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