Php Program to multiply two matrices

Given two matrices, the task to multiply them. Matrices can either be square or rectangular.

Examples:

Input : mat1[][] = {{1, 2}, 
                   {3, 4}}
        mat2[][] = {{1, 1}, 
                    {1, 1}}
Output : {{3, 3}, 
          {7, 7}}
Input : mat1[][] = {{2, 4}, 
                    {3, 4}}
        mat2[][] = {{1, 2}, 
                    {1, 3}}       
Output : {{6, 16}, 
          {7, 18}}

Multiplication of Square Matrices : 
The below program multiplies two square matrices of size 4*4, we can change N for different dimensions. 

PHP

<?php
// PHP program to multiply two
// square matrices.

// This function multiplies mat1[][] and
// mat2[][], and stores the result in res[][]
function multiply(&$mat1, &$mat2, &$res)
{
    $N = 4;
    for ($i = 0; $i < $N; $i++)
    {
        for ($j = 0; $j < $N; $j++)
        {
            $res[$i][$j] = 0;
            for ($k = 0; $k < $N; $k++)
                $res[$i][$j] += $mat1[$i][$k] *
                                $mat2[$k][$j];
        }
    }
}

// Driver Code
$mat1 = array(array(1, 1, 1, 1),
              array(2, 2, 2, 2),
              array(3, 3, 3, 3),
              array(4, 4, 4, 4));

$mat2 = array(array(1, 1, 1, 1),
              array(2, 2, 2, 2),
              array(3, 3, 3, 3),
              array(4, 4, 4, 4));

multiply($mat1, $mat2, $res);
$N = 4;
echo ("Result matrix is
");
for ($i = 0; $i < $N; $i++)
{
    for ($j = 0; $j < $N; $j++)
    {
        echo ($res[$i][$j]);
        echo(" ");
    }
    echo ("
");
}

// This code is contributed
// by Shivi_Aggarwal
?>

Output

Result matrix is 
10 10 10 10 
20 20 20 20 
30 30 30 30 
40 40 40 40

Time complexity: O(n³). It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O(n²)

Multiplication of Rectangular Matrices : 
We use pointers in C to multiply to matrices. Please refer to the following post as a prerequisite of the code.
How to pass a 2D array as a parameter in C?

PHP

<?php
// PHP program to multiply two
// rectangular matrices

// Multiplies two matrices mat1[][]
// and mat2[][] and prints result.
// (m1) x (m2) and (n1) x (n2) are
// dimensions of given matrices.
function multiply($m1, $m2, $mat1,
                  $n1, $n2, $mat2)
{
    for ($i = 0; $i < $m1; $i++)
    {
        for ($j = 0; $j < $n2; $j++)
        {
            $res[$i][$j] = 0;
            for ($x = 0; $x < $m2; $x++)
            {
                $res[$i][$j] += $mat1[$i][$x] *
                                $mat2[$x][$j];
            }
        }
    }
    for ($i = 0; $i < $m1; $i++)
    {
        for ($j = 0; $j < $n2; $j++)
        {
            echo $res[$i][$j] . " ";
        }
        echo "
";
    }
}

// Driver code
$mat1 = array( array( 2, 4 ), array( 3, 4 ));
$mat2 = array( array( 1, 2 ), array( 1, 3 ));
$m1 = 2;
$m2 = 2;
$n1 = 2;
$n2 = 2;

//Function call
multiply($m1, $m2, $mat1, $n1, $n2, $mat2);

// This code is contributed by rathbhupendra
?>

Output

6 16 
7 18

Time complexity: O(n³). It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O(m1 * n2)

Please refer complete article on Program to multiply two matrices for more details!