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https://github.com/Karaka-Management/phpOMS.git
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798 lines
17 KiB
PHP
798 lines
17 KiB
PHP
<?php
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/**
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* Orange Management
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*
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* PHP Version 7.2
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*
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* @package phpOMS\Math\Matrix
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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 phpOMS\Math\Matrix
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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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* @return void
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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], $this->matrix[$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], $this->matrix[$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<int, array<int, mixed>>
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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 sub matrix array.
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*
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* @param int $iRow Start row
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* @param int $lRow End row
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* @param int $iCol Start col
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* @param int $lCol End col
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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 getSubMatrix(int $iRow, int $lRow, int $iCol, int $lCol) : Matrix
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{
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$X = [[]];
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for ($i = $iRow; $i <= $lRow; ++$i) {
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for ($j = $iCol; $j <= $lCol; ++$j) {
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$X[$i - $iRow][$j - $iCol] = $this->matrix[$i][$j];
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}
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}
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$matrix = new self();
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$matrix->setMatrix($X);
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return $matrix;
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}
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/**
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* Get sub matrix array.
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*
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* @param array<int> $rows Row indices
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* @param array<int> $cols Row indices
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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 getSubMatrixByColumnsRows(array $rows, array $cols) : Matrix
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{
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$X = [[]];
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$rlength = \count($rows);
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$clength = \count($cols);
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for ($i = 0; $i < $rlength; ++$i) {
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for ($j = 0; $j < $clength; ++$j) {
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$X[$i][$j] = $this->matrix[$rows[$i]][$cols[$j]];
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}
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}
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$matrix = new self();
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$matrix->setMatrix($X);
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return $matrix;
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}
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/**
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* Get sub matrix array.
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*
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* @param int $iRow Start row
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* @param int $lRow End row
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* @param array<int> $cols Row indices
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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 getSubMatrixByColumns(int $iRow, int $lRow, array $cols) : Matrix
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{
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$X = [[]];
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$length = \count($cols);
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for ($i = $iRow; $i <= $lRow; ++$i) {
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for ($j = 0; $j < $length; ++$j) {
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$X[$i - $iRow][$j] = $this->matrix[$i][$cols[$j]];
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}
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}
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$matrix = new self();
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$matrix->setMatrix($X);
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return $matrix;
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}
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/**
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* Get sub matrix array.
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*
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* @param array<int> $rows Row indices
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* @param int $iCol Start col
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* @param int $lCol End col
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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 getSubMatrixByRows(array $rows, int $iCol, int $lCol) : Matrix
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{
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$X = [[]];
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$length = \count($rows);
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for ($i = 0; $i < $length; ++$i) {
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for ($j = $iCol; $j <= $lCol; ++$j) {
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$X[$i][$j - $iCol] = $this->matrix[$rows[$i]][$j];
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}
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}
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$matrix = new self();
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$matrix->setMatrix($X);
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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<int, array<int, mixed>>
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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 $this->matrix;
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}
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/**
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* Is symmetric.
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*
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* @return bool
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*
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* @since 1.0.0
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*/
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public function isSymmetric() : bool
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{
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$isSymmetric = true;
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for ($j = 0; ($j < $this->m) & $isSymmetric; ++$j) {
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for ($i = 0; ($i < $this->n) & $isSymmetric; ++$i) {
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$isSymmetric = ($this->matrix[$i][$j] === $this->matrix[$j][$i]);
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}
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}
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return $isSymmetric;
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}
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/**
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* Get matrix rank.
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*
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* @return int
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*
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* @since 1.0.0
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*/
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public function rank() : int
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{
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$matrix = $this->matrix;
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$mDim = $this->m;
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$nDim = $this->n;
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if ($this->m > $this->n) {
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$mDim = $this->n;
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$nDim = $this->m;
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$matrix = \array_map(null, ...$matrix);
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}
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$rank = $mDim;
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for ($row = 0; $row < $rank; ++$row) {
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if (isset($matrix[$row][$row]) && $matrix[$row][$row] !== 0) {
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for ($col = 0; $col < $mDim; ++$col) {
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if ($col !== $row) {
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$mult = $matrix[$col][$row] / $matrix[$row][$row];
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for ($i = 0; $i < $rank; ++$i) {
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$matrix[$col][$i] -= $mult * $matrix[$row][$i];
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}
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}
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}
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} else {
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$reduce = true;
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for ($i = $row + 1; $i < $mDim; ++$i) {
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if (isset($matrix[$i][$row]) && $matrix[$i][$row] !== 0) {
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$this->swapRow($matrix, $row, $i, $rank);
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$reduce = false;
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break;
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}
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}
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if ($reduce) {
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--$rank;
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for ($i = 0; $i < $mDim; ++$i) {
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$matrix[$i][$row] = $matrix[$i][$rank];
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}
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--$row;
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}
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}
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}
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return $rank;
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}
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/**
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* Swap values in rows
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*
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* @param array<array> $matrix Matrix reference to modify
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* @param int $row1 Row to swap
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* @param int $row2 Row to swap
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* @param int $col Max col to swap to
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*
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* @return void
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*
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* @since 1.0.0
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*/
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private function swapRow(array &$matrix, int $row1, int $row2, int $col) : void
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{
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for ($i = 0; $i < $col; ++$i) {
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$temp = $matrix[$row1][$i];
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$matrix[$row1] = $matrix[$row2][$i];
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$matrix[$row2] = $temp;
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}
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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<int, array<int|float>> $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 $this->add($value->mult(-1));
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} elseif (!is_string($value) && is_numeric($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_string($value) && is_numeric($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_string($value) && is_numeric($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);
|
|
|
|
return $matrix;
|
|
}
|
|
|
|
/**
|
|
* Trianglize matrix.
|
|
*
|
|
* @param array<int, array<int|float>> $arr Matrix to trianglize
|
|
*
|
|
* @return int Det sign
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
private function upperTrianglize(array &$arr) : int
|
|
{
|
|
$n = $this->n;
|
|
$sign = 1;
|
|
|
|
for ($i = 0; $i < $n; ++$i) {
|
|
$max = 0;
|
|
|
|
for ($j = $i; $j < $n; ++$j) {
|
|
if (\abs($arr[$j][$i]) > \abs($arr[$max][$i])) {
|
|
$max = $j;
|
|
}
|
|
}
|
|
|
|
if ($max) {
|
|
$sign = -$sign;
|
|
$temp = $arr[$i];
|
|
$arr[$i] = $arr[$max];
|
|
$arr[$max] = $temp;
|
|
}
|
|
|
|
if (!$arr[$i][$i]) {
|
|
return 0;
|
|
}
|
|
|
|
for ($j = $i + 1; $j < $n; ++$j) {
|
|
$r = $arr[$j][$i] / $arr[$i][$i];
|
|
|
|
if (!$r) {
|
|
continue;
|
|
}
|
|
|
|
for ($c = $i; $c < $n; ++$c) {
|
|
$arr[$j][$c] -= $arr[$i][$c] * $r;
|
|
}
|
|
}
|
|
}
|
|
|
|
return $sign;
|
|
}
|
|
|
|
/**
|
|
* Inverse matrix.
|
|
*
|
|
* @param int $algorithm Algorithm for inversion
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws InvalidDimensionException
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function inverse(int $algorithm = InverseType::GAUSS_JORDAN) : Matrix
|
|
{
|
|
return $this->solve(new IdentityMatrix($this->m));
|
|
}
|
|
|
|
/**
|
|
* Solve matrix
|
|
*
|
|
* @param Matrix $B Matrix/Vector b
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function solve(Matrix $B) : Matrix
|
|
{
|
|
$M = $this->m === $this->n ? new LUDecomposition($this) : new QRDecomposition($this);
|
|
|
|
return $M->solve($B);
|
|
}
|
|
|
|
/**
|
|
* 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]);
|
|
}
|
|
}
|