]\n"
     ]
    }
   ],
   "source": [
    "# Last column of array\n",
    "a = np.column_stack((np.eye(10), np.zeros(10)))\n",
    "print(a[:, -1])\n",
    "\n",
    "a = np.arange(10)\n",
    "# Every 2nd element from 4th to last index to 10\n",
    "print(a[-4:10:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 5 3 1]\n"
     ]
    }
   ],
   "source": [
    "# start from 3rd element from the end and count backwards by 2\n",
    "a = np.arange(10)\n",
    "print(a[-3::-2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To index in a matrix across dimensions, use `:` for each axis that you are \"ignoring\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[-0.13217796 -1.4992006 ]\n",
      "  [ 1.51180475 -0.08302459]\n",
      "  [ 1.06665064  1.78287524]]\n",
      "\n",
      " [[ 0.67966369  1.424192  ]\n",
      "  [ 0.73777     1.20346446]\n",
      "  [ 0.68110987  0.35752176]]\n",
      "\n",
      " [[-0.07503073 -0.11775053]\n",
      "  [-0.1204558   0.30488683]\n",
      "  [ 1.57130886  0.17487111]]]\n",
      "[[-1.4992006  -0.08302459  1.78287524]\n",
      " [ 1.424192    1.20346446  0.35752176]\n",
      " [-0.11775053  0.30488683  0.17487111]]\n"
     ]
    }
   ],
   "source": [
    "x = np.random.randn(3,3,2)\n",
    "print(x)\n",
    "\n",
    "# get all elements with index 1 in the third dimension\n",
    "print(x[:, :, 1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also access specific elements by passing an array of indices to an array. This is called fancy indexing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3 2 3]\n",
      " [5 4 5]\n",
      " [8 1 2]]\n",
      "Elements at (0,0) and (2,1):  [3 1]\n"
     ]
    }
   ],
   "source": [
    "data = np.array([[3,2,3],[5,4,5],[8,1,2]])\n",
    "print(data)\n",
    "\n",
    "row = np.array([0,2])\n",
    "col = np.array([0,1])\n",
    "\n",
    "print('Elements at (0,0) and (2,1): ', data[row, col])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stacking and Concatenation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if you want to join existing arrays together, or join a newly created array to one that already exists?\n",
    "Several functions come in handy: \n",
    "\n",
    "To stack one array on top of another, use `np.vstack`:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 1.]\n",
      " [1. 1. 1. 1.]]\n",
      "[[1. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 1.]\n",
      " [1. 1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.eye(4)\n",
    "b = np.ones((1,4))\n",
    "stacked = np.vstack((a, b))\n",
    "\n",
    "print(stacked)\n",
    "\n",
    "# alternatively, use shorthand\n",
    "print(np.r_[a,b])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To stack them horizontally, you can similarly call `np.hstack`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 3. 3.]\n",
      " [0. 1. 0. 3. 3.]\n",
      " [0. 0. 1. 3. 3.]]\n",
      "[[1. 0. 0. 3. 3.]\n",
      " [0. 1. 0. 3. 3.]\n",
      " [0. 0. 1. 3. 3.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.eye(3)\n",
    "b = np.full((3,2),3)\n",
    "stacked = np.hstack((a, b))\n",
    "\n",
    "print(stacked)\n",
    "\n",
    "# alternatively, use shorthand\n",
    "print(np.c_[a,b])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These can be useful to call if you're incrementally appending to an array over a loop, especially if the number of iterations is not known beforehand."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range(0, 5)\n",
      "[[3. 3. 3.]\n",
      " [3. 3. 3.]\n",
      " [3. 3. 3.]\n",
      " [3. 3. 3.]\n",
      " [3. 3. 3.]]\n"
     ]
    }
   ],
   "source": [
    "iter = int(np.round(np.random.uniform(0,1,1) * 10))\n",
    "\n",
    "arr = np.empty((0,3))\n",
    "row = np.full((1,3),3)\n",
    "print(range(iter))\n",
    "for c in list(range(int(iter))):\n",
    "  arr = np.vstack((arr, row))\n",
    "\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One caveat to keep in mind is stacking 1d arrays onto higher dimensional arrays. This is a failure case if np.hstack is applied naively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "all the input arrays must have same number of dimensions, but the array at index 0 has 2 dimension(s) and the array at index 1 has 1 dimension(s)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_49856/1003724156.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0meye\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mhstack\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Roaming\\Python\\Python39\\site-packages\\numpy\\core\\shape_base.py\u001b[0m in \u001b[0;36mhstack\u001b[1;34m(tup)\u001b[0m\n\u001b[0;32m    344\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0m_nx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mconcatenate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marrs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    345\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 346\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0m_nx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mconcatenate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marrs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    347\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    348\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mconcatenate\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: all the input arrays must have same number of dimensions, but the array at index 0 has 2 dimension(s) and the array at index 1 has 1 dimension(s)"
     ]
    }
   ],
   "source": [
    "x = np.array([1,2,3,4,5])\n",
    "y = np.eye(5)\n",
    "\n",
    "print(np.hstack((y,x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You have to take care to either explicitly keep the number of dimensions consistent if sticking with `np.hstack`, or use the convenience function `np.column_stack` instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reshaping and using np.stack:\n",
      "  [[1. 0. 0. 0. 3.]\n",
      " [0. 1. 0. 0. 2.]\n",
      " [0. 0. 1. 0. 1.]\n",
      " [0. 0. 0. 1. 5.]]\n",
      "Using convenience function np.column_stack:\n",
      "  [[1. 0. 0. 0. 3.]\n",
      " [0. 1. 0. 0. 2.]\n",
      " [0. 0. 1. 0. 1.]\n",
      " [0. 0. 0. 1. 5.]]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([3,2,1,5])\n",
    "y = np.eye(4)\n",
    "\n",
    "# Keeping number of dimensions consistent\n",
    "print('Reshaping and using np.stack:\\n ', np.hstack((y, x[:, None])))\n",
    "\n",
    "# using convenience functions\n",
    "print('Using convenience function np.column_stack:\\n ', np.column_stack((y,x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logic operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result of [100 OR 10, 010 OR 001]:  [6 3]\n",
      "Result of [100 OR 10, 010 OR 001]:  [6 3]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ True,  True])"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# BITWISE\n",
    "x = np.array([4,2])\n",
    "y = np.array([2,1])\n",
    "\n",
    "# result is 110 in binary (6)\n",
    "print('Result of [100 OR 10, 010 OR 001]: ', x | y)\n",
    "print('Result of [100 OR 10, 010 OR 001]: ', x | y)\n",
    "\n",
    "# LOGICAL\n",
    "# # elementwise boolean comparisons\n",
    "\n",
    "np.logical_and(x, y)\n",
    "np.logical_not(x, y)\n",
    "np.logical_xor(x, y)\n",
    "np.logical_or(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercise caution when performing boolean operations using infix operators on numeric numpy arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_49856/1889443628.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"
     ]
    }
   ],
   "source": [
    "x = np.zeros((4,2))\n",
    "y = np.array([[1,1],[1,0],[0,0],[0,1]])\n",
    "print(x or y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the same type of call is, however, fine for a boolean array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ True False  True  True  True]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([True, False, False, True, True])\n",
    "y = np.array([False, False, True, True, True])\n",
    "print(x | y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## np.array vs. np.matrix - whats the difference?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might encounter code that uses `np.matrix` instead of `np.array`, often in older codebases. Though you can perform a lot of the same manipulations on either, these are not equivalent. \n",
    "\n",
    "`np.matrix` provides some convenience methods for linear algebraic operations that have succint syntax."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converting matrix to ndarray:\n",
      " [[3 2 1]\n",
      " [8 2 4]\n",
      " [2 1 2]]\n",
      "Taking the inverse of a matrix:\n",
      " [[ 2.77555756e-17  2.50000000e-01 -5.00000000e-01]\n",
      " [ 6.66666667e-01 -3.33333333e-01  3.33333333e-01]\n",
      " [-3.33333333e-01 -8.33333333e-02  8.33333333e-01]]\n",
      "Taking the conjugate transpose of a matrix:\n",
      " [[3 8 2]\n",
      " [2 2 1]\n",
      " [1 4 2]]\n"
     ]
    }
   ],
   "source": [
    "# convert ndarray to matrix\n",
    "x = np.array([[3,2,1],[8,2,4],[2,1,2]])\n",
    "x_mat = np.asmatrix(x)\n",
    "\n",
    "# convert matrix to ndarray\n",
    "print('Converting matrix to ndarray:\\n', x_mat.A)\n",
    "\n",
    "#inverse\n",
    "print('Taking the inverse of a matrix:\\n', x_mat.I)\n",
    "\n",
    "#conjugate\n",
    "print('Taking the conjugate transpose of a matrix:\\n', x_mat.H)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keep in mind that while convenient, this functionality is soon to be deprecated and is not recommended by the developers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Views"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many convenience functions and methods in NumPy for accessing different views of the same data, aside from using slicing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`atleast_1d`, `atleast_2d` and `atleast_3d` are useful for taking a higher dimensional view of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1D view of scalar:  [3]\n",
      "2D view of 1D array:\n",
      " [2 3]\n",
      "3D view of 2D array:\n",
      " [[[2]\n",
      "  [3]\n",
      "  [6]]\n",
      "\n",
      " [[5]\n",
      "  [2]\n",
      "  [1]]]\n"
     ]
    }
   ],
   "source": [
    "scalar_to_1d = np.atleast_1d(3)\n",
    "print('1D view of scalar: ', scalar_to_1d)\n",
    "\n",
    "to_2d = np.atleast_1d([2,3])\n",
    "print('2D view of 1D array:\\n', to_2d)\n",
    "\n",
    "to_3d = np.atleast_3d([[2,3,6],[5,2,1]])\n",
    "print('3D view of 2D array:\\n', to_3d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more control over the desired shape of your output, you can also reshape it explicitly to a compatible shape (i.e., same number of elements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.51554864  0.97920968  1.13369491 -1.20841794]\n",
      " [ 0.05588986 -0.85682848  0.05641216  1.02201355]\n",
      " [ 2.0585612  -0.06168255 -1.63309948  1.29429777]\n",
      " [-0.58304522 -0.52133003 -0.18223653 -0.30994011]] \n",
      "\n",
      "[[-1.51554864  0.97920968]\n",
      " [ 1.13369491 -1.20841794]\n",
      " [ 0.05588986 -0.85682848]\n",
      " [ 0.05641216  1.02201355]\n",
      " [ 2.0585612  -0.06168255]\n",
      " [-1.63309948  1.29429777]\n",
      " [-0.58304522 -0.52133003]\n",
      " [-0.18223653 -0.30994011]] \n",
      "\n",
      "[[-0.35600938 -0.59387011]\n",
      " [ 0.86311487  0.94756519]] \n",
      "\n",
      "[[[[[[-0.35600938]]]]]\n",
      "\n",
      "\n",
      "\n",
      "\n",
      " [[[[[-0.59387011]]]]]\n",
      "\n",
      "\n",
      "\n",
      "\n",
      " [[[[[ 0.86311487]]]]]\n",
      "\n",
      "\n",
      "\n",
      "\n",
      " [[[[[ 0.94756519]]]]]]\n"
     ]
    }
   ],
   "source": [
    "a = np.random.randn(4,4)\n",
    "print(a, '\\n')\n",
    "\n",
    "# same number of elements\n",
    "print(np.reshape(a, (8,2)), '\\n')\n",
    "\n",
    "# 2D to 4D\n",
    "a = np.random.randn(2,2)\n",
    "print(a, '\\n')\n",
    "print(a.reshape(4,1,1,1,1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other manipulations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes you may want to represent all the elements of an array as a 1d list. We can do this in two ways -- `ravel` or `flatten`.\n",
    "While they both have the same functionality, their behavior is different. Furthermore, `ravel` is a library level function and can take 'array-like' structures as input, while `flatten` is a method that can *only be used on ndarrays*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np.ravel` returns a flattened *view* of the input array whenever possible. That means if you decide to modify its output in-place later down the line, you may inadvertantly mutate your original input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transformed output using input  [3 1 2 3 5 7 2 5 1]\n",
      " Representation in memory: \n",
      " [[[3 1 2]\n",
      "  [3 5 7]\n",
      "  [2 5 1]]]\n",
      "Transformed output using input list of lists:  \n",
      "[3 1 2 3 5 7 2 5 1]\n"
     ]
    }
   ],
   "source": [
    "# ravel numpy array\n",
    "x = np.array([[[3,1,2],[3,5,7],[2,5,1]]])\n",
    "y = np.ravel(x)\n",
    "print('Transformed output using input  {}\\n Representation in memory: \\n {}'.format(y, y.base))\n",
    "\n",
    "# ravel list of lists\n",
    "x = [[[3,1,2],[3,5,7],[2,5,1]]]\n",
    "y = np.ravel(x)\n",
    "print('Transformed output using input list of lists:  \\n{}'.format(y, y.base))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np.flatten` *always* returns a flattened copy of the original input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transformed output using input: [3 1 2 3 5 7 2 5 1]\n",
      "Representation in memory: None\n"
     ]
    }
   ],
   "source": [
    "# ravel numpy array\n",
    "x = np.array([[[3,1,2],[3,5,7],[2,5,1]]])\n",
    "y = x.flatten()\n",
    "print('Transformed output using input: {}\\nRepresentation in memory: {}'.format(y, y.base))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np.insert` and `np.delete` can be used to add or remove rows/columns in an array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original array:\n",
      " [[1 1 1]\n",
      " [1 1 1]]\n",
      "Insert column of 2s at index 1:\n",
      "  [[1 2 1 1]\n",
      " [1 2 1 1]]\n",
      "Original array:\n",
      " [[1 1 1 1]\n",
      " [1 1 1 1]\n",
      " [1 1 1 1]\n",
      " [1 1 1 1]]\n",
      "Delete a column:\n",
      "  [[1 1 1]\n",
      " [1 1 1]\n",
      " [1 1 1]\n",
      " [1 1 1]]\n"
     ]
    }
   ],
   "source": [
    "a = np.full((2,3), 1)\n",
    "print('Original array:\\n', a)\n",
    "print('Insert column of 2s at index 1:\\n ', np.insert(a, 1, 2, axis=1))\n",
    "\n",
    "a = np.full((4,4), 1)\n",
    "print('Original array:\\n', a)\n",
    "print('Delete a column:\\n ', np.delete(a, 1, axis=1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have redundant dimensions of size 1, you can use `np.squeeze` to get rid of them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x has shape (1, 1, 7) and is [[[3 1 2 3 4 5 6]]]\n",
      "x has shape (7,) and is [3 1 2 3 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[[3,1,2,3,4,5,6]]])\n",
    "print('x has shape {} and is {}'.format(x.shape, x))\n",
    "\n",
    "x_squoze = np.squeeze(x)\n",
    "print('x has shape {} and is {}'.format(x_squoze.shape, x_squoze))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np.unique` can be used to return a sorted *list* of the unique elements of an array, the *indices* of unique elements in an array, or the *count of each* unique element."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique elements:  [1 2 3]\n",
      "Tuple of unique elements and indices:  (array([1, 2, 3]), array([0, 1, 2], dtype=int64))\n",
      "Tuple of unique elements and counts:  (array([1, 2, 3]), array([1, 3, 5], dtype=int64))\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2,3],[3,3,2],[3,2,3]])\n",
    "\n",
    "# return unique elements\n",
    "print('Unique elements: ', np.unique(x))\n",
    "\n",
    "# additionally return indices of first occurences of unique elements\n",
    "print('Tuple of unique elements and indices: ', np.unique(x, return_index=True))\n",
    "\n",
    "# additionally return count of unique elements\n",
    "print('Tuple of unique elements and counts: ', np.unique(x, return_counts=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aggregations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original array:\n",
      "  [[[3. 2. 5.]\n",
      "  [5. 4. 2.]\n",
      "  [5. 5. 5.]]\n",
      "\n",
      " [[3. 2. 5.]\n",
      "  [5. 4. 2.]\n",
      "  [5. 5. 5.]]]\n",
      "Total sum:  72.0\n",
      "Sum along axis 2:\n",
      "  [[10. 11. 15.]\n",
      " [10. 11. 15.]]\n",
      "Sum along axis 0:\n",
      "  [[ 6.  4. 10.]\n",
      " [10.  8.  4.]\n",
      " [10. 10. 10.]]\n",
      "Sum along axes 0 and 1:\n",
      "  [26. 22. 24.]\n"
     ]
    }
   ],
   "source": [
    "x = np.zeros((2,3,3)) + np.array([[[3,2,5],[5,4,2],[5,5,5]]])\n",
    "print('Original array:\\n ', x)\n",
    "\n",
    "# sum over all elements\n",
    "print('Total sum: ', np.sum(x))\n",
    "# sum along axis\n",
    "print('Sum along axis 2:\\n ', np.sum(x, axis=2))\n",
    "print('Sum along axis 0:\\n ', np.sum(x, axis=0))\n",
    "print('Sum along axes 0 and 1:\\n ', np.sum(x, axis=(0,1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the most common causes of confusion is the direction the operation is taken on when setting the axis argument. Operations are executed in the direction that the axis *increments*, not in the direction the axis spans. For example, the 0th axis increments by row, so adding along the 0th axis would add down a column, NOT across a row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n",
      "Sum along the 0th axis: \n",
      " [3. 3. 3. 3. 3. 3. 3. 3. 3. 3.]\n"
     ]
    }
   ],
   "source": [
    "x = np.ones((3,10))\n",
    "print(x)\n",
    "\n",
    "print('Sum along the 0th axis: \\n', np.sum(x, axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many other aggegation operations are supported."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean:  3.111111111111111\n",
      "Standard Deviation  1.594744454934147\n",
      "Variance 2.5432098765432096\n",
      "Product 36000000.0\n",
      "Argmin/Argmax: 3, 2\n",
      "Min/Max: 1.0, 5.0\n"
     ]
    }
   ],
   "source": [
    "x = np.zeros((2,3,3)) + np.array([[[3,2,5],[1,4,2],[1,5,5]]])\n",
    "\n",
    "# sum over all elements\n",
    "print('Mean: ', np.mean(x))\n",
    "print('Standard Deviation ', np.std(x))\n",
    "print('Variance', np.var(x))\n",
    "print('Product', np.prod(x))\n",
    "print('Argmin/Argmax: {}, {}'.format(np.argmin(x), np.argmax(x)))\n",
    "print('Min/Max: {}, {}'.format(np.min(x), np.max(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Mathematical Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard pythonic infix operators work between two NumPy arrays as you would expect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3. 2. 2.]\n",
      " [2. 3. 2.]\n",
      " [2. 2. 3.]]\n",
      "[[2. 0. 0.]\n",
      " [0. 2. 0.]\n",
      " [0. 0. 2.]]\n",
      "[[0.5 0.  0. ]\n",
      " [0.  0.5 0. ]\n",
      " [0.  0.  0.5]]\n",
      "[[-1. -2. -2.]\n",
      " [-2. -1. -2.]\n",
      " [-2. -2. -1.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.eye(3, 3)\n",
    "b = np.full((3,3), 2)\n",
    "\n",
    "print(a + b)\n",
    "print(a * b)\n",
    "print(a / b)\n",
    "print(a - b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### np.dot, np.multiply, np.matmul"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A common source of confusion is the difference among each of these functions. In some situations they compute exactly the same thing, while in others they give completely different results.\n",
    "\n",
    "\n",
    "- `np.multiply` is for *elementwise* multiplication between two arrays. \n",
    "- `np.dot` computes the standard dot product between two N-dimensional vectors.\n",
    "- `np.matmul` computes standard matrix multiplication. Remember to use the infix operator '@' for readability.\n",
    "\n",
    "\n",
    "`np.multiply` and `np.dot` yield the same result when the arguments are two 2D arrays. For ***all other combinations*** of arguments, where one input is N-dimensional (with N>2), the calculations are as defined above.\n",
    "\n",
    "Furthermore, broadcasting works slightly diffrent between the two, and you cannot use a scalar argument with `np.multiply`, whereas scalars are accepted for `np.dot`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 6  6  6]\n",
      "  [ 8  8 12]\n",
      "  [ 2  2  2]]\n",
      "\n",
      " [[ 6  4  6]\n",
      "  [ 8 10 12]\n",
      "  [ 2  2  2]]\n",
      "\n",
      " [[ 2  8 14]\n",
      "  [ 8  4 12]\n",
      "  [ 2  2  2]]]\n",
      "Dot product:  [[[[18 18 18]\n",
      "   [18 18 18]\n",
      "   [18 18 18]]\n",
      "\n",
      "  [[28 28 28]\n",
      "   [28 28 28]\n",
      "   [28 28 28]]\n",
      "\n",
      "  [[ 6  6  6]\n",
      "   [ 6  6  6]\n",
      "   [ 6  6  6]]]\n",
      "\n",
      "\n",
      " [[[16 16 16]\n",
      "   [16 16 16]\n",
      "   [16 16 16]]\n",
      "\n",
      "  [[30 30 30]\n",
      "   [30 30 30]\n",
      "   [30 30 30]]\n",
      "\n",
      "  [[ 6  6  6]\n",
      "   [ 6  6  6]\n",
      "   [ 6  6  6]]]\n",
      "\n",
      "\n",
      " [[[24 24 24]\n",
      "   [24 24 24]\n",
      "   [24 24 24]]\n",
      "\n",
      "  [[24 24 24]\n",
      "   [24 24 24]\n",
      "   [24 24 24]]\n",
      "\n",
      "  [[ 6  6  6]\n",
      "   [ 6  6  6]\n",
      "   [ 6  6  6]]]]\n",
      "Matrix multiply:  [[[18 18 18]\n",
      "  [28 28 28]\n",
      "  [ 6  6  6]]\n",
      "\n",
      " [[16 16 16]\n",
      "  [30 30 30]\n",
      "  [ 6  6  6]]\n",
      "\n",
      " [[24 24 24]\n",
      "  [24 24 24]\n",
      "  [ 6  6  6]]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[[3,3,3],\n",
    "            [4,4,6],\n",
    "            [1,1,1]],\n",
    "            [[3,2,3],\n",
    "            [4,5,6],\n",
    "            [1,1,1]],\n",
    "            [[1,4,7],\n",
    "            [4,2,6],\n",
    "            [1,1,1]]])\n",
    "b = np.full((3,3,3), 2)\n",
    "\n",
    "# elementwise multiply\n",
    "print(a * b)\n",
    "\n",
    "# dot product\n",
    "print('Dot product: ', np.dot(a, b))\n",
    "\n",
    "# matrix multiply\n",
    "print('Matrix multiply: ', a @ b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear algebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many standard unary operations on matrices are all supported.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transpose: \n",
      " [[1 3]\n",
      " [2 4]]\n",
      "Inverse: \n",
      " [[-2.   1. ]\n",
      " [ 1.5 -0.5]]\n",
      "Determinant:  -2.0000000000000004\n",
      "Dot product:  60\n",
      "Dot product:  60\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]])\n",
    "\n",
    "\n",
    "\n",
    "# transpose\n",
    "print('Transpose: \\n', x.T)\n",
    "\n",
    "# inverse\n",
    "print('Inverse: \\n', np.linalg.inv(x))\n",
    "\n",
    "# determinant\n",
    "print('Determinant: ', np.linalg.det(x))\n",
    "\n",
    "# dot product\n",
    "x = np.array([3,5])\n",
    "y = np.array([5,9])\n",
    "\n",
    "print('Dot product: ', np.dot(x, y))\n",
    "print('Dot product: ', x.dot(y))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the eigenvectors and/or eigenvalues of a matrix, use the function `np.linalg.eig`. This will return a tuple of the form `(eigenvalues, eigenvectors)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Get eigenvectors of a matrix: \n",
      " [[-0.82456484 -0.41597356]\n",
      " [ 0.56576746 -0.90937671]]\n",
      "Get eigenvalues of a matrix: \n",
      " [-0.37228132  5.37228132]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]])\n",
    "\n",
    "val, vec = np.linalg.eig(x)\n",
    "# eigenvectors\n",
    "print('Get eigenvectors of a matrix: \\n', vec)\n",
    "\n",
    "# eigenvalues\n",
    "print('Get eigenvalues of a matrix: \\n', val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To take an Lp norm, use `np.linalg.norm`. If p is not specified, the default is 2 if you are taking the norm of a vector (Euclidean distance). Norms on matrices are not defined the same way as for vectors! Refer to the documentation for specifics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L1 norm:  11.0\n",
      "L1 norm:  6.244997998398398\n",
      "L3 norm:  5.4401218254147965\n",
      "L4 norm:  5.185427592735\n",
      "\n",
      "\n",
      "2-norm 6.723711277716526\n",
      "Frobenius norm:  6.855654600401044\n"
     ]
    }
   ],
   "source": [
    "# Vector norms\n",
    "x = np.array([3,5,1,2])\n",
    "print('L1 norm: ', np.linalg.norm(x, ord=1))\n",
    "print('L1 norm: ', np.linalg.norm(x))\n",
    "print('L3 norm: ', np.linalg.norm(x, ord=3))\n",
    "print('L4 norm: ', np.linalg.norm(x, ord=4))\n",
    "\n",
    "print('\\n')\n",
    "  \n",
    "# Matrix norms\n",
    "x = np.array([[3,5],[3,2]])\n",
    "print('2-norm', np.linalg.norm(x, ord=2))\n",
    "print('Frobenius norm: ', np.linalg.norm(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LU, Cholesky, and QR decompositions are all supported:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LU Decomposition: \n",
      "\n",
      "(array([[-2.79182316e-01,  8.08895055e-01,  9.69348229e-02,\n",
      "         5.08281088e-01],\n",
      "       [-8.10078065e-01,  8.50435017e-02, -8.89473370e-04,\n",
      "        -5.80120970e-01],\n",
      "       [-1.34332727e-01, -2.53385991e-01,  9.46336978e-01,\n",
      "         1.48985172e-01],\n",
      "       [ 4.97780554e-01,  5.23690684e-01,  3.08300458e-01,\n",
      "        -6.18799979e-01]]),\n",
      " array([11.65767451,  8.92348545,  3.57084552,  0.84799452]),\n",
      " array([[-2.79182316e-01, -8.10078065e-01, -1.34332727e-01,\n",
      "         4.97780554e-01],\n",
      "       [ 8.08895055e-01,  8.50435017e-02, -2.53385991e-01,\n",
      "         5.23690684e-01],\n",
      "       [ 9.69348229e-02, -8.89473370e-04,  9.46336978e-01,\n",
      "         3.08300458e-01],\n",
      "       [ 5.08281088e-01, -5.80120970e-01,  1.48985172e-01,\n",
      "        -6.18799979e-01]]))\n"
     ]
    }
   ],
   "source": [
    "import pprint\n",
    "x = np.array([[7, 3, -1, 2],\n",
    "           [3, 8, 1, -4],\n",
    "            [-1, 1, 4, -1],\n",
    "             [2, -4, -1, 6]])\n",
    "print('LU Decomposition: \\n')\n",
    "pprint.pprint(np.linalg.lu(x))\n",
    "\n",
    "# print('Cholesky Decomposition: \\n')\n",
    "# pprint.pprint(np.linalg.cholesky(x))\n",
    "\n",
    "# print('SVD: \\n')\n",
    "# pprint.pprint(np.linalg.svd(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Filtering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many ways you can filter values out or from existing arrays, based on conditions that do not relate to ranges over indices.\n",
    "\n",
    "One is a *boolean mask*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mask out all values less than or equal to 9: \n",
      " [[False False False]\n",
      " [False False False]\n",
      " [ True  True False]]\n",
      "Filtered values: \n",
      " [ 10 100] \n",
      "\n",
      "Mask out all elements x that are not equal to x - 1 * 2: \n",
      " [[ True  True False]\n",
      " [False  True False]\n",
      " [False False  True]]\n",
      "Filtered values: \n",
      " [2 2 2 2] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[2,2,8],[9,2,1],[10,100,2]])\n",
    "mask = x > 9\n",
    "print('Mask out all values less than or equal to 9: \\n', mask)\n",
    "print('Filtered values: \\n' , x[mask], '\\n')\n",
    "\n",
    "mask = (x - 1) * 2 == x\n",
    "print('Mask out all elements x that are not equal to x - 1 * 2: \\n', mask)\n",
    "print('Filtered values: \\n' , x[mask], '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use `np.where` to get either the indices of an array that satisfy a condition, or a modified version of the array that extracts elements from two different arrays based on a condition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3 3 3]\n",
      " [2 3 1]\n",
      " [3 9 2]]\n",
      "Indices that satisfy a condition:\n",
      "  (array([1, 1, 2, 2], dtype=int64), array([0, 2, 1, 2], dtype=int64))\n",
      "Element values that satisfy a condition:\n",
      "  [2 1 9 2]\n",
      "Array modified based on condition:\n",
      "  [[0. 0. 0.]\n",
      " [1. 0. 1.]\n",
      " [0. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "# get indices of elements that satisfy condition, and slice using those indices\n",
    "x = np.array([[3,3,3],[2,3,1],[3,9,2]])\n",
    "print(x)\n",
    "print('Indices that satisfy a condition:\\n ', np.where(x != 3))\n",
    "print('Element values that satisfy a condition:\\n ', x[np.where(x != 3)])\n",
    "\n",
    "# returned copy of array, modified based on condition\n",
    "pos = np.ones((3,3))\n",
    "neg = np.zeros((3,3))\n",
    "\n",
    "print('Array modified based on condition:\\n ', np.where(x != 3,pos,neg))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the indices returned by `np.where` are formatted as a tuple of arrays. Each array in the ith tuple element corresponds to a matrix index along the ith axis. So in the example above, the indices returned are `(1,0), (1,2), (2,1), and (2,2)`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if you want to randomly generate new data points? Some common use-cases would be the generation of synthetic data, testing whether some point transformation function works, or just trying to model a distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from a multivariate Gaussian distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "An array of shape (4, 2, 5), with values from a multivariate Gaussian:\n",
      "[[[-0.60143227 -2.6137123   1.75978469 -0.3747837  -0.208937  ]\n",
      "  [ 0.84830705  0.31005252 -0.23223041  1.07410926  0.1211707 ]]\n",
      "\n",
      " [[ 1.04649546  0.04280614 -0.0968234  -0.51818672  0.67387909]\n",
      "  [ 0.68297098 -1.14339678 -0.43194097  1.20284071 -0.50435208]]\n",
      "\n",
      " [[ 0.10352752  2.09221188  0.84059257  0.95882453 -1.05070489]\n",
      "  [ 0.8561377  -0.05123853  0.25801183  1.92347036  1.07524303]]\n",
      "\n",
      " [[-0.55080133  0.45353134  0.10567007 -0.09577899  2.12731078]\n",
      "  [ 0.23649591  0.82009635  1.17463516 -1.24304543 -0.44394244]]]\n"
     ]
    }
   ],
   "source": [
    "sampled_points = np.random.randn(4,2,5)\n",
    "print('An array of shape {}, with values from a multivariate Gaussian:\\n{}'.format(sampled_points.shape, sampled_points))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Choosing elements randomly from a discrete set, with a chosen pmf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[82 91 82]\n"
     ]
    }
   ],
   "source": [
    "sampled_elements = np.random.choice([82,46,64,91], size=3, p=[0.5, 0.15, 0.05, 0.3])\n",
    "print(sampled_elements)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from a uniform distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "An array of shape (10,), with values from a uniform distribution between 0 and 5\n",
      "[1.06140995 3.12063989 2.58304995 3.34417705 4.07561498 1.24413537\n",
      " 2.09634393 0.50876819 1.56925548 0.87190493]\n"
     ]
    }
   ],
   "source": [
    "sampled_points = np.random.uniform(0,5,10)\n",
    "print('An array of shape {}, with values from a uniform distribution between 0 and 5\\n{}'.format(sampled_points.shape, sampled_points))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ufuncs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ufuncs, or universal functions, are vectorized operations that can be performed elementwise and can be broadcast over arrays. Some useful built-in ufuncs are demonstrated below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5x5 ndrray with values added at matrix indices (0,0) and (4,3): \n",
      " [[2. 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. 1. 1.]]\n",
      "1D array with values added at indices 0,2,3: \n",
      " [-3 -5  1  2 -4]\n",
      "Accumulate multiplications:  [ 2  6 30]\n",
      "Accumulate additions:  [ 6  7 20]\n"
     ]
    }
   ],
   "source": [
    "# add to specific elements\n",
    "x = np.eye(5)\n",
    "np.add.at(x, ((0,4),(0,3)), 1)\n",
    "print('5x5 ndrray with values added at matrix indices (0,0) and (4,3): \\n {}'.format(x))\n",
    "\n",
    "# set specific elements negative\n",
    "x = np.array([3,5,1,2,4])\n",
    "idx = (x, [0,2,3])\n",
    "np.negative.at(x, [0,1,4])\n",
    "print('1D array with values added at indices 0,2,3: \\n {}'.format(x))\n",
    "\n",
    "# outer product\n",
    "np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))\n",
    "\n",
    "# accumulate np.accumulate\n",
    "print('Accumulate multiplications: ', np.multiply.accumulate([2, 3, 5]))\n",
    "print('Accumulate additions: ', np.add.accumulate([6,1,13]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NumPy has support for user-defined, custom ufuncs. However, this requires some knowledge of Cython or C++ as well, which is out of scope. Refer to the following link for more information:\n",
    "\n",
    "https://numpy.org/doc/stable/user/c-info.ufunc-tutorial.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accessing array attributes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes you may want to get meta information about a NumPy array -- its shape, size, dimension, or whether it is a view or a copy. You can easily access this information directly through the array's attributes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of x:  (3, 4)\n",
      "Data type:  int32\n",
      "Number of dimensions:  2\n",
      "Total number of elements:  12\n",
      "Representation in memory:  None\n"
     ]
    }
   ],
   "source": [
    "# shape and dimension info\n",
    "x = np.array([[3,5,4,4],[5,8,1,2],[3,2,3,5]])\n",
    "print('Shape of x: ', x.shape)\n",
    "print('Data type: ', x.dtype)\n",
    "print('Number of dimensions: ', x.ndim)\n",
    "print('Total number of elements: ', x.size)\n",
    "\n",
    "# check if copy/view. None if copy, view otherwise\n",
    "print('Representation in memory: ', x.base)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Good practices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Several good practices to keep in mind:\n",
    "1. **Don't use for-loops if you can use a vectorized operation instead.** This completely defeats the purpose of using NumPy for fast calculation.\n",
    "2. **Make sure to consider if you are modifying a view or a copy.** You don't want to be changing data that has no business being changed, or not changing any data at all.\n",
    "3. **Preallocate when possible.** It is usually more efficient to instantiate a fixed-size array, rather than to incrementally change its size while stacking rows or columns onto it over a loop.\n",
    "4. **Opt for using infix operators.** These keep your code readable and pain-free to debug."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://matplotlib.org/stable/api/index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "plt.style.use('default')\n",
    "\n",
    "# Sample 100 xy points from normal distribution\n",
    "x= np.linspace(-3,3, 100)\n",
    "y = np.cos(2*x) + 3.2\n",
    "\n",
    "ax.plot(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, you can create plots by calling analogous functions from the pyplot module directly, without creating an `Axes` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|Plot Type | Function|\n",
    "|---|----|\n",
    "|Line plot|`plot`|\n",
    "|Scatter plot|`scatter`|\n",
    "|Bar chart|`bar`|\n",
    "|Step|`step`|\n",
    "|Pie chart|`pie`|\n",
    "|Histogram|`hist`|\n",
    "|Fill|`fill_between`|\n",
    "|Scatter plot with error bars|`errorbar`|\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting multiple data series on the same plot is easy -- simply call the plotting function again with different input data. We can also clarify which series is which by adding a legend and setting the labels of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x22bc98a0790>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x= np.random.randn(100,100)\n",
    "x2 = (np.linspace(-2,2,100), np.full((100,), 1.5))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x[0], x[1], label='Series 1');\n",
    "ax.scatter(x2[0], x2[1], label='Series 2');\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Styling a plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can customize the style of plot elements in several ways:\n",
    "  1. Directly through the `Axes` object\n",
    "  2. Through the `rcParams` attribute of matplotlib\n",
    "  3. Using keyword arguments passed to the plotting function\n",
    "  4. Within the `fmt` string.\n",
    "  5. Through `matplotlib.pyplot`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "\n",
    "fig, ax = plt.subplots(1,3)\n",
    "\n",
    "#rcParams\n",
    "mpl.rcParams['figure.figsize'] = (8,4)\n",
    "\n",
    "# pyplot style\n",
    "plt.setp(ax, xlim=[-1,0], ylim=[0,1], xlabel='Time')\n",
    "plt.suptitle('Example plots')\n",
    "\n",
    "# OO style\n",
    "ax[0].set_title('Line')\n",
    "ax[1].set_title('Scatter')\n",
    "ax[2].set_title('Step')\n",
    "ax[0].set_ylabel('Position')\n",
    "\n",
    "# kwarg\n",
    "ax[0].plot(x[0], x[1], linestyle='--');\n",
    "ax[1].scatter(x[0], x[1], color='g');\n",
    "\n",
    "# fmt string\n",
    "ax[2].step(x[0], x[1], '+-.c');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|Property|kwarg|\n",
    "|---|---|\n",
    "|Line color|`color`|\n",
    "|Line style|`linestyle`|\n",
    "|Linewidth|`linewidth`|\n",
    "|Marker type|`marker`|\n",
    "|Marker size|`markersize`|\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|Symbol|Plot Element|Value|\n",
    "|---|---|---|\n",
    "|x|Marker|X|\n",
    "|+|Marker|Plus|\n",
    "|o|Marker|Circle|\n",
    "|p|Marker|Pentagon|\n",
    "|*|Marker|Star|\n",
    "|s|Marker|Square|\n",
    "|D|Marker|Diamond|\n",
    "|^|Marker|Triangle|\n",
    "|r|Color|Red|\n",
    "|g|Color|Green|\n",
    "|b|Color|Blue|\n",
    "|m|Color|Magenta|\n",
    "|c|Color|Cyan|\n",
    "|y|Color|Yellow|\n",
    "|--|Line|Dashed| \n",
    "|-.|Line|Dash-dot|\n",
    "|:|Line|Dotted|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subplots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To include more than one plot in a single figure, you can pass the number of rows and columns as arguments to `plt.subplot`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nrows is the first argument, ncols is the second\n",
    "fig, ax = plt.subplots(2,2)\n",
    "x = np.arange(0,5,0.1)\n",
    "y = np.sin(x)\n",
    "ax[0, 0].plot(x, y);\n",
    "ax[0, 1].plot(x + 3,y);\n",
    "ax[1, 0].plot(x,y*2);\n",
    "ax[1, 1].plot(x +3 ,y + 3);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Built in stylesheets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matplotlib's default visuals may feel outdated, especially to those of you used to data visualization in R (ggplot!). Matplotlib has several stylesheets with a more \"modern\" look:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 648x216 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "st = ['default', 'ggplot', 'seaborn']\n",
    "\n",
    "x = np.linspace(0,4)\n",
    "y = x**2 - 2.5\n",
    "for s in st:\n",
    "    fig,[ax1,ax2,ax3] = plt.subplots(1,3, figsize=(9,3))\n",
    "    plt.style.use(s)\n",
    "    plt.suptitle('Example plot using {}'.format(s))\n",
    "    ax1.step(x,y)\n",
    "    ax2.scatter(x,y)\n",
    "    ax3.hist(x,y)\n",
    "      \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This package includes a lot of useful statistical functions -- probability distributions, statistical tests, summary statistics, and other functionality. There is support for modeling of both continuous and discrete random variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a distribution over a continuous random variable, you create a range of input values and call the `pdf` function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multivariate Gaussian distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import multivariate_normal\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "x = np.linspace(-10, 10, 100)\n",
    "ax.plot(x, multivariate_normal.pdf(x),\n",
    "       'r-', lw=2, label='norm pdf');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Distributions over discrete RVs have slightly different syntax, where you call `ppf` to create your inputs and `pmf` to get the outputs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Binomial distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x24778421640>"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "n, p = 5, 0.4\n",
    "x = np.arange(binom.ppf(0.01, n, p), binom.ppf(0.99, n, p))\n",
    "ax.plot(x, binom.pmf(x, n, p), 'bo', ms=8);\n",
    "ax.vlines(x, 0, binom.pmf(x, n, p), colors='b', lw=5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other common distributions that are included:\n",
    "\n",
    "\n",
    "1. `scipy.stats.poisson`: Poisson distribution \n",
    "2. `scipy.stats.norm`: 1-D Gaussian distribution\n",
    "3. `scipy.stats.beta`: Beta distribution \n",
    "4. `scipy.stats.dirichlet`: Dirichlet distribution \n",
    "5. `scipy.stats.weibull_min`: Weibull distribution "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scipy.fft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+2.41421356j 1.-2.41421356j 1.-0.41421356j 1.+0.41421356j]\n",
      "[15.+0.j  2.+7.j -7.+0.j]\n"
     ]
    }
   ],
   "source": [
    "from scipy.fft import fft, rfft, irfft\n",
    "\n",
    "# Fast fourier transform\n",
    "arr = np.exp(2j * np.pi * np.arange(4) / 8)\n",
    "print(fft(arr))\n",
    "\n",
    "# 1D discrete real fast fourier transform\n",
    "arr = [3,2,1,9]\n",
    "print(rfft(arr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scipy.linalg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mostly analogous to np.linalg, although implementations of some operations may differ. See the relevant NumPy section above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scipy.special"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This module includes several functions commonly used in machine learning implementations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scipy.special.softmax`\n",
    "\n",
    "`scipy.special.log_softmax`\n",
    "\n",
    "Normalizing logits in the output of an RNN:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distribution:\n",
      "  [0.02604922 0.03600327 0.01388308 0.11734198 0.02559839 0.2211749\n",
      " 0.02548176 0.04654198 0.05915248 0.42877294]\n",
      "[-3.64776758 -3.3241455  -4.27708419 -2.14266268 -3.66522582 -1.50880148\n",
      " -3.66979254 -3.06740061 -2.82763681 -0.84682777]\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import softmax, log_softmax\n",
    "\n",
    "data = np.random.randn(10)\n",
    "print('Distribution:\\n ', softmax(data))\n",
    "print(log_softmax(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scipy.special.logsumexp`\n",
    "\n",
    "To help perform computation in a numerically stable way (the \"logsumexp\" trick)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculation prone to instability\n",
      " inf\n",
      "Calculation with logsumexp\n",
      " 1001.0986122886682\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Bryan\\AppData\\Local\\Temp/ipykernel_49856/1068758318.py:5: RuntimeWarning: overflow encountered in exp\n",
      "  print('Calculation prone to instability\\n', (np.log(np.sum(np.exp(data)))))\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import logsumexp\n",
    "import math\n",
    "\n",
    "data = np.array([1000, 1000, 1000])\n",
    "print('Calculation prone to instability\\n', (np.log(np.sum(np.exp(data)))))\n",
    "print('Calculation with logsumexp\\n', logsumexp(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scipy.special.gamma`\n",
    "\n",
    "Calculating mean wind speed for a wind turbine using a weibull distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean winspeed is 9.47618493681721\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import gamma\n",
    "c, k = 10.7, 2.2\n",
    "U_bar =  c * gamma(1 + 1/k)\n",
    "print(\"Mean winspeed is {}\".format(U_bar))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scipy.special.xlogy`\n",
    "\n",
    "Calculating entropy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entropy: -0.3579322767129623\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import xlogy\n",
    "\n",
    "# hot dogs are equal to 2\n",
    "possible_hot_dogs = np.array([1,5,2,24,39,1,2])\n",
    "\n",
    "p = np.count_nonzero(possible_hot_dogs == 2)\n",
    "n = possible_hot_dogs.shape[0] - p\n",
    "H = xlogy(p / (p+n), p/(p+n))\n",
    "\n",
    "print('Entropy: {}'.format(H))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other Native Python Libraries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This section lists some other useful Python standard libraries. Example codes are forthcoming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [argparse](https://docs.python.org/3/library/argparse.html): Enables parsing of command line arguments at runtime.\n",
    "- [itertools](https://docs.python.org/3/library/itertools.html): Common functions for combinatorics.\n",
    "- [os](https://docs.python.org/3/library/os.html),[pathlib](https://docs.python.org/3/library/pathlib.html): Libraries for creating relative and absolute path strings to reference files.\n",
    "- [pickle](https://docs.python.org/3/library/pickle.html): Useful for saving and serializing data.\n",
    "- [math](https://docs.python.org/3/library/math.html): Math library.\n",
    "- [timeit](https://docs.python.org/3/library/timeit.html): Easily track the runtime of your code.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3rd-party libraries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [tqdm](https://github.com/tqdm/tqdm): display informative progress bars.\n",
    "- [rich](https://github.com/Textualize/rich): `pprint` on steroids. Useful for the poweruser that wants to print detailed, structured, visually appealing output.\n",
    "- [numba](https://numba.pydata.org/) Python JIT compilation.\n",
    "- [pytest](https://docs.pytest.org/en/7.1.x/) generate robust unit tests."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimizations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## JAX\n",
    "\n",
    "https://github.com/google/jax\n",
    "\n",
    "JAX is a library that allows for accelerated NumPy-like computations. While NumPy is fast, it only allows computations on CPU.\n",
    "JAX allows you to perform NumPy-like computations on accelerators like GPUs and TPUs. It leverages just-in-time compilation and can often be used as a drop-in replacement for NumPy.\n",
    "\n",
    "**NOTE:** You need a UNIX system to run this out-of-the box. If you're on Windows, you can use WSL2, or you need to compile the binary yourself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Repeat a 2x1 array of values sampled from a 1D normal, across a matrix of shape `(200,100)`.\n",
    "2. Create an ndarray of shape `(5,2,4)` filled with the number 9. Add 1 to the elements at position `(0,1,1)`, `(2,0,3)`, and `(1,2,2)`. Then create a flattened view of it without making a copy.\n",
    "3. Create a positive semidefinite matrix and check its eigenvalues. Then sum the values in each row.\n",
    "4. Implement maximum likelihood estimation over a dataset without any for loops.\n",
    "5. Create a 5x5 matrix with the number 8 along the diagonal.\n",
    "6. Sample 50 points from a Poisson distribution in one line.\n",
    "7. Convert the nested list `[[3,2,-1],[1,6,3],[2,-4,0]]` to a NumPy array, then take its inverse.\n",
    "8. Given the array `np.array([[3,4,5,1],[5,4,2,1],[5,2,4,8],[9,1,2,0]])`, filter all unique elements that have a count of greater than 2.\n",
    "9. Create three plots in the same figure, each with different plotted data, but with the same limits. The first should be y=sin(3x), the second y=3x^2 + 4, and the third a 3D surface plot of your choosing.\n",
    "10. Add 3 to every 3rd element in a 5x5 matrix filled with values drawn from a Bernoulli distribution (p=0.25)."
   ]
  }
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