{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Refresher  \n",
    "\n",
    "This document summarizes what you need to know about Python for doing CS homeworks in Jupyter Notebooks. \n",
    "\n",
    "There are three sections:\n",
    "\n",
    "- **Basic Python Programming** shows you all the basic features you need to get started\n",
    "- **Advanced Python** explains a number of advanced features which everyone should know about after the first week\n",
    "- **Appendices** present a number of special topics which may or may not be useful, depending on your project\n",
    "\n",
    "For a brief introduction to using Jupyter Notebooks, \n",
    "\n",
    "I also refer you to the tutorial notebooks on Latex, Markdown, Numpy, and Pandas. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Python Programming"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First Lesson in Python: Variables and assignment statements\n",
    "\n",
    "Python is an **interpreted** language, which means is mostly acts like a calculator,\n",
    "accepting *definitions* of variables and functions, and *expressions* which are evaluated\n",
    "in the context of the global definitions. \n",
    "\n",
    "Defining variables is done using the equals sign. You must line up the beginning of each statement,\n",
    "and you don't need a semicolon. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "6\n",
      "[4, 5]\n"
     ]
    }
   ],
   "source": [
    "x = 4\n",
    "y = x + 2\n",
    "a = [4,5]\n",
    "\n",
    "print(x)\n",
    "print(y)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Types and variables\n",
    "\n",
    "Python, like many interpreted languages, is \"weakly-typed,\" that is, values have types, but\n",
    "variables are NOT declared with a type, and in general, you can assign any type of value to\n",
    "any variable. \n",
    "\n",
    "Here are some examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "2.3\n",
      "True\n",
      "hi there\n"
     ]
    }
   ],
   "source": [
    "x = 4\n",
    "\n",
    "print(x)\n",
    "\n",
    "x = 2.3\n",
    "\n",
    "print(x)\n",
    "\n",
    "x = True\n",
    "\n",
    "print(x)\n",
    "\n",
    "x = \"hi there\"\n",
    "\n",
    "print(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Types are checked when variables are used, and may generate errors at execution time:"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Screen%20Shot%202023-01-10%20at%2010.08.02%20AM.png](attachment:Screen%20Shot%202023-01-10%20at%2010.08.02%20AM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Second lesson in Python: IF statements and how to indicate scope and nested context\n",
    "\n",
    "The most distinctive feature of Python is\n",
    "that it does not use an \"end of line\" character, and uses indentation to indicate nested contexts--what in other languages might be indicated with curly braces `{....}`:\n",
    "\n",
    "Java:\n",
    "\n",
    "    if(count < 20) {\n",
    "         final_count = count;\n",
    "         System.out.println(\"count =\", count);\n",
    "    }\n",
    "    \n",
    "Python:\n",
    "\n",
    "    if(count < 20):\n",
    "        final_count = count\n",
    "        print(\"count =\"count)\n",
    "        \n",
    "What is other languages is indicated using opening and closing parentheses (or curly braces)\n",
    "is indicated in Python by a tab-indented line.  The nesting level of a nested statement is\n",
    "indicated by its alignment on the page, NOT by the presence of opening and closing characters such\n",
    "as `{....}`. \n",
    "\n",
    "Therefore you will need to pay attention to where statements line up rather than what\n",
    "characters surround it. \n",
    "\n",
    "The other difference is that at the end of the conditional expression, a colon (:) will introduce\n",
    "the nested code block. \n",
    "\n",
    "Here are some examples of conditional statements. \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1 is greater than  2\n",
      "x2 is NOT greater than 2\n",
      "5 <= x3 < 8 \n"
     ]
    }
   ],
   "source": [
    "x1 = 5\n",
    "\n",
    "if(x1 >2):\n",
    "    print(\"x1 is greater than  2\")\n",
    "\n",
    "x2 = 1\n",
    "if(x2 >2):\n",
    "    print(\"x2 is greater than  2\")\n",
    "else:\n",
    "    print(\"x2 is NOT greater than 2\")\n",
    "    \n",
    "x3 = 7\n",
    "if(x3 < 2):\n",
    "    print(\"x3 < 2\")\n",
    "elif(x3 < 5):\n",
    "    print(\"2 <= x3 < 5\")\n",
    "elif(x3 < 8):\n",
    "    print(\"5 <= x3 < 8 \")\n",
    "else:\n",
    "    print(\"x3 >= 8\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Third lesson in Python: lists as the primary data structure\n",
    "\n",
    "Python, like most interpreted languages, makes heavy use of lists rather than arrays. What's the difference? Mostly, that lists can change shape, and (because of weak typing) can hold any kind of data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = [1,2,3,4]\n",
    "B = [\"hi\", \"there\", \"Paul\"]\n",
    "C = [a,'hi', True,[2,'b']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hi', 'there', 'Paul']\n"
     ]
    }
   ],
   "source": [
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4, 5], 'hi', True, [2, 'b']]\n"
     ]
    }
   ],
   "source": [
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paul\n",
      "Paul\n"
     ]
    }
   ],
   "source": [
    "# Pulling stuff out of lists\n",
    "\n",
    "print(B[2])\n",
    "\n",
    "# Using negative indices (going right to left)\n",
    "\n",
    "print(B[-1])     # last element of the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hi', 'there', 'Wayne']\n"
     ]
    }
   ],
   "source": [
    "# Replacing elements of lists\n",
    "\n",
    "B[2] = 'Wayne'\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can use ranges of indices to extract parts of lists. Just remember that the second number in\n",
    "the range is always 1 more than the last index you want. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['there', 'Wayne']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['hi', 'there']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['there', 'Wayne']"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['hi', 'there', 'Wayne']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The two most useful operations on lists\n",
    "\n",
    "Here are two ways you will manipulate lists most often. For additional functions, see the section **Useful List Functions** in **Advanced Python** below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hi', 'there', 'Wayne', 'how', 'are', 'you']\n"
     ]
    }
   ],
   "source": [
    "# append two lists using +\n",
    "\n",
    "D = B + ['how','are','you']\n",
    "print( D )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hi is in the list\n"
     ]
    }
   ],
   "source": [
    "# Check if an object is a member of a list using in\n",
    "\n",
    "if( 'hi' in D ):\n",
    "    print('hi is in the list')\n",
    "else:\n",
    "    print('hi is not in the list')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Strings can be manipulated as lists\n",
    "\n",
    "Strings have their own set of associated functions, but basically they are just lists of characters, and\n",
    "you can call many (but not all) list functions on them. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = \"Hi there Wayne\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'y'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "' ther'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[2:7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Addendum to Third Lesson:  Tuples \n",
    "\n",
    "An alternative to lists is *tuples*, which are essentially immutable lists, i.e., once created, they can not be modified; this turns out to be necessary in some cases. Mostly, you can just treat them like lists, \n",
    "as shown here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = (\"hi\", \"there\", \"Paul\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('there', 'Paul')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('hi', 'there')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('there', 'Paul')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(D)"
   ]
  },
  {
   "attachments": {
    "Screen%20Shot%202023-01-10%20at%2010.29.50%20AM.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But if you try to change a tuple's contents, you will get an error:\n",
    "\n",
    "![Screen%20Shot%202023-01-10%20at%2010.29.50%20AM.png](attachment:Screen%20Shot%202023-01-10%20at%2010.29.50%20AM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fourth Lesson:  Loops: while and for\n",
    "\n",
    "The while statement should cause no problems, just remember to indent and\n",
    "use a colon (:) at the end of the condition, which introduces the intended\n",
    "code block:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "x = 4\n",
    "while(x < 10):\n",
    "    print(x)\n",
    "    x += 1                # Python does not allow \"++x\" so you'll have to do this to increment a variable\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### For loops\n",
    "\n",
    "for loops iterate over the elements of a list, which may be created by the `range(...)` function. Just remember\n",
    "that the upper bound in a range is always 1 more than the last number you want to produce:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "for k in [1,2,3,5]:\n",
    "    print(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(10))        # a single number is assumed to be an upper bound with a starting value of 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(2,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 5, 8]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(2,10,3))      # a third argument is the skip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fifth Lesson:  Defining functions\n",
    "\n",
    "Functions are defined using the keyword `def` and using the colon and indented block syntax\n",
    "we have seen above.  Functions which return a value must use `return`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 5 5\n"
     ]
    }
   ],
   "source": [
    "def f(x):\n",
    "    print(x,x,x)\n",
    "    \n",
    "f(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def is_even(x):\n",
    "    if(x % 2 == 0):\n",
    "        return True\n",
    "    else:\n",
    "        return False\n",
    "    \n",
    "is_even(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "here is a definition\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'Hi there, Paul'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"here is a definition\")\n",
    "\n",
    "def sayHi(name):\n",
    "    return \"Hi there, \" + name\n",
    "\n",
    "sayHi('Paul')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Functions introduce a local scope for variables which are not available outside the function, just\n",
    "as in Java and other languages.  You may refer to variables outside the scope, but if you want\n",
    "to assign to them, you have to declare them as **global**. If you don't do this, you will get an error!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "N = 5\n",
    "\n",
    "def add2N(x):\n",
    "    global N\n",
    "    N = N + x\n",
    "    \n",
    "add2N(2)\n",
    "\n",
    "print(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Advanced Features of Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Useful List Functions\n",
    "\n",
    "Here are some examples of useful functions that work on lists. There are two important things to remember\n",
    "about calling a function on a list, the first having to do with the syntax and the second having to\n",
    "do with the effect of the function:\n",
    "\n",
    "1. Functions will be called in one of two ways, either as a function:\n",
    "\n",
    "    n = max(C)\n",
    "    \n",
    "or using the dot notation familiar from object-oriented languages such as Java:\n",
    "\n",
    "    k = C.index(3)\n",
    "    \n",
    "2. Functions may return a value (perhaps another list), leaving the original list unchanged:\n",
    "\n",
    "    C1 = C.copy()\n",
    "    \n",
    "or they may modify the list \"in place\" and return <code>None</code>. In this case, you use them\n",
    "as \"imperative\"statements that modify the list:\n",
    "\n",
    "    C.append(6)\n",
    "    \n",
    "**Note that functions which modify the original list will always use the \"dot notation.\"**\n",
    "    \n",
    "Here are examples of the most useful functions which return values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n",
      "2\n",
      "3\n",
      "5\n",
      "1\n",
      "[1, 2, 3, 3, 4, 4, 5]\n",
      "[5, 4, 4, 3, 3, 2, 1]\n",
      "[1, 3, 4, 2, 3, 4, 5]\n",
      "[1, 3, 4, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "C = [1,3,4,2,3,4,5]\n",
    "\n",
    "# Return the length of the list\n",
    "\n",
    "print(len(C))\n",
    "\n",
    "# Return a count of how many times a given element occurs in the list\n",
    "\n",
    "print(C.count(4))\n",
    "\n",
    "# Return the index of the first occurrence of an element (error if not found)\n",
    "\n",
    "print(C.index(2))\n",
    "\n",
    "# Return the largest/smallest element in the list\n",
    "\n",
    "print(max(C))\n",
    "print(min(C))\n",
    "\n",
    "# Return a sorted copy of the list, in ascending order by default\n",
    "\n",
    "print(sorted(C))\n",
    "print(sorted(C,reverse=True))\n",
    "\n",
    "# Return a copy of the list (two different ways)\n",
    "\n",
    "print(C.copy())\n",
    "print(C[:])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are two useful functions which change the list in place and return None. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 4, 2, 3, 4, 5, 12]\n",
      "[1, 2, 3, 3, 4, 4, 5, 12]\n",
      "[12, 5, 4, 4, 3, 3, 2, 1]\n"
     ]
    }
   ],
   "source": [
    "# Add a new element to the end of the list\n",
    "\n",
    "C.append(12)\n",
    "print(C)\n",
    "\n",
    "# Sort the list in place\n",
    "\n",
    "C.sort()\n",
    "print(C)\n",
    "\n",
    "C.sort(reverse=True)\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List Comprehensions\n",
    "\n",
    "A list comprehension is a great way to create lists with a minimum of fuss and bugs. \n",
    "The basic idea is that instead of creating a list by specifying every step, say like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a list of the first 10 squares\n",
    "\n",
    "L = [0] * 10         # create a list of 10 zeros\n",
    "\n",
    "for k in range(len(L)):\n",
    "    L[k] = (k+1)**2\n",
    "L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "you can do it all in one line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]\n"
     ]
    }
   ],
   "source": [
    "L1 = [  (k+1)**2  for k in range(len(L))  ]\n",
    "print(L1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea is to collect together all instances of the expression at the beginning, for all values of k produces\n",
    "by the for. Some examples may clarify. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5070673275206681, 0.3273805686543323, 0.8412274449804783, 0.835724182196044, 0.35999478038816213, 0.17099486665971741, 0.7854551215753977, 0.8151163509924048, 0.07280493543428213, 0.4540995910610309]\n"
     ]
    }
   ],
   "source": [
    "from random import random            # The function random() returns a random double in the range [0..1)\n",
    "\n",
    "L2 = [  random()  for k in range(10)  ]\n",
    "print(L2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use multiple for loops:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['0A', '0B', '0C', '0D', '0E', '1A', '1B', '1C', '1D', '1E', '2A', '2B', '2C', '2D', '2E', '3A', '3B', '3C', '3D', '3E', '4A', '4B', '4C', '4D', '4E']\n"
     ]
    }
   ],
   "source": [
    "D = ['0','1','2','3','4']\n",
    "L = ['A','B','C','D','E']\n",
    "     \n",
    "X = [ d + el for d in D for el in L ]\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, watch out, because the order of the **for**'s must be the same as if you were writing a loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = [ [ 1,2,3] , [4,5,6], [7,8,9]]\n",
    "\n",
    "Tall = [ x for lst in T for x in lst ]\n",
    "\n",
    "Tall"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List comprehensions can do a lot, especiallly if you use conditions in the \"loop\" part:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[63, 241, 7, 43, 99, 132, 6, -3, 71, 235, 24, 66]\n",
      "[7, 43, 6, -3, 24]\n",
      "[63, 241, 99, 132, 71, 235, 66]\n"
     ]
    }
   ],
   "source": [
    "L3 = [63,241,7,43,99,132,6,-3,71,235,24,66]  \n",
    "\n",
    "# let's pick 63 as the \"pivot\" for quicksort and partition the list into those\n",
    "# numbers less than 63 and those greater or equal:\n",
    "\n",
    "left = [ x for x in L3 if x < 63 ]\n",
    "right = [ x for x in L3 if x >= 63 ]\n",
    "\n",
    "print(L3)\n",
    "print(left)\n",
    "print(right)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-3, 6, 7, 24, 43, 63, 66, 71, 99, 132, 235, 241]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  List comprehensions can be used to write very complicated algorithms with very few lines of code!\n",
    "\n",
    "def quicksort(L):\n",
    "    if(L == []):\n",
    "        return []\n",
    "    else:\n",
    "        pivot = L[0]\n",
    "        left  = [ x for x in L[1:] if x < pivot ]       # partition list around pivot\n",
    "        right = [ x for x in L[1:] if x >= pivot ] \n",
    "        return (  quicksort(left) + [pivot] + quicksort(right) )\n",
    "\n",
    "quicksort(L3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sets\n",
    "\n",
    "A set in mathematics is a collection of elements in which there are no duplicates and order does not matter.\n",
    "In Python, we can create sets, which are implemented by hash tables, and are much more efficient than lists, if\n",
    "a set is really what you want. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{2, 3, 4, 5}\n",
      "{3, 4}\n",
      "\n",
      "True\n",
      "True\n",
      "\n",
      "{2, 3, 4, 5, 7}\n",
      "{2, 4, 5, 7}\n",
      "\n",
      "A = {'d', 'c', 'a'}\n",
      "B = {'d', 2, 'c'}\n",
      "C = {1, 2, 3}\n",
      "\n",
      "A U B = {'d', 2, 'a', 'c'}\n",
      "B U C = {'d', 2, 1, 3, 'c'}\n",
      "A U B U C = {'d', 2, 1, 3, 'a', 'c'}\n",
      "A.union() = {'d', 'c', 'a'}\n",
      "\n",
      "A n B = {'d', 'c'}\n",
      "B n C = {2}\n",
      "A n C = set()      <- this is how empty set can be represented\n",
      "C n A n B = set()\n",
      "\n",
      "A - B = {'a'}\n",
      "B - A = {2}\n",
      "A - C = {'d', 'a', 'c'}\n"
     ]
    }
   ],
   "source": [
    "# create a set\n",
    "S= {2,3,4,5}\n",
    "print(S)\n",
    "\n",
    "# duplicates are ignored\n",
    "T = { 3, 4,3 }\n",
    "print(T)\n",
    "print()\n",
    "\n",
    "# membership test\n",
    "print( (3 in S) )\n",
    "\n",
    "# subset test\n",
    "print(  (T.issubset(S)) )\n",
    "print()\n",
    "\n",
    "# add an element to a set\n",
    "S.add(7)\n",
    "print(S)\n",
    "\n",
    "# remove an element from a set\n",
    "S.remove(3)\n",
    "print(S)\n",
    "print()\n",
    "\n",
    "# create a new set using set operations union, intersection, and set difference\n",
    "\n",
    "A = {'a', 'c', 'd'}\n",
    "B = {'c', 'd', 2 }\n",
    "C = {1, 2, 3}\n",
    "\n",
    "print('A =',A)\n",
    "print('B =',B)\n",
    "print('C =',C)\n",
    "print()\n",
    "\n",
    "print('A U B =', A.union(B))\n",
    "print('B U C =', B.union(C))\n",
    "print('A U B U C =', A.union(B, C))\n",
    "print('A.union() =', A.union())              # just make a copy\n",
    "print()\n",
    "\n",
    "# return a new set which is the intersecction of others\n",
    "print('A n B =',B.intersection(A))\n",
    "print('B n C =',B.intersection(C))\n",
    "print('A n C =',A.intersection(C),'     <- this is how empty set can be represented')\n",
    "print('C n A n B =',C.intersection(A, B))\n",
    "print()\n",
    "\n",
    "# return a new set which is the set difference with another\n",
    "print('A - B =',A.difference(B))\n",
    "print('B - A =',B.difference(A))\n",
    "print('A - C =',A.difference(C))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dictionaries\n",
    "\n",
    "A dictionary is a data structures which stores (key,value) pairs (typically implemented as a hash table).\n",
    "This is a great data structure for storing information about objects without having to muck around with lists.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': 2, 'c': 8, 'b': 1}\n",
      "{}\n"
     ]
    }
   ],
   "source": [
    "D = { 'a' : 2, 'c' : 8, 'b' : 1}      # Dictionary storing, say, how many times a letter appears in a string\n",
    "print(D)\n",
    "E = {}        # empty dictionary\n",
    "print(E)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Basic Dictionary Operations\n",
    "\n",
    "Most of the manipulation of dictionaries looks like array or list manipulation\n",
    "but using the keys instead of the position of the elements in the list. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the value associated with a particular key\n",
    "D['c']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 4, 'c': 8, 'b': 1, 'z': 23}"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Insert a key-value pair \n",
    "D['a'] = 4\n",
    "D['z'] = 23\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 4, 'c': 8, 'b': 1, 'z': 25}"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# update a value associated with a key by doing both\n",
    "D['z'] = D['z'] + 2\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['a', 'c', 'b', 'z'])\n",
      "['a', 'c', 'b', 'z']\n",
      "[4, 8, 1, 25]\n"
     ]
    }
   ],
   "source": [
    "### Miscellaneous functions\n",
    "\n",
    "# get all keys\n",
    "print( D.keys() )\n",
    "print( list(D.keys()) )       # to just get a list\n",
    "\n",
    "# get all values\n",
    "print( list(D.values()) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "# Default values for dictionaries\n",
    "\n",
    "# simplest: use the function get(...)\n",
    "x = D.get('q',0)         # first argument to get is the key, the second is the default\n",
    "                         # value if the key is not in the dictionary\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "# The second way is to use a different kind of dictionary, which you have to import,\n",
    "# and then define a function to return the default value\n",
    "\n",
    "from collections import defaultdict\n",
    "\n",
    "def get_default():\n",
    "    return 0\n",
    "\n",
    "A = defaultdict(get_default)\n",
    "\n",
    "A['a'] = 5\n",
    "print( A['a'] )\n",
    "print( A['b'] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter creates a dictionary giving the frequency counts of each element in the list.\n",
      "Counter({3: 5, 4: 5, 2: 2, 5: 2, 8: 1})\n",
      "The list has 5 instances of the number 3.\n"
     ]
    }
   ],
   "source": [
    "### Calculating frequency counts using a dictionary\n",
    "\n",
    "from collections import Counter       \n",
    "\n",
    "F = Counter([3,4,2,3,4,5,4,3,2,3,4,5,4,3,8])\n",
    "\n",
    "print(\"Counter creates a dictionary giving the frequency counts of each element in the list.\")\n",
    "print(F)\n",
    "\n",
    "n = 3\n",
    "print(\"The list has\",F[n], 'instances of the number '+ str(n) + '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting and Graphing\n",
    "\n",
    "The <code>scatter(...)</code> function is used to display points from a list of x values and the associated y values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This is the list of points: [(1, 2), (2, 3), (3, 6), (4, 8)]\n",
      "They must be input to the function as separate lists:\n",
      "\tX = [1, 2, 3, 4]\n",
      "\tY = [2, 3, 6, 8] \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEWCAYAAABsY4yMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAcY0lEQVR4nO3dfZxcZX338c83mwAbwETJqiQ8pFKNgmASV4xShQISrNwSMVUs+EDh5qXeUhWMNtbbh6rFGrWF+tQIKhTBgsboTYFoVaAg4J0nCaCxYhIhAbI8LAmwYBJ+/eNcC5NhdnZ2d87szpXv+/WaV2bOOXOu35mz+c6Za85cRxGBmZnlZ9xoF2BmZuVwwJuZZcoBb2aWKQe8mVmmHPBmZplywJuZZcoBbzuR9ElJl9SZf7uko1pXUX2STpH049Guo5+kj0q6oM78d0m6oZU1tYqk4yQtLWndX5L07jLWnTMH/Bgn6WRJt0h6VNLmdP+9kjQa9UTEIRFxbbPXm4Jvh6RHJG2RtFrSCQ3U852IOG4IbZQarhHxDxFxRmpvuqSQNL7MNoei1hu4pGslndGE1f8D8Lm0zv0kPSTpzyra2T9Ne2VV+5J0vaSPV01/p6Q7JU0EFgF/J2m3JtS5y3DAj2GSzgHOo/jjfj7wPODdwBFAzT90SR0tK7D5boqIvYDJwIXA5ZKeM7ol2WAkdUh6BTApIm4GiIi7gY8AF0jaIy36r8C3IuKWyudH8WvL04GzJR2S1tkFfAE4IyIei4h7gN8Ab2zJRuUiInwbgzdgEvAo8OZBlvs28DXgqrT8scAbgFXAFuAu4JMVy08HAjgT2ATcA5xTMf+TwOXAxcBW4Hagu2L+euDYBpednerYClwB/DvwmQG2413ADRWP90x1dqfX4mKgB9gAfAwYN8DzguJN8L+Bh4CvAAJeAjwO7AAeAXrT8n8B3JFq3Ah8aID6NgAvT/dPTe0cnB6fASyteE0uSff/kJZ7JN1e1V8vRXg9BKwDXl9n/34k1bUVWAsck6Z3AB8F7kzzVgD7p3nnpf2+JU1/TZp+PPBHYFuq51fAZ9Nr8nia9uW07IuBnwAPpnbfMsjf3MeBC6pqF/Bz4FzgnanWiXW2dQFwM8WB52XA16vm/x3FG8So//9sl9uoF+DbADum+M+4HRg/yHLfBh6mOKofB+wBHAUcmh4fBtwHzEvLT0+hcxlFiB5KEZyVof14Cr6O9J/z5or21jeyLMUnjA3A+4EJwEkpXAYNeGB8et5Wng73HwJ7p/p/C5xe/bz0OIArKT4FHJC27fhay6Zp9/B0AD4bmD1AfReT3giBxSms3lMx74MVr8klVa/1+Krt3Ab87/SavYfijVY12pxBEdRTK9Z3ULq/AFiTlhHwMmCfNO9UYJ/0Op4D3AvsUV1fRTvXUhwp9z/eM7V7WlrHbOB+4JA6f3NXAAtqbMNBadmHgKMH+VvuAG4BllC8Oe5dNf8kYOVo/99sp5u7aMauKcD9EbG9f4KkX0jqldQn6bUVy/4wIm6MiCcj4vGIuDYi1qTHt1KE+ZFV6/9URDwaEWuAbwFvq5h3Q0RcFRE7gH+jCI+BDLTsHIpwOD8itkXEEuCXg2zzHEm9FIH0NuBNFEeVbwUWRsTWiFgPfBF4e531fC4ieiPiDxRHkDPrLLsNOFjSsyLioYhYOcBy1/H0a/gaijez/sdHpvmN2hAR30iv2UXAvhTdb9V2ALun+iZExPqIuDPNOwP4WESsjcKvIuIBgIi4JCIeiIjtEfHFtI4ZQ6jvBGB9RHwrrWMl8H1gfsUyO/3NUbyhbq21rRRvYFuA6+s1ml6Pv6bY72dFRPX6tqZ2rEEO+LHrAWBK5Rd0EfHqiJic5lXuu7sqnyjplZJ+LqlH0sMUXRZTqtZf+ZwNwNSKx/dW3H8M2KPOF4UDLTsV2Bjp0KtWnTXcHBGTI2JKRMyJiP9Mdfd/Gqisd1qd9VTXtFedZd9M8Qlkg6TrJL1qgOWuA14j6fkUR5r/DhwhaTrFp4zVddoYsL6IeCzdfUaNEfE74AMUR92bJX1XUv9+2p/iU8QzSDpH0q8lPZzeMCfxzP1fz4HAK9PBRG9axykU3wP1q96XD1F8wqr2txR/r5uBDw3WcETcnu7eXmP23kDvYOuwpzngx66bgCeAExtYtnpI0EuBH1H0yU4Cvk7xMb7S/hX3D6A4ymqme4BpVWf77D/QwnXcT3GUfWDFtAMo+qWH6hlDp0bE/4+IE4HnAkspvlN45hOLsH0M+Bvg+nR0eS/Fdxk3RMSTjbQ35IIjLo2IP6PY/gD+Mc26i6L7YyeSXkPRb/8W4NnpgOBhnt7/tWqqnnYXcF16s+2/7RUR76nznFuBF1XVcjBFV9IZFF+iflTSC+tt7yBeQvG9gTXIAT9GRUQv8Cngq5LmS9pL0jhJMyn6SOvZG3gwIh6XdDjwVzWW+b+SJqazFk6jOCJtppsouhjeJ2m8pBOBw4e6kvSx/XLgs5L2lnQgcDYw4Ln6ddwH7Nd/qp2k3dJ59JMiYhtFN8KOOs+/DngfT3fHXFv1uFoP8CTwgmHUiqQZko6WtDvFdx19FfVdAHxa0gvTaYaHSdqHYt9vT22PT6cePqtitfcB0yWNq5pWWeOVwIskvV3ShHR7haSX1Cn3Kiq6AdP6LwQ+HxG/SV2F5wOL+9/00ymb1w7hJTkSuHoIy+/yHPBjWER8niLMPkzxEfc+ilPNPgL8os5T3wv8vaStFGc31DoqvQ74HfBT4AsR0dQfC0XEHym+FDud4mP1qRTB8cQwVncWxdkav6c4A+VS4JvDWM/PKD763yvp/jTt7cB6SVsourJOrfP86ygC9PoBHu8kdb98FrgxdXXMGWK9u1OcV34/xaeF51KcOQPwJYr9+mOKN6YLgU5gGUUI/paiK+txdu5OuSL9+4Ck/u8bzgPmp3PUz0+fTo4DTqb4ZHcvxSeH3QcqNPXTP1xxjvv7gYnA5ysW+zRFN0//Off7Azc28kJI2hc4mOJTljVIO3eRWu5Sn/E6YELlF7gtavsWilPfvtXKdq01JB0HvDci5jW4/GqK0z4faGDZLwJ3RsRXR1TkLsYBv4tpZcBLOpLiHOr7Kb6k+zrwgih+tGJmJRszP6G2LM2g6EbYi+KMj/kOd7PW8RG8mVmm/CWrmVmmxlQXzZQpU2L69OmjXYaZWdtYsWLF/RHRVWvemAr46dOns3z58tEuw8ysbUjaMNA8d9GYmWXKAW9mlikHvJlZphzwZmaZcsCbmWWq1LNoJH2QYmChoLj6zGnp4gBmZru8pas2smjZWjb19jF1cicL5s5g3qx6lzoYmtKO4CVNoxg7uzsiXkpxkYSTy2rPzKydLF21kYVL1rCxt48ANvb2sXDJGpauGs6lDmoru4tmPNCZrvAzkeZfVMLMrC0tWraWvm07X36gb9sOFi1b27Q2Sgv4iNhIceX4P1Bc3efhWmOOSzpT0nJJy3t6esoqx8xsTNnU2zek6cNRZhfNsykuN/cnFNfn3FPSMy6mEBGLI6I7Irq7umr+2tbMLDtTJ3cOafpwlNlFcyywLiJ60uXQlgCvLrE9M7O2sWDuDDondOw0rXNCBwvmzmhaG2WeRfMHYI6kiRTXkjwG8EAzZmbw1NkyZZ5FU1rAR8Qtkr4HrKS4CPAqYHFZ7ZmZtZt5s6Y1NdCrlXoefER8AvhEmW2YmVlt/iWrmVmmHPBmZplywJuZZcoBb2aWKQe8mVmmHPBmZplywJuZZcoBb2aWKQe8mVmmHPBmZplywJuZZcoBb2aWKQe8mVmmHPBmZplywJuZZcoBb2aWKQe8mVmmHPBmZplywJuZZcoBb2aWKQe8mVmmHPBmZplywJuZZcoBb2aWqdICXtIMSasrblskfaCs9szMbGfjy1pxRKwFZgJI6gA2Aj8oqz0zM9tZq7pojgHujIgNLWrPzGyX16qAPxm4rNYMSWdKWi5peU9PT4vKMTPLX+kBL2k34I3AFbXmR8TiiOiOiO6urq6yyzEz22W04gj+9cDKiLivBW2ZmVnSioB/GwN0z5iZWXlKDXhJE4HXAUvKbMfMzJ6ptNMkASLiMWCfMtswM7Pa/EtWM7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsU+PLXLmkycAFwEuBAP46Im4qs00zq23pqo0sWraWTb19TJ3cyYK5M5g3a9pol2UlKjXggfOAayJivqTdgIklt2dmNSxdtZGFS9bQt20HABt7+1i4ZA2AQz5jpXXRSHoW8FrgQoCI+GNE9JbVnpkNbNGytU+Fe7++bTtYtGztKFVkrVBmH/wLgB7gW5JWSbpA0p7VC0k6U9JySct7enpKLMds17Wpt29I0y0PZQb8eGA28LWImAU8Cvxt9UIRsTgiuiOiu6urq8RyzHZdUyd3Dmm65aHMgL8buDsibkmPv0cR+GbWYgvmzqBzQsdO0zondLBg7oxRqshaYUgBL2lc6lsfVETcC9wlqf8v6BjgjiHWZ2ZNMG/WNM496VCmTe5EwLTJnZx70qH+gjVzg55FI+lS4N3ADmAFMEnSlyJiUQPrPwv4TjqD5vfAaSMp1syGb96saQ70XUwjR/AHR8QWYB5wFXAA8PZGVh4Rq1P/+mERMS8iHhp+qWZmNhSNBPwESRMoAv6HEbGN4kdLZmY2hjUS8P8KrAf2BK6XdCCwpcyizMxs5Abtg4+I84HzKyZtkPTn5ZVkZmbNMOgRvKTnSbpQ0tXp8cHAO0uvzMzMRqSRLppvA8uAqenxb4EPlFSPmZk1SSMBPyUiLgeeBIiI7RSnTJqZ2RjWSMA/Kmkf0pkzkuYAD5dalZmZjVgjwwWfDfwIOEjSjUAXML/UqszMbMQaOYtmpaQjgRmAgLXpXHgzMxvDGhmq4B1Vk2ZLIiIuLqkmMzNrgka6aF5RcX8PikHDVgIOeDOzMayRLpqzKh9LmgT8W2kVmZlZUwxnPPjHgBc2uxAzM2uuRvrg/x9PDy42DjgYuLzMoszMbOQa6YP/QsX97cCGiLi7pHrMzKxJGumDv64VhZiZWXMNGPCStlJ73HcBERENXbrPzMxGx4ABHxF7t7IQMzNrrkb64AGQ9FyK8+ABiIg/lFKRmZk1RSPjwb9R0n8D64DrKK7udHXJdZmZ2Qg1ch78p4E5wG8j4k8ofsl6Y6lVmZnZiDUS8Nsi4gFgnKRxEfFzYGa5ZZmZ2Ug10gffK2kv4HrgO5I2U5wPb2ZmY9iAR/CS5kvaAziRYniCDwLXAHcC/6s15ZmZ2XDVO4I/BfgqRahfBvw4Ii4aysolrQe2Ulzib3tEdA+zTjMzG6IBj+Aj4k3AnwI/Bf4GuEvS1yS9doht/HlEzHS4m5m1Vt0vWSNiS0RcFBGvBw4FVgP/IumuVhRnZmbD19BwwZKeDZwEvBV4DvD9BtcfwI8lrZB05gDrPlPScknLe3p6GlytmZkNpt5YNHsD84C3AbMpLrz9GeDnEVFrjJpajoiITelXsD+R9JuIuL5ygYhYDCwG6O7ubnS9ZmY2iHpfsq4DlgFfA64ZzoW2I2JT+nezpB8Ah1OcbmlmZiWrF/AHRMRjw12xpD2BcRGxNd0/Dvj74a7PzMyGpt5oksMO9+R5wA8k9bdzaURcM8J1mplZgxoeTXKoIuL3wMvKWr+ZmdVX75esb2llIWZm1lz1TpN8h6RrJL2gZdWYmVnT1OuDP0HSPOA/JF1KcTbNkxXzHyy/PDMzG666ffARsVTSOopTG0/n6Wu0BuAjezOzMazeD512Bz4GzAdOiYgrW1aVmZmNWL0++FuBDmC2w93MrP3U66J5U0Tc0bJKzMysqeoNF+xwNzNrYw2NJmlmZu3HAW9mlqlBA17SiyT9VNJt6fFhkj5WfmlmZjYSjRzBfwNYCGwDiIhbgZPLLMrMzEaukYCfGBG/rJq2vYxizMyseRoJ+PslHUT6Fauk+cA9pVZlZmYj1shwwf+H4pJ6L5a0keJKT6eWWpWZmY3YoAGfxnU/tvIKTeWXZWZmIzVowKcxad4MTAfGpys0ERG+/J6Z2RjWSBfND4GHgRXAE+WWY2ZmzdJIwO8XEceXXomZmTVVI2fR/ELSoaVXYmZmTVVvPPjbKK7gNB44TdLvKbpoBEREHNaaEs3MbDjqddFMA2a2qA4zM2uyegG/LiI2tKwSMzNrqnoB/1xJZw80MyK+VEI9ZmbWJPUCvgPYi6LPfdgkdQDLgY0RccJI1mVmZo2rF/D3NOnHTO8Hfg08qwnrMjOzBtU7TXJER+4AkvYD3gBcMNJ1mZnZ0NQL+GOasP5/Bj5McbplTZLOlLRc0vKenp4mNGlmZlD/otsPjmTFkk4ANkfEinrLRcTiiOiOiO6urq6RNGlmZhXKvCbrEcAbJa0HvgscLemSEtszM7MKpQV8RCyMiP0iYjrFJf5+FhEeR97MrEXKPII3M7NR1MhokiMWEdcC17aiLTMzK/gI3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NMOeDNzDLlgDczy9T4slYsaQ/gemD31M73IuITZbVnY8fSVRtZtGwtm3r7mDq5kwVzZzBv1rTRLstsl1NawANPAEdHxCOSJgA3SLo6Im4usU0bZUtXbWThkjX0bdsBwMbePhYuWQPgkDdrsdK6aKLwSHo4Id2irPZsbFi0bO1T4d6vb9sOFi1bO0oVme26Su2Dl9QhaTWwGfhJRNxSY5kzJS2XtLynp6fMcqwFNvX2DWm6mZWn1ICPiB0RMRPYDzhc0ktrLLM4Irojorurq6vMcqwFpk7uHNJ0MytPS86iiYhe4Frg+Fa0Z6NnwdwZdE7o2Gla54QOFsydMUoVme26Sgt4SV2SJqf7ncCxwG/Kas/GhnmzpnHuSYcybXInAqZN7uTckw71F6xmo6DMs2j2BS6S1EHxRnJ5RFxZYns2RsybNc2BbjYGlBbwEXErMKus9ZuZWX3+JauZWaYc8GZmmXLAm5llygFvZpYpB7yZWaYc8GZmmXLAm5llygFvZpYpB7yZWaYc8GZmmXLAm5llygFvZpYpB7yZWaYc8GZmmXLAm5llygFvZpYpB7yZWaYc8GZmmXLAm5llygFvZpYpB7yZWaYc8GZmmXLAm5llygFvZpap8WWtWNL+wMXA84EngcURcV6z21m6aiOLlq1lU28fUyd3smDuDObNmtbsZszM2k5pAQ9sB86JiJWS9gZWSPpJRNzRrAaWrtrIwiVr6Nu2A4CNvX0sXLIGwCFvZru80rpoIuKeiFiZ7m8Ffg00NXUXLVv7VLj369u2g0XL1jazGTOzttSSPnhJ04FZwC015p0pabmk5T09PUNa76beviFNNzPblZQe8JL2Ar4PfCAitlTPj4jFEdEdEd1dXV1DWvfUyZ1Dmm5mtispNeAlTaAI9+9ExJJmr3/B3Bl0TujYaVrnhA4WzJ3R7KbMzNpOmWfRCLgQ+HVEfKmMNvq/SPVZNGZmz1TmWTRHAG8H1khanaZ9NCKuamYj82ZNc6CbmdVQWsBHxA2Aylq/mZnV51+ympllygFvZpYpB7yZWaYc8GZmmVJEjHYNT5HUA2wY5tOnAPc3sZzRlMu25LId4G0Zi3LZDhjZthwYETV/JTqmAn4kJC2PiO7RrqMZctmWXLYDvC1jUS7bAeVti7tozMwy5YA3M8tUTgG/eLQLaKJctiWX7QBvy1iUy3ZASduSTR+8mZntLKcjeDMzq+CANzPLVFsFvKRvStos6bYB5kvS+ZJ+J+lWSbNbXWOjGtiWoyQ9LGl1un281TU2QtL+kn4u6deSbpf0/hrLtMV+aXBbxvx+kbSHpF9K+lXajk/VWKZd9kkj2zLm90klSR2SVkm6ssa85u6XiGibG/BaYDZw2wDz/wK4mmIUyznALaNd8wi25SjgytGus4Ht2BeYne7vDfwWOLgd90uD2zLm90t6nfdK9ydQXCpzTpvuk0a2Zczvk6p6zwYurVVzs/dLWx3BR8T1wIN1FjkRuDgKNwOTJe3bmuqGpoFtaQvR2MXV22K/NLgtY156nR9JDyekW/XZFO2yTxrZlrYhaT/gDcAFAyzS1P3SVgHfgGnAXRWP76YN/4NWeFX6aHq1pENGu5jB1Lm4etvtl3oXiqcN9kvqBlgNbAZ+EhFtu08a2BZog32S/DPwYeDJAeY3db/kFvC1LjDSru/2KynGmHgZ8C/A0tEtp75BLq7eVvtlkG1pi/0SETsiYiawH3C4pJdWLdI2+6SBbWmLfSLpBGBzRKyot1iNacPeL7kF/N3A/hWP9wM2jVItIxIRW/o/mkZxmcMJkqaMclk1NXBx9bbZL4NtSzvtF4CI6AWuBY6vmtU2+6TfQNvSRvvkCOCNktYD3wWOlnRJ1TJN3S+5BfyPgHekb6LnAA9HxD2jXdRwSHq+JKX7h1PsqwdGt6pnSjUOdnH1ttgvjWxLO+wXSV2SJqf7ncCxwG+qFmuXfTLotrTDPgGIiIURsV9ETAdOBn4WEadWLdbU/VLmRbebTtJlFN+YT5F0N/AJii9diIivA1dRfAv9O+Ax4LTRqXRwDWzLfOA9krYDfcDJkb5mH2NqXlwdOADabr80si3tsF/2BS6S1EERdpdHxJWS3g1tt08a2ZZ22CcDKnO/eKgCM7NM5dZFY2ZmiQPezCxTDngzs0w54M3MMuWANzPLlAPe2oKkfSpGC7xX0sZ0v1fSHSNY79mSLqx4fIqk/6haZrqkuyWNq5q+Op13XWu90zXASKFmreKAt7YQEQ9ExMz0k/WvA/+U7s9k4HE9GnE+8HJJR6Qf1HwGOKuq7fUU44O8pn+apBcDe0fEL0fQtlmpHPCWgw5J31AxXviP0y8ekXSQpGskrZD0XymUdxIR24H3Al8BPg98MyJ+X6ONyyh+fdjvZOCydKT+X5JWpturq58o6V2Svlzx+EpJR6X7x0m6KT33ijQODpI+J+kOFWOCf2G4L4zt2hzwloMXAl+JiEOAXuDNafpi4KyIeDnwIeCrtZ4cEb+gGBr4WIqQr+VyYJ6k/l9/v5ViPJHNwOsiYnaadn6jRafxUj4GHJuevxw4W9JzgDcBh0TEYRSfKsyGrK2GKjAbwLqIWJ3urwCmpyPhVwNXpGFKAHav9eS0bDfFUBFdFAM+7SQi7pV0O3CMpPuAbRFxm6RJwJclzQR2AC8aQt1zgIOBG1ONuwE3AVuAx4EL0vcBz7jyj1kjHPCWgycq7u8AOik+nfamfvrBfAq4BLgP+CfgLwdYrr+b5r50H+CD6fHLUpuP13jednb+tLxH+lcU45u/rfoJ6cvbY1J77wOObmA7zHbiLhrLUhrHfZ2kv4SnrnX5surlJB1KcYWdf6To0jlQ0usGWO33KQaC6u+eAZgE3BMRT1IMVNZR43nrgZmSxknaH+g/8+Zm4AhJf5pqmSjpRekTxaQ09O0HKL5INhsyB7zl7BTgdEm/Am6nuBzaU9IQs18DPhgRj6eQfi9wnqTdqleWxiO/GbgvItalyV8F3inpZorumUdr1HEjsA5YA3yB4gIVREQP8C6KL2tvTet+McX1YK9M066j+JRgNmQeTdLMLFM+gjczy5QD3swsUw54M7NMOeDNzDLlgDczy5QD3swsUw54M7NM/Q8PqaYvg7grCgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# To plot the points (1,2), (2,3), (3,6), (4,8) we would list the x values and the corresponding y values:\n",
    "X = [1,2,3,4]\n",
    "Y = [2,3,6,8]\n",
    "\n",
    "print(\"\\nThis is the list of points:\",list(zip(X,Y)))\n",
    "print(\"They must be input to the function as separate lists:\")\n",
    "print(\"\\tX =\",X)\n",
    "print(\"\\tY =\",Y,\"\\n\")\n",
    "\n",
    "plt.scatter(X,Y)\n",
    "plt.title('Graphing Points with scatter(X,Y)')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Plotting curves\n",
    "\n",
    "If you call <code>plot(...)</code> instead of <code>scatter(...)</code> you will display a curve created by connecting the points with straight lines. Essentially you can only plot straight lines between points, but if the points are close together, you will not notice, and it will look like a smooth curve. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import sin\n",
    "\n",
    "# To plot a curve through the points (1,2), (2,3), (3,6), (4,8) we would use: \n",
    "plt.plot([1,2,3,4], [2,3,6,8])\n",
    "plt.title('A Sequence of Straight Lines')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "X = np.linspace(1,20,100)            # returns a list of 100 equally-spaced values in the range [1..20]\n",
    "Y = [sin(x) for x in X]\n",
    "plt.plot(X,Y)\n",
    "plt.title('A Smooth-Looking Curve')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you leave out the $X$ values, `plot(...)` will assume that you want the x-axis labeled 0, 1, ..., (len(X)-1),\n",
    "corresponding to the labels on an array or list:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a list against the indices\n",
    "Y = [2,3,6,8]\n",
    "\n",
    "plt.plot(Y)\n",
    "plt.title('Graphing lines with plot(Y)')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to do both, you can simply call both functions before you call show(). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([1,2,3,4], [2,3,6,8])\n",
    "plt.plot([1,2,3,4], [2,3,6,8])\n",
    "plt.title('A Curve Through Some Points, Showing the Points')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to draw a single line from $(x_1,y_1)$ to $(x_2,y_2)$ you can plot $[x_1,x_2]$ and $[y_1,y_2].$\n",
    "\n",
    "Here we have added a zero line to our sin curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(1,20,100)            # returns a list of 100 equally-spaced values in the range [1..20]\n",
    "Y = [np.sin(x) for x in X]\n",
    "plt.plot(X,Y)\n",
    "plt.plot([0,20],[0,0])\n",
    "plt.title('A Smooth-Looking Curve')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bar Charts\n",
    "\n",
    "If we do the exact same thing as we did with a simple plot, but use the function <code>bar(...)</code> we get a bar chart:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To plot the points (1,2), (2,3), (3,6), (4,8) we would list the x values and the corresponding y values:\n",
    "plt.figure(num=None, figsize=(8, 6))\n",
    "plt.bar([1,2,3,4], [2,3,6,8])\n",
    "plt.title('A Bar Chart')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "If the Y axis is probabilities (in the range 0 .. 1), we get a distribution of the probabilities among the outcomes of an experiment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the distribution of probabilities for a coin flip:\n",
    "x = [0,1]\n",
    "y = [0.5, 0.5]\n",
    "labels = ['Heads', 'Tails']\n",
    "\n",
    "plt.figure(num=None, figsize=(8, 6))\n",
    "plt.xticks(x, labels)\n",
    "plt.bar(x,y)\n",
    "plt.title('Probability Distribution for Coin Flips')\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xlabel(\"Outcomes\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a few tweaks, you can create an attractive bar chart for arbitrary probability distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MJEmSJPWewUiSJElS7xmMJEmSJPWewUiSJElS7xmMJEmSJPWewUiSJElS7xmMJEmSJPWewUiSJElS7xmMJEmSJPWewUiSJElS7xmMJEmSJPWewUiSJElS73UajJIckeTqJJuSnDrO+scmuTTJnUneNM76kSRfS3Jxl3VKkiRJ6rfOglGSEeAM4EhgBXBskhVjNrsZeD3wngmaORnY2FWNkiRJkgTd9hgdBmyqqmuq6i7gAuDowQ2q6saqWgdsH7tzkiXA7wAf6rBGSZIkSeo0GC0Gtgw839ouG9bfAG8G7pnGmiRJkiTpProMRhlnWQ21Y7IKuLGqLh9i2+OTrE+yftu2bTtboyRJkiR1Goy2AksHni8Brhty36cCz09yLc0QvGcm+eh4G1bVWVW1sqpWLly48P7UK0mSJKmnugxG64DlSQ5JshdwDLBmmB2r6o+qaklVHdzu99mqenl3pc5RIwtI0tnPoiXLZvsMJUmSpBmxZ1cNV9XdSU4CLgFGgHOqakOSE9r1q5McCKwH9gXuSfIGYEVV3dpVXfPKju0cdEp3M5lvPm1VZ21LkiRJu5POghFAVa0F1o5Ztnrg8Q00Q+wma+PzwOc7KE+SJEmSgI6/4FWSJEmS5gKDkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6j2DkSRJkqTeMxhJkiRJ6r1Og1GSI5JcnWRTklPHWf/YJJcmuTPJmwaWL03yuSQbk2xIcnKXdUqSJEnqtz27ajjJCHAG8BxgK7AuyZqq+tbAZjcDrwdeMGb3u4E3VtUVSfYBLk/y6TH7SpIkSdK06LLH6DBgU1VdU1V3ARcARw9uUFU3VtU6YPuY5ddX1RXt458AG4HFHdYqSZIkqce6DEaLgS0Dz7eyC+EmycHAocBlE6w/Psn6JOu3bdu2K3VKkiRJ6rkug1HGWVY71UDyEODjwBuq6tbxtqmqs6pqZVWtXLhw4S6UKUmSJKnvugxGW4GlA8+XANcNu3OSBTSh6GNVddE01yZJkiRJP9dlMFoHLE9ySJK9gGOANcPsmCTA2cDGqnpvhzVKkiRJUnez0lXV3UlOAi4BRoBzqmpDkhPa9auTHAisB/YF7knyBmAF8KvAK4CrklzZNvmWqlrbVb2SJEmS+quzYATQBpm1Y5atHnh8A80Qu7G+xPj3KEmSJEnStOv0C14lSZIkaS4wGEmSJEnqPYORJjaygCSd/ixasmy2z1KSJEnq9h4jzXE7tnPQKRd3eojNp63qtH1JkiRpGPYYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3us0GCU5IsnVSTYlOXWc9Y9NcmmSO5O8aWf2lSRJkqTp0lkwSjICnAEcCawAjk2yYsxmNwOvB96zC/tKkiRJ0rTossfoMGBTVV1TVXcBFwBHD25QVTdW1Tpg+87uK0mSJEnTZahglGRVkp0NUYuBLQPPt7bLpnXfJMcnWZ9k/bZt23ayREmSJEkavsfoGOA7Sd6d5HFD7pNxltV071tVZ1XVyqpauXDhwiGblyRJkqR/N1QwqqqXA4cC3wXObSdMOD7JPpPsthVYOvB8CXDdkHXdn30lSZIkaacMPTyuqm4FPk5zv88i4IXAFUleN8Eu64DlSQ5JshdNr9OaIQ93f/aVJEmSpJ2y5zAbJXk+cBzwSOAjwGFVdWOSBwEbgfeP3aeq7k5yEnAJMAKcU1UbkpzQrl+d5EBgPbAvcE+SNwArqurW8fa9n+cqSZIkSeMaKhgBLwb+uqq+OLiwqu5I8uqJdqqqtcDaMctWDzy+gWaY3FD7SpIkSVIXhh1Kd/3YUJTkNICq+sy0VyVJkiRJM2jYYPSccZYdOZ2FqKdGFpCks59FS5bN9hlKkiRpDph0KF2S/wK8Fnhkkm8MrNoH+HKXhakndmznoFMu7qz5zaet6qxtSZIkzR9T3WP0t8D/Af4SOHVg+U+q6ubOqpIkSZKkGTRVMKqqujbJiWNXJHmo4UiSJEnSfDBMj9Eq4HKggAysK+ARHdUlSZIkSTNm0mBUVavafw+ZmXIkSZIkaeZNNfnCEydbX1VXTG85kiRJkjTzphpK91eTrCvgmdNYiyRJkiTNiqmG0v3WTBUiSZIkSbNlqqF0z6yqzyZ50Xjrq+qibsqSJEmSpJkz1VC6pwOfBZ43zroCDEaSJEmS5ryphtK9tf33uJkpR5IkSZJm3h7DbJTkgCSnJ7kiyeVJ3pfkgK6LkyRJkqSZMFQwAi4AtgH/AXhx+/jvuypKkiRJkmbSVPcYjXpoVb1j4Pk7k7ygg3okSZIkacYN22P0uSTHJNmj/Xkp8KkuC5MkSZKkmTLVdN0/oZl9LsB/BT7artoDuA14a6fVSZIkSdIMmGpWun1mqhBJkiRJmi3D3mNEkv2B5cDeo8uq6otdFCVJkiRJM2moYJTkNcDJwBLgSuBw4FLgmZ1VJkmSJEkzZNjJF04GngRsrqrfAg6lmbJbkiRJkua8YYPRz6rqZwBJHlBV3wYe011ZkiRJkjRzhr3HaGuS/YBPAJ9O8iPguq6KkiRJkqSZNFQwqqoXtg/fluRzwC8A/9RZVZIkSZI0g3ZmVronAr9B871GX66quzqrSpIkSZJm0FD3GCX5b8B5wAHAw4Bzk/xJl4VJkiRJ0kwZtsfoWODQgQkY3gVcAbyzq8IkSZIkaaYMOyvdtQx8sSvwAOC7U+2U5IgkVyfZlOTUcdYnyent+m+0w/VG1/1Bkg1Jvpnk75LsPXZ/SZIkSZoOkwajJO9PcjpwJ7AhyYeTnAt8E7htin1HgDOAI4EVwLFJVozZ7EhgeftzPHBmu+9i4PXAyqp6PDACHLOT5yZJkiRJQ5lqKN369t/Lgf89sPzzQ7R9GLCpqq4BSHIBcDTwrYFtjgbOr6oCvpJkvySLBmp7YJLtwINwenBJkiRJHZk0GFXVeaOPk+wFPLp9enVVbZ+i7cXAloHnW4EnD7HN4qpan+Q9wPeAnwL/XFX/PMXxpPsaWUCSTg9x4OKlXL/1e50eQ5IkSd0aavKFJM+gmZXuWiDA0iS/X1VfnGy3cZbVMNsk2Z+mN+kQ4BbgH5K8vKo+Ok5tx9MMw2PZsmWTnod6aMd2Djrl4k4Psfm0VZ22L0mSpO4NO/nCXwG/XVVPr6qnAc8F/nqKfbYCSweeL+G+w+Em2ubZwL9V1ba2Z+oi4NfHO0hVnVVVK6tq5cKFC4c8HUmSJEn6d8MGowVVdfXok6r6V2DBFPusA5YnOaQdhncMsGbMNmuAV7az0x0O/LiqrqcZQnd4kgelGQf1LGDjkLVKkiRJ0k4Z9nuMLk9yNvCR9vnLaCZkmFBV3Z3kJOASmlnlzqmqDUlOaNevBtYCRwGbgDuA49p1lyW5kOa7ku4GvgactTMnJkmSJEnDGjYYnQCcSDOFdoAvAh+caqeqWksTfgaXrR54XG274+37VuCtQ9YnSZIkSbtsymCUZA/g8vb7hN7bfUmSJEmSNLOmvMeoqu4Bvp7EKd8kSZIkzUvDDqVbBGxI8lXg9tGFVfX8TqqSJEmSpBk0bDB6e6dVSJIkSdIsmjQYJdmbZuKFRwFXAWdX1d0zUZgkSZIkzZSp7jE6D1hJE4qOpPmiV0mSJEmaV6YaSreiqn4FoP0eo692X5IkSZIkzaypeoy2jz5wCJ0kSZKk+WqqHqNfS3Jr+zjAA9vnofl+1n07rU6SJEmSZsCkwaiqRmaqEEmSJEmaLVN+waskSZIkzXcGI0mSJEm9ZzCSJEmS1HsGI0mSJEm9ZzCSJEmS1HsGI0mSJEm9ZzCSJEmS1HsGI0mSJEm9ZzCSJEmS1HsGI+n+GllAks5+Fi1ZNttnKEmSNO/tOdsFSHPeju0cdMrFnTW/+bRVnbUtSZKkhj1GkiRJknrPYCRJkiSp9wxGkiRJknrPYCRJkiSp9wxGkiRJknrPYCRJkiSp9wxGkiRJknrPYCRJkiSp9zoNRkmOSHJ1kk1JTh1nfZKc3q7/RpInDqzbL8mFSb6dZGOSp3RZqyRJkqT+6iwYJRkBzgCOBFYAxyZZMWazI4Hl7c/xwJkD694H/FNVPRb4NWBjV7VKkiRJ6rcue4wOAzZV1TVVdRdwAXD0mG2OBs6vxleA/ZIsSrIv8DTgbICququqbumwVkmSJEk91mUwWgxsGXi+tV02zDaPALYB5yb5WpIPJXnweAdJcnyS9UnWb9u2bfqqlyRJktQbXQajjLOshtxmT+CJwJlVdShwO3Cfe5QAquqsqlpZVSsXLlx4f+qVJEmS1FNdBqOtwNKB50uA64bcZiuwtaoua5dfSBOUJEmSJGnadRmM1gHLkxySZC/gGGDNmG3WAK9sZ6c7HPhxVV1fVTcAW5I8pt3uWcC3OqxVkiRJUo/t2VXDVXV3kpOAS4AR4Jyq2pDkhHb9amAtcBSwCbgDOG6gidcBH2tD1TVj1kmSJEnStOksGAFU1Vqa8DO4bPXA4wJOnGDfK4GVXdYnSZIkSdDxF7xKkiRJ0lxgMJIkSZLUewYjaXc3soAknf4sWrJsts9SkiRpVnV6j5GkabBjOwedcnGnh9h82qpO25ckSdrd2WMkSZIkqfcMRpIkSZJ6z2AkSZIkqfcMRpIkSZJ6z2AkSZIkqfcMRpIkSZJ6z2AkSZIkqfcMRpIkSZJ6z2AkSZIkqfcMRpIkSZJ6z2AkSZIkqfcMRpIkSZJ6z2AkSZIkqfcMRpIkSZJ6z2AkSZIkqfcMRpJgZAFJOvtZtGTZbJ+hJEnSpPac7QIk7QZ2bOegUy7urPnNp63qrG1JkqTpYI+RJEmSpN4zGEmSJEnqPYORJEmSpN4zGEmSJEnqPYORJEmSpN4zGEmSJEnqPYORJEmSpN7rNBglOSLJ1Uk2JTl1nPVJcnq7/htJnjhm/UiSryXp7gtWJEmSJPVeZ8EoyQhwBnAksAI4NsmKMZsdCSxvf44Hzhyz/mRgY1c1SpIkSRJ022N0GLCpqq6pqruAC4Cjx2xzNHB+Nb4C7JdkEUCSJcDvAB/qsEZJkiRJ6jQYLQa2DDzf2i4bdpu/Ad4M3DPZQZIcn2R9kvXbtm27XwVLkiRJ6qcug1HGWVbDbJNkFXBjVV0+1UGq6qyqWllVKxcuXLgrdUqSJEnquS6D0VZg6cDzJcB1Q27zVOD5Sa6lGYL3zCQf7a5USZIkSX3WZTBaByxPckiSvYBjgDVjtlkDvLKdne5w4MdVdX1V/VFVLamqg9v9PltVL++wVkldGllAks5+Fi1ZNttnKEmS5rg9u2q4qu5OchJwCTACnFNVG5Kc0K5fDawFjgI2AXcAx3VVj6RZtGM7B53S3az7m09b1VnbkiSpHzoLRgBVtZYm/AwuWz3wuIATp2jj88DnOyhPkiRJkoCOv+BVkiRJkuYCg5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5EkSZKk3jMYSZIkSeo9g5GkuW9kAUk6/Vm0ZNlsn6UkSerQnrNdgCTdbzu2c9ApF3d6iM2nreq0fUmSNLvsMZIkSZLUewYjSZIkSb1nMJIkSZLUewYjSZIkSb1nMJIkSZLUewYjSZIkSb1nMJIkSZLUewYjSZIkSb1nMJKkYYwsIElnP4uWLJvtM5Qkqdf2nO0CJGlO2LGdg065uLPmN5+2qrO2JUnS1OwxkiRJktR7BiNJkiRJvWcwkiRJktR7BiNJkiRJvWcwkiRJktR7BiNJkiRJvWcwkqTdQcffk+R3JUmSNLlOv8coyRHA+4AR4ENV9a4x69OuPwq4A3hVVV2RZClwPnAgcA9wVlW9r8taJWlWdfw9SeB3JUmSNJnOeoySjABnAEcCK4Bjk6wYs9mRwPL253jgzHb53cAbq+pxwOHAiePsK0mSJEnTosuhdIcBm6rqmqq6C7gAOHrMNkcD51fjK8B+SRZV1fVVdQVAVf0E2Ags7rBWSZIkST3WZTBaDGwZeL6V+4abKbdJcjBwKHDZ9JcoSZIkSd0Go4yzrHZmmyQPAT4OvKGqbh33IMnxSdYnWb9t27ZdLlaSJElSf3UZjLYCSweeLwGuG3abJAtoQtHHquqiiQ5SVWdV1cqqWrlw4cJpKVySJElSv3QZjNYBy5MckmQv4BhgzZht1gCvTONw4MdVdX07W93ZwMaqem+HNUpSf3Q8JbjTgUuS5rLOpuuuqruTnARcQjNd9zlVtSHJCe361cBamqm6N9FM131cu/tTgVcAVyW5sl32lqpa21W9kjTvdTwluNOBS5Lmsk6/x6gNMmvHLFs98LiAE8fZ70uMf/+RJEmSJE27LofSSZIkSdKcYDCSJEmS1HsGI0mSJEm9ZzCSJE2Pjme9c+Y7SVKXOp18QZLUIx3PegfOfCdJ6o49RpIkSZJ6z2AkSZIkqfcMRpIkSZJ6z2AkSZo7Op7gwckdJKm/nHxBkjR3dDzBg5M7SFJ/2WMkSZIkqfcMRpIkSZJ6z2AkSdIov6RWknrLe4wkSRrll9RKUm/ZYyRJkiSp9wxGkiTNJKccl6TdkkPpJEmaSU45Lkm7JXuMJEmSJPWewUiSpPnEmfUkaZc4lE6SpPnEmfUkaZfYYyRJknaOE0hImofsMZIkSTvHCSQkzUP2GEmSpN2L90lJmgX2GEmSpN2L90lJmgX2GEmSpP7xPilJY9hjJEmS+qfr+6Te80KSdNY+wIGLl3L91u91egypTwxGkiRJ020mhgN2HL4MXuobg5EkSdJcZK+XNK06DUZJjgDeB4wAH6qqd41Zn3b9UcAdwKuq6oph9pUkSVKH7PVSz3QWjJKMAGcAzwG2AuuSrKmqbw1sdiSwvP15MnAm8OQh95UkSdJcNg96vUb22psdd/2ss/YNdzOnyx6jw4BNVXUNQJILgKOBwXBzNHB+VRXwlST7JVkEHDzEvpIkSdLEZmjqd8Pd5OZKuOsyGC0Gtgw830rTKzTVNouH3FeSJEma3+ZDuJsj3xuWprOmg4aTlwDPrarXtM9fARxWVa8b2OZTwF9W1Zfa558B3gw8Yqp9B9o4Hji+ffoY4OpOTggeBtzUUdvafXid+8Nr3Q9e5/7wWveD17k/urzWB1XVwrELu+wx2gosHXi+BLhuyG32GmJfAKrqLOCs+1vsVJKsr6qVXR9Hs8vr3B9e637wOveH17ofvM79MRvXeo8O214HLE9ySJK9gGOANWO2WQO8Mo3DgR9X1fVD7itJkiRJ06KzHqOqujvJScAlNFNun1NVG5Kc0K5fDaylmap7E8103cdNtm9XtUqSJEnqt06/x6iq1tKEn8FlqwceF3DisPvOss6H62m34HXuD691P3id+8Nr3Q9e5/6Y8Wvd2eQLkiRJkjRXdHmPkSRJkiTNCQajKSQ5IsnVSTYlOXW261F3klyb5KokVyZZP9v1aHokOSfJjUm+ObDsoUk+neQ77b/7z2aNmh4TXOu3Jfl++76+MslRs1mj7r8kS5N8LsnGJBuSnNwu9309j0xynX1PzzNJ9k7y1SRfb6/129vlM/6edijdJJKMAP8KPIdmavF1wLFV9a1ZLUydSHItsLKq/H6EeSTJ04DbgPOr6vHtsncDN1fVu9o/eOxfVafMZp26/ya41m8Dbquq98xmbZo+SRYBi6rqiiT7AJcDLwBehe/reWOS6/xSfE/PK0kCPLiqbkuyAPgScDLwImb4PW2P0eQOAzZV1TVVdRdwAXD0LNckaSdU1ReBm8csPho4r318Hs3/bDXHTXCtNc9U1fVVdUX7+CfARmAxvq/nlUmus+aZatzWPl3Q/hSz8J42GE1uMbBl4PlWfFPOZwX8c5LLkxw/28WoU7/Ufmca7b+/OMv1qFsnJflGO9TO4VXzSJKDgUOBy/B9PW+Nuc7ge3reSTKS5ErgRuDTVTUr72mD0eQyzjLHHs5fT62qJwJHAie2w3IkzW1nAo8EngBcD/zVrFajaZPkIcDHgTdU1a2zXY+6Mc519j09D1XVjqp6ArAEOCzJ42ejDoPR5LYCSweeLwGum6Va1LGquq7990bgf9MMpdT89IN2/ProOPYbZ7kedaSqftD+D/ce4H/i+3peaO9D+Djwsaq6qF3s+3qeGe86+56e36rqFuDzwBHMwnvaYDS5dcDyJIck2Qs4BlgzyzWpA0ke3N7cSZIHA78NfHPyvTSHrQF+v338+8AnZ7EWdWj0f6qtF+L7es5rb9Q+G9hYVe8dWOX7eh6Z6Dr7np5/kixMsl/7+IHAs4FvMwvvaWelm0I7DeTfACPAOVX157NbkbqQ5BE0vUQAewJ/67WeH5L8HfAM4GHAD4C3Ap8A/hewDPge8JKq8qb9OW6Ca/0MmiE3BVwL/OfRMeuam5L8BvAvwFXAPe3it9Dcf+L7ep6Y5Dofi+/peSXJr9JMrjBC02nzv6rqz5IcwAy/pw1GkiRJknrPoXSSJEmSes9gJEmSJKn3DEaSJEmSes9gJEmSJKn3DEaSJEmSes9gJEmaNUmWJPlkku8k+W6S97XfGzfZPm+ZqfokSf1hMJIkzYr2CxwvAj5RVcuBRwMPAab6DjGDkSRp2hmMJEmz5ZnAz6rqXICq2gH8AfDqJK9N8oHRDZNcnOQZSd4FPDDJlUk+1q57ZZJvJPl6ko+0yw5K8pl2+WeSLGuXfzjJmUk+l+SaJE9Pck6SjUk+PHC8305yaZIrkvxDkoe0y9+V5Fttu++ZoddJkjQD9pztAiRJvfXLwOWDC6rq1iTfY4L/P1XVqUlOqqonACT5ZeCPgadW1U1JHtpu+gHg/Ko6L8mrgdOBF7Tr9qcJZc8H/hF4KvAaYF2SJwBbgT8Bnl1Vtyc5BfivbVB7IfDYqqok+03DayBJ2k0YjCRJsyVA7cTy8TwTuLCqbgKoqpvb5U8BXtQ+/gjw7oF9/rENNlcBP6iqqwCSbAAOBpYAK4AvN6P92Au4FLgV+BnwoSSfAi4eskZJ0hxgMJIkzZYNwH8YXJBkX2Ap8GPuPdx77wnaGDZEDW5zZ/vvPQOPR5/vCewAPl1Vx97nYMlhwLOAY4CTaIKZJGke8B4jSdJs+QzwoCSvBEgyAvwV8GHgGuAJSfZIshQ4bGC/7UkWDLTx0iQHtG2MDqX7fzThBeBlwJd2oq6vAE9N8qi2zQcleXR7n9EvVNVa4A3AE3aiTUnSbs4eI0nSrGiHs70Q+GCSP6X5Y91amlnn7gL+DbgK+CZwxcCuZwHfSHJFVb0syZ8DX0iyA/ga8Crg9cA5Sf4Q2AYctxN1bUvyKuDvkjygXfwnwE+ATybZm6an6g927cwlSbujVA07jFuSJEmS5ieH0kmSJEnqPYORJEmSpN4zGEmSJEnqPYORJEmSpN4zGEmSJEnqPYORJEmSpN4zGEmSJEnqPYORJEmSpN77/71a1izLsGHTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Show the distribution of probabilities for flipping two dice\n",
    "x = [k for k in range(1,30)]\n",
    "y = [5**(k-1)*6**(-k) for k in x]\n",
    "\n",
    "plt.figure(num=None, figsize=(14, 6))\n",
    "plt.bar(x,y, width=1.0,edgecolor='black')\n",
    "plt.title('Probability Distribution for tossing a die until a 6')\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xlabel(\"Outcomes\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Histograms\n",
    "- If you give a list of values to <code>hist(...)</code> it will create a histogram counting how many of each value occur; this list can be unordered;\n",
    "- You will get a cleaner display if you specify where the edges of the bins are, and make sure the edges of the bins are visible, as shown in this example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(num=None, figsize=(8, 6))\n",
    "plt.hist([1,2,4,2,6,2,4,5,6,4,6,3,4,3],bins=[0.5,1.5,2.5,3.5,4.5,5.6,6.5],edgecolor='black')\n",
    "plt.title('Sample Histogram')\n",
    "plt.xlabel(\"Outcomes\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Customizing Your Plots\n",
    "\n",
    "One thing you have probably noticed is that when you write \"bare-bones\" code such as we have above, certain\n",
    "defaults are used for the size and layout of the figure and the style of the drawing. One of the most noticable is that when you draw multiple lines, Matplotlib will change the color each time you call the same function (notice that this doesn't happen when calling a different function, e.g., plot followed by scatter). \n",
    "\n",
    "#### Using Colors\n",
    "\n",
    "Matplotlib cycles through a sequence of 10 colors, which is fine if that is what you want. For my taste, they are pretty ugly, and in the next section we will show you how to use the colors you want. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The 10 Matplotlib color sequence, starting at 12 o'clock and going clockwise:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"\\nThe 10 Matplotlib color sequence, starting at 12 o\\'clock and going clockwise:\")\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "for k in np.arange(0,2*np.pi,np.pi/20):                 # arange is like range, except it allows you to use floats\n",
    "    plt.plot([0,np.sin(k)],[0,np.cos(k)],lw=4)\n",
    "plt.title('Line Colors',fontsize=14)\n",
    "plt.xlim([-1.2,1.2])\n",
    "plt.ylim([-1.2,1.2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an example where we simply change the colors of the plot using the appropriate parameter; see a complete list of colors here: https://matplotlib.org/2.0.2/api/colors_api.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8e20434a30>]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 712x712 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# EXAMPLE: Plotting a square with lines of different colors\n",
    "plt.figure(num=None, figsize=(8, 8), dpi=89)\n",
    "plt.plot([0,1],[0,0],color='red') # Line connecting (0,0) to (1,0)\n",
    "plt.plot([0,0],[0,1],color='green') # Line connecting (0,0) to (0,1)\n",
    "plt.plot([0,1],[1,1],color='orange') # Line connecting (0,1) to (1,1)\n",
    "plt.plot([1,1],[0,1],color='black') # Line connecting (1,0) to (1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Changing the Style of Plots\n",
    "\n",
    "Here is an example showing how to\n",
    "\n",
    "  - change the size of the whole figure\n",
    "  - change the color of lines or points\n",
    "  - change the style of lines or points\n",
    "  \n",
    "To see a complete list of lines styles see:  https://matplotlib.org/2.0.2/api/lines_api.html\n",
    "\n",
    "To see a complete list of colors see: https://matplotlib.org/2.0.2/api/colors_api.html\n",
    "\n",
    "To see a complete list of marker (point) styles see:  https://matplotlib.org/2.0.2/api/markers_api.html#module-matplotlib.markers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# EXAMPLE: Plotting a square via lines \n",
    "plt.figure(figsize=(12, 12))             # the size is (horizontal, vertical)\n",
    "plt.title(\"Line Colors and Styles\",fontsize=16)\n",
    "plt.plot([0,10],[0,0],  color='red') # Line connecting (0,0) to (1,0)\n",
    "plt.plot([0,0],[0,10],  color='green') # Line connecting (0,0) to (0,1)\n",
    "plt.plot([0,10],[10,10],color='orange') # Line connecting (0,1) to (1,1)\n",
    "plt.plot([10,10],[0,10],color='black') # Line connecting (1,0) to (1,1)\n",
    "plt.plot([1,9],[9,9], linewidth=5)    # give a linewidth in points, default is 1.0\n",
    "plt.plot([1,9],[8,8], linewidth=5,color = '#eaafff')    # for custom color give the RGB value in hex\n",
    "plt.plot([1,9],[7,7], linewidth=5,color='0.75') # for grey give the percentage of white in quotes\n",
    "plt.plot([1,9],[6,6], lw=4,linestyle='--') # Linestyles\n",
    "plt.plot([1,9],[5,5], lw=3,linestyle='-.') # Linestyles\n",
    "plt.plot([1,9],[4,4], lw=2,linestyle=':') # Linestyles\n",
    "\n",
    "plt.scatter(range(1,10),[3.5]*9,marker='.')  # various markers, if you don't specify the colors it will cycle\n",
    "plt.scatter(range(1,10),[3]*9,marker='o')    # through a bunch of colors, starting with blue, orange, green, etc.\n",
    "plt.scatter(range(1,10),[2.5]*9,marker='x')\n",
    "plt.scatter(range(1,10),[2]*9,marker='s')\n",
    "plt.scatter(range(1,10),[1.5]*9,marker='^')\n",
    "plt.scatter(range(1,10),[1]*9,marker='D')\n",
    "print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Et Cetera\n",
    "\n",
    "Then you can start getting obsessive, adding gridlines, changing the background color,  adding legends, text, and so on. \n",
    "\n",
    "Another nice feature of matplotlib is that you can insert simple Latex commands into titles and text....."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [i for i in range(11)]\n",
    "y = [i**2 for i in x]\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $x = x^2$')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.grid()\n",
    "plt.plot(x,y)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $y = x^2$')\n",
    "plt.grid(color='w')                # grid of white lines -- don't use points with this, they look funny\n",
    "plt.gca().set_facecolor('0.95')    # background of light grey\n",
    "plt.plot(x,y,color='b')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $y = x^2$')\n",
    "plt.grid(color='r',alpha=0.1)       # alpha sets the transparency, 0 = invisible and 1 = normal           \n",
    "plt.plot(x,y,color='r',lw=0.5,label='Curve')\n",
    "plt.scatter(x,y,color='r',marker='o',label='Points')\n",
    "plt.legend()\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $y = x^2$',fontsize=16)\n",
    "plt.xlabel(\"X\",fontsize=14)\n",
    "plt.ylabel(\"Y\",rotation=0,fontsize=14)\n",
    "plt.grid(color='0.95')\n",
    "plt.text(0,90,\"The title has been enlarged from default 12 points to 16 points.\")\n",
    "plt.text(0,80,\"Notice that the $y$ axis label is rotated to be upright, \\nand the x and y labels are also bigger, at 14 points.\")   # lower left corner of text string is at point (0,60)\n",
    "plt.text(0,60,\"When drawing points and lines together it looks \\nbetter if you make the lines thinner.\")\n",
    "plt.text(0,40,\"Honestly I think it is also better to just use\\nthe default marker (circles) when you draw \\nlines, these triangles are kinda fussy\\nand they don't seem to be centered on \\nthe data point.\")\n",
    "plt.plot(x,y,color='b',lw=0.5)\n",
    "plt.scatter(x,y,color='b',marker='^')\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optional Arguments to Functions\n",
    "\n",
    "Python allows a lot of flexibility when you define functions; in particular,\n",
    "it allows you to define functions with a variable number of arguments,\n",
    "and optional arguments with default values. This simplifies the syntax\n",
    "when you have a function which you want to use in a variety of contexts;\n",
    "many of the statistical functions operation in this way, for example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All the arguments: (2, 2, 5, 4, 7, -3)\n",
      "Number of arguments: 6\n",
      "Last argument: -3\n",
      "Sum =  17\n",
      "\n",
      "All the arguments: (4,)\n",
      "Number of arguments: 1\n",
      "Last argument: 4\n",
      "Sum =  4\n",
      "\n",
      "All the arguments: ()\n",
      "Number of arguments: 0\n",
      "Sum =  0\n"
     ]
    }
   ],
   "source": [
    "# Variable number of arguments, this looks a lot like how it is done in C\n",
    "\n",
    "# The following function collects together all its arguments into a tuple,\n",
    "# which can then be accessed as usual inside the function\n",
    "\n",
    "def my_sum(*args):\n",
    "    print('All the arguments:', args)\n",
    "    print('Number of arguments:', len(args))\n",
    "    if len(args) > 0:\n",
    "        print('Last argument:', args[-1])\n",
    "    return sum(args)\n",
    "        \n",
    "print('Sum = ', my_sum(2,2,5,4,7,-3))\n",
    "print()\n",
    "print('Sum = ', my_sum(4))\n",
    "print()\n",
    "print('Sum = ', my_sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = 5 , a = 3 , m = 7 , b = 1\n",
      "2\n",
      "\n",
      "x = 5 , a = 2137 , m = 6827 , b = 0\n",
      "3858\n",
      "\n",
      "x = 15 , a = 23 , m = 6827 , b = 0\n",
      "345\n",
      "\n",
      "x = 15 , a = 7 , m = 11 , b = 0\n",
      "6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Optional Arguments with Default Values\n",
    "\n",
    "# You may give arguments with default values using\n",
    "# an initialization in the definition, as shown here:\n",
    "\n",
    "#           x is a normal parameter, you MUST supply it \n",
    "#                          m is optional, if you leave it out it will get the default\n",
    "#                                         b ditto\n",
    "def LC_Hash(x, a = 2137, m = 6827, b = 0):\n",
    "    print('x =',x, ', a =',a, ', m =',m, ', b =',b)\n",
    "    return ((a * x) % m) + b\n",
    "\n",
    "# Here we give all four values\n",
    "\n",
    "print( LC_Hash( 5, 3, 7, 1) )         # x <- 5, a <- 3, m <- 7, b <- 1\n",
    "print()\n",
    "\n",
    "# Here we give only first, rest will take optional values\n",
    "\n",
    "print( LC_Hash( 5 ) )         # x <- 5, a <- 3, m <- 7, b <- 1\n",
    "print()\n",
    "\n",
    "# Here we give first two\n",
    "\n",
    "print( LC_Hash( 15, 23 ) )        \n",
    "print()\n",
    "\n",
    "# Here we give only first three\n",
    "\n",
    "print( LC_Hash( 15, 7, 11 ) )         # x <- 5, a <- 3, m <- 7, b <- 1\n",
    "print()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = 15 , a = 11 , m = 23 , b = 3\n",
      "7\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Is best to give values for a prefix of the arguments, in order, and not skip around\n",
    "# When in doubt, use the name of the parameter\n",
    "\n",
    "print( LC_Hash( 15, 11, m = 23, b = 3 ) )      \n",
    "print()"
   ]
  },
  {
   "attachments": {
    "Screen%20Shot%202020-01-31%20at%207.14.28%20PM.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basically, Python matches the parameters and arguments by position, and THEN by\n",
    "name:\n",
    "<pre>\n",
    "print( LC_Hash( 15, 11,  m = 23, b = 3 ) )      \n",
    "     \n",
    "   by position: ****** |\n",
    "   by name:            | +++++++++++++\n",
    "\n",
    "\n",
    "</pre>\n",
    "\n",
    "\n",
    "If you try to do the reverse, it will complain:\n",
    "\n",
    "\n",
    "![Screen%20Shot%202020-01-31%20at%207.14.28%20PM.png](attachment:Screen%20Shot%202020-01-31%20at%207.14.28%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Passing lists or functions as parameters to functions\n",
    "\n",
    "Remember that parameter passing in python is by reference. Thus if you pass an array into\n",
    "a subroutine, and modify the array in the subroutine, the modifications will still be in effect after the subroutine exits\n",
    "(i.e., modifying an array creates side-effects).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4]\n",
      "[5, 2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "def changeList(L):\n",
    "    L[0] = 5\n",
    "    \n",
    "Lst = [1,2,3,4]\n",
    "\n",
    "print(Lst)\n",
    "changeList(Lst)\n",
    "print(Lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Passing a function into another function\n",
    "\n",
    "def plus_one(x):\n",
    "    return x + 1\n",
    "\n",
    "def g(f,x):\n",
    "    return f(x)\n",
    "\n",
    "g(plus_one,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shallow vs Deep Copies of Lists\n",
    "\n",
    "This discussion is based on the one found <a href=\"https://www.afternerd.com/blog/python-copy-list/\">here</a>.\n",
    "\n",
    "The question is:\n",
    "\n",
    "> How do you make a copy of a list?\n",
    "\n",
    "The answer depends on what you mean by a *copy*!  If you mean another reference to the same list, that is called a **shallow copy** (like the fact that my oldest son is called \"John\" or \"JH\" -- two names for the same person),\n",
    "just assign the list to another name:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4]\n",
      "[1, 2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "A = [1,2,3,4]\n",
    "B = A\n",
    "print(A)\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But to see that there is only one list (which now has two names), just make changes to each:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 2, 3, 4]\n",
      "['a', 2, 3, 4]\n",
      "\n",
      "['a', 2, 3, 'c']\n",
      "['a', 2, 3, 'c']\n"
     ]
    }
   ],
   "source": [
    "A = [1,2,3,4]\n",
    "B = A\n",
    "\n",
    "A[0] = 'a'\n",
    "\n",
    "print(A)\n",
    "print(B)\n",
    "print()\n",
    "\n",
    "B[3] = 'c'\n",
    "\n",
    "print(A)\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A shallow copy only copies the *reference* to the list, not the list contents:\n",
    " \n",
    "         A = [1,2,3,4]        \n",
    "                             A -> [1,2,3,4]\n",
    "                             \n",
    "         B = A \n",
    "                             A -> [1,2,3,4]  <- B\n",
    "                             \n",
    "         A[0] = 'a'\n",
    "                             A -> ['a',2,3,4]  <- B \n",
    "                             \n",
    "         B[3] = 'c'\n",
    "                             A -> ['a',2,3,'c']  <- B \n",
    "                             "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make a **deep copy** of a list, making an entirely new list with new elements, you can use\n",
    "a slice, a list constructor, or Python3's `copy` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 2, 3, 4]\n",
      "[1, 'b', 3, 4]\n",
      "[1, 2, 'c', 4]\n",
      "[1, 2, 3, 'd']\n"
     ]
    }
   ],
   "source": [
    "A = [1,2,3,4]\n",
    "\n",
    "# Copying a list by slicing\n",
    "B = A[:]\n",
    "\n",
    "# Copying a list using the list constructor\n",
    "C = list(A)\n",
    "\n",
    "# Copying a list using Python3's copy function:\n",
    "D = A.copy()\n",
    "\n",
    "# These are all different lists:\n",
    "\n",
    "A[0] = 'a'\n",
    "B[1] = 'b'\n",
    "C[2] = 'c'\n",
    "D[3] = 'd'\n",
    "\n",
    "print(A)\n",
    "print(B)\n",
    "print(C)\n",
    "print(D)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A deep copy makes an entirely new list:\n",
    " \n",
    "         A = [1,2,3,4]        \n",
    "                             A -> [1,2,3,4]\n",
    "                             \n",
    "         B = A[:] \n",
    "                             A -> [1,2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             \n",
    "         C = list(A)\n",
    "                             A -> [1,2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             C -> [1,2,3,4]\n",
    "                             \n",
    "         D = list(A)\n",
    "                             A -> [1,2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             C -> [1,2,3,4] \n",
    "                             D -> [1,2,3,4]\n",
    "                             \n",
    "         A[0] = 'a'\n",
    "                             A -> ['a',2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             C -> [1,2,3,4] \n",
    "                             D -> [1,2,3,4]\n",
    "\n",
    "         B[1] = 'b'\n",
    "                             A -> ['a',2,3,4] \n",
    "                             B -> [1,'b',3,4] \n",
    "                             C -> [1,2,3,4] \n",
    "                             D -> [1,2,3,4]\n",
    "                             \n",
    "               --and so on--"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Features/Bugs of Python to Watch out for\n",
    "\n",
    "There are three things about Python that you need to know, if you\n",
    "are more familiar with a language like Java or C. \n",
    "\n",
    "(1) Python is an **interpreted** language, which means it are processed\n",
    "in a \"Read-Eval-Print\" loop: \n",
    "input expressions or definitions or assignment statements are read, evaluated,\n",
    "and the result printed out, and then it starts all over again with the next expression. \n",
    "You can see the order in which the cells were evaluated by looking at the number in square braces to the left: \n",
    "\n",
    "    In [87]:\n",
    "\n",
    "(2)  Python is a **weakly-typed** language, which means that values have types (of course) but \n",
    "variables don't have to be declared with a type and only contain values of that type.\n",
    "Any variable can represent any type of value. \n",
    "\n",
    "\n",
    "(3) Python maintains a **global memory** of all definitions (function \n",
    "definitions, and assignment statements), which is maintained until\n",
    "you terminate or restart the kernel.    This feature causes a lot of problems!\n",
    "\n",
    "Features (2) and (3) make it difficult to keep track of the variables\n",
    "in your program, and are the major source of bugs when you are\n",
    "first learning Python.  Unfortunately, Jupyter notebooks do not\n",
    "help, and in fact make these features more difficult to handle. \n",
    "We will develop strategies to minimize\n",
    "these problems. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Managing variables in a weakly-typed language (feature 2)\n",
    "\n",
    "\n",
    "Python does not force all variables to be declared with a type, as in Java and C,\n",
    "and this leads to problems. The main problem is that you create a variable\n",
    "accidentally with the same name, but different meaning. Here\n",
    "is a variable X being used in three different ways. Confusing? YES. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "hi\n",
      "['hi', 'folks']\n"
     ]
    }
   ],
   "source": [
    "X = 4\n",
    "print(X)\n",
    "\n",
    "X = 'hi'\n",
    "print(X)\n",
    "\n",
    "X = [X, 'folks']              # The second X refers to the previous definition \n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might think this is not a big deal, but if you make a habit of using only a small number of variable names\n",
    "such as X, Y, x, k, i, etc. and if these occur over the WHOLE range of your notebook, you will almost certainly have some confusion somewhere about what a variable means. \n",
    "\n",
    "Even worse, Python allows you to redefine the standard names of functions, so the following, if you uncomment the last two lines, \n",
    "creates a confusing bug:\n",
    "\n",
    "#### TODO:  \n",
    "\n",
    "In the next cell, remove the hash mark from the last two lines, to \"uncomment\" them. Run the cell, and observe that it\n",
    "seems fine. \n",
    "\n",
    "Now run it once more: it will generate a weird error, because the call to the constructor <code>list</code>\n",
    "is now calling a list [2,5,4]. You've destroyed the binding between the variable list and its definition\n",
    "in the standard library. \n",
    "\n",
    "Finally, put the hash marks back in, and hit `Restart & Run All` from the `Kernel` menu. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>NOTE:  IF YOU GET A WEIRD BUG THAT MAKES NO SENSE, DO `Kernel -> Restart & Run All` BEFORE DOING ANYTHING ELSE. IT OFTEN FIXES THE PROBLEM.</b> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Punchline:  Use as few global variables as possible. Do NOT reuse common names (X, i, lst) as global variables. Do NOT use the  `sum`, `list`, `sqrt` as variable names, as these are <b> function names</b> predefined in Python. \n",
    "\n",
    "Either write a function for each problem, storing everything as local variables, or give each global variable a unique name by adding the number of the problem. \n",
    "\n",
    "Example:  Suppose you have the following code which is your solution to a Problem Four in a homework:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 6]\n",
      "[2, 5, 4]\n"
     ]
    }
   ],
   "source": [
    "A = [2,3,4]\n",
    "B = A + [6]                 \n",
    "print(B)\n",
    "\n",
    "X = [2,5,4]\n",
    "print(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 6]\n",
      "[2, 5, 4]\n"
     ]
    }
   ],
   "source": [
    "# Here is a way of avoiding global variables by wrapping everything in a function (all variables local)\n",
    "\n",
    "def solution4():\n",
    "    A = [2,3,4]\n",
    "    B = A + [6]                 \n",
    "    print(B)\n",
    "\n",
    "    X = [2,5,4]\n",
    "    print(X) \n",
    "    \n",
    "solution4()             # be sure to call it! \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 6]\n",
      "[2, 5, 4]\n"
     ]
    }
   ],
   "source": [
    "# Or simply add the problem number to the name:\n",
    "\n",
    "A4 = [2,3,4]\n",
    "B4 = A4 + [6]                 \n",
    "print(B4)\n",
    "\n",
    "X4 = [2,5,4]\n",
    "print(X4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Caveat:</b> You do NOT need to do this for all variables, since local variables in for loops or functions\n",
    "are not a problem. Use the usual variables x,y,i, X, etc. for local variables; there is\n",
    "no problem with these. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Managing the global list of variable bindings (feature 3)\n",
    "\n",
    "Python is an interpreted language (feature 1) which uses a \"Read-Eval-Print\" loop to read\n",
    "an expression, evaluate it, and print out the value. For definitions, such as\n",
    "assignments and function definitions, there is also a change to the global master list\n",
    "which holds all variable and function definitions. \n",
    "\n",
    "    To see the (long) list of global variable bindings, call the function globals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "#globals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you use unique global variable names, you should not have too much trouble with this,\n",
    "but still there are strange things that happen if you don't know about this feature. \n",
    "The problem is about \"old values\" which were stored in the past, even if you don't need them. \n",
    "\n",
    "Let us look at one example to show the problem, and you can keep a watch out for this.\n",
    "\n",
    "Suppose you write the following and run it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now there is a binding in the global memory:  <code>   X = [1,2,3]   </code>\n",
    "\n",
    "But then suppose you change your mind and delete this statement. The problem is\n",
    "that the binding is NOT removed unless you **Restart** the Kernel (in the Kernel menu). \n",
    "\n",
    "Thus, four hours later, you have completely forgotten about this X, and you write this\n",
    "code, but you make a very small error, and leave out the '1' in 'X1'.  It's hard\n",
    "to see that the single character is missing, and when you run it, PYTHON \n",
    "STILL HAS THE BINDING FOR X AND YOU WON'T KNOW ABOUT THE ERROR EXCEPT FOR THE RESULT\n",
    "BEING WRONG.  You'll have to see the missing '1'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2]\n"
     ]
    }
   ],
   "source": [
    "X1 = ['a','b','c','d','e','f','g']\n",
    "\n",
    "print( X[:2] )        # expecting to see ['a','b']  but Python finds the old value of X and doesn't complain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### PUNCHLINE:   If you have a nasty bug that you can't figure out, try Restart and Run All from the Kernel menu.  ALWAYS Restart and Run All before submitting to make sure everything works as it is supposed to. "
   ]
  },
  {
   "attachments": {
    "Screen%20Shot%202021-05-24%20at%205.55.43%20PM.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Floating-Point Arithmetic\n",
    "\n",
    "This section will summarize a few important points from the lecture notes in CS 132:\n",
    "\n",
    "       https://www.cs.bu.edu/fac/snyder/cs132-book/L02Numerics.html\n",
    "\n",
    "Python has both integer and floating point types. Integers, as long as they are not too large, can be stored precisely; however, real numbers (such as $\\pi$), can only be approximated by storing the number in scientific notation in binary:\n",
    "\n",
    "![Screen%20Shot%202021-05-24%20at%205.55.43%20PM.png](attachment:Screen%20Shot%202021-05-24%20at%205.55.43%20PM.png)\n",
    "\n",
    "Because only a fixed number of bits are used, most real numbers cannot be represented exactly in a computer.\n",
    "\n",
    "Another way of saying this is that, usually, a floating point number is an approximation of some particular real number.\n",
    "\n",
    "Generally when we try to store a real number in a computer, what we wind up storing is the closest floating point number that the computer can represent.\n",
    "\n",
    "Problems arise when we work with floating point numbers and confuse them with real numbers, thereby forgetting that most of the time we are not storing the real number exactly, but only a floating point number that is close to it.\n",
    "\n",
    "Let’s look at some examples. First:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ((1/8)*8)-1\n",
    "a = 1/8\n",
    "b = 8\n",
    "c = 1\n",
    "(a*b)-c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that 1/8, 8, and 1 can all be stored exactly in IEEE-754 floating point format.\n",
    "\n",
    "So, we are storing the inputs exactly (1/8, 8 and 1), computing the results exactly, yielding \n",
    "\n",
    "  $$(1/8)∗8=1$$\n",
    "\n",
    "and representing the result exactly (zero).\n",
    "\n",
    "OK, here is another example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ((1/7)*7)-1\n",
    "a = 1/7\n",
    "b = 7\n",
    "c = 1\n",
    "a * b - c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the situation is different.\n",
    "\n",
    "1/7 can not be stored exactly in floating point format.\n",
    "\n",
    "In binary, 1/7 is 0.001001⎯⎯⎯⎯⎯⎯⎯⎯⎯, an infinitely repeating pattern that clearly cannot be represented in a finite sequence of bits.\n",
    "\n",
    "Nonetheless, the computation (1/7)∗7 still yields exactly 1.0.\n",
    "\n",
    "Why? Because the rounding of 0.001001⎯⎯⎯⎯⎯⎯⎯⎯⎯ to its closest floating point representation, when multiplied by 7, yields a value whose closest floating point representation is 1.0.\n",
    "\n",
    "Now, let’s do something that seems very similar:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.3877787807814457e-17"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ((1/70)*7)-0.1\n",
    "a = 1/70\n",
    "b = 7\n",
    "c = 0.1\n",
    "a * b - c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, neither 1/70 nopr 0.1 can be stored exactly.\n",
    "\n",
    "More importantly, the process of rounding 1/70 to its closest floating point representation, then multiplying by 7, yields a number whose closest floating point representation is not 0.1\n",
    "\n",
    "However, that floating point representation is very close to 0.1.\n",
    "\n",
    "Let’s look at the difference: -1.3877787807814457e-17.\n",
    "\n",
    "This is about $−1\\cdot 10^{−17}$ =  -0.0000000000000001.\n",
    "\n",
    "Compared to 0.1, this is a very small number. The relative error abs(-0.0000000000000001 / 0.1) is about $10^{−16}$.\n",
    "\n",
    "This suggests that when a floating point calculation is not exact, the error (in a relative sense) is usually very small."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Punchline 1:  Do not compare floating point numbers for equality¶\n",
    "\n",
    "Two floating point computations that should yield the same result mathematically, may not do so due to rounding error.\n",
    "\n",
    "However, in general, if two numbers should be equal, the relative error of the difference in the floating point should be small.\n",
    "\n",
    "So, instead of asking whether two floating numbers are equal, we should ask whether the relative error of their difference is small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3877787807814457e-16"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 7\n",
    "b = 1/10\n",
    "c = 1/a\n",
    "r1 = a * b * c\n",
    "r2 = b * c * a\n",
    "np.abs(r1-r2)/r1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "finfo(resolution=1e-15, min=-1.7976931348623157e+308, max=1.7976931348623157e+308, dtype=float64)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.finfo('float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "print(r1 == r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead, when comparing floating-point values, we should test whether they\n",
    "are \"close enough.\" \n",
    "This test is needed often enough that numpy has a function that implements it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isclose(r1, r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Punchline 2:  Beware of ill-conditioned problems¶\n",
    "\n",
    "An ill-conditioned problem is one in which the outputs depend in a very sensitive manner on the inputs.\n",
    "\n",
    "That is, a small change in the inputs can yield a very large change in the outputs.\n",
    "\n",
    "The simplest example is computing 1/(𝑎−𝑏)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r1 is 0.1\n",
      "r2 is very close to r1\n",
      "r3 is 0.1001\n",
      "1/(r1 - r2) = 7.205759403792794e+16\n",
      "1/(r3 - r2) = 9999.999999998327\n"
     ]
    }
   ],
   "source": [
    "print(f'r1 is {r1}')\n",
    "print(f'r2 is very close to r1')\n",
    "r3 = r1 + 0.0001\n",
    "print(f'r3 is 0.1001')\n",
    "print(f'1/(r1 - r2) = {1/(r1 - r2)}')\n",
    "print(f'1/(r3 - r2) = {1/(r3 - r2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a is close to b, small changes in either make a big difference in the output.\n",
    "\n",
    "Because the inputs to your problem may not be exact, if the problem is ill-conditioned, the outputs may be wrong by a large amount.\n",
    "\n",
    "Later on in CS 132 we will see that the notion of ill-conditioning applies to matrix problems too, and in particular comes up when we solve certain problems involving matrices.\n",
    "\n",
    "#### Punchline 3: Relative error can be magnified during subtractions¶\n",
    "\n",
    "Two numbers, each with small relative error, can yield a value with large relative error if subtracted.\n",
    "\n",
    "Let’s say we represent a = 1.2345 as 1.2345002 – the relative error is 0.0000002.\n",
    "\n",
    "Let’s say we represent b = 1.234 as 1.2340001 – the relative error is 0.0000001.\n",
    "\n",
    "Now, subtract a - b: the result is .0005001.\n",
    "\n",
    "What is the relative error? 0.005001 - 0.005 / 0.005 = 0.0002\n",
    "\n",
    "The relative error of the result is 1000 times larger than the relative error of the inputs.\n",
    "\n",
    "Here’s an example in practice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9e-08\n",
      "8.999999989711682e-08\n",
      "1.1431464011915431e-09\n"
     ]
    }
   ],
   "source": [
    "a = 1.23456789\n",
    "b = 1.2345678\n",
    "print(0.00000009)\n",
    "print(a-b)\n",
    "print(np.abs(a-b-0.00000009)/ 0.00000009)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know the relative error in the inputs is on the order of $10^{−16}$, but the relative error of the output is on the order of $10^{−9}$ – i.e., a million times larger.\n",
    "\n",
    "A good summary that covers additional issues is at https://docs.python.org/2/tutorial/floatingpoint.html."
   ]
  }
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