# Matrix arithmetic PHP Class

During my studies in AI I wanted to solve the XOR problem; I wanted just to do a quick test so I started writing the code in PHP. Solving that problem I ended up to write a class that handles matrix operations as well.

Since there is no reason to use AI with PHP (I’ll explain this in another article) I share with you the class that handle the matrix operations.

In this article I’m going to show you some of the methods of the class **Matrix** and how to use them.

With this class you can sum or subtract two matrices, dot products or product by value, transpose and many other operations.

In the following examples is assumed that the file *Matrix.php* is included and the `Matrix`

class is instantiated as `$lib`

:

`$lib = new Matrix;`

As Numpy (a Python library), the matrix is an array of arrays; a matrix is defined as following:

```
include “Matrix.php"
$lib = new Matrix;
// matrix 3×3
$matrix = [
[1 , 2 , 3],
[4 , 5 , 6],
[7 , 8 , 9]
];
// matrix 3×1 with a row
$matrix = [
[1 , 2 , 3]
];
// vector
$vector = [
[1],
[2],
[3]
];
// scalar
$scalar = [
[15]
];
// or more simply
$scalar = 15;
```

#### Matrix Transpose

The method `matrixTranspose`

returns the transpose of a matrix. Example:

```
$matrix = [
[1 , 2],
[3 , 4]
];
$matrix_transp = $lib->matrixTranspose($matrix);
sm($matrix_transp); // it shows the matrix the result in a nice way
```

#### Dot product

The function `matrixDotProduct`

has in input two matrices and it gives in output the dot product. If the two matrices are not compatible with each other an exception will be thrown.

```
$m1 = [
[1 , 2 , 3],
[4 , 5 , 6]
];
$m2 = [
[1 , 2],
[3 , 4],
[5 , 6]
];
$result = $lib->matrixDotProduct($m1,$m2);
sm($result); // it shows the matrix the result in a nice way
```

#### RELU, SIGMOID, TANH, LOG operation

The method `matrixOperation`

performs in each element of the given matrix the operation: RELU, SIGMOID, LOG (natural logarithm), NEGATIVE, TANH. In the following example we are going to perform SIGMOID to each element of `$matrix`

:

```
$matrix = [
[1 , 2],
[4 , 5]
];
$result = $lib->matrixOperation('sigmoid’, $matrix);
sm($result);
// This is what sm shows
// | 0.731 0.881 |
// | 0.982 0.993 |
```

#### Multiplie a matrix for a scalar value

The method `matrixTimesValue`

multiplies a scalar value to all the elements of a given matrix. The first parameter is the matrix and the second is the number (or a matrix 1×1 dimension).

```
$matrix = [
[1 , 2],
[4 , 5]
];
$result = $lib->matrixTimesValue($matrix, 10);
// Result of $matrix * 10
// | 10 20 |
// | 40 50 |
```

#### Matrix addition

The method `matrixSum`

performs the addiction of two gives matrices as parameters.

```
$m1 = [
[1 , 2],
[3 , 4]
];
$m2 = [
[11 , 12],
[13 , 14]
];
$result = $lib->matrixSum($m1, $m2);
// Result
// | 12 14 |
// | 16 18 |
```

#### Product value by value

This is a different from DOT product; it multiplies two matrices with same dimensions value by value _

```
$m1 = [
[1 , 2],
[3 , 4]
];
$m2 = [
[2 , 3],
[5 , 4]
];
$result = $lib->matrixProductValueByValue($m1, $m2);
// Result
// | 2 6 |
// | 15 16 |
```