Javascript Program for Diagonally Dominant Matrix

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". 

Example:

// 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))
    console.log("YES");
else
    console.log("NO");

YES

Complexity Analysis:

• Time Complexity: O(N²)
• Auxiliary Space: O(1)

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