Day 6: Vector and Matrices¶

Today we will learn about two important data types of numpy library which is similar to vectors and matrices. Array and matrices stores data similar to lists but they suitable for mathematical operations like dot product and matrix multiplication.

Day 6: Vector and Matrices

1. Array¶

Here we will learn about array which is similar to vectors in mathematics.

1.1 Importing array¶

Similar to other python library we can import array as the following methods

import array
import array as arr
from array import *

Note

We will use only the second method in this course.

1.2 Creating Array elements¶

To make an array in python we use the following functions.

import array as arr
a = arr.array ('d' ,[1,2,3,4,5])
print(a)

This will create a array with variable a contains five elements 1 to 5. Here d denote the data type of float. For other datatype you can use the following table.

Code	C Type	Python Type	Min bytes
b	signed char	int	1
B	unsigned char	int	1
u	Py_UNICODE	Unicode	2
h	signed short	int	2
H	unsigned short	int	2
i	signed int	int	2
I	unsigned int	int	2
l	signed long	int	4
L	unsigned long	int	4
f	float	float	4
d	double	float	8

Tip

You can convert any list of number to an array simply using d as in above code.

1.3 Accessing elements of array¶

Element: To access the an element of the array a, we use the following command

import array as arr
a = arr.array ('d' ,[1,2,3,4,5])
print(a[2])  # counting starts with 0
print(a[-2]) # count from last

3
4

Slicing: Similar to the list and strings we can obtain a continuous part of an array

import array as arr

a=arr.array('d', [6.8, 5.9, 9.8, 2.4, 3.3])
print(a[1:3]) # prints the part of array start with index 1 and end before 3

array('d', [5.9, 9.8])

1.4 Basic Array operations¶

len: Length of an array can be computed using len function as follows

import array as arr
a = arr.array ('d' ,[1,2,3,4,5])
print(len(a)) # prints length of array a

Concatenation: We can join two array with + operation.

import array as arr

a = arr.array('d',[1.2, 5.8, 6.4])
b = arr.array('d',[1.3, 6])
c = a + b # array c will have elements of a and b
print(c)

Array c =  array('d', [1.2, 5.8, 6.4, 1.3, 6.0])

1.5 Method on array¶

append: Similar to the list the append is used to add a single element at the end of an array.

import array as arr
a = arr.array ('d' ,[1,2,3,4,5])
a.append(23) # appends 23 at the end of array a
print(a)

array('d', [1.0, 2.0, 3.0, 4.0, 5.0, 23.0])

extend: It is used when you want to add more than one element at the end of an array.

import array as arr
a = arr.array ('d' ,[4,5])
a.extend([23, 4.15, 6.7]) # extend array a using list
print(a)
b = arr.array ('d' ,[23, 4.15, 6.7])
a.extend(b) # extend array a using another array b
print(a)

array('d', [4.0, 5.0, 23.0, 4.15, 6.7])
array('d', [4.0, 5.0, 23.0, 4.15, 6.7, 23.0, 4.15, 6.7])

insert: - used when you want to add an element at a specific position in an array.

import array as arr
a = arr.array ('d' ,[1.2,2,3.14,4,5])
a.insert(1, 2.73) # insert 2.73 at position 1 (count with 0)
print(a)

array('d', [1.2, 2.73, 2.0, 3.14, 4.0, 5.0])

pop: It is used when you want to remove an element and return it. We can provide optional argument to remove an element with given index.

import array as arr
a = arr.array('d', [4, 3, 5, 6.7, 3.5])
print(a.pop()) # remove the last element
print(a.pop(1)) # remove index 1 element (count with 0)
print(a)

3.5
3.0
array('d', [4.0, 5.0, 6.7])

remove: : It is used when you want to remove an element with a specific value without returning it.

import array as arr
a = arr.array('d', [4, 3, 5, 6.7, 3.5])
print(a.remove(5)) # remove element 5, but produce no output
print(a) # prints array a after removing element 5

None
array('d', [4.0, 3.0, 6.7, 3.5])

1.6 Looping through an array¶

Similar to list and string we can use for loops or while loops to go through each elements of a list one by one.

for To iterates over the items of an array specified we can use for as follows

import array as arr

a = arr.array('d', [6.8, 5.9, 9.8, 2.4, 3.3])
for i in a:
    # you can use each element on your desire
    print(i**2) # printing square of each element

46.239999999999995
34.81
96.04000000000002
5.76
10.889999999999999

2. Matrices in Python¶

Matrices in python can be achieved using one of the following ways

Nested Lists
Numpy Arrays
Numpy Matrices

Now we will learn them one by one

2.1 Nested List¶

We can used nested list to store data similar to matrices.

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
print(matrix)

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

Warning

Nested list doesn't work similar to matrices in mathematics. They are simply table and operations are limited by list functions.

2.2 Numpy Arrays¶

Similar to nested list, we can use array inside array to store data in matrices.

import numpy as np

a = np.array([[1.2, 2.1],[3.6, 4.3]])
print(a)

[[1.2 2.1]
[3.6 4.3]]

2.2.1 Operation on matrices¶

Addition: We use + to achieve addition of similar size matrices.

import numpy as np

a = np.array([[1, 2], [3, 4]])
b = np.array([[10, 20], [30, 40]])
print(a + b)

[[11 22]
[33 44]]

Matrix multiplication: We use * to achieve addition of similar size matrices.

import numpy as np

a = np.array([[1, 2], [3, 4]])
b = np.array([[10, 20], [30, 40]])
print(a * b)

[[ 10  40]
[ 90 160]]

Transpose: We can transpose a matrix using the transpose function of numpy library.

import numpy as np

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

[[1 2 3]
[4 5 6]]
[[1 4]
[2 5]
[3 6]]

2.3 Numpy Matrices¶

Numpy matrix is a class in nunpy library to handle matrices and mathematical operations related to them.

2.3.1 creating a matrix from a string¶

The main advantage of this class is that it has flexible method of creating matrices and slicing them.

import numpy as np

a = np.matrix("1, 2; 3, 4")
b = np.matrix([[10, 20],[30, 40]])
print(a)
print(b)

[[1 2]
 [3 4]]
[[10 20]
 [30 40]]

2.3.2 Operations on Numpy Matrices¶

The operation on numpy matrices are similar to the matrices we make using numpy arrays.