NUMPY

INTRODUCTION  TO AN ARRAY IN PROGRAMMING LANGUAGE:-

Array is a container which can hold a fix number of items and these items should be of the same type. Most of the data structures make use of arrays to implement their algorithms. Following are the important terms to understand the concept of Array.

• Element − Each item stored in an array is called an element.
• Index − Each location of an element in an array has a numerical index,                      which is used to identify the element.
• Thus, An array is a special variable, which can hold more than one value at a time. i.e. An array can hold many values under a single name, and you can access the values by referring to an index number.
• Note: Python does not have built-in support for Arrays, but Python Lists can be used instead.

Introduction to NumPy

• NumPy, which stands for Numerical Python, is a library consisting of multidimensional array objects and a collection of routines for processing those arrays. Using NumPy, mathematical and logical operations on arrays can be performed.
• The most important object defined in NumPy is an N-dimensional array type called ndarray. It describes the collection of items of the same type. Items in the collection can be accessed using a zero-based index.

Creating 1D ndarray

The following example creates an 1D ndarray using a list.

import numpy as np

a = np.array([1,2,3,4])

print(a)

print('Dimension:',a.shape)# dimension of the array- (4 rows for 1 D array)

print('Datatype:',a.dtype)

print('Size of each element:', a.itemsize, 'bytes')

OUTPUT:

[1 2 3 4] Dimension: (4,) Datatype: int64 Size of each element: 8 bytes

We can create an array with smaller size by mentioning the dtype specifically to int16 or int8

import numpy as np

a = np.array([1,2,3,4], dtype='int8')

print(a.dtype)

print('Size of each element:', a.itemsize, 'byte')

OUTPUT:

int8 Size of each element: 1 byte

Creating ndarrays using fromiter()

• fromiter() function can be create a numpy array using any iterable (that can be traversed through) object like string, list or a dictionary
• The following examples illustrate the use of fromiter() method

#This example creates an array of unicode charactersrs from a string

#The dtype needs to be exclusively given (Unicode 2 bytes)

import numpy as np

st ="NUMPY"

arr = np.fromiter(st, dtype='U2')

print(arr)

#This example creates an array of integers from a loop

itr = (x*x for x in range(1,8))

arr = np.fromiter(itr, dtype='int8')

print(arr)

#This example will create a dictionary of keys of a dictionary

dic = {'A':10, 'B':20, 'C':20}

arr = np.fromiter(dic, dtype='U2')

print(arr)

#The last example will create an arry selecting only first 5 charecters of the string

#For this we need to set the count attribute to a desired value

st = "PYTHONLANG"

arr = np.fromiter(st, dtype='U2', count=5)

print(arr)

OUTPUT :

['N' 'U' 'M' 'P' 'Y'] [ 1 4 9 16 25 36 49] ['A' 'B' 'C'] ['P' 'Y' 'T' 'H' 'O']

Accessing elements of 1D array

We use 0 based indexing for accessing the elements of an ndarray

import numpy as np

a = np.array([1,2,3,4], dtype='int8')

print('The first element:',a[0])

print('The last element:',a[3])

OUTPUT:

The first element: 1 The last element: 4

Creating 2D ndarray

We can pass a 2D list in the array() function of numpy to create a 2D ndarray as shown below.

import numpy as np

b = np.array([[1,2,3],[4,5,6],[7,8,9]])

print(b)

print('The shape is:',b.shape)

OUTPUT:

[[1 2 3] [4 5 6] [7 8 9]] The shape is: (3, 3)

Accessing the elements of 2D array

The following examples illustrates the use of 0 based indexing on 2D array

import numpy as np

b = np.array([[1,2,3],[4,5,6],[7,8,9]])

print(b)

print('first row:',b[0])

print('First row 1st element:',b[0][0])

print('Third row 3rd element:',b[2][2]) 

print('Second row 1st element:',b[1,0])

OUTPUT:

[[1 2 3] [4 5 6] [7 8 9]] first row: [1 2 3] First row 1st element: 1 Third row 3rd element: 9 Second row 1st element: 4

Creating matrices with numpy functions

Creating matrix of 0s using the zeros() function.

Observe that the dtype of the resulting matrix of zeros is float64

import numpy as np

b = np.zeros((3,3)) # Creates a 3x3 matrix with zeros

print(b)

print(b.dtype)

OUTPUT:

[[0. 0. 0.] [0. 0. 0.] [0. 0. 0.]] float64

Creating the matrix of 1s using the ones() function

import numpy as np

b = np.ones((3,3)) # Creates a 3x3 matrix with ones

print(b)

print(b.dtype)

OUTPUT:

[[1. 1. 1.] [1. 1. 1.] [1. 1. 1.]] float64

Creating a matrix using full() function

This function accepts two parameters - size as tuple and the data value as a number

import numpy as np

b = np.full((2,2), 8) # Creates a 2x2 constant matrix with 8

print(b)

OUTPUT:

[[8 8] [8 8]]

Creating an identity matrix using eye() function

This method accepts one parameter as the size of the identity matrix.

import numpy as np

b = np.eye(3) # Creates an identity matrix

print(b)

OUTPUT:

[[1. 0. 0.] [0. 1. 0.] [0. 0. 1.]]

Creating matrix with random() funcion

• Random numbers can be generated using the random library of numpy.
• The following statement creates a a 2x2 matrix using random.random() funcion

import numpy as np

b = np.random.random((2,2)) # Creates an random number matrix

print(b)

OUTPUT:

[[0.53352925 0.48243526] [0.51794348 0.46761645]]

Using arange() function to create numpy array

#Using arange function to create a numpy array

import numpy as np

# creates an array of integers from 0 to 9

b = np.arange(10) 

print(b)

# creates an array of floats from 1 to 10

a = np.arange(1,11, dtype=float) 

print(a)

# Creates an array with interval of 0.1

c = np.arange(2,3, 0.1)

print(c) 

OUTPUT:

[0 1 2 3 4 5 6 7 8 9]

[ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.] [2. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9]

Slicing of numpy arrays

• Slicing of numpy arrays creates sub-arrays from and existing array
• Any modification done in the subarray is reflected back in the main array

#Slicing of numpy arrays

#Resultant array will always be a sub-array of the original array

import numpy as np

a = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])

b = a[0:2] # slice consists of only first two row (excludes row three)

print('b:',b)

c = a[1:2] # Slice consists of only second row

print('c:',c)

d = a[0:1,0:4] # Slice consists of entire first row (first row all columns)

print('d:',d)

e = a[0:1,0:2] # Slice consists of first row and first two columns

print('e:',e)

f = a[0:1,2:4] # Slice consists of first row and columns three and four

print('f:',f)

OUTPUT:

b: [[1 2 3 4] [5 6 7 8]] c: [[5 6 7 8]] d: [[1 2 3 4]] e: [[1 2]] f: [[3 4]]

Some more examples of slicing in numpy arrays

#Slicing of numpy arrays

import numpy as np

a = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])

b = a[1:2,0:4]                 # Slice consists of second row all columns

print('b:',b)

c = a[1:2,1:2]                 # Slice consists of second row second column

print('c:',c)

d = a[:2,0:2]                   # Slice consists of two rows first[1,2] and second[5,6]

print('d:',d)

e = a[:2,1:3]                  # Slice consists of two rows first[2,3] and second[6,7]

print('e:',e)

f = a[1:3,2:4]                              # Slice consists of two rows first[7,8] and second[11,12]

print('f:',f)

OUTPUT:

b: [[5 6 7 8]] c: [[6]] d: [[1 2] [5 6]] e: [[2 3] [6 7]] f: [[ 7 8] [11 12]]

Creating a new arbitry array from an existing one using indexing

#Indexing will create a new arbitry array from the original array

import numpy as np

a = np.array([[1,2], [3, 4], [5, 6]])

print(a.shape)

b = a[[0,1,2],[0,1,0]] # The resultant array will have shape (3,)

print(b)

print(b.shape)

OUTPUT:

(3, 2) [1 4 5] (3,)

Changing the value in a slice will also create a change in original array

#Changing the values in an array resulting from slice

import numpy as np

a = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])

b = a[0:2,1:3] #Sliced array

print(b)

b[0,0]=20 # Changing the value in the slice

print(b)

print(a) # The change is getting reflected in the original array

OUTPUT:

[[2 3] [6 7]] [[20 3] [ 6 7]] [[ 1 20 3 4] [ 5 6 7 8] [ 9 10 11 12]]

Joining two numpy arrays using concatenate() function

#Joining two numpy arrays

import numpy as np

a = np.array([[1,2],[2,4]])

b = np.array([[7,8]])

#Joing as row

c = np.concatenate((a,b), axis=0)

print(c)

#Joinging as column

d = np.concatenate((a,b.T), axis=1)

print(d)

OUTPUT:

[[1 2] [2 4] [7 8]] [[1 2 7] [2 4 8]]

Arithmatic operations on numpy arrays

• Unlike lists the aritmatic operations on numpy arrays are vector operations
• Addition, subtraction, simple multipliction, matrix multiplication, division, square root
• Addition of two arrays: np.add(a,b) or a+b
• Subtraction of two arrays: np.subtract(a,b) or a-b
• Simple multiplication: np.multiply(a,b) or a*b
• Division of two arrays: np.divide(a,b) or a/b
• Matrix multiplication: np.dot(a,b) or a.dot(b)

#Numpy arithmatic operations

import numpy as np

a = np.array([[1,2],[3,4]], dtype=np.int32)

b = np.array([[5,6],[7,8]], dtype=np.int32)

print(a+b)

print(np.add(a,b))

print(a-b)

print(np.subtract(a,b))

print(a*b) # Multiplies corresponding elements

print(np.multiply(a,b))

print(a/b)

print(np.divide(a,b))

print(np.sqrt(a))

# Actual Matrix multiplication

print(a.dot(b))

print(np.dot(a,b))

OUTPUT:

[[ 6 8] [10 12]] [[ 6 8] [10 12]] [[-4 -4] [-4 -4]] [[-4 -4] [-4 -4]] [[ 5 12] [21 32]] [[ 5 12] [21 32]] [[0.2 0.33333333] [0.42857143 0.5 ]] [[0.2 0.33333333] [0.42857143 0.5 ]] [[1. 1.41421356] [1.73205081 2. ]] [[19 22] [43 50]] [[19 22] [43 50]]

Row and column sum of array elements using sum() function

• for axis=0 there will be row sum
• for axis=1 there will be column sum

#numpy sum() function

a = np.array([[1,2],[3,4]], dtype=np.int32)

print(np.sum(a, axis=0))

print(np.sum(a, axis=1))

[4 6] [3 7]