Php 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”. 

PHP

<?php
// PHP Program to check whether
// given matrix is Diagonally
// Dominant Matrix.

// check the given  matrix
// is Diagonally Dominant Matrix or not.
function isDDM( $m, $n)
{
    // for each row
    for ($i = 0; $i < $n; $i++)

    {
        // for each column, finding
        // sum of each row.
        $sum = 0;
        for ( $j = 0; $j < $n; $j++)
            $sum += abs($m[$i][$j]);

        // removing the diagonal element.
        $sum -= abs($m[$i][$i]);

        // checking if diagonal element
        // is less than sum of non-diagonal
        // element.
        if (abs($m[$i][$i]) < $sum)
            return false;
    }

    return true;
}

// Driver Code
$n = 3;
$m = array(array( 3, -2, 1 ),
           array( 1, -3, 2 ),
           array( -1, 2, 4 ));

if((isDDM($m, $n)))
echo "YES";
else
echo"NO";

// This code is contributed by SanjuTomar
?>

Output :

YES

Time Complexity: O(N²)

Auxiliary Space: O(1)

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