py-datascience-handbook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9ccd786a",
   "metadata": {},
   "source": [
    "# Python Data Science Handbook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "18b6f390",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Users/vincentprudhomme/OneDrive - ETS/2021/Python\n"
     ]
    }
   ],
   "source": [
    "#Import librairies and packages\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import textwrap\n",
    "#import pyodbc #pyodbc is not available in IPython\n",
    "import os\n",
    "import sys\n",
    "from timeit import default_timer as timer\n",
    "import scipy\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib\n",
    "import sklearn\n",
    "#import seaborn as sns #seaborn is not available in IPython\n",
    "#import bokeh as bok #bokeh is not available in IPython\n",
    "from math import pi\n",
    "import scipy\n",
    "from scipy import special\n",
    "import math\n",
    "plt.style.use('ggplot')\n",
    "from matplotlib.pyplot import figure\n",
    "print(os.getcwd()) # Display project rep"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a02ea4c2",
   "metadata": {},
   "source": [
    "# Chapter 2: Introduction to NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "1b099a36",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
     ]
    }
   ],
   "source": [
    "L = list(range(10))\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "04cdedad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(L) #display the type of L - L is a list i.e. a container that hold many Python objects like... integers or strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "7ef38442",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(L[0]) #display the type of the object 0 in the list L "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "e468dcb6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']\n"
     ]
    }
   ],
   "source": [
    "#for similary, a list of strings (in this case the numbers are set as strings)\n",
    "L2 = [str(c) for c in L]\n",
    "print(L2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "8b263f55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "str"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(L2[0]) #return the type of the object at position 0 (range is 0 to 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "2bc5095d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#because of python's dynamic typing, we can even create heterogenous list i.e with string and int or bool.\n",
    "L3 = [True, '2', 3.0, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "675658c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[bool, str, float, int]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[type(item) for item in L3] #return the list of types for each items in the list L3\n",
    "# every item in a list is Python object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "e4f1f5e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import array \n",
    "L = list(range(10))\n",
    "A = array.array('i', L)\n",
    "A\n",
    "#here 'i' is a type code indicating the contents are integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "adf82052",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ford', 'Volvo', 'BMW']\n"
     ]
    }
   ],
   "source": [
    "#Python arrays - Arrays are used to store multiple values in one single variable.\n",
    "#this is a 1D array i.e only 1 row\n",
    "cars = ['Ford','Volvo','BMW']\n",
    "print(cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "aeeef9d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(cars) #return the lengh of the array - There's 3 objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "ae9c9d5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Add and element to the car list - array\n",
    "cars.append('Toyota')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "38438b3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "ca2ad488",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ford\n"
     ]
    }
   ],
   "source": [
    "#Get the value of the first array item - Array indexing: accessing single elements\n",
    "x = cars[0]\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "cb4af385",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Toyota'"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To index the end of the array, you can use negative indices - Toyota is the last object of the list\n",
    "cars[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "7bba53d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 2. 3. 4.]\n"
     ]
    }
   ],
   "source": [
    "x4 = np.array([1,2,3,4], dtype='float32')\n",
    "print(x4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "a4588022",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.  3.  4.  5.  6.]\n",
      " [ 4.  5.  6.  7.  8.]\n",
      " [ 6.  7.  8.  9. 10.]]\n"
     ]
    }
   ],
   "source": [
    "x5 = np.array([range(i, i + 5) for i in [2, 4, 6]], dtype='float32')\n",
    "print(x5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "fe97116f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.      3.1416  4.      5.      6.    ]\n",
      " [ 4.      5.      6.      7.      8.    ]\n",
      " [ 6.      7.      8.      9.     10.    ]]\n"
     ]
    }
   ],
   "source": [
    "x5[0,1] = 3.1416\n",
    "print(x5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "eea92449",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.14, 3.14, 3.14, 3.14, 3.14],\n",
       "       [3.14, 3.14, 3.14, 3.14, 3.14],\n",
       "       [3.14, 3.14, 3.14, 3.14, 3.14]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a 3x5 array filled with 3.14 \n",
    "# np.ones - full of ones\n",
    "# np.zeros - full of zeros\n",
    "# np.aranges - # Create an array filled with a linear sequence. Starting at 0, ending at 20, stepping by 2 np.arange(0, 20, 2) \n",
    "# nplinspace - Create an array of five values evenly spaced between 0 and 1 np.linspace(0, 1, 5)\n",
    "np.full((3, 5), 3.14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "de018bfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.60846394, 0.7179427 , 0.43036406],\n",
       "       [0.25241011, 0.97572458, 0.1197632 ],\n",
       "       [0.20856888, 0.23983126, 0.39034023]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a 3x3 array of uniformly distributed # random values between 0 and 1\n",
    "np.random.random((3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "ec38ac29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.01044915,  0.31737152, -1.30840814],\n",
       "       [-0.97496232,  1.57774258, -0.87026069],\n",
       "       [ 0.91052841,  1.36337822,  0.03155953]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a 3x3 array of normally distributed random values # with mean 0 and standard deviation 1\n",
    "np.random.normal(0,1, (3, 3))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "0a1e41ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0) #seed for reproducibility\n",
    "#define variable \n",
    "x1 = np.random.randint(10, size=6) #ouput is a one-dimension 1D array with 6 objects and the int var are rand between 0 to 10\n",
    "x2 = np.random.randint(10, size=(3,4)) #output is a two-dimension 2D array i.e a 3x4 matrix  and the int var are and between 0 to 10\n",
    "x3 = np.random.randint(10, size=(3,4,5)) #output is tree-dimension 3D array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "68ee5a51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 3, 3, 7, 9])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "f49c65d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "60f40520",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4],\n",
       "       [7, 6, 8, 8],\n",
       "       [1, 6, 7, 7]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#In a multidimensional array, you access items using a comma-separated tuple of indices\n",
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "a56fa0d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "58323a8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "x2[0,0] = 12 #modify the value of this index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "76a3c370",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12,  5,  2,  4],\n",
       "       [ 7,  6,  8,  8],\n",
       "       [ 1,  6,  7,  7]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "10f1657e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x3 ndim:  3\n",
      "x3 shape: (3, 4, 5)\n",
      "x3 size:  60\n",
      "dtype:  int64\n"
     ]
    }
   ],
   "source": [
    "print('x3 ndim: ', x3.ndim) #number of dimension, in this case 3\n",
    "print('x3 shape:', x3.shape) #shape is the size, in this case, 3x4x5\n",
    "print('x3 size: ', x3.size) #number of object, in this case 60\n",
    "print('dtype: ', x3.dtype) #type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "c6882ce3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itemsize 8 bytes\n",
      "nbytes 480 bytes\n"
     ]
    }
   ],
   "source": [
    "print('itemsize', x3.itemsize, 'bytes') #size of each array\n",
    "print('nbytes', x3.nbytes, 'bytes') #total size of the array\n",
    "#in general, we expect that nbytes is equal to itemsize times size\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "0ca8336d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#16-10-2021 : Page 44 - #The NumPy slicing syntax follows that of the standard Python list; to access a slice of an array x, use this: x[start:stop:step]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "4774bf2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Note - There's a difference between Python List and NumPy Librairy Array's - unlike Python lists, NumPy arrays have a fixed type\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "f0edd559",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The NumPy slicing syntax follows that of the standard Python list; to access a slice of an array x, use this - \n",
    "#x[start:stop:step] - accessing an array of an array i.e. sub-array? \n",
    "x6 = np.arange(10) #genarate a linear array of 10 objects\n",
    "x6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "e700724c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5, 6])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x6[4:7] #Exemple - access the middle subarray -> 4 = 'start' and 7 = 'stop', by default step = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "170804f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12,  5,  2,  4],\n",
       "       [ 7,  6,  8,  8],\n",
       "       [ 1,  6,  7,  7]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Multi-dimensional slices work in the same way, with multiple slices separated by commas. \n",
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "0274a96d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12,  5,  2],\n",
       "       [ 7,  6,  8]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Access two rows and three colums \n",
    "x2[:2,:3] #Exemple: x[row,column]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "737a7af9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12  5  2  4]\n"
     ]
    }
   ],
   "source": [
    "#First row of x2\n",
    "print(x2[0,:]) #or print(x2[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "8afe9f02",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12  5  2  4]\n",
      " [ 7  6  8  8]\n",
      " [ 1  6  7  7]]\n"
     ]
    }
   ],
   "source": [
    "#How to extract a 2x2 sub-array (array of an array)\n",
    "print(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "64809384",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12  5]\n",
      " [ 7  6]]\n"
     ]
    }
   ],
   "source": [
    "x2_sub=x2[:2,:2] #2x2 matrix\n",
    "print(x2_sub)\n",
    "#it possible afterward to change directly the sub-array and it will change de main array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "9409179b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[99  5]\n",
      " [ 7  6]]\n"
     ]
    }
   ],
   "source": [
    "x2_sub[0,0] = 99\n",
    "print(x2_sub)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "a4b50ffb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[99  5  2  4]\n",
      " [ 7  6  8  8]\n",
      " [ 1  6  7  7]]\n"
     ]
    }
   ],
   "source": [
    "print(x2)"
   ]
  },
  {
   "cell_type": "raw",
   "id": "5030c0f1",
   "metadata": {},
   "source": [
    "Creating copies of arrays\n",
    "\n",
    "It is sometimes useful to instead explicitly copy the data within an array or a subarray. This can be most easily done with the copy() method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "38391cb1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[99  5]\n",
      " [ 7  6]]\n"
     ]
    }
   ],
   "source": [
    "x2_sub_copy = x2[:2,:2].copy() #Create a copy of a 2x2 sub-array \n",
    "#We now modify this subarray, the original array is not touched \n",
    "print(x2_sub_copy)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "95bbb7a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[3 2 1]\n"
     ]
    }
   ],
   "source": [
    "#Concatenation of arrays\n",
    "x = np.array([1, 2, 3])\n",
    "y = np.array([3, 2, 1])\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "3b494c45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 3, 2, 1])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([x,y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "e93d23c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 3 2 1]\n"
     ]
    }
   ],
   "source": [
    "xy = np.concatenate([x,y])\n",
    "print(xy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "cd5911dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  3  2  1 99 99 99]\n"
     ]
    }
   ],
   "source": [
    "#You can also concatenate more than two arrays at once:\n",
    "z = [99,99,99]\n",
    "xyz = np.concatenate([x,y,z])\n",
    "print(xyz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "83399a2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [6, 5, 4],\n",
       "       [3, 2, 1]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#np.concatenate can also be used for two-dimensional arrays (matrix concatenate)\n",
    "grid1 = np.array([[1,2,3],[4,5,6]])\n",
    "grid2 = np.array([[6,5,4],[3,2,1]])\n",
    "np.concatenate([grid1, grid2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "adec05cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 6, 5, 4],\n",
       "       [4, 5, 6, 3, 2, 1]])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([grid1, grid2], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "56a4d7f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [9, 8, 7],\n",
       "       [6, 5, 4]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#np.vstack[x, grid] - add a 1d array to a 2d array (vertical)\n",
    "#np.hstack[grid,y] - add a 1d array to a 2d array (horizontal)\n",
    "#np.dstack will stack arrays along the third axi (3d)\n",
    "x = np.array([1,2,3])\n",
    "grid = np.array([[9,8,7],[6,5,4]])\n",
    "(np.vstack([x,grid]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "1897e20c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3] [99 99] [3 2 1]\n"
     ]
    }
   ],
   "source": [
    "x=[1,2,3,99,99,3,2,1] \n",
    "x1, x2, x3 = np.split(x, [3, 5]) #Split a 1d array\n",
    "print(x1, x2, x3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "dd39ab47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#split a grid array (matrix)\n",
    "#np.hsplit or np.vsplit\n",
    "grid = np.arange(16).reshape(4,4) #Reshape in a 4x4 matrix - Linear range 0 to 16.\n",
    "grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "8fb887b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2 3]\n",
      " [4 5 6 7]]\n",
      "[[ 8  9 10 11]\n",
      " [12 13 14 15]]\n"
     ]
    }
   ],
   "source": [
    "upper, lower = np.vsplit(grid, [2]) # Vertical split in half\n",
    "print(upper)\n",
    "print(lower)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "3ab9dc73",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "\n",
    "def compute_reciprocals(values): #definition of a function? \n",
    "    output = np.empty(len(values))\n",
    "    for i in range(len(values)):\n",
    "        output[i] = 1.0/values[i]\n",
    "        return output\n",
    "    \n",
    "    values = np.random.randint(1,10, size=5)\n",
    "    compute_reciprocals(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "0358a283",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.22 µs ± 99.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "big_array = np.random.randint(1,100, size=1000000)\n",
    "%timeit compute_reciprocals(big_array) #function compute_reciproccals is used again..or UFuncs?"
   ]
  },
  {
   "cell_type": "raw",
   "id": "414bed6b",
   "metadata": {},
   "source": [
    "Computations using vectorization through ufuncs are nearly always more efficient than their counterpart implemented through Python loops, especially as the arrays grow in size. \n",
    "\n",
    "Ufuncs exist in two flavors: unary ufuncs, which operate on a single input, and binary ufuncs, which operate on two inputs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "20f901f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [0 1 2 3]\n",
      "x + 5 = [5 6 7 8]\n",
      "x - 5 = [-5 -4 -3 -2]\n",
      "x * 2 = [0 2 4 6]\n",
      "x / 2 = [0.  0.5 1.  1.5]\n",
      "x // 2 = [0 0 1 1]\n",
      "Output array = [-1.   -2.25 -4.   -6.25]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(4) \n",
    "print(\"x =\", x)\n",
    "print(\"x + 5 =\", x + 5) \n",
    "print(\"x - 5 =\", x - 5) \n",
    "print(\"x * 2 =\", x * 2)\n",
    "print(\"x / 2 =\", x / 2)\n",
    "print(\"x // 2 =\", x // 2) # floor division\n",
    "#a ** operator for exponentiation, and a % operator for modulus:\n",
    "#Ufuncs - Make use of Python’s native arithmetic operators. \n",
    "print('Output array =',-(0.5*x + 1) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "45ddf645",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3]\n",
      "[2 3 4 5]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "y = np.add(x,2) #add +2 to each object of the array\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "58caffd2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 1 0 1 2]\n",
      "[2 1 0 1 2]\n"
     ]
    }
   ],
   "source": [
    "#tranform values into absolute values\n",
    "x = np.array([-2,-1,0,1,2])\n",
    "print(abs(x)) \n",
    "#or np.absolute(x)\n",
    "print(np.absolute(x))\n",
    "#it can handle complexe number like 4-3j"
   ]
  },
  {
   "cell_type": "raw",
   "id": "e38da892",
   "metadata": {},
   "source": [
    "For large calculations, it is sometimes useful to be able to specify the array where the result of the calculation will be stored. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "db5a100d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array x times 10 = [ 0 10 20 30 40]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(5)\n",
    "y = np.multiply(x, 10)\n",
    "print('Array x times 10 =', y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "931ebd77",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5]\n",
      "120\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(1, 6)\n",
    "np.add.reduce(x) #Reduce is for aggreation. add is for addition of a value into the array. add.reduce is a sum of the array\n",
    "y = np.multiply.reduce(x) #reduce added to multiply - multiply the object in the array\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "f909b06f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  6, 10, 15])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Store all the intermediate results of the computation, we can instead use accumulate. \n",
    "np.add.accumulate(x) # 1x2 = 3, 2x3 = 6... :/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "522409a9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generation of a random array of 100 obj. = [0.60846394 0.7179427  0.43036406 0.25241011 0.97572458 0.1197632\n",
      " 0.20856888 0.23983126 0.39034023 0.61318864 0.8603706  0.34645385\n",
      " 0.2939397  0.39274799 0.69444295 0.71234984 0.64181726 0.14519247\n",
      " 0.91796933 0.02800916 0.53171561 0.34500616 0.80695872 0.07155939\n",
      " 0.20794804 0.24551118 0.77437728 0.45116519 0.08043329 0.09711552\n",
      " 0.06215684 0.16934182 0.468866   0.87884932 0.09785878 0.12446372\n",
      " 0.42253024 0.39034562 0.35621026 0.99663284 0.55823601 0.84371046\n",
      " 0.78986544 0.99105381 0.28137886 0.01765187 0.6559858  0.61765416\n",
      " 0.17973144 0.84749539 0.46820265 0.97459109 0.60303019 0.31209932\n",
      " 0.63006004 0.93992516 0.36891447 0.86732999 0.45108972 0.67813826\n",
      " 0.82235473 0.21737642 0.21458453 0.75687255 0.891968   0.91821687\n",
      " 0.85946    0.50718748 0.10660595 0.64094331 0.78333905 0.28045269\n",
      " 0.2888203  0.39869403 0.21810444 0.41660806 0.69813452 0.81783624\n",
      " 0.72199978 0.28087945 0.0323053  0.10372152 0.53005891 0.69079487\n",
      " 0.99206462 0.19107554 0.80362599 0.27757786 0.95501989 0.34106202\n",
      " 0.05331828 0.90524432 0.82573516 0.47536596 0.20202806 0.90823836\n",
      " 0.73882912 0.97343133 0.04370114 0.75900897]\n",
      "Sum of the 100 objects in the array = 50.88772629915091\n"
     ]
    }
   ],
   "source": [
    "L = np.random.random(100) #generate a random array of 100 objects - real numbers\n",
    "print('Generation of a random array of 100 obj. =', L)\n",
    "print('Sum of the 100 objects in the array =', sum(L)) #or np.sum(L) works too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "2c1a8cde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.88772629915093"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.reduce(L) #seems to work too...? But not exactly the same number."
   ]
  },
  {
   "cell_type": "raw",
   "id": "487c2dfa",
   "metadata": {},
   "source": [
    "Comments: Because it executes the operation in compiled code, NumPy’s version of the operation is computed much more quickly -  the sum function and the np.sum function are not identical, which can sometimes lead to confusion! In particular, their optional arguments have differ‐ ent meanings, and np.sum is aware of multiple array dimensions,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "3e088e7a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "223 ms ± 5.34 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit min(big_array), max(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "39d067fe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.02 ms ± 36.1 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit np.min(big_array), np.max(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "f3edbce1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Numpy returns an ouput in 2.03 ms and Python native function return an output in 222 ms. Delta of 20 ms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "7bfc5401",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3x4 random matrix = [[0.13531095 0.88282561 0.3126663  0.49555108]\n",
      " [0.9552979  0.81778172 0.49902653 0.22465879]\n",
      " [0.89005733 0.30654364 0.37441302 0.75259926]]\n"
     ]
    }
   ],
   "source": [
    "#Multi-dimensional aggregates\n",
    "M = np.random.random((3,4)) #Generate a 3x4 random matrix\n",
    "print('3x4 random matrix =', M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "7680226e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.646732129985812"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum() #Sum of the 2d array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "1128c57c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.13531095, 0.30654364, 0.3126663 , 0.22465879])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.min(axis=0) #return the minimum value within each column by specifying axis=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "2bb99b7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Introducing Broadcasting\n",
    "#Recall that for arrays of the same size, binary operations are performed on an element-by-element basis:\n",
    "a = np.array([0,1,2])\n",
    "b = np.array([5,5,5])\n",
    "a+b\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "f763d05e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Broadcasting allows these types of binary operations to be performed on arrays of dif‐ ferent sizes—for example, we can just as easily add a scalar (think of it as a zero- dimensional array) to an array\n",
    "a+5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "73c7649d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.ones((3,3))\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "4586caa6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [1., 2., 3.],\n",
       "       [1., 2., 3.]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M+a #Here the one-dimensional array a is stretched, or broadcast, across the second dimension in order to match the shape of M."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "549fb85d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Plotting a two-dimensional function\n",
    "# x and y have 50 steps from 0 to 5\n",
    "x = np.linspace(0,5,50)\n",
    "y = np.linspace(0,5,50)[:, np.newaxis]\n",
    "z = np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)\n",
    "#in this case z=f(x,y) i.e a multi-dimensional function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "e54e377f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f8e9464afd0>"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(z, origin='lower', extent=[0,5,0,5], cmap='viridis') #note: extent is the parameter of the graph\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "ff9e4dc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Comparison Operators as ufuncs\n",
    "x = np.array([1,2,3,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "f1438173",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True, False, False, False])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < 3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "8c9941f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 3, 3],\n",
       "       [7, 9, 3, 5],\n",
       "       [2, 4, 7, 6]])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "x = rng.randint(10, size=(3,4))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "000f0449",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [ True,  True, False, False],\n",
       "       [False, False,  True, False]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x > 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "0f057a56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To count the number of True entrie in a Boolean array, np.count_nonzero is useful\n",
    "#np.any\n",
    "#np.all\n",
    "np.count_nonzero(x<6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "de0d0ac3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>STATION</th>\n",
       "      <th>STATION_NAME</th>\n",
       "      <th>DATE</th>\n",
       "      <th>PRCP</th>\n",
       "      <th>SNWD</th>\n",
       "      <th>SNOW</th>\n",
       "      <th>TMAX</th>\n",
       "      <th>TMIN</th>\n",
       "      <th>AWND</th>\n",
       "      <th>WDF2</th>\n",
       "      <th>WDF5</th>\n",
       "      <th>WSF2</th>\n",
       "      <th>WSF5</th>\n",
       "      <th>WT01</th>\n",
       "      <th>WT05</th>\n",
       "      <th>WT02</th>\n",
       "      <th>WT03</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140101</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>72</td>\n",
       "      <td>33</td>\n",
       "      <td>12</td>\n",
       "      <td>340</td>\n",
       "      <td>310</td>\n",
       "      <td>36</td>\n",
       "      <td>40</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140102</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>106</td>\n",
       "      <td>61</td>\n",
       "      <td>32</td>\n",
       "      <td>190</td>\n",
       "      <td>200</td>\n",
       "      <td>94</td>\n",
       "      <td>116</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140103</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>89</td>\n",
       "      <td>28</td>\n",
       "      <td>26</td>\n",
       "      <td>30</td>\n",
       "      <td>50</td>\n",
       "      <td>63</td>\n",
       "      <td>72</td>\n",
       "      <td>1</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140104</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>78</td>\n",
       "      <td>6</td>\n",
       "      <td>27</td>\n",
       "      <td>40</td>\n",
       "      <td>40</td>\n",
       "      <td>45</td>\n",
       "      <td>58</td>\n",
       "      <td>1</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140105</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>83</td>\n",
       "      <td>-5</td>\n",
       "      <td>37</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>67</td>\n",
       "      <td>76</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140106</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>78</td>\n",
       "      <td>-5</td>\n",
       "      <td>26</td>\n",
       "      <td>210</td>\n",
       "      <td>210</td>\n",
       "      <td>112</td>\n",
       "      <td>125</td>\n",
       "      <td>1</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140107</td>\n",
       "      <td>122</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>83</td>\n",
       "      <td>50</td>\n",
       "      <td>16</td>\n",
       "      <td>160</td>\n",
       "      <td>150</td>\n",
       "      <td>45</td>\n",
       "      <td>54</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140108</td>\n",
       "      <td>97</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>100</td>\n",
       "      <td>72</td>\n",
       "      <td>46</td>\n",
       "      <td>180</td>\n",
       "      <td>180</td>\n",
       "      <td>107</td>\n",
       "      <td>143</td>\n",
       "      <td>1</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140109</td>\n",
       "      <td>58</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>94</td>\n",
       "      <td>56</td>\n",
       "      <td>63</td>\n",
       "      <td>210</td>\n",
       "      <td>230</td>\n",
       "      <td>143</td>\n",
       "      <td>183</td>\n",
       "      <td>1</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>GHCND:USW00024233</td>\n",
       "      <td>SEATTLE TACOMA INTERNATIONAL AIRPORT WA US</td>\n",
       "      <td>20140110</td>\n",
       "      <td>43</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>128</td>\n",
       "      <td>83</td>\n",
       "      <td>70</td>\n",
       "      <td>200</td>\n",
       "      <td>200</td>\n",
       "      <td>134</td>\n",
       "      <td>183</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "      <td>-9999</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             STATION                                STATION_NAME      DATE  \\\n",
       "0  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140101   \n",
       "1  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140102   \n",
       "2  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140103   \n",
       "3  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140104   \n",
       "4  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140105   \n",
       "5  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140106   \n",
       "6  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140107   \n",
       "7  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140108   \n",
       "8  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140109   \n",
       "9  GHCND:USW00024233  SEATTLE TACOMA INTERNATIONAL AIRPORT WA US  20140110   \n",
       "\n",
       "   PRCP  SNWD  SNOW  TMAX  TMIN  AWND  WDF2  WDF5  WSF2  WSF5  WT01  WT05  \\\n",
       "0     0     0     0    72    33    12   340   310    36    40 -9999 -9999   \n",
       "1    41     0     0   106    61    32   190   200    94   116 -9999 -9999   \n",
       "2    15     0     0    89    28    26    30    50    63    72     1 -9999   \n",
       "3     0     0     0    78     6    27    40    40    45    58     1 -9999   \n",
       "4     0     0     0    83    -5    37    10    10    67    76 -9999 -9999   \n",
       "5     3     0     0    78    -5    26   210   210   112   125     1 -9999   \n",
       "6   122     0     0    83    50    16   160   150    45    54 -9999 -9999   \n",
       "7    97     0     0   100    72    46   180   180   107   143     1 -9999   \n",
       "8    58     0     0    94    56    63   210   230   143   183     1 -9999   \n",
       "9    43     0     0   128    83    70   200   200   134   183 -9999 -9999   \n",
       "\n",
       "   WT02  WT03  \n",
       "0 -9999 -9999  \n",
       "1 -9999 -9999  \n",
       "2 -9999 -9999  \n",
       "3 -9999 -9999  \n",
       "4 -9999 -9999  \n",
       "5 -9999 -9999  \n",
       "6 -9999 -9999  \n",
       "7 -9999 -9999  \n",
       "8 -9999 -9999  \n",
       "9 -9999 -9999  "
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np \n",
    "import pandas as pd\n",
    "\n",
    "pd.read_csv('/Users/vincentprudhomme/OneDrive - ETS/2021/Python/data/seattle2014.csv')\n",
    "rainfall.head(10)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "4ad43b2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(365,)"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#use Pandas to extract rainfall inches as NumPy array\n",
    "\n",
    "rainfall = pd.read_csv('/Users/vincentprudhomme/OneDrive - ETS/2021/Python/data/seattle2014.csv')['PRCP'].values\n",
    "inches = rainfall/254 #1/10mm -> inches\n",
    "inches.shape\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "b3e854ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([245.,  14.,  13.,  17.,   8.,   6.,   5.,   6.,   4.,   3.,   7.,\n",
       "          6.,   3.,   3.,   3.,   4.,   4.,   2.,   4.,   0.,   0.,   1.,\n",
       "          1.,   1.,   0.,   0.,   0.,   2.,   1.,   1.,   0.,   0.,   0.,\n",
       "          0.,   0.,   0.,   0.,   0.,   0.,   1.]),\n",
       " array([0.        , 0.04596457, 0.09192913, 0.1378937 , 0.18385827,\n",
       "        0.22982283, 0.2757874 , 0.32175197, 0.36771654, 0.4136811 ,\n",
       "        0.45964567, 0.50561024, 0.5515748 , 0.59753937, 0.64350394,\n",
       "        0.6894685 , 0.73543307, 0.78139764, 0.8273622 , 0.87332677,\n",
       "        0.91929134, 0.96525591, 1.01122047, 1.05718504, 1.10314961,\n",
       "        1.14911417, 1.19507874, 1.24104331, 1.28700787, 1.33297244,\n",
       "        1.37893701, 1.42490157, 1.47086614, 1.51683071, 1.56279528,\n",
       "        1.60875984, 1.65472441, 1.70068898, 1.74665354, 1.79261811,\n",
       "        1.83858268]),\n",
       " <a list of 40 Patch objects>)"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set() # set plot styles\n",
    "\n",
    "plt.hist(inches, 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "83b7a45f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((inches > 0.5) & (inches < 1)) #display the number (sum) of days with rainfall between 0.5 and 1.0 inches\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "01ba885b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of days without rain:  215\n",
      "Number of days with rain:  150\n"
     ]
    }
   ],
   "source": [
    "print('Number of days without rain: ', np.sum(inches == 0))\n",
    "print('Number of days with rain: ', np.sum(inches != 0))"
   ]
  },
  {
   "cell_type": "raw",
   "id": "bc1f6768",
   "metadata": {},
   "source": [
    "Boolean Arrays as Mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "2f24f4f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 3, 3],\n",
       "       [7, 9, 3, 5],\n",
       "       [2, 4, 7, 6]])"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[5,0,3,3],[7,9,3,5],[2,4,7,6]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "dbe10288",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True,  True,  True],\n",
       "       [False, False,  True, False],\n",
       "       [ True,  True, False, False]])"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < 5 #return which one is less than 5"
   ]
  },
  {
   "cell_type": "raw",
   "id": "43f076d0",
   "metadata": {},
   "source": [
    "#Now to select these values from the array, we can simply index on this Boolean array; this is known as a masking operation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "ad966e9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 3, 3, 2, 4])"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[x<5] #index only the value less than 5 (those who meet the condition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "2e46f670",
   "metadata": {},
   "outputs": [],
   "source": [
    "#construct a mask of all rainy days\n",
    "rainy = (inches > 0)\n",
    "#construct a mask of all summer days (june 21st is he 172nd day)\n",
    "summer = (np.arange(365) - 172 < 90) & (np.arange(365) - 172 > 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "72fb7b5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.Median precip on rainy days in 2014 (inches): 0.19488188976377951\n",
      "2.Median precip on summer days in 2014 (inches): 0.0\n",
      "3.Maximum precip on summer days in 2014 (inches): 0.8503937007874016\n",
      "4.Maximum precip on non-summer rainy days (inches): 0.20078740157480315\n"
     ]
    }
   ],
   "source": [
    "print('1.Median precip on rainy days in 2014 (inches):', np.median(inches[rainy])) #rainy = inches > 0\n",
    "print('2.Median precip on summer days in 2014 (inches):', np.median(inches[summer]))\n",
    "print('3.Maximum precip on summer days in 2014 (inches):', np.max(inches[summer]))\n",
    "print('4.Maximum precip on non-summer rainy days (inches):', np.median(inches[rainy & ~summer])) # ~ means bitwise not"
   ]
  },
  {
   "cell_type": "raw",
   "id": "35b5e4e3",
   "metadata": {},
   "source": [
    "Using the Keywords and/or Versus the Operators &/|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "0c3f1b5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, False)"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool(42), bool(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "893500f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, False,  True,  True])"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([1, 0, 1, 0, 1, 0], dtype=bool)\n",
    "B = np.array([1, 1, 1, 0, 1, 1], dtype = bool)\n",
    "\n",
    "A|B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "a0394ccc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False, False,  True,  True,  True, False,\n",
       "       False])"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(10)\n",
    "(x>4)&(x<8)"
   ]
  },
  {
   "cell_type": "raw",
   "id": "a2d00ba9",
   "metadata": {},
   "source": [
    "Fancy Indexing \n",
    "Exploring Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "705d9106",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[51 92 14 71 60 20 82 86 74 74]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "rand = np.random.RandomState(42)\n",
    "x = rand.randint(100, size=10)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "da40cec4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([71, 86, 60])"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind = [3,7,4] # return the number in the array at the position 3, 7 and 4\n",
    "x[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "28fca644",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[71, 86],\n",
       "       [60, 20]])"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#With fancy indexing, the shape of the result reflects the shape of the index arrays rather than the shape of the array being indexed:\n",
    "ind = np.array([[3, 7], [4, 5]])\n",
    "x[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "21583552",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Fancy indexing also works in multiple dimensions. - Consider the following array\n",
    "X = np.arange(12).reshape((3,4))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "f9874cee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  5, 11])"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row = np.array([0, 1, 2])\n",
    "col = np.array([2, 1, 3])\n",
    "X[row, col]\n",
    "#if we combine a column vector and a row vector within the indices, we get a two-dimensional result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43145638",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Restart at page 80 - Chapter 2: Introduction to Numpy"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.4 ('base')",
   "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": "3.7.4"
  },
  "vscode": {
   "interpreter": {
    "hash": "80ed3414b9407e1c1714391c25463e0e1f8cf1716594c4f3219a3635151a7068"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}