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name : Matrix.php <?php /** * * Class for the management of Matrices * * @copyright Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix) * @license https://opensource.org/licenses/MIT MIT */ namespace Matrix; use Generator; use Matrix\Decomposition\LU; use Matrix\Decomposition\QR; /** * Matrix object. * * @package Matrix * * @property-read int $rows The number of rows in the matrix * @property-read int $columns The number of columns in the matrix * @method Matrix antidiagonal() * @method Matrix adjoint() * @method Matrix cofactors() * @method float determinant() * @method Matrix diagonal() * @method Matrix identity() * @method Matrix inverse() * @method Matrix minors() * @method float trace() * @method Matrix transpose() * @method Matrix add(...$matrices) * @method Matrix subtract(...$matrices) * @method Matrix multiply(...$matrices) * @method Matrix divideby(...$matrices) * @method Matrix divideinto(...$matrices) * @method Matrix directsum(...$matrices) */ class Matrix { protected $rows; protected $columns; protected $grid = []; /* * Create a new Matrix object from an array of values * * @param array $grid */ final public function __construct(array $grid) { $this->buildFromArray(array_values($grid)); } /* * Create a new Matrix object from an array of values * * @param array $grid */ protected function buildFromArray(array $grid): void { $this->rows = count($grid); $columns = array_reduce( $grid, function ($carry, $value) { return max($carry, is_array($value) ? count($value) : 1); } ); $this->columns = $columns; array_walk( $grid, function (&$value) use ($columns) { if (!is_array($value)) { $value = [$value]; } $value = array_pad(array_values($value), $columns, null); } ); $this->grid = $grid; } /** * Validate that a row number is a positive integer * * @param int $row * @return int * @throws Exception */ public static function validateRow(int $row): int { if ((!is_numeric($row)) || (intval($row) < 1)) { throw new Exception('Invalid Row'); } return (int)$row; } /** * Validate that a column number is a positive integer * * @param int $column * @return int * @throws Exception */ public static function validateColumn(int $column): int { if ((!is_numeric($column)) || (intval($column) < 1)) { throw new Exception('Invalid Column'); } return (int)$column; } /** * Validate that a row number falls within the set of rows for this matrix * * @param int $row * @return int * @throws Exception */ protected function validateRowInRange(int $row): int { $row = static::validateRow($row); if ($row > $this->rows) { throw new Exception('Requested Row exceeds matrix size'); } return $row; } /** * Validate that a column number falls within the set of columns for this matrix * * @param int $column * @return int * @throws Exception */ protected function validateColumnInRange(int $column): int { $column = static::validateColumn($column); if ($column > $this->columns) { throw new Exception('Requested Column exceeds matrix size'); } return $column; } /** * Return a new matrix as a subset of rows from this matrix, starting at row number $row, and $rowCount rows * A $rowCount value of 0 will return all rows of the matrix from $row * A negative $rowCount value will return rows until that many rows from the end of the matrix * * Note that row numbers start from 1, not from 0 * * @param int $row * @param int $rowCount * @return static * @throws Exception */ public function getRows(int $row, int $rowCount = 1): Matrix { $row = $this->validateRowInRange($row); if ($rowCount === 0) { $rowCount = $this->rows - $row + 1; } return new static(array_slice($this->grid, $row - 1, (int)$rowCount)); } /** * Return a new matrix as a subset of columns from this matrix, starting at column number $column, and $columnCount columns * A $columnCount value of 0 will return all columns of the matrix from $column * A negative $columnCount value will return columns until that many columns from the end of the matrix * * Note that column numbers start from 1, not from 0 * * @param int $column * @param int $columnCount * @return Matrix * @throws Exception */ public function getColumns(int $column, int $columnCount = 1): Matrix { $column = $this->validateColumnInRange($column); if ($columnCount < 1) { $columnCount = $this->columns + $columnCount - $column + 1; } $grid = []; for ($i = $column - 1; $i < $column + $columnCount - 1; ++$i) { $grid[] = array_column($this->grid, $i); } return (new static($grid))->transpose(); } /** * Return a new matrix as a subset of rows from this matrix, dropping rows starting at row number $row, * and $rowCount rows * A negative $rowCount value will drop rows until that many rows from the end of the matrix * A $rowCount value of 0 will remove all rows of the matrix from $row * * Note that row numbers start from 1, not from 0 * * @param int $row * @param int $rowCount * @return static * @throws Exception */ public function dropRows(int $row, int $rowCount = 1): Matrix { $this->validateRowInRange($row); if ($rowCount === 0) { $rowCount = $this->rows - $row + 1; } $grid = $this->grid; array_splice($grid, $row - 1, (int)$rowCount); return new static($grid); } /** * Return a new matrix as a subset of columns from this matrix, dropping columns starting at column number $column, * and $columnCount columns * A negative $columnCount value will drop columns until that many columns from the end of the matrix * A $columnCount value of 0 will remove all columns of the matrix from $column * * Note that column numbers start from 1, not from 0 * * @param int $column * @param int $columnCount * @return static * @throws Exception */ public function dropColumns(int $column, int $columnCount = 1): Matrix { $this->validateColumnInRange($column); if ($columnCount < 1) { $columnCount = $this->columns + $columnCount - $column + 1; } $grid = $this->grid; array_walk( $grid, function (&$row) use ($column, $columnCount) { array_splice($row, $column - 1, (int)$columnCount); } ); return new static($grid); } /** * Return a value from this matrix, from the "cell" identified by the row and column numbers * Note that row and column numbers start from 1, not from 0 * * @param int $row * @param int $column * @return mixed * @throws Exception */ public function getValue(int $row, int $column) { $row = $this->validateRowInRange($row); $column = $this->validateColumnInRange($column); return $this->grid[$row - 1][$column - 1]; } /** * Returns a Generator that will yield each row of the matrix in turn as a vector matrix * or the value of each cell if the matrix is a column vector * * @return Generator|Matrix[]|mixed[] */ public function rows(): Generator { foreach ($this->grid as $i => $row) { yield $i + 1 => ($this->columns == 1) ? $row[0] : new static([$row]); } } /** * Returns a Generator that will yield each column of the matrix in turn as a vector matrix * or the value of each cell if the matrix is a row vector * * @return Generator|Matrix[]|mixed[] */ public function columns(): Generator { for ($i = 0; $i < $this->columns; ++$i) { yield $i + 1 => ($this->rows == 1) ? $this->grid[0][$i] : new static(array_column($this->grid, $i)); } } /** * Identify if the row and column dimensions of this matrix are equal, * i.e. if it is a "square" matrix * * @return bool */ public function isSquare(): bool { return $this->rows === $this->columns; } /** * Identify if this matrix is a vector * i.e. if it comprises only a single row or a single column * * @return bool */ public function isVector(): bool { return $this->rows === 1 || $this->columns === 1; } /** * Return the matrix as a 2-dimensional array * * @return array */ public function toArray(): array { return $this->grid; } /** * Solve A*X = B. * * @param Matrix $B Right hand side * * @throws Exception * * @return Matrix ... Solution if A is square, least squares solution otherwise */ public function solve(Matrix $B): Matrix { if ($this->columns === $this->rows) { return (new LU($this))->solve($B); } return (new QR($this))->solve($B); } protected static $getters = [ 'rows', 'columns', ]; /** * Access specific properties as read-only (no setters) * * @param string $propertyName * @return mixed * @throws Exception */ public function __get(string $propertyName) { $propertyName = strtolower($propertyName); // Test for function calls if (in_array($propertyName, self::$getters)) { return $this->$propertyName; } throw new Exception('Property does not exist'); } protected static $functions = [ 'adjoint', 'antidiagonal', 'cofactors', 'determinant', 'diagonal', 'identity', 'inverse', 'minors', 'trace', 'transpose', ]; protected static $operations = [ 'add', 'subtract', 'multiply', 'divideby', 'divideinto', 'directsum', ]; /** * Returns the result of the function call or operation * * @param string $functionName * @param mixed[] $arguments * @return Matrix|float * @throws Exception */ public function __call(string $functionName, $arguments) { $functionName = strtolower(str_replace('_', '', $functionName)); // Test for function calls if (in_array($functionName, self::$functions, true)) { return Functions::$functionName($this, ...$arguments); } // Test for operation calls if (in_array($functionName, self::$operations, true)) { return Operations::$functionName($this, ...$arguments); } throw new Exception('Function or Operation does not exist'); } }