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NumPy Part 2

Array indexing

  1. NumPy mainly offers three ways to index into arrays.

  • Slicing Based Indexing

  • Integer Based Indexing

  • Boolean Based Indexing

Accessing a single element

  • Use [] for accessing the elements inside the array

Example 1

*** index starts from 0



Slicing Based Indexing

  • Similar to Python lists, numpy arrays can be sliced. As elements inside the arras are indexed

  • Since arrays may be multidimensional, you must specify a slice for each dimension of the array

  • A slice of an array is a view into the same data, so modifying it will modify the original array

  • When you index into numpy arrays using slicing, the resulting array view will always be a subarray of the original array.


Accessing multiple element from 2d array


  • In 2 dimensional we have rows as one dimension and columns as other dimension (Matrix)

  • Rows and Columns index starts from 0


  • So whenever we are doing slicing we have to provide slicing for both rows as well as for columns





*** ending index not included


Example 2


1 ROW AND 1 COLUMN


Example 3


"N" ROWS AND "M" COLUMNS





Integer array indexing

  • Integer array indexing allows you to construct arbitrary arrays using the data from another array

  • Means no change in the original array if we do any change in the sub array

  • yield an array of lower rank than the original array

  • Since arrays may be multidimensional, you must specify an Integer array indexing for each dimension of the array


Example 4



Boolean Based indexing

  • Boolean array indexing lets you pick out arbitrary elements of an array

  • Means no change in the original array if we do any change in the extracted array

  • This type of indexing is used to select the elements of an array that satisfy some condition

  • It can also be called masking

Example 5


Example 6



Mathematical Operations on Arrays

  • Basic mathematical functions can be applied on arrays

  • This mathematical functions operate elementwise on arrays

  • This mathematical operation are available as both as operators and function in numpy module

Addition (+ or add() )

  • We can use + operator to do elementwise addition

  • Or we can use add() functions in the NumPy module

Example 7


Subtraction (- or subtract() )

  • We can use - operator to do elementwise subtraction

  • Or we can use subtract() functions in the NumPy module

Example 8




Multiplication (* or multiply() )

  • We can use * operator to do elementwise multiplication

  • Or we can use multiply() functions in the NumPy module

Example 9



dot() (to get inner product)

  • * is elementwise multiplication, not matrix multiplication

  • To do matrix multiplication we have to use dot() function provided by numpy module

  • dot() functions computes the inner products

  • Whenever we are using this dot() function we have to follow matrix multiplication to rule

  • For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

  • The resulting matrix, has the number of rows of the first and the number of columns of the second matrix as its final shape

  • So if you don't follow the above rule then we will get an error


Example 10




Example 11




Broadcasting


  • Broadcasting is a powerful mechanism that allows numpy to work with arrays of different shapes when performing arithmetic operations.

  • Frequently we have a smaller array and a larger array, and we want to use the smaller array multiple times to perform some operation on the larger array

  • whenever we are doing computation on different shapes of array then numpy automatically uses this broadcasting technique

  • Broadcasting in a simple way we can understand it as duplicating the rows or column to match the shape of the larger array

  • In the below figure we have an array having a shape (3,3) means 3 rows and 3 columns and other array having a shape of (3,) means a single row having 3 elements so when we do multiplication on both the arrays the array with shape (3,) will duplicate the rows 2 times to match the larger array shaped as (3,3)


Example 11

Example 12

Example 13



Division (/ or divide() )

  • We can use / operator to do elementwise division

  • Or we can use divide() functions in the NumPy module

Example 14


Square Root (sqrt() )

  • We can use sqrt() function to get square root of each element in an array

Example 15

Different Functions For Performing Computations On Arrays


sum(array object , axis)

  • We can use sum() function to get sum of all elements

  • axis (its and optional parameter) parameters has two values 0 (column wise sum) , 1 (rows wise sum)

  • If we don't use axis parameter then the sum function will return sum of all the elements in the array

Example 16


prod(array object , axis)

  • We can use prod() function to get product of all elements

  • axis (its and optional parameter) parameters has two values 0 (column wise product) , 1 (rows wise product)

  • If we don't use axis parameter then the prod function will return product of all the elements in the array

Example 17



cumsum(array object , axis)

  • We can use cumsum() function to get the cumulative sum of the elements .

  • axis (its and optional parameter) parameters has two values 0 (column wise cumulative sum ) , 1 (rows wise cumulative sum )

Example 18


cumprod(array object , axis)

  • We can use cumprod() function to get the cumulative product of the elements .

  • axis (its and optional parameter) parameters has two values 0 (column wise cumulative product ) , 1 (rows wise cumulative product )

Example 19


round(array object , decimals)

  • Evenly round to the given number of decimals

  • decimal parameter is nothing but the Number of decimal places to round to (default: 0)

Example 20


Descriptive statistics on the ndarray


mean()

  • Computes the mean of ndarray

  • axis parameter can be used to compute mean row wise(1) or column wise(0)

  • If axis parameter is not used while computing the mean then mean will be computed for total elements inside the array

Example 21



median()

  • Computes the median of ndarray

  • axis parameter can be used to compute mean row wise(1) or column wise(0)

  • If axis parameter is not used while computing the median then median will be computed for total elements inside the array

Example 22


std() Standard Deviation

  • Computes the standard deviation of ndarray

  • axis parameter can be used to compute mean row wise(1) or column wise(0)

  • If axis parameter is not used while computing the standard deviation then standard deviation will be computed for total elements inside the array

Example 23

min()

  • Computes the minimum value of ndarray

  • axis parameter can be used to compute mean row wise(1) or column wise(0)

  • If axis parameter is not used while computing the minimum value then minimum value will be computed from the total elements inside the array

Example 24

argmin()

  • Gets the index of minimum value in the ndarray

Example 24


max()

  • Computes the maximum value of ndarray

  • axis parameter can be used to compute mean row wise(1) or column wise(0)

  • If axis parameter is not used while computing the maximum value then maximum value will be computed from the total elements inside the array

Example 25

argmax()

  • Gets the index of maximum value in the ndarray

Example 26

Extras:-

Transpose A Matrix

  • We can transpose a matrix(2d) by using T

  • It can be also used as a reshape function

  • taking the transpose of a rank 1 array does nothing

Example 27

Tile Function

  • Tile function is used to create a new array by repeating the array column wise or row wise

  • Tile function takes two important arguments

    • array

    • repetitions along axis (should be given in a tuple format)

      • (row wise repetitions ,column wise repetitions)

      • (2,3) -- repeat 2 times row wise and three times column wise

Example 28


Create An Empty Array With The Same Shape Of Other Array

  • We can create an empty array with the same shape of other array by using empty_like()

Example 29


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