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<?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');

    }

}