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

Step to implement Square Matrix Multiplication:

1. Initialize Matrix Dimensions
2. Define the Multiplication Function
3. Initialize Result Matrix
   • For each element in the result matrix res, initialize it to 0.
4. Perform Multiplication
   • Use three nested loops:
     • The outer loop iterates over rows of mat1.
     • The middle loop iterates over columns of mat2.
     • The inner loop iterates over columns of mat1 and rows of mat2.
     • For each element res[i][j]res[i][j]res[i][j], sum the products of corresponding elements from mat1 row and mat2 column: res[i][j]+=mat1[i][k]×mat2[k][j]res[i][j] += mat1[i][k] \times mat2[k][j]res[i][j]+=mat1[i][k]×mat2[k][j]
5. Print Result Matrix
   • Iterate through the res matrix and print each element.

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 
?>

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

Complexity Analysis:

• Time complexity: O(n³).
  It can be optimized using Strassen’s Matrix Multiplication
• Auxiliary Space: O(n²)

Multiplication of Rectangular Matrices

Steps to implement Rectangular Matrices Multiplication :

1. Define Matrix Dimensions
2. Initialize Result Matrix
3. Matrix Multiplication Logic
   • Use three nested loops:
     • The outer loop iterates over the rows of mat1 (index i).
     • The middle loop iterates over the columns of mat2 (index j).
     • The inner loop iterates over the columns of mat1 and rows of mat2 (index x).
   • For each element res[i][j]res[i][j]res[i][j], compute the sum of products of corresponding elements from the row of mat1 and the column of mat2:
     res[i][j]+=mat1[i][x]×mat2[x][j]
4. Print Result Matrix
   • Iterate through the res matrix and print each element, formatting the output as a matrix.

<?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
?>

6 16 
7 18

Complexity Analysis:

• Time complexity: O(n3).
  It can be optimized using Strassen’s Matrix Multiplication
• Auxiliary Space: O(m1 * n2).