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 liststest_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]# printing original listprint("The original list : " + str(test_list))# zip() to get all elements # sum() / len() gives mean# extracts column meanres = [sum(idx) / len(idx) for idx in zip(*test_list)]# extracts all elements meanres = sum(res) / len(res) # printing result print("Matrix Mean : " + str(res)) |
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 comprehensionfrom statistics import mean# initializing liststest_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]# printing original listprint("The original list : " + str(test_list))# zip() to get all elements # mean() gives mean# extracts column meanres = [mean(idx) for idx in zip(*test_list)]# extracts all elements meanres = mean(res) # printing result print("Matrix Mean : " + str(res)) |
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 Meanimport statistics# initializing liststest_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]# printing original listprint("The original list : " + str(test_list))x=[]for i in test_list: x.extend(i)res=statistics.mean(x)# printing resultprint("Matrix Mean : " + str(res)) |
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 npimport numpy as np# Define the matrix as a list of liststest_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 |
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 matrixtest_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]# Printing original matrixprint("The original matrix : ")for row in test_list: print(row)# Calculating mean# using nested looptotal_sum = 0count = 0for row in test_list: for num in row: total_sum += num count += 1# calculating meanres = total_sum / count# printing resultprint("Matrix Mean : " + str(res)) |
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 matrixtest_list = [[5, 6, 3], [8, 3, 1], [9, 10, 4], [8, 4, 2]]# printing original matrixprint("The original matrix : ")for row in test_list: print(row)# using reduce() function to calculate sum of all elementstotal_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 matrixcount = len([num for row in test_list for num in row])# calculating meanres = total_sum / count# printing resultprint("Matrix Mean : " + str(res)) |
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.
