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

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

5.47723

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Improved By : mohit kumar 29, AnkitRai01