Matrices with PHP
Implementation of Matrix Operations with PHP
In PHP it can be written as a class Matrix with implementation of a set of matrix operations.
This class is a PHP implementation of matrix operations commonly used in linear algebra and, by extension, in various AI and machine learning algorithms. It provides a robust set of methods for performing matrix calculations, making it a valuable tool for developers working on AI projects in PHP.
Example of Class Matrix
class Matrix {
private $matrix;
private $rows;
private $cols;
public function __construct(array $matrix) {
$this->matrix = $matrix;
$this->rows = count($matrix);
$this->cols = count($matrix[0]);
}
public function rank(): int {
$epsilon = 1e-10; // Threshold for considering a value as zero
$ref = $this->reducedEchelonForm();
$rank = 0;
for ($i = 0; $i < $this->rows; $i++) {
for ($j = 0; $j < $this->cols; $j++) {
if (abs($ref->matrix[$i][$j]) > $epsilon) {
$rank++;
break;
}
}
}
return $rank;
}
public function add(Matrix $other): Matrix {
if ($this->rows !== $other->rows || $this->cols !== $other->cols) {
throw new Exception("Matrices must have the same dimensions for addition.");
}
$result = [];
for ($i = 0; $i < $this->rows; $i++) {
for ($j = 0; $j < $this->cols; $j++) {
$result[$i][$j] = $this->matrix[$i][$j] + $other->matrix[$i][$j];
}
}
return new Matrix($result);
}
public function subtract(Matrix $other): Matrix {
if ($this->rows !== $other->rows || $this->cols !== $other->cols) {
throw new Exception("Matrices must have the same dimensions for subtraction.");
}
$result = [];
for ($i = 0; $i < $this->rows; $i++) {
for ($j = 0; $j < $this->cols; $j++) {
$result[$i][$j] = $this->matrix[$i][$j] - $other->matrix[$i][$j];
}
}
return new Matrix($result);
}
public function scalarMultiply($scalar): Matrix {
$result = [];
for ($i = 0; $i < $this->rows; $i++) {
for ($j = 0; $j < $this->cols; $j++) {
$result[$i][$j] = $this->matrix[$i][$j] * $scalar;
}
}
return new Matrix($result);
}
public function multiply(Matrix $other): Matrix {
if ($this->cols !== $other->rows) {
throw new Exception("Number of columns in the first matrix must equal the number of rows in the second matrix.");
}
$result = [];
for ($i = 0; $i < $this->rows; $i++) {
for ($j = 0; $j < $other->cols; $j++) {
$result[$i][$j] = 0;
for ($k = 0; $k < $this->cols; $k++) {
$result[$i][$j] += $this->matrix[$i][$k] * $other->matrix[$k][$j];
}
}
}
return new Matrix($result);
}
public function transpose(): Matrix {
$result = [];
for ($i = 0; $i < $this->cols; $i++) {
for ($j = 0; $j < $this->rows; $j++) {
$result[$i][$j] = $this->matrix[$j][$i];
}
}
return new Matrix($result);
}
public function determinant(): float {
if ($this->rows !== $this->cols) {
throw new Exception("Determinant can only be calculated for square matrices.");
}
if ($this->rows === 1) {
return $this->matrix[0][0];
}
if ($this->rows === 2) {
return $this->matrix[0][0] * $this->matrix[1][1] - $this->matrix[0][1] * $this->matrix[1][0];
}
$det = 0;
for ($j = 0; $j < $this->cols; $j++) {
$det += (($j % 2 == 0) ? 1 : -1) * $this->matrix[0][$j] * $this->cofactor(0, $j)->determinant();
}
return $det;
}
private function cofactor($row, $col): Matrix {
$result = [];
$r = 0;
for ($i = 0; $i < $this->rows; $i++) {
if ($i == $row) continue;
$c = 0;
for ($j = 0; $j < $this->cols; $j++) {
if ($j == $col) continue;
$result[$r][$c] = $this->matrix[$i][$j];
$c++;
}
$r++;
}
return new Matrix($result);
}
public function inverse(): Matrix {
$det = $this->determinant();
if ($det == 0) {
throw new Exception("Matrix is not invertible.");
}
$adjoint = $this->adjoint();
return $adjoint->scalarMultiply(1 / $det);
}
private function adjoint(): Matrix {
$result = [];
for ($i = 0; $i < $this->rows; $i++) {
for ($j = 0; $j < $this->cols; $j++) {
$result[$j][$i] = (($i + $j) % 2 == 0 ? 1 : -1) * $this->cofactor($i, $j)->determinant();
}
}
return new Matrix($result);
}
private function reducedEchelonForm(): Matrix {
$ref = $this->matrix;
$lead = 0;
for ($r = 0; $r < $this->rows; $r++) {
if ($lead >= $this->cols) {
return new Matrix($ref);
}
$i = $r;
while ($ref[$i][$lead] == 0) {
$i++;
if ($i == $this->rows) {
$i = $r;
$lead++;
if ($this->cols == $lead) {
return new Matrix($ref);
}
}
}
$temp = $ref[$i];
$ref[$i] = $ref[$r];
$ref[$r] = $temp;
$lv = $ref[$r][$lead];
for ($j = 0; $j < $this->cols; $j++) {
$ref[$r][$j] /= $lv;
}
for ($i = 0; $i < $this->rows; $i++) {
if ($i != $r) {
$lv = $ref[$i][$lead];
for ($j = 0; $j < $this->cols; $j++) {
$ref[$i][$j] -= $lv * $ref[$r][$j];
}
}
}
$lead++;
}
return new Matrix($ref);
}
public function cofactorMatrix(): Matrix {
$result = [];
for ($i = 0; $i < $this->rows; $i++) {
for ($j = 0; $j < $this->cols; $j++) {
$result[$i][$j] = (($i + $j) % 2 == 0 ? 1 : -1) * $this->cofactor($i, $j)->determinant();
}
}
return new Matrix($result);
}
public function adjugateMatrix(): Matrix {
return $this->cofactorMatrix()->transpose();
}
public function toString(): string {
$result = "";
for ($i = 0; $i < $this->rows; $i++) {
$result .= "[" . implode(", ", $this->matrix[$i]) . "]\n";
}
return $result;
}
}Example of Use:
$matrix1 = new Matrix([[1, 2], [3, 4]]);
$matrix2 = new Matrix([[5, 6], [7, 8]]);
echo "Matrix 1:\n" . $matrix1->toString() . "\n";
echo "Matrix 2:\n" . $matrix2->toString() . "\n";
echo "Rank of Matrix 1: " . $matrix1->rank() . "\n\n";
echo "Rank of Matrix 2: " . $matrix1->rank() . "\n\n";
echo "Addition:\n" . $matrix1->add($matrix2)->toString() . "\n";
echo "Subtraction:\n" . $matrix1->subtract($matrix2)->toString() . "\n";
echo "Scalar multiplication (by 2):\n" . $matrix1->scalarMultiply(2)->toString() . "\n";
echo "Matrix multiplication:\n" . $matrix1->multiply($matrix2)->toString() . "\n";
echo "Transpose of Matrix 1:\n" . $matrix1->transpose()->toString() . "\n";
echo "Determinant of Matrix 1: " . $matrix1->determinant() . "\n\n";
echo "Cofactor Matrix of Matrix 1:\n" . $matrix1->cofactorMatrix()->toString() . "\n";
echo "Adjugate Matrix of Matrix 1:\n" . $matrix1->adjugateMatrix()->toString() . "\n";
echo "Inverse of Matrix 1:\n" . $matrix1->inverse()->toString() . "\n";To try this code yourself, install the example files from the official GitHub repository: https://github.com/apphp/ai-with-php-examples
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