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Mathematical Operations in Python with Numpy

This article was published as a part of the Data Science Blogathon 

Introduction

Numpy which stands for Numeric Python is a Python library used for working with arrays. It also has functions for working in the domain of linear algebra, Fourier transform, and matrices.

NumPy was created in 2005 by Travis Oliphant as an open-source project and one can use it freely.

mathematical operations in numpy

Why Numpy?

Numpy is a Python library that is written in Python, but the parts that require fast computation are written in C or C++. For this reason, working with Numpy array is much faster than working with Python lists.

Numpy being an open-source project has thousands of contributors working to keep NumPy fast, friendly, and bug-free. Numpy is hugely popular these days due to its use in various fields and tasks.

Uses of numpy

Uses of Numpy :

Numpy has numerous uses. Normal arithmetic and statistical operations are simple to implement Numpy. Various trigonometric calculations can also be done. Other uses are broadcasting, linear algebra, matrix operations, stacking, copying and manipulating arrays.

NumPy contains a multi-dimensional array and matrix data structures, making large scale calculations simple and easy.

numpy arrays explained
Numpy Arrays explained (https://predictivehacks.com/tips-about-numpy-arrays/)

Numpy has random number generators which can be used for various tasks like noise generation for signals for just random probability generations and other mathematical tasks.

Numpy Basics :

Let us start with the basics of Numpy.

import numpy as np
#numpy array  
a= np.array([34,67,8,5,33,90,23]) 
print(a)

Output: [34 67 8 5 33 90 23]

#type
type(a)

Output: numpy.ndarray

print(a[2])

Output : 8

b=np.array([[77, 38, 9], [10, 11, 12]])
print(b)

Output:

[[77 38 9]

[10 11 12]]

Now, we look at some interesting functions in NumPy.

Ones: Creates a NumPy array according to the parameters given, with all elements being 1.

np.ones(5)

array([1., 1., 1., 1., 1.])

np.ones([6,7])

Output:

array([[1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1.]])

Zeros: Creates a NumPy array according to the parameters given, with all elements being 0.

np.zeros(7)

Output :  array([0., 0., 0., 0., 0., 0., 0.])

These functions are simple, they can be used to create sample arrays which are often needed for various computational purposes.

eye: Let us now look at the eye function. This function returns a 2-D array with ones on the diagonal and zeros elsewhere.

np.eye(5)

Output:

array([[1., 0., 0., 0., 0.],

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

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

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

[0., 0., 0., 0., 1.]])

Similarly, the diag() function creates a 2D array with the elements passed as diagonal elements and other elements being zero.

y=np.array([6,78,3,56,89])
np.diag(y)

Output:

array([[ 6, 0, 0, 0, 0],

[ 0, 78, 0, 0, 0],

[ 0, 0, 3, 0, 0],

[ 0, 0, 0, 56, 0],

[ 0, 0, 0, 0, 89]])

Let us try some more interesting functions. These are self-explanatory.

np.array([1, 2, 3,7] * 3)

Output : array([1, 2, 3, 7, 1, 2, 3, 7, 1, 2, 3, 7])

np.repeat([1, 4, 2, 3], 5)

Output : array([1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3])

p = np.ones([2, 3], int)
print(p)

Output :

[[1 1 1]

[1 1 1]]

With vstack(), we can vertically append data, and with hstack(), we can horizontally stack data. Let us try out some examples.

np.vstack([p, 2*p])

Output :

array([[1, 1, 1],

[1, 1, 1],

[2, 2, 2],

[2, 2, 2]])

np.vstack([3*p, 2*p, 6.5*p,4.6*p])

Output :

array([[3. , 3. , 3. ],

[3. , 3. , 3. ],

[2. , 2. , 2. ],

[2. , 2. , 2. ],

[6.5, 6.5, 6.5],

[6.5, 6.5, 6.5],

[4.6, 4.6, 4.6],

[4.6, 4.6, 4.6]])

np.hstack([2*p,5.5*p,9*p])

Output:

array([[2. , 2. , 2. , 5.5, 5.5, 5.5, 9. , 9. , 9. ],

[2. , 2. , 2. , 5.5, 5.5, 5.5, 9. , 9. , 9. ]])

Numpy Mathematical Computation :

Let us get onto working with NumPy in various mathematical computations.

import numpy as np
a=np.array([4,6,8])
b=np.array([8,9,7])

c=a+b

print(c)

Output: [12 15 15]

Now, we go for an element by element multiplication.

a=np.array([4,6,8])
b=np.array([8,9,7])

c=a*b

print(c)

Output : [32 54 56]

Element by element division.

a=np.array([4,6,8])
b=np.array([8,9,7])

c=a/b

print(c)

Output: [0.5         0.66666667 1.14285714]

We calculate the dot product now.

c=np.array([6,7,5,8])
d=np.array([4,3,7,8])

ans=c.dot(d)  #dot product

print(ans)

Output : 144

Let us now, look at how to create multi-dimensional numpy arrays.

z=np.array([[5,7,5,4,5],[6,2,3,4,6]])

print(z)

Output:

[[5 7 5 4 5]

[6 2 3 4 6]]

Getting the transpose.

print(z.T)

Output :

[[5 6]

[7 2]

[5 3]

[4 4]

[5 6]]

Let us create a list by giving a few parameters. The first and second parameter will be for determining the range and the third will be for the interval.

h=np.arange(4,90,5)
print(h)

Output: [ 4 9 14 19 24 29 34 39 44 49 54 59 64 69 74 79 84 89]

Now, let us look at some standard functions.

output

Let us carry some computations over multi-dimensional arrays.

test = np.random.randint(0,10,(4,3))
print(test)

Output:

[[5 0 2]
[3 6 0]
[5 7 7]
[0 5 9]]

Here 0 and 10 indicate the range, and 4,3 is the shape of the matrix/2D array.

test2 = np.random.randint(90,120,(8,3))
test2

Output:

array([[106, 103, 104],
[ 96, 93, 106],
[110, 108, 115],
[117, 106, 114],
[ 91, 102, 103],
[ 98, 104, 92],
[112, 99, 105],
[115, 111, 118]])

for row in test2:
    print(row)

Output:

[106 103 104] [ 96 93 106] [110 108 115] [117 106 114] [ 91 102 103] [ 98 104 92] [112 99 105] [115 111 118]

test3 = test2**2
test3

Output:

array([[11236, 10609, 10816],
[ 9216, 8649, 11236],
[12100, 11664, 13225],
[13689, 11236, 12996],
[ 8281, 10404, 10609],
[ 9604, 10816, 8464],
[12544, 9801, 11025],
[13225, 12321, 13924]], dtype=int32)

for i, j in zip(test2, test3):
    print(i,'+',j,'=',i+j)

Output:

[106 103 104] + [11236 10609 10816] = [11342 10712 10920]
[ 96 93 106] + [ 9216 8649 11236] = [ 9312 8742 11342]
[110 108 115] + [12100 11664 13225] = [12210 11772 13340]
[117 106 114] + [13689 11236 12996] = [13806 11342 13110]
[ 91 102 103] + [ 8281 10404 10609] = [ 8372 10506 10712]
[ 98 104 92] + [ 9604 10816 8464] = [ 9702 10920 8556]
[112 99 105] + [12544 9801 11025] = [12656 9900 11130]
[115 111 118] + [13225 12321 13924] = [13340 12432 14042]

Conclusion

Thus, we can see that NumPy can be used for various types of mathematical calculations and the important thing is that the computation time is much less than python lists. This helps while working in real-life cases with millions of data points.

Numpy array is also very convenient to use with a lot of data manipulation tricks and methods.

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