mirror of
https://github.com/Karaka-Management/phpOMS.git
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756 lines
16 KiB
PHP
756 lines
16 KiB
PHP
<?php
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/**
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* Orange Management
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*
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* PHP Version 7.1
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*
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* @package TBD
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* @copyright Dennis Eichhorn
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* @license OMS License 1.0
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* @version 1.0.0
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* @link http://website.orange-management.de
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*/
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declare(strict_types = 1);
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namespace phpOMS\Math\Matrix;
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use phpOMS\Math\Matrix\Exception\InvalidDimensionException;
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/**
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* Matrix class
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*
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* @package Framework
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* @license OMS License 1.0
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* @link http://website.orange-management.de
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* @since 1.0.0
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*/
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class Matrix implements \ArrayAccess, \Iterator
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{
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/**
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* Matrix.
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*
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* @var array
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* @since 1.0.0
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*/
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protected $matrix = [];
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/**
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* Columns.
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*
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* @var int
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* @since 1.0.0
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*/
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protected $n = 0;
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/**
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* Rows.
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*
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* @var int
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* @since 1.0.0
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*/
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protected $m = 0;
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/**
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* Iterator position.
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*
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* @var int
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* @since 1.0.0
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*/
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protected $position = 0;
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/**
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* Constructor.
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*
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* @param int $m Rows
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* @param int $n Columns
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*
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* @since 1.0.0
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*/
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public function __construct(int $m = 1, int $n = 1)
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{
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$this->n = $n;
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$this->m = $m;
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for ($i = 0; $i < $m; $i++) {
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$this->matrix[$i] = array_fill(0, $n, 0);
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}
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}
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/**
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* Set value.
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*
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* @param int $m Row
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* @param int $n Column
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* @param int $value Value
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*
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* @throws InvalidDimensionException
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*
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* @since 1.0.0
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*/
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public function set(int $m, int $n, $value) /* : void */
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{
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if (!isset($this->matrix[$m][$n])) {
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throw new InvalidDimensionException($m . 'x' . $n);
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}
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$this->matrix[$m][$n] = $value;
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}
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/**
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* Get value.
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*
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* @param int $m Row
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* @param int $n Column
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*
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* @return mixed
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*
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* @throws InvalidDimensionException
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*
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* @since 1.0.0
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*/
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public function get(int $m, int $n)
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{
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if (!isset($this->matrix[$m][$n])) {
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throw new InvalidDimensionException($m . 'x' . $n);
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}
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return $this->matrix[$m][$n];
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}
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/**
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* Transpose matrix.
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*
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* @return Matrix
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*
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* @since 1.0.0
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*/
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public function transpose() : Matrix
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{
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$matrix = new Matrix($this->n, $this->m);
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$matrix->setMatrix(array_map(null, ...$this->matrix));
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return $matrix;
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}
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/**
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* Get matrix array.
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*
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* @return array
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*
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* @since 1.0.0
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*/
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public function getMatrix() : array
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{
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return $this->matrix;
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}
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/**
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* Get matrix array.
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*
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* @return array
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*
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* @since 1.0.0
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*/
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public function toArray() : array
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{
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return $this->matrix;
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}
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/**
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* Get matrix rank.
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*
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* @return int
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*
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* @since 1.0.0
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*/
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public function rank() : int
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{
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return 0;
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}
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/**
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* Set matrix array.
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*
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* @param array $matrix Matrix
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*
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* @return Matrix
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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public function setMatrix(array $matrix) : Matrix
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{
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$this->m = count($matrix);
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$this->n = count($matrix[0] ?? 1);
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$this->matrix = $matrix;
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return $this;
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}
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/**
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* Subtract right.
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*
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* @param mixed $value Value
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*
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* @return Matrix
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*
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* @throws \InvalidArgumentException
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*
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* @since 1.0.0
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*/
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public function sub($value) : Matrix
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{
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if ($value instanceOf Matrix) {
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return $this->add($this->mult(-1));
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} elseif (is_scalar($value)) {
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return $this->add(-$value);
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}
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throw new \InvalidArgumentException('Type');
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}
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/**
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* Add right.
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*
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* @param mixed $value Value
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*
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* @return Matrix
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*
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* @throws \InvalidArgumentException
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*
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* @since 1.0.0
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*/
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public function add($value) : Matrix
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{
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if ($value instanceOf Matrix) {
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return $this->addMatrix($value);
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} elseif (is_scalar($value)) {
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return $this->addScalar($value);
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}
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throw new \InvalidArgumentException();
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}
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/**
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* Add matrix.
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*
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* @param Matrix $matrix Matrix to add
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*
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* @return Matrix
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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private function addMatrix(Matrix $matrix) : Matrix
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{
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if ($this->m !== $matrix->getM() || $this->n !== $matrix->getN()) {
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throw new InvalidDimensionException($matrix->getM() . 'x' . $matrix->getN());
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}
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$matrixArr = $matrix->getMatrix();
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$newMatrixArr = $this->matrix;
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foreach ($newMatrixArr as $i => $vector) {
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foreach ($vector as $j => $value) {
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$newMatrixArr[$i][$j] += $matrixArr[$i][$j];
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}
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}
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$newMatrix = new Matrix($this->m, $this->n);
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$newMatrix->setMatrix($newMatrixArr);
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return $newMatrix;
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}
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/**
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* Get matrix rows.
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*
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* @return int
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*
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* @since 1.0.0
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*/
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public function getM() : int
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{
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return $this->m;
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}
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/**
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* Get matrix columns.
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*
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* @return int
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*
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* @since 1.0.0
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*/
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public function getN() : int
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{
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return $this->n;
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}
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/**
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* Add scalar.
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*
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* @param mixed $scalar Scalar
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*
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* @return Matrix
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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private function addScalar($scalar) : Matrix
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{
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$newMatrixArr = $this->matrix;
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foreach ($newMatrixArr as $i => $vector) {
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foreach ($vector as $j => $value) {
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$newMatrixArr[$i][$j] += $scalar;
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}
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}
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$newMatrix = new Matrix($this->m, $this->n);
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$newMatrix->setMatrix($newMatrixArr);
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return $newMatrix;
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}
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/**
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* Multiply right.
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*
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* @param mixed $value Factor
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*
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* @return Matrix
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*
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* @throws \InvalidArgumentException
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*
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* @since 1.0.0
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*/
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public function mult($value) : Matrix
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{
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if ($value instanceOf Matrix) {
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return $this->multMatrix($value);
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} elseif (is_scalar($value)) {
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return $this->multScalar($value);
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}
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throw new \InvalidArgumentException('Type');
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}
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/**
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* Multiply matrix.
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*
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* @param Matrix $matrix Matrix to multiply with
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*
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* @return Matrix
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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private function multMatrix(Matrix $matrix) : Matrix
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{
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$nDim = $matrix->getN();
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$mDim = $matrix->getM();
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if ($this->n !== $mDim) {
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throw new InvalidDimensionException($mDim . 'x' . $nDim);
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}
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$matrixArr = $matrix->getMatrix();
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$newMatrix = new Matrix($this->m, $nDim);
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$newMatrixArr = $newMatrix->getMatrix();
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for ($i = 0; $i < $this->m; $i++) { // Row of $this
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for ($c = 0; $c < $nDim; $c++) { // Column of $matrix
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$temp = 0;
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for ($j = 0; $j < $mDim; $j++) { // Row of $matrix
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$temp += $this->matrix[$i][$j] * $matrixArr[$j][$c];
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}
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$newMatrixArr[$i][$c] = $temp;
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}
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}
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$newMatrix->setMatrix($newMatrixArr);
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return $newMatrix;
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}
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/**
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* Multiply matrix.
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*
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* @param mixed $scalar Scalar value
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*
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* @return Matrix
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*
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* @throws \Exception
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*
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* @since 1.0.0
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*/
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private function multScalar($scalar) : Matrix
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{
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$newMatrixArr = $this->matrix;
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foreach ($newMatrixArr as $i => $vector) {
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foreach ($vector as $j => $value) {
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$newMatrixArr[$i][$j] *= $scalar;
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}
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}
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$newMatrix = new Matrix($this->m, $this->n);
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$newMatrix->setMatrix($newMatrixArr);
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return $newMatrix;
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}
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/**
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* Upper triangulize matrix.
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*
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* @return Matrix
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*
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* @since 1.0.0
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*/
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public function upperTriangular() : Matrix
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{
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$matrix = new Matrix($this->n, $this->n);
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$matrixArr = $this->matrix;
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$this->upperTrianglize($matrixArr);
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$matrix->setMatrix($matrixArr);
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return $matrix;
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}
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/**
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* Trianglize matrix.
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*
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* @param array $arr Matrix to trianglize
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*
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* @return int Det sign
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*
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* @since 1.0.0
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*/
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private function upperTrianglize(array &$arr) : int
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{
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$n = count($arr);
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$sign = 1;
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for ($i = 0; $i < $n; $i++) {
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$max = 0;
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for ($j = $i; $j < $n; $j++) {
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if (abs($arr[$j][$i]) > abs($arr[$max][$i])) {
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$max = $j;
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}
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}
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if ($max) {
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$sign = -$sign;
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$temp = $arr[$i];
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$arr[$i] = $arr[$max];
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$arr[$max] = $temp;
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}
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if (!$arr[$i][$i]) {
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return 0;
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}
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for ($j = $i + 1; $j < $n; $j++) {
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$r = $arr[$j][$i] / $arr[$i][$i];
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if (!$r) {
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continue;
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}
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for ($c = $i; $c < $n; $c++) {
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$arr[$j][$c] -= $arr[$i][$c] * $r;
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}
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}
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}
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return $sign;
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}
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/**
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* Lower triangulize matrix.
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*
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* @return Matrix
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*
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* @since 1.0.0
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*/
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public function lowerTriangular() : Matrix
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{
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// todo: implement
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return new Matrix($this->m, $this->n);
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}
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/**
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* Inverse matrix.
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*
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* @param int $algorithm Algorithm for inversion
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*
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* @return Matrix
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*
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* @throws InvalidDimensionException
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*
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* @since 1.0.0
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*/
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public function inverse(int $algorithm = InverseType::GAUSS_JORDAN) : Matrix
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{
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return $this->solve(new IdentityMatrix($this->m, $this->m));
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}
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/**
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* Inverse matrix using gauss jordan.
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*
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* @return Matrix
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*
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* @since 1.0.0
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*/
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private function inverseGaussJordan() : Matrix
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{
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$newMatrixArr = $this->matrix;
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// extending matrix by identity matrix
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for ($i = 0; $i < $this->n; $i++) {
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for ($j = $this->n; $j < $this->n * 2; $j++) {
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if ($j === ($i + $this->n)) {
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$newMatrixArr[$i][$j] = 1;
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} else {
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$newMatrixArr[$i][$j] = 0;
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}
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}
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}
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$mDim = count($newMatrixArr);
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$nDim = count($newMatrixArr[0]);
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// pivoting
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$newMatrixArr = $this->diag($newMatrixArr);
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/* create unit matrix */
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for ($i = 0; $i < $mDim; $i++) {
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$temp = $newMatrixArr[$i][$i];
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for ($j = 0; $j < $nDim; $j++) {
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$newMatrixArr[$i][$j] = $newMatrixArr[$i][$j] / $temp;
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}
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}
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/* removing identity matrix */
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for ($i = 0; $i < $mDim; $i++) {
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$newMatrixArr[$i] = array_slice($newMatrixArr[$i], $mDim);
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}
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$newMatrix = new Matrix($this->n, $this->n);
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$newMatrix->setMatrix($newMatrixArr);
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return $newMatrix;
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}
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public function diagonalize() : Matrix
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{
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$newMatrix = new Matrix($this->m, $this->n);
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$newMatrix->setMatrix($this->diag($this->matrix));
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return $newMatrix;
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}
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public function solve(Matrix $B) : Matrix
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{
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$M = $this->m === $this->n ? new LUDecomposition($this) : new QRDecomposition($this);
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return $M->solve($B);
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}
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private function gaussElimination($b) : Matrix
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{
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$mDim = count($b);
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$matrix = $this->matrix;
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for ($col = 0; $col < $mDim; $col++) {
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$j = $col;
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$max = $matrix[$j][$j];
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for ($i = $col + 1; $i < $mDim; $i++) {
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$temp = abs($matrix[$i][$col]);
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if ($temp > $max) {
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$j = $i;
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$max = $temp;
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}
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}
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if ($col != $j) {
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$temp = $matrix[$col];
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$matrix[$col] = $matrix[$j];
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$matrix[$j] = $temp;
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$temp = $b[$col];
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$b[$col] = $b[$j];
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$b[$j] = $temp;
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}
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for ($i = $col + 1; $i < $mDim; $i++) {
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$temp = $matrix[$i][$col] / $matrix[$col][$col];
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for ($j = $col + 1; $j < $mDim; $j++) {
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$matrix[$i][$j] -= $temp * $matrix[$col][$j];
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}
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$matrix[$i][$col] = 0;
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$b[$i] -= $temp * $b[$col];
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}
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}
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$x = [];
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for ($col = $mDim - 1; $col >= 0; $col--) {
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$temp = $b[$col];
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for ($j = $mDim - 1; $j > $col; $j--) {
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$temp -= $x[$j] * $matrix[$col][$j];
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}
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$x[$col] = $temp / $matrix[$col][$col];
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}
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$solution = new self(count($x), count($x[0]));
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$solution->setMatrix($x);
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return $solution;
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}
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/**
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* Diagonalize matrix.
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*
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* @param array $arr Matrix to diagonalize
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*
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* @return array
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*
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* @since 1.0.0
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*/
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private function diag(array $arr) : array
|
|
{
|
|
$mDim = count($arr);
|
|
$nDim = count($arr[0]);
|
|
|
|
for ($i = $mDim - 1; $i > 0; $i--) {
|
|
if ($arr[$i - 1][0] < $arr[$i][0]) {
|
|
for ($j = 0; $j < $nDim; $j++) {
|
|
$temp = $arr[$i][$j];
|
|
$arr[$i][$j] = $arr[$i - 1][$j];
|
|
$arr[$i - 1][$j] = $temp;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* create diagonal matrix */
|
|
for ($i = 0; $i < $mDim; $i++) {
|
|
for ($j = 0; $j < $mDim; $j++) {
|
|
if ($j !== $i) {
|
|
$temp = $arr[$j][$i] / $arr[$i][$i];
|
|
|
|
for ($c = 0; $c < $nDim; $c++) {
|
|
$arr[$j][$c] -= $arr[$i][$c] * $temp;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return $arr;
|
|
}
|
|
|
|
/**
|
|
* Calculate det.
|
|
*
|
|
* @return float
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function det() : float
|
|
{
|
|
$L = new LUDecomposition($this);
|
|
return $L->det();
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function current()
|
|
{
|
|
return $this->offsetGet($this->position);
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function offsetGet($offset)
|
|
{
|
|
$row = (int) ($offset / $this->m);
|
|
|
|
return $this->matrix[$row][$offset - $row * $this->n];
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function next()
|
|
{
|
|
++$this->position;
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function key()
|
|
{
|
|
return $this->position;
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function valid()
|
|
{
|
|
return $this->offsetExists($this->position);
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function offsetExists($offset)
|
|
{
|
|
$row = (int) ($offset / $this->m);
|
|
|
|
return isset($this->matrix[$row][$offset - $row * $this->n]);
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function rewind()
|
|
{
|
|
$this->position = 0;
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function offsetSet($offset, $value)
|
|
{
|
|
$row = (int) ($offset / $this->m);
|
|
$this->matrix[$row][$offset - $row * $this->n] = $value;
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function offsetUnset($offset)
|
|
{
|
|
$row = (int) ($offset / $this->m);
|
|
unset($this->matrix[$row][$offset - $row * $this->n]);
|
|
}
|
|
|
|
} |