Python – Get Matrix Mean

Last Updated : 11 May, 2023

Given a Matrix, Find its mean.

Input : test_list = [[5, 6, 7], [7, 5, 6]] Output : 6.0 Explanation : 36 / 6 = 6.0
Input : test_list = [[5, 6, 7, 4, 8]] Output : 6.0 Explanation : 30 / 5 = 6.0

Method #1 : Using list comprehension + sum() + len() + zip()

The combination of above functions can be used to solve this problem. In this, we perform the mean calculation using sum() and len(), zip() along with * operator does task of extracting each element of rows of matrix.

Python3

# Python3 code to demonstrate working of 
# Matrix Mean
# Using list comprehension + sum() + len() + zip()
 
# initializing lists
test_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
 
# printing original list
print("The original list : " + str(test_list))
 
# zip() to get all elements 
# sum() / len() gives mean
# extracts column mean
res = [sum(idx) / len(idx) for idx in zip(*test_list)]
 
# extracts all elements mean
res = sum(res) / len(res)
     
# printing result 
print("Matrix Mean : " + str(res))

Output

The original list : [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
Matrix Mean : 5.25

Method #2 : Using mean() + zip() + list comprehension

This is another method in which this task can be performed. In this, we extract mean using inbuilt method of mean()

Python3

# Python3 code to demonstrate working of 
# Matrix Mean
# Using mean() + zip() + list comprehension
from statistics import mean
 
# initializing lists
test_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
 
# printing original list
print("The original list : " + str(test_list))
 
# zip() to get all elements 
# mean() gives mean
# extracts column mean
res = [mean(idx) for idx in zip(*test_list)]
 
# extracts all elements mean
res = mean(res)
     
# printing result 
print("Matrix Mean : " + str(res))

Output

The original list : [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
Matrix Mean : 5.25

Method #3 : Using extend() and mean() method of statistics module

Python3

# Python3 code to demonstrate working of
# Matrix Mean
import statistics
# initializing lists
test_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
 
# printing original list
print("The original list : " + str(test_list))
x=[]
for i in test_list:
    x.extend(i)
res=statistics.mean(x)
# printing result
print("Matrix Mean : " + str(res))

Output

The original list : [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
Matrix Mean : 5.25

Method #4: Using numpy

Here’s a step-by-step algorithm for calculating the mean of a matrix:

Initialize the matrix as a list of lists.
Convert the matrix to a NumPy array using np.array().
Calculate the mean of the NumPy array using np.mean().
Print the result to the console using print().

Python3

# Import the numpy library as np
import numpy as np
 
# Define the matrix as a list of lists
test_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
 
# Converting the matrix to a NumPy array using np.array()
arr = np.array(test_list)
 
# Calculating the matrix using np.mean()
res = np.mean(arr)
 
# Printing esult to the console using print()
print("Matrix Mean : " + str(res))
 
# This code is contributed by Vinay Pinjala

Output

The original list : [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
Matrix Mean : 5.25

Time complexity: O(n^2). This is because there are two main operations that dominate the time complexity: initializing the matrix and converting it to a NumPy array. Initializing the matrix takes O(n^2) time, where n is the size of the matrix. Converting the matrix to a NumPy array also takes O(n^2) time. Calculating the mean of the NumPy array and printing the result to the console take constant time. Therefore, the overall time complexity is O(n^2).

Auxilairy space: O(n^2). This is because the matrix takes O(n^2) space in memory, and the NumPy array also takes O(n^2) space in memory. The mean of the NumPy array is stored in a single variable, which takes O(1) space. There are no additional data structures used in this algorithm. Therefore, the overall space complexity is O(n^2).

Method 5: Using nested loops

Initialize a 2D list named test_list with integer values.
Now printing the original matrix using a for loop to iterate through each row in test_list and print each row.
Initializing two variables total_sum and count to zero.
Using nested loops, iterate through each element in test_list, add the value of each element to total_sum, and increment the value of count by 1 for each element.
Calculating the mean of the matrix by dividing total_sum by count and assign it to the variable res.
Printing the calculated mean of the matrix as a string concatenated with “Matrix Mean : “.

Python3

# Python3 code to demonstrate working of
# Matrix Mean
 
# initializing matrix
test_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
 
# Printing original matrix
print("The original matrix : ")
 
for row in test_list:
    print(row)
 
# Calculating mean
# using nested loop
total_sum = 0
count = 0
 
for row in test_list:
    for num in row:
        total_sum += num
        count += 1
 
# calculating mean
res = total_sum / count
 
# printing result
print("Matrix Mean : " + str(res))

Output

The original matrix : 
[5, 6, 3]
[8, 3, 1]
[9, 10, 4]
[8, 4, 2]
Matrix Mean : 5.25

Time complexity: O(n^2), where n is the number of elements in the matrix
Auxiliary space: O(1)

Method #7: Using the reduce() function from the functools module

Approach:

Import the functools module using the import statement: import functools
Define a lambda function that takes two arguments, x and y, and returns their sum: lambda x, y: x + y
Use the reduce() function from functools to calculate the sum of all the elements in the matrix: total_sum = functools.reduce(lambda x, y: x + y, [num for row in test_list for num in row])
Use the len() function to calculate the total number of elements in the matrix: count = len([num for row in test_list for num in row])
Calculate the mean of the matrix by dividing the total_sum by the count: res = total_sum / count
Print the result: print(“Matrix Mean : ” + str(res))

Python3

import functools
 
# initializing matrix
test_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]
 
# printing original matrix
print("The original matrix : ")
for row in test_list:
    print(row)
 
# using reduce() function to calculate sum of all elements
total_sum = functools.reduce(
    lambda x, y: x + y, [num for row in test_list for num in row])
 
# calculating total number of elements in the matrix
count = len([num for row in test_list for num in row])
 
# calculating mean
res = total_sum / count
 
# printing result
print("Matrix Mean : " + str(res))

Output

The original matrix : 
[5, 6, 3]
[8, 3, 1]
[9, 10, 4]
[8, 4, 2]
Matrix Mean : 5.25

Time complexity: O(n^2), where n is the number of rows or columns in the matrix.
Auxiliary space: O(1), since we are only storing a few variables to calculate the mean.

Suggest improvement

Python | Numpy matrix.getA()

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