0_PythonBasics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PYTHON BASICS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. CORE PYTHON"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A **variable** is anything (its name cannot start by a number etc.!) to which a value is assigned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = 2      # The value of b is an integer\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = b*2.0  # Now the value of b is a float\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Printing Output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Output can be displayed with the print function **￼print**(*object1*, *object2*,...) that converts *object1*, *object2*, and so on, to strings and prints them on the same line, separated by spaces. The **newline character ’\\n’** can be used to force a new line. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.998 book ['a', 'b', 'c', 4.0]\n"
     ]
    }
   ],
   "source": [
    "a = 12.998\n",
    "b = \"book\"\n",
    "c = ['a','b','c',4.]\n",
    "print(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 12.998 \n",
      " b = book \n",
      " c = ['a', 'b', 'c', 4.0]\n"
     ]
    }
   ],
   "source": [
    "print('a =',a,'\\n','b =',b,'\\n','c =',c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Formatting print"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Output can be formatted with the *format method*. The simplest form of the conversion statement is<br/>\n",
    "￼￼￼<center>*print('{:fmt1} {:fmt2}...'.format(arg1,arg2,...))*</center>\n",
    "\n",
    "where *fmt1, fmt2,...* are the format specifications for *arg1, arg2,...*, respectively. \n",
    "\n",
    "Typically used format specifications are<br/>\n",
    "* *wd* for an integer<br/>\n",
    "* *w.df* for floating point notation<br/>\n",
    "* *w.de* for exponential notation\n",
    "\n",
    "where *w* is the width of the field and *d* is the number of digits after the decimal point. The output is right justified in the specified field and padded with blank spaces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "123.46\n",
      "123.4568\n",
      "123.46 123.4568\n"
     ]
    }
   ],
   "source": [
    "a = 123.456789\n",
    "print('{:6.2f}'.format(a))\n",
    "print('{:8.4f}'.format(a))\n",
    "print('{:6.2f} {:8.4f}'.format(a,a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    987\n",
      "0000987\n",
      "n=    987 n=0000987\n"
     ]
    }
   ],
   "source": [
    "n = 987\n",
    "print('{:7d}'.format(n))    # Pad with spaces\n",
    "print('{:07d}'.format(n))   # Pad with zeros\n",
    "print('n={:7d} n={:07d}'.format(n,n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2e+02\n",
      "         1.2e+02\n",
      "0000000001.2e+02\n",
      "1.2e+02\n",
      "1.23e+02\n",
      "1.235e+02\n",
      "1.2345679e+02\n",
      "1.2e+02 1.23e+02 1.235e+02 1.2345679e+02\n"
     ]
    }
   ],
   "source": [
    "print('{:6.1e}'.format(a))\n",
    "print('{:16.1e}'.format(a))\n",
    "print('{:016.1e}'.format(a))\n",
    "print('{:6.1e}'.format(a))\n",
    "print('{:7.2e}'.format(a))\n",
    "print('{:8.3e}'.format(a))\n",
    "print('{:13.7e}'.format(a))\n",
    "print('{:6.1e} {:7.2e} {:8.3e} {:13.7e}'.format(a,a,a,a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arithmetic Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Addition = + <br/>\n",
    "Subtraction = - <br/>\n",
    "Multiplication = * <br/>\n",
    "Division = / <br/>\n",
    "Exponentiation = ** <br/>\n",
    "Modular division = %"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.5\n",
      "-2.5\n",
      "37.5\n",
      "0.6666666666666666\n",
      "174692.81074217107\n",
      "2.5\n"
     ]
    }
   ],
   "source": [
    "x = 5\n",
    "y = 7.5\n",
    "print(x+y)\n",
    "print(x-y)\n",
    "print(x*y)\n",
    "print(x/y)\n",
    "print(x**y)\n",
    "print(y%x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Augmented assignment operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x += y is equivalent to x = x + y <br/>\n",
    "x -= y is equivalent to x = x - y <br/>\n",
    "x * = y is equivalent to x = x * y <br/>\n",
    "x /= y is equivalent to x = x / y <br/>\n",
    "x ** = y is equivalent to x = x ** y <br/>\n",
    "x %= y is equivalent to x = x % y <br/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Strings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Strings** are enclosed between double quotes or single quotes (when nested quotes need to alternate)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Hello World! \\n The first thing 'everybody says' when learning to code\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "string1 = \"Hello World! \\n The first thing 'everybody says' when learning to code\"\n",
    "string1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello World! \n",
      " The first thing 'everybody says' when learning to code\n"
     ]
    }
   ],
   "source": [
    "print(string1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H\n"
     ]
    }
   ],
   "source": [
    "print(string1[0])   # The first character of string1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "e\n"
     ]
    }
   ],
   "source": [
    "print(string1[-1])  # The last character of string1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ello World! \n",
      " The fi\n"
     ]
    }
   ],
   "source": [
    "print(string1[1:21])  # Slicing string1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello World! \n",
      " The first thing 'everybody says' when learning to code in any language\n"
     ]
    }
   ],
   "source": [
    "string2='in any language'\n",
    "print(string1 + ' ' + string2)   # Concatenation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello World! \n",
      " The first thing 'everybody says' when learning to codein any language\n"
     ]
    }
   ],
   "source": [
    "print(string1 + string2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i\n"
     ]
    }
   ],
   "source": [
    "print(string2[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Strings are IMMUTABLE!\n",
    "# Uncommenting and running the following gives an error!\n",
    "\n",
    "# string2[0] = ' i'\n",
    "# print(string2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lists"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A **list** is a mutable sequence of any objects, separated by commas and enclosed in square brackets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 2.0, 3.0, 4.0]\n"
     ]
    }
   ],
   "source": [
    "a = [1.0, 2.0, 3.0]\n",
    "\n",
    "a.append(4.0)        # Appending an element (at the end of the list)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.5, 2.0, 3.0, 4.0]\n"
     ]
    }
   ],
   "source": [
    "a.insert(1,1.5)      # Inserting an eleemt at some position (here the second)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "print(len(a))        # Length of a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0]                 # First element of the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[-1]                # Last element of the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.0, 3.0]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:4]               # Slice of a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.5, 1.0, 1.0, 1.0, 4.0]\n"
     ]
    }
   ],
   "source": [
    "# Lists are MUTABLE!\n",
    "\n",
    "a[2:4] = [1.0, 1.0, 1.0]   # Modify selected elements\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The range list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1 = range(5)\n",
    "list(r1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 4, 5, 6, 7, 8]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2 = range(2,9)\n",
    "list(r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 12, 14, 16, 18]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r3 = range(10,20,2)\n",
    "list(r3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tuples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A **tuple** is an immutable sequence of arbitrary objects, separated by commas and enclosed in parentheses. If the tuple contains a single object, a final comma is required; for example, x = (2,). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mary\n",
      "John\n",
      "[6, 23, 68]\n"
     ]
    }
   ],
   "source": [
    "t = ('Mary','John',[6,23,68])\n",
    "print(t[0])\n",
    "print(t[1])\n",
    "print(t[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Mary', 'John')\n",
      "('John', [6, 23, 68])\n"
     ]
    }
   ],
   "source": [
    "# Slicing\n",
    "\n",
    "print(t[0:2])\n",
    "print(t[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Mary', 'John', [6, 23, 68], -1)\n"
     ]
    }
   ],
   "source": [
    "s = (-1,)         # Appending an element (at the end of the tuple)\n",
    "print(t + s)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# No direct insertion of elements in a tuple (immutability)!\n",
    "# Uncommenting and running the following gives an error!\n",
    "\n",
    "# t[0:2] = ('Mary', 'John', 'Jack')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Mary', 'John', 'Jack', [6, 23, 68])\n"
     ]
    }
   ],
   "source": [
    "# However, this can be overcome by the following trick!\n",
    "\n",
    "lt=list(t)\n",
    "lt.insert(2,'Jack')\n",
    "tt=tuple(lt)\n",
    "print(tt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "str"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x='Hi'\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "str"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x='100.22'\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10.5\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10.5+2j\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=[10.5,2]\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tuple"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=(10.5,2)\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conversions between types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "str"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10\n",
    "y=str(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x='10'\n",
    "y=int(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x='10'\n",
    "y=float(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.6\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x='10.6'\n",
    "y=float(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10\n",
    "y=float(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10+0j)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10\n",
    "y=complex(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "str"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10.5\n",
    "y=str(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10.5\n",
    "y=int(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10.5+0j)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=10.5\n",
    "y=complex(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10.5+1j)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y=complex(10.5,1)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10.5, 2)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tuple"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=[10.5,2]\n",
    "y=tuple(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.5, 2]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=(10.5,2)\n",
    "y=list(x)\n",
    "print(y)\n",
    "type(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logical Operations (Comparisons)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All these are Boolean operators, i.e., they are only evaluated as True or False:\n",
    "\n",
    "\"==\" is equal to <br/>\n",
    "\"!=\" is not equal to (i.e., different than) <br/>\n",
    "\">\" is greater than <br/>\n",
    "\">=\" is greater than or equal to <br/>\n",
    "\"<\" is less than <br/>\n",
    "\"<=\" is less than or equal to "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 2\n",
    "b = 1.77\n",
    "c = '2'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "print(a < b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print(a >= b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "print(a == c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print(a != c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print((a > b) and (a != c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print((a > b) or (a == b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "print((a <= b) or (a == b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Built-In Mathematical Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**abs(number)** is the absolute value of the number<br/>\n",
    "**max(sequence)** is the maximum element of a sequence (list or tuple)<br/>\n",
    "**min(sequence)** is the minimum element of a sequence (list or tuple)<br/>\n",
    "**round(float,n)** rounds the float to (integer) n decimal places"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.688779163215974"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(10.5+2j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0001"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max([1,2,2.0001])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.897"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(7.89654023,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.142"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "pi=math.pi\n",
    "round(pi,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reading Input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intrinsic function for accepting user input is ￼*input(prompt )*. Notice that the input string should be quotted if it is a string, unless it is a number. Notice also that there should be a space at the end of the command!\n",
    "\n",
    "It displays the prompt and then reads a line of input that is converted to a string. To convert the string into a numerical value use the function *eval(string)*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input a: 'cat'\n",
      "'cat' <class 'str'>\n",
      "cat <class 'str'>\n"
     ]
    }
   ],
   "source": [
    "a = input('Input a: ') # Input the string of a word (here 'cat')\n",
    "print(a, type(a))           \n",
    "b = eval(a)\n",
    "print(b,type(b)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input a: 3.14\n",
      "3.14 <class 'str'>\n",
      "3.14 <class 'float'>\n"
     ]
    }
   ],
   "source": [
    "a = input('Input a: ') # Input the string of a number (here 3.14)\n",
    "print(a, type(a))           \n",
    "b = eval(a)\n",
    "print(b,type(b)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input a: int(3.14)\n",
      "int(3.14) <class 'str'>\n",
      "3 <class 'int'>\n"
     ]
    }
   ],
   "source": [
    "a = input('Input a: ') # Input the string of a number (here int(3.14))\n",
    "print(a, type(a))           \n",
    "b = eval(a)\n",
    "print(b,type(b)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditional loops (if)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 is even\n",
      "1 is odd\n",
      "2 is even\n",
      "3 is odd\n",
      "4 is even\n",
      "5 is odd\n",
      "6 is even\n",
      "7 is odd\n",
      "8 is even\n",
      "9 is odd\n"
     ]
    }
   ],
   "source": [
    "for i in range(0,10):\n",
    "    if i%2 == 0:\n",
    "        print(i,'is even')\n",
    "    else:\n",
    "        print(i,'is odd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4 is even and negative\n",
      "-3 is odd and negative\n",
      "-2 is even and negative\n",
      "-1 is odd and negative\n",
      "0 is even and zero\n",
      "1 is odd and positive\n",
      "2 is even and positive\n",
      "3 is odd and positive\n"
     ]
    }
   ],
   "source": [
    "for i in range(-4,4):\n",
    "    if i%2 == 0 and i < 0:\n",
    "        print(i,'is even and negative')\n",
    "    elif i%2 == 0 and i > 0:\n",
    "        print(i,'is even and positive')\n",
    "    elif i%2 != 0 and i < 0:\n",
    "        print(i,'is odd and negative')\n",
    "    elif i%2 != 0 and i > 0:\n",
    "        print(i,'is odd and positive')\n",
    "    else:\n",
    "        print(i,'is even and zero')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type an from 1 to 10: 5\n",
      "You failed to guess the right number in your effort 1/4\n",
      "Type an from 1 to 10: 2\n",
      "You failed to guess the right number in your effort 2/4\n",
      "Type an from 1 to 10: 7\n",
      "Type an from 1 to 10: 4\n",
      "You failed to guess the right number 10 in your 4 efforts.\n"
     ]
    }
   ],
   "source": [
    "# The \"break\" statement terminates the loop:\n",
    "\n",
    "import random\n",
    "x=random.randint(1,10)\n",
    "# guess = eval(input('Type an from 1 to 10: '))\n",
    "for i in range(0,4):\n",
    "    guess = eval(input('Type an from 1 to 10: '))\n",
    "    if guess != x and i < 2:\n",
    "        print('You failed to guess the right number in your effort %i/4' %(i+1))\n",
    "    if guess != x and i == 3:\n",
    "        print('You failed to guess the right number %i in your 4 efforts.' %x)\n",
    "    if guess == x:\n",
    "        print(\"Congrats, you've guessed the right number %i in your effort %i/4!\" %(x,i+1))\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For loops (iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 7]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = []\n",
    "for i in range(1,10,3):\n",
    "    a.append(i)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jack has position 1 in the list\n",
      "Jill has position 2 in the list\n",
      "Tim has position 3 in the list\n",
      "Dave has position 4 in the list\n"
     ]
    }
   ],
   "source": [
    "persons = ['Jack', 'Jill', 'Tim', 'Dave']\n",
    "for i in range(len(persons)):\n",
    "    print(persons[i],'has position',i+1,'in the list')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 6, 9, 12, 15, 18]\n"
     ]
    }
   ],
   "source": [
    "# The \"continue\" statement allows us to skip the remaining part of a for loop (iteration):\n",
    "\n",
    "x = []\n",
    "for i in range(1,20):\n",
    "    if i%3 != 0: \n",
    "        continue\n",
    "    x.append(i)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### While loops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 0.5, 0.3333333333333333, 0.25, 0.2, 0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111, 0.1]\n"
     ]
    }
   ],
   "source": [
    "m = 10\n",
    "n = 1\n",
    "a = []\n",
    "while n <= m:\n",
    "    a.append(1/n)\n",
    "    n = n + 1\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error Control"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # If you were running the following command:\n",
    "\n",
    "# c=1/0\n",
    "\n",
    "# # you would receive the following error:\n",
    "\n",
    "# ZeroDivisionError                         Traceback (most recent call last)\n",
    "# <ipython-input-80-e3767d549fe3> in <module>\n",
    "#       1 # If you were running the following command:\n",
    "#       2 \n",
    "# ----> 3 c=1/0\n",
    "\n",
    "# ZeroDivisionError: division by zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divizion by zero is undefined!\n"
     ]
    }
   ],
   "source": [
    "# To avoid this error:\n",
    "\n",
    "try:\n",
    "    c = 1/0\n",
    "except ZeroDivisionError:\n",
    "    print('Divizion by zero is undefined!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (Python) Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Functions without arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def squares(numeric_seqence):\n",
    "    a=[]\n",
    "    for i in numeric_seqence:\n",
    "        a.append(i**2)\n",
    "    return a\n",
    "\n",
    "squares(range(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Functions with arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "75.0000010000278"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cubicf(x):\n",
    "    return x**3\n",
    "\n",
    "def derivativecf(f,x,h):\n",
    "    df=(f(x+h)-f(x-h))/(2.0*h)\n",
    "    return df\n",
    "\n",
    "derivativecf(cubicf,x=5,h=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7999999995730867"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import atan\n",
    "derivativecf(atan,x=0.5,h=0.0001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Functions with default arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6400000029938013"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def secondderivativecf(f,x,h=0.0001):\n",
    "    ddf=(f(x+h)-2.0*f(x)+f(x-h))/h**2\n",
    "    return ddf\n",
    "\n",
    "secondderivativecf(atan,x=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lambda Statement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the function has the form of an expression, it can be defined with the lambda statement<br/>\n",
    "<center>func name = lambda param1, param2,...: expression</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = lambda x,y : x**2 + y**2\n",
    "c(3,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "75.0000010000278"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = lambda x,h : (cubicf(x+h)-cubicf(x-h))/(2.0*h)\n",
    "d(5,0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7999999995730867"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "da = lambda x,h : (atan(x+h)-atan(x-h))/(2.0*h)\n",
    "da(0.5,0.0001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6400000029938013"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dda = lambda x,h : (atan(x+h)-2.0*atan(x)+atan(x-h))/h**2\n",
    "dda(0.5,0.0001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The math (and cmath) Module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh', 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'erf', 'erfc', 'exp', 'expm1', 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum', 'gamma', 'gcd', 'hypot', 'inf', 'isclose', 'isfinite', 'isinf', 'isnan', 'ldexp', 'lgamma', 'log', 'log10', 'log1p', 'log2', 'modf', 'nan', 'pi', 'pow', 'radians', 'remainder', 'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'tau', 'trunc']\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print([x for x in dir(math) if \"__\" not in x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "log of 2.5 = 0.9162907318741551\n",
      "approximate log of 2.5 = 0.92\n",
      "square root of 2.5 = 1.5811388300841898\n",
      "approximate square root of 2.5 = 1.581\n",
      "sine of 2.5 = 0.5984721441039564\n",
      "approximate sine of 2.5 = 0.5985\n",
      "ceiling of 2.5 = 3\n"
     ]
    }
   ],
   "source": [
    "x=2.5\n",
    "print(\"log of\",x,'=',math.log(x))\n",
    "print(\"approximate log of\",x,'=','{:.2f}'.format(math.log(x)))\n",
    "print(\"square root of\",x,'=',math.sqrt(x))\n",
    "print(\"approximate square root of\",x,'=','{:.3f}'.format(math.sqrt(x)))\n",
    "print(\"sine of\",x,'=',math.sin(x))\n",
    "print(\"approximate sine of\",x,'=','{:.4f}'.format(math.sin(x)))\n",
    "print(\"ceiling of\",x,'=',math.ceil(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The numpy Module"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The complete set of functions in numpy is far too long to be printed in its entirety. The following list is limited to the most commonly used functions:\n",
    "\n",
    "[’complex’, ’float’, ’abs’, ’append’, arccos’,\n",
    "’arccosh’, ’arcsin’, ’arcsinh’, ’arctan’, ’arctan2’,\n",
    "’arctanh’, ’argmax’, ’argmin’, ’cos’, ’cosh’, ’diag’,\n",
    "’diagonal’, ’dot’, ’e’, ’exp’, ’floor’, ’identity’,\n",
    "’inner, ’inv’, ’log’, ’log10’, ’max’, ’min’,\n",
    "’ones’, ’outer’, ’pi’, ’prod’ ’sin’, ’sinh’, ’size’,\n",
    "’solve’, ’sqrt’, ’sum’, ’tan’, ’tanh’, ’trace’,\n",
    "’transpose’, ’vectorize’,’zeros’]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Creating Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2. -1.]\n",
      " [-1.  3.]]\n"
     ]
    }
   ],
   "source": [
    "# From lists\n",
    "\n",
    "a = [[2.0, -1.0],[-1.0, 3.0]]\n",
    "b = np.array(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2 -1]\n",
      " [-1  3]]\n"
     ]
    }
   ],
   "source": [
    "# Integer values\n",
    "\n",
    "a = [[2.0, -1.0],[-1.0, 3.0]]\n",
    "bi = np.array(a,int)\n",
    "print(bi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0.]\n",
      " [0. 0.]\n",
      " [0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Array of zeroes (of size 3x2)\n",
    "\n",
    "zero_array = np.zeros((3,2))\n",
    "print(zero_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "# Array of ones (of size 3x4)\n",
    "\n",
    "ones_array = np.ones((3,4))\n",
    "print(ones_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### arange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4]\n",
      "[2 4 6 8]\n",
      "[2. 4. 6. 8.]\n",
      "[0. 0. 0. 0. 0.]\n",
      "[0 0 0 0 0]\n",
      "[1. 1. 1.]\n",
      "[1 1 1]\n",
      "[[1. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.arange(5))\n",
    "print(np.arange(2,10,2))\n",
    "print(np.arange(2.0,10.0,2.0))\n",
    "print(np.zeros(5))\n",
    "print(np.zeros((5),int))\n",
    "print(np.ones(3))\n",
    "print(np.ones((3),int))\n",
    "print(np.identity(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Accessing and Changing Array Elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((3,3))\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.]\n",
      " [ 0.  4.  0.]\n",
      " [ 0.  8. -3.]]\n"
     ]
    }
   ],
   "source": [
    "a[0] = [1, 2, 3]   # Change a row\n",
    "a[1,1] = 4         # Change an element\n",
    "a[2,1:] = [8,-3]   # Change part of a row\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Operations on Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.33333333  0.66666667  1.        ]\n",
      " [ 0.          1.33333333  0.        ]\n",
      " [ 0.          2.66666667 -1.        ]]\n"
     ]
    }
   ],
   "source": [
    "print(a/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.  0.  1.]\n",
      " [-2.  2. -2.]\n",
      " [-2.  6. -5.]]\n"
     ]
    }
   ],
   "source": [
    "print(a-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.23606798 2.44948974 2.64575131]\n",
      " [2.         2.82842712 2.        ]\n",
      " [2.         3.46410162 1.        ]]\n"
     ]
    }
   ],
   "source": [
    "a=a+4\n",
    "print(np.sqrt(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.28366219  0.96017029  0.75390225]\n",
      " [-0.65364362 -0.14550003 -0.65364362]\n",
      " [-0.65364362  0.84385396  0.54030231]]\n"
     ]
    }
   ],
   "source": [
    "print(np.cos(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4. -2.  1.]\n",
      " [-2.  4. -2.]\n",
      " [ 1. -2.  3.]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[4,-2,1],[-2,4,-2],[1,-2,3]],float)\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4. 4. 3.]\n"
     ]
    }
   ],
   "source": [
    "# Principal Diagonal\n",
    "\n",
    "print(np.diagonal(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2. -2.]\n"
     ]
    }
   ],
   "source": [
    "# First Lower Dubdiagonal\n",
    "\n",
    "print(np.diagonal(A,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2. -2.]\n"
     ]
    }
   ],
   "source": [
    "# First Upper Dubdiagonal\n",
    "\n",
    "print(np.diagonal(A,-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.0\n"
     ]
    }
   ],
   "source": [
    "# Trace\n",
    "\n",
    "print(np.trace(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.0 4.0\n"
     ]
    }
   ],
   "source": [
    "# Minimum, maximum elements\n",
    "\n",
    "print(np.amin(A),np.amax(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 1] [0 1 2]\n"
     ]
    }
   ],
   "source": [
    "# Indices of max, min column elements\n",
    "\n",
    "print(np.argmin(A,axis=0),np.argmax(A,axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 1] [0 1 2]\n"
     ]
    }
   ],
   "source": [
    "# Indices of max, min row elements\n",
    "\n",
    "print(np.argmin(A,axis=1),np.argmax(A,axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Inner product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A = \n",
      " [[1 2]\n",
      " [3 2]]\n",
      "B = \n",
      " [[1 1]\n",
      " [2 2]]\n",
      "x = [7 3]\n",
      "y = [2 1]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1,2],[3,2]])\n",
    "B = np.array([[1,1],[2,2]])\n",
    "x = np.array([7,3])\n",
    "y = np.array([2,1])\n",
    "\n",
    "print('A = \\n',A)\n",
    "print('B = \\n',B)\n",
    "print('x =',x)\n",
    "print('y =',y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "inner product of A, B = \n",
      " [[ 3  6]\n",
      " [ 5 10]]\n",
      "inner product of x, A = \n",
      " [13 27]\n",
      "inner product of B, y = \n",
      " [3 6]\n",
      "inner product of x, y = \n",
      " 17\n",
      "inner product of x, y = 17\n"
     ]
    }
   ],
   "source": [
    "print(\"inner product of A, B = \\n\",np.inner(A,B))\n",
    "print(\"inner product of x, A = \\n\",np.inner(x,A))\n",
    "print(\"inner product of B, y = \\n\",np.inner(B,y))\n",
    "print(\"inner product of x, y = \\n\",np.inner(x,y))\n",
    "print(\"inner product of x, y =\",np.inner(x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Outer product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "outer product of A, B = \n",
      " [[1 1 2 2]\n",
      " [2 2 4 4]\n",
      " [3 3 6 6]\n",
      " [2 2 4 4]]\n",
      "outer product of x, A = \n",
      " [[ 7 14 21 14]\n",
      " [ 3  6  9  6]]\n",
      "outer product of B, y = \n",
      " [[2 1]\n",
      " [2 1]\n",
      " [4 2]\n",
      " [4 2]]\n",
      "outer product of x, y = \n",
      " [[14  7]\n",
      " [ 6  3]]\n",
      "outer product of x, y = \n",
      " [[14  7]\n",
      " [ 6  3]]\n"
     ]
    }
   ],
   "source": [
    "print(\"outer product of A, B = \\n\",np.outer(A,B))\n",
    "print(\"outer product of x, A = \\n\",np.outer(x,A))\n",
    "print(\"outer product of B, y = \\n\",np.outer(B,y))\n",
    "print(\"outer product of x, y = \\n\",np.outer(x,y))\n",
    "print(\"outer product of x, y = \\n\",np.outer(x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dot product "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot product of A, B = \n",
      " [[5 5]\n",
      " [7 7]]\n",
      "dot product of x, A = \n",
      " [16 20]\n",
      "dot product of B, y = \n",
      " [3 6]\n",
      "dot product of x, y = \n",
      " 17\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(\"dot product of A, B = \\n\",np.dot(A,B))\n",
    "print(\"dot product of x, A = \\n\",np.dot(x,A))\n",
    "print(\"dot product of B, y = \\n\",np.dot(B,y))\n",
    "print(\"dot product of x, y = \\n\",np.dot(x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transposing and Inversing Arrays and Solving Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[ 4.0, -2.0,  1.0], \\\n",
    "              [-2.0,  4.0, -2.0], \\\n",
    "              [ 1.0, -2.0,  3.0]])\n",
    "b = np.array([1.0, 4.0, 2.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv,solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4. -2.  1.]\n",
      " [-2.  4. -2.]\n",
      " [ 1. -2.  3.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.transpose(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.33333333 0.16666667 0.        ]\n",
      " [0.16666667 0.45833333 0.25      ]\n",
      " [0.         0.25       0.5       ]]\n"
     ]
    }
   ],
   "source": [
    "print(inv(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  2.5 2. ]\n"
     ]
    }
   ],
   "source": [
    "print(solve(A,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vectorizing Mathematical Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Say we want to compute the following sum:\n",
    "\n",
    "$$s = \\sum_{i=0}^{100} \\sqrt{\\frac{i\\pi}{100}} \\sin \\frac{i\\pi}{100}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "77.51389798916522\n"
     ]
    }
   ],
   "source": [
    "# Direct way\n",
    "\n",
    "x = 0.0; s = 0.0\n",
    "for i in range(101):\n",
    "    s = s + math.sqrt(x)*math.sin(x)\n",
    "    x = x + 0.01*math.pi\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "77.5138979891651\n"
     ]
    }
   ],
   "source": [
    "# Vectorized version\n",
    "\n",
    "x = np.arange(0.0, 1.001*np.pi, 0.01*np.pi)\n",
    "print(sum(np.sqrt(x)*np.sin(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Deep Copying Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make an independent copy of a numpy array a, use the copy method: b = a.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4. -2.  1.]\n",
      " [-2.  4. -2.]\n",
      " [ 1. -2.  3.]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[ 4.0, -2.0,  1.0], \\\n",
    "              [-2.0,  4.0, -2.0], \\\n",
    "              [ 1.0, -2.0,  3.0]])\n",
    "AA = A.copy()\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[104.  98. 101.]\n",
      " [ 98. 104.  98.]\n",
      " [101.  98. 103.]]\n"
     ]
    }
   ],
   "source": [
    "A=A+100\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4. -2.  1.]\n",
      " [-2.  4. -2.]\n",
      " [ 1. -2.  3.]]\n"
     ]
    }
   ],
   "source": [
    "print(AA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting with matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0.0,6.2,0.2)\n",
    "\n",
    "fig=plt.figure(figsize=(7,7))\n",
    "\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(x,np.sin(x));\n",
    "plt.xlabel('x');\n",
    "plt.ylabel('sin(x)');\n",
    "\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(x,np.cos(x));\n",
    "plt.xlabel('x');\n",
    "plt.ylabel('cos(x)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(7,5))\n",
    "\n",
    "plt.plot(x,np.sin(x),x,np.cos(x));\n",
    "plt.xlabel('x');\n",
    "plt.ylabel('y');\n",
    "plt.legend(('sine','cosine'),loc = 0);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}