Python – Matrix Custom Multiplier

Sometimes, while working with data, we can have a problem in which we need to multiply each row of matrix with a different multiplier. This kind of application is important in data science domain. Lets discuss certain ways in which this task can be performed. 

Method #1 : Using loop + zip() The combination of above functions can be used to perform this task. In this, we iterate through each row and perform the task of multiplication using zip(). 

Python3

# Python3 code to demonstrate
# Matrix Custom Multiplier
# using loop + zip()

# Initializing list
test_list1 = [[1, 3], [5, 6], [8, 9]]
test_list2 = [4, 3, 6]

# printing original lists
print("The original list 1 is : " + str(test_list1))
print("The original list 2 is : " + str(test_list2))

# Matrix Custom Multiplier
# using loop + zip()
res = []
for mul, sub in zip(test_list2, test_list1):
    temp = []
    for ele in sub:
        temp.append(mul * ele)
    res.append(temp)

# printing result
print ("Matrix after custom multiplication : " + str(res))

Output

The original list 1 is : [[1, 3], [5, 6], [8, 9]]
The original list 2 is : [4, 3, 6]
Matrix after custom multiplication : [[4, 12], [15, 18], [48, 54]]

Time complexity: O(n^2), where n is the length of the longest sublist in test_list1.
Auxiliary space: O(n^2), to store the result list res.

Method #2 : Using list comprehension + zip() The combination of above methods can be used to solve this problem. In this, we just iterate through the list and perform the task of multiplication in one liner. 

Python3

# Python3 code to demonstrate
# Matrix Custom Multiplier
# using list comprehension + zip()

# Initializing list
test_list1 = [[1, 3], [5, 6], [8, 9]]
test_list2 = [4, 3, 6]

# printing original lists
print("The original list 1 is : " + str(test_list1))
print("The original list 2 is : " + str(test_list2))

# Matrix Custom Multiplier
# using list comprehension + zip()
res = [[mul * ele for ele in sub] for mul, sub in zip(test_list2, test_list1)]

# printing result
print ("Matrix after custom multiplication : " + str(res))

Output

The original list 1 is : [[1, 3], [5, 6], [8, 9]]
The original list 2 is : [4, 3, 6]
Matrix after custom multiplication : [[4, 12], [15, 18], [48, 54]]

Time complexity: O(n^2), where n is the number of elements in the matrix.

Auxiliary space: O(n^2), since a new matrix of the same size is created to store the result.

Method #3 : Using Numpy

We can use Numpy library to perform this task. Numpy library provides a function “multiply()” which is used to perform the element wise multiplication of two arrays.

Python3

# Python3 code to demonstrate
# Matrix Custom Multiplier
# using Numpy

# Importing Numpy library
import numpy as np

# Initializing list
test_list1 = [[1, 3], [5, 6], [8, 9]]
test_list2 = [4, 3, 6]

# printing original lists
print("The original list 1 is : " + str(test_list1))
print("The original list 2 is : " + str(test_list2))
test_list2 = np.array([4, 3, 6])[:, np.newaxis]
# Matrix Custom Multiplier
# using Numpy
res = np.multiply(test_list1, test_list2)

# printing result
print("Matrix after custom multiplication : " + str(res))
#This code is contributed by Edula Vinay Kumar Reddy

Output :

The original list 1 is : [[1, 3], [5, 6], [8, 9]]
The original list 2 is : [4, 3, 6]
Matrix after custom multiplication : [[ 4 9]
[15 18]
[48 54]]

Time Complexity: O(mn), where m is the number of rows and n is the number of columns.
Auxiliary Space: O(mn)

Method #4 : Using for loops

Python3

# Python3 code to demonstrate
# Matrix Custom Multiplier

# Initializing list
test_list1 = [[1, 3], [5, 6], [8, 9]]
test_list2 = [4, 3, 6]

# printing original lists
print("The original list 1 is : " + str(test_list1))
print("The original list 2 is : " + str(test_list2))

# Matrix Custom Multiplier
res = []
for i in range(0,len(test_list1)):
    x=[]
    for j in range(0,len(test_list1[i])):
        x.append(test_list1[i][j]*test_list2[i])
    res.append(x)
# printing result
print ("Matrix after custom multiplication : " + str(res))

Output

The original list 1 is : [[1, 3], [5, 6], [8, 9]]
The original list 2 is : [4, 3, 6]
Matrix after custom multiplication : [[4, 12], [15, 18], [48, 54]]

Time Complexity: O(mn), where m is the number of rows and n is the number of columns.
Auxiliary Space: O(mn)

Method #5: Using the map() function

This implementation uses the lambda function inside the map() function to perform the multiplication on each element of the sub-lists. The outer map() function applies the lambda function to each element of both input lists using the zip() function. Finally, the result is converted to a list using the list() function.

Python3

# Python3 code to demonstrate
# Matrix Custom Multiplier
# using map() function

# Initializing list
test_list1 = [[1, 3], [5, 6], [8, 9]]
test_list2 = [4, 3, 6]

# printing original lists
print("The original list 1 is : " + str(test_list1))
print("The original list 2 is : " + str(test_list2))

# Matrix Custom Multiplier
# using map() function
res = list(map(lambda x, y: list(map(lambda a: a*x, y)), test_list2, test_list1))

# printing result
print ("Matrix after custom multiplication : " + str(res))

Output

The original list 1 is : [[1, 3], [5, 6], [8, 9]]
The original list 2 is : [4, 3, 6]
Matrix after custom multiplication : [[4, 12], [15, 18], [48, 54]]

The time complexity of this code is O(n^2), where n is the length of the longest sub-list in the input list test_list1.
The space complexity of this code is O(n^2), where n is the length of the longest sub-list in the input list test_list1. 

Method #9: Using pandas

Step-by-step approach:

• Import pandas library
• Create a pandas DataFrame using the first list “test_list1“
• Multiply the DataFrame with the second list “test_list2” using the multiply() method of DataFrame
• Get the resulting matrix as a numpy array using the values attribute of the DataFrame
• Convert the numpy array back to a list using the tolist() method of numpy array.

Below is the implementation of the above approach:

Python3

# Python3 code to demonstrate
# Matrix Custom Multiplier
# using pandas

# import pandas and numpy
import pandas as pd
import numpy as np

# Initializing list
test_list1 = [[1, 3], [5, 6], [8, 9]]
test_list2 = [4, 3, 6]

# Create a pandas DataFrame
df = pd.DataFrame(test_list1)

# Multiply the DataFrame with the second list
res_df = df.multiply(test_list2, axis=0)

# Get the resulting matrix as a numpy array
res_np = res_df.values

# Convert the numpy array back to a list
res = res_np.tolist()

# printing result
print ("Matrix after custom multiplication : " + str(res))

Output: 

Matrix after custom multiplication : [[4, 12], [15, 18], [48, 54]]

Time complexity: O(n^2), where n is the number of elements in the largest dimension of the matrix (either number of rows or columns).
Auxiliary space: O(n^2), since the matrix multiplication operation requires creating a new matrix of size n x n