Finding the Frobenius Norm of a given matrix

Given an M * N matrix, the task is to find the Frobenius Norm of the matrix. The Frobenius Norm of a matrix is defined as the square root of the sum of the squares of the elements of the matrix.

Example:

Input: mat[][] = {{1, 2}, {3, 4}}
Output: 5.47723
sqrt(1² + 2² + 3² + 4²) = sqrt(30) = 5.47723

Input: mat[][] = {{1, 4, 6}, {7, 9, 10}}
Output: 16.8226

Approach: Find the sum of squares of the elements of the matrix and then print the square root of the calculated value.

Below is the implementation of the above approach:

CPP

// C++ implementation of the approach 
#include <bits/stdc++.h> 
using namespace std; 
  
const int row = 2, col = 2; 
  
// Function to return the Frobenius 
// Norm of the given matrix 
float frobeniusNorm(int mat[row][col]) 
{ 
  
    // To store the sum of squares of the 
    // elements of the given matrix 
    int sumSq = 0; 
    for (int i = 0; i < row; i++) { 
        for (int j = 0; j < col; j++) { 
            sumSq += pow(mat[i][j], 2); 
        } 
    } 
  
    // Return the square root of 
    // the sum of squares 
    float res = sqrt(sumSq); 
    return res; 
} 
  
// Driver code 
int main() 
{ 
    int mat[row][col] = { { 1, 2 }, { 3, 4 } }; 
  
    cout << frobeniusNorm(mat); 
  
    return 0; 
} 

Java

// Java implementation of the approach  
class GFG 
{ 
      
    final static int row = 2, col = 2;  
      
    // Function to return the Frobenius  
    // Norm of the given matrix  
    static float frobeniusNorm(int mat[][])  
    {  
      
        // To store the sum of squares of the  
        // elements of the given matrix  
        int sumSq = 0;  
        for (int i = 0; i < row; i++)  
        {  
            for (int j = 0; j < col; j++)  
            {  
                sumSq += (int)Math.pow(mat[i][j], 2);  
            }  
        }  
      
        // Return the square root of  
        // the sum of squares  
        float res = (float)Math.sqrt(sumSq);  
        return res;  
    }  
      
    // Driver code  
    public static void main (String[] args) 
    {  
        int mat[][] = { { 1, 2 }, { 3, 4 } };  
      
        System.out.println(frobeniusNorm(mat));  
      
    }  
} 
  
// This code is contributed by AnkitRai01 

Python3

# Python3 implementation of the approach 
from math import sqrt 
row = 2
col = 2
  
# Function to return the Frobenius 
# Norm of the given matrix 
def frobeniusNorm(mat): 
  
    # To store the sum of squares of the 
    # elements of the given matrix 
    sumSq = 0
    for i in range(row): 
        for j in range(col): 
            sumSq += pow(mat[i][j], 2) 
  
    # Return the square root of 
    # the sum of squares 
    res = sqrt(sumSq) 
    return round(res, 5) 
  
# Driver code 
  
mat = [ [ 1, 2 ], [ 3, 4 ] ] 
  
print(frobeniusNorm(mat)) 
  
# This code is contributed by mohit kumar 29 

C#

// C# implementation of the approach  
using System; 
  
class GFG 
{ 
      
    static int row = 2, col = 2;  
      
    // Function to return the Frobenius  
    // Norm of the given matrix  
    static float frobeniusNorm(int [,]mat)  
    {  
      
        // To store the sum of squares of the  
        // elements of the given matrix  
        int sumSq = 0;  
        for (int i = 0; i < row; i++)  
        {  
            for (int j = 0; j < col; j++)  
            {  
                sumSq += (int)Math.Pow(mat[i, j], 2);  
            }  
        }  
      
        // Return the square root of  
        // the sum of squares  
        float res = (float)Math.Sqrt(sumSq);  
        return res;  
    }  
      
    // Driver code  
    public static void Main () 
    {  
        int [,]mat = { { 1, 2 }, { 3, 4 } };  
      
        Console.WriteLine(frobeniusNorm(mat));  
    }  
} 
  
// This code is contributed by AnkitRai01 

Output:

5.47723

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My Personal Notes

CPP

Java

Python3

C#

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