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Javascript Program for Diagonally Dominant Matrix

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In mathematics, a square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix A is diagonally dominant if 
 

For example, The matrix 
 

is diagonally dominant because 
|a11| ? |a12| + |a13| since |+3| ? |-2| + |+1| 
|a22| ? |a21| + |a23| since |-3| ? |+1| + |+2| 
|a33| ? |a31| + |a32| since |+4| ? |-1| + |+2|
Given a matrix A of n rows and n columns. The task is to check whether matrix A is diagonally dominant or not.
Examples : 
 

Input : A = { { 3, -2, 1 },
              { 1, -3, 2 },
              { -1, 2, 4 } };
Output : YES
Given matrix is diagonally dominant
because absolute value of every diagonal
element is more than sum of absolute values
of corresponding row.

Input : A = { { -2, 2, 1 },
              { 1, 3, 2 },
              { 1, -2, 0 } };
Output : NO

 

The idea is to run a loop from i = 0 to n-1 for the number of rows and for each row, run a loop j = 0 to n-1 find the sum of non-diagonal element i.e i != j. And check if diagonal element is greater than or equal to sum. If for any row, it is false, then return false or print “No”. Else print “YES”. 
 

Javascript




<script>
 
// JavaScript Program to check whether given matrix
// is Diagonally Dominant Matrix.
 
    // check the given matrix is Diagonally
    // Dominant Matrix or not.
    function isDDM(m, n)
    {
        // for each row
        for (let i = 0; i < n; i++)
        {       
        
            // for each column, finding
            //sum of each row.
            let sum = 0;
            for (let j = 0; j < n; j++)            
                sum += Math.abs(m[i][j]);       
        
            // removing the diagonal element.
            sum -= Math.abs(m[i][i]);
        
            // checking if diagonal element is less
            // than sum of non-diagonal element.
            if (Math.abs(m[i][i]) < sum)
                return false;
          
        }
   
        return true;
    }
 
// Driver code   
          
        let n = 3;
        let m = [[ 3, -2, 1 ],
                      [ 1, -3, 2 ],
                      [ -1, 2, 4 ]];
        
        if (isDDM(m, n))
             document.write("YES") ;
        else 
           document.write("NO");
             
</script>


Output : 

YES

Time Complexity: O(N2)

Auxiliary Space: O(1)

Please refer complete article on Diagonally Dominant Matrix for more details!



Last Updated : 12 Jan, 2023
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