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phpOMS/Math/Matrix/Matrix.php

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<?php
/**
* Karaka
*
* PHP Version 8.0
*
* @package phpOMS\Math\Matrix
* @copyright Dennis Eichhorn
* @license OMS License 1.0
* @version 1.0.0
* @link https://karaka.app
*/
declare(strict_types=1);
namespace phpOMS\Math\Matrix;
use phpOMS\Math\Matrix\Exception\InvalidDimensionException;
/**
* Matrix class
*
* @package phpOMS\Math\Matrix
* @license OMS License 1.0
* @link https://karaka.app
* @since 1.0.0
*
* @phpstan-implements \ArrayAccess<string, mixed>
* @phpstan-implements \Iterator<string, mixed>
*/
class Matrix implements \ArrayAccess, \Iterator
{
/**
* Epsilon for float comparison.
*
* @var float
* @since 1.0.0
*/
public const EPSILON = 4.88e-04;
/**
* Matrix.
*
* @var array<int, array<int, int|float>>
* @since 1.0.0
*/
protected array $matrix = [];
/**
* Columns.
*
* @var int<0, max>
* @since 1.0.0
*/
protected int $n = 0;
/**
* Rows.
*
* @var int<0, max>
* @since 1.0.0
*/
protected int $m = 0;
/**
* Iterator position.
*
* @var int
* @since 1.0.0
*/
protected int $position = 0;
/**
* Constructor.
*
* @param int<0, max> $m Rows
* @param int<0, max> $n Columns
*
* @since 1.0.0
*/
public function __construct(int $m = 1, int $n = 1)
{
$this->n = $n;
$this->m = $m;
for ($i = 0; $i < $m; ++$i) {
$this->matrix[$i] = \array_fill(0, $n, 0);
}
}
/**
* Create matrix from array
*
* @param array $matrix Matrix array
*
* @return self
*
* @since 1.0.0
*/
public static function fromArray(array $matrix) : self
{
$m = new self();
$m->setMatrix($matrix);
return $m;
}
/**
* Set value.
*
* @param int $m Row
* @param int $n Column
* @param int|float $value Value
*
* @return void
*
* @throws InvalidDimensionException
*
* @since 1.0.0
*/
public function set(int $m, int $n, int | float $value) : void
{
if (!isset($this->matrix[$m], $this->matrix[$m][$n])) {
throw new InvalidDimensionException($m . 'x' . $n);
}
$this->matrix[$m][$n] = $value;
}
/**
* Get value.
*
* @param int $m Row
* @param int $n Column
*
* @return int|float
*
* @throws InvalidDimensionException
*
* @since 1.0.0
*/
public function get(int $m, int $n = 0) : int | float
{
if (!isset($this->matrix[$m], $this->matrix[$m][$n])) {
throw new InvalidDimensionException($m . 'x' . $n);
}
return $this->matrix[$m][$n];
}
/**
* Transpose matrix.
*
* @return Matrix
*
* @since 1.0.0
*/
public function transpose() : self
{
$matrix = new self($this->n, $this->m);
$matrix->setMatrix(\array_map(null, ...$this->matrix));
return $matrix;
}
/**
* Get matrix array.
*
* @return array<int, array<int, mixed>>
*
* @since 1.0.0
*/
public function getMatrix() : array
{
return $this->matrix;
}
/**
* Get sub matrix array.
*
* @param int $iRow Start row
* @param int $lRow End row
* @param int $iCol Start col
* @param int $lCol End col
*
* @return Matrix
*
* @since 1.0.0
*/
public function getSubMatrix(int $iRow, int $lRow, int $iCol, int $lCol) : self
{
$X = [[]];
for ($i = $iRow; $i <= $lRow; ++$i) {
for ($j = $iCol; $j <= $lCol; ++$j) {
$X[$i - $iRow][$j - $iCol] = $this->matrix[$i][$j];
}
}
$matrix = new self();
$matrix->setMatrix($X);
return $matrix;
}
/**
* Get sub matrix array.
*
* @param int[] $rows Row indices
* @param int[] $cols Row indices
*
* @return Matrix
*
* @since 1.0.0
*/
public function getSubMatrixByColumnsRows(array $rows, array $cols) : self
{
$X = [[]];
$rlength = \count($rows);
$clength = \count($cols);
for ($i = 0; $i < $rlength; ++$i) {
for ($j = 0; $j < $clength; ++$j) {
$X[$i][$j] = $this->matrix[$rows[$i]][$cols[$j]];
}
}
$matrix = new self();
$matrix->setMatrix($X);
return $matrix;
}
/**
* Get sub matrix array.
*
* @param int $iRow Start row
* @param int $lRow End row
* @param int[] $cols Row indices
*
* @return Matrix
*
* @since 1.0.0
*/
public function getSubMatrixByColumns(int $iRow, int $lRow, array $cols) : self
{
$X = [[]];
$length = \count($cols);
for ($i = $iRow; $i <= $lRow; ++$i) {
for ($j = 0; $j < $length; ++$j) {
$X[$i - $iRow][$j] = $this->matrix[$i][$cols[$j]];
}
}
$matrix = new self();
$matrix->setMatrix($X);
return $matrix;
}
/**
* Get sub matrix array.
*
* @param int[] $rows Row indices
* @param int $iCol Start col
* @param int $lCol End col
*
* @return Matrix
*
* @since 1.0.0
*/
public function getSubMatrixByRows(array $rows, int $iCol, int $lCol) : self
{
$X = [[]];
$length = \count($rows);
for ($i = 0; $i < $length; ++$i) {
for ($j = $iCol; $j <= $lCol; ++$j) {
$X[$i][$j - $iCol] = $this->matrix[$rows[$i]][$j];
}
}
$matrix = new self();
$matrix->setMatrix($X);
return $matrix;
}
/**
* Get matrix array.
*
* @return array<int, array<int, int|float>>
*
* @since 1.0.0
*/
public function toArray() : array
{
return $this->matrix;
}
/**
* Is symmetric.
*
* @return bool
*
* @since 1.0.0
*/
public function isSymmetric() : bool
{
$isSymmetric = true;
for ($j = 0; ($j < $this->m) & $isSymmetric; ++$j) {
for ($i = 0; ($i < $this->n) & $isSymmetric; ++$i) {
$isSymmetric = ($this->matrix[$i][$j] === $this->matrix[$j][$i]);
}
}
return $isSymmetric;
}
/**
* Get matrix rank.
*
* @return int
*
* @since 1.0.0
*/
public function rank() : int
{
$matrix = $this->matrix;
$mDim = $this->m;
$nDim = $this->n;
$rank = 0;
$selected = \array_fill(0, $mDim, false);
for ($i = 0; $i < $nDim; ++$i) {
for ($j = 0; $j < $mDim; ++$j) {
if (!$selected[$j] && \abs($matrix[$j][$i]) > self::EPSILON) {
break;
}
}
if ($j === $mDim) {
continue;
}
++$rank;
$selected[$j] = true;
for ($p = $i + 1; $p < $nDim; ++$p) {
$matrix[$j][$p] /= $matrix[$j][$i];
}
for ($k = 0; $k < $mDim; ++$k) {
if ($k !== $j && \abs($matrix[$k][$i]) > self::EPSILON) {
for ($p = $i + 1; $p < $nDim; ++$p) {
$matrix[$k][$p] -= $matrix[$j][$p] * $matrix[$k][$i];
}
}
}
}
return $rank;
}
/**
* Set matrix array.
*
* @param array<int, array<int|float>> $matrix Matrix
*
* @return Matrix
*
* @throws \Exception
*
* @since 1.0.0
*/
public function setMatrix(array $matrix) : self
{
$this->m = \count($matrix);
$this->n = !\is_array($matrix[0] ?? 1) ? 1 : \count($matrix[0]);
$this->matrix = $matrix;
return $this;
}
/**
* Subtract right.
*
* @param int|float|self $value Value
*
* @return Matrix
*
* @since 1.0.0
*/
public function sub(int | float | self $value) : self
{
if (\is_numeric($value)) {
return $this->addScalar(-$value);
}
return $this->add($value->mult(-1));
}
/**
* Add right.
*
* @param int|float|self $value Value
*
* @return Matrix
*
* @since 1.0.0
*/
public function add(int | float | self $value) : self
{
if (\is_numeric($value)) {
return $this->addScalar($value);
}
return $this->addMatrix($value);
}
/**
* Add matrix.
*
* @param Matrix $matrix Matrix to add
*
* @return Matrix
*
* @since 1.0.0
*/
private function addMatrix(self $matrix) : self
{
if ($this->m !== $matrix->getM() || $this->n !== $matrix->getN()) {
throw new InvalidDimensionException($matrix->getM() . 'x' . $matrix->getN());
}
$matrixArr = $matrix->getMatrix();
$newMatrixArr = $this->matrix;
foreach ($newMatrixArr as $i => $vector) {
foreach ($vector as $j => $value) {
$newMatrixArr[$i][$j] += $matrixArr[$i][$j];
}
}
$newMatrix = new self($this->m, $this->n);
$newMatrix->setMatrix($newMatrixArr);
return $newMatrix;
}
/**
* Get matrix rows.
*
* @return int<0, max>
*
* @since 1.0.0
*/
public function getM() : int
{
return $this->m;
}
/**
* Get matrix columns.
*
* @return int<0, max>
*
* @since 1.0.0
*/
public function getN() : int
{
return $this->n;
}
/**
* Add scalar.
*
* @param int|float $scalar Scalar
*
* @return Matrix
*
* @since 1.0.0
*/
private function addScalar(int | float $scalar) : self
{
$newMatrixArr = $this->matrix;
foreach ($newMatrixArr as $i => $vector) {
foreach ($vector as $j => $value) {
$newMatrixArr[$i][$j] += $scalar;
}
}
$newMatrix = new self($this->m, $this->n);
$newMatrix->setMatrix($newMatrixArr);
return $newMatrix;
}
/**
* Multiply right.
*
* @param int|float|self $value Factor
*
* @return Matrix
*
* @since 1.0.0
*/
public function mult(int | float | self $value) : self
{
if (\is_numeric($value)) {
return $this->multScalar($value);
}
return $this->multMatrix($value);
}
/**
* Multiply matrix.
*
* @param Matrix $matrix Matrix to multiply with
*
* @return Matrix
*
* @since 1.0.0
*/
private function multMatrix(self $matrix) : self
{
$nDim = $matrix->getN();
$mDim = $matrix->getM();
if ($mDim !== $this->n) {
throw new InvalidDimensionException($mDim . 'x' . $nDim);
}
$matrixArr = $matrix->getMatrix();
$newMatrix = new self($this->m, $nDim);
$newMatrixArr = $newMatrix->getMatrix();
for ($i = 0; $i < $this->m; ++$i) { // Row of $this
for ($c = 0; $c < $nDim; ++$c) { // Column of $matrix
$temp = 0;
for ($j = 0; $j < $mDim; ++$j) { // Row of $matrix
$temp += ($this->matrix[$i][$j] ?? 0) * ($matrixArr[$j][$c] ?? 0);
}
$newMatrixArr[$i][$c] = $temp;
}
}
$newMatrix->setMatrix($newMatrixArr);
return $newMatrix;
}
/**
* Multiply matrix.
*
* @param int|float $scalar Scalar value
*
* @return Matrix
*
* @since 1.0.0
*/
private function multScalar(int | float $scalar) : self
{
$newMatrixArr = $this->matrix;
foreach ($newMatrixArr as $i => $vector) {
foreach ($vector as $j => $value) {
$newMatrixArr[$i][$j] *= $scalar;
}
}
$newMatrix = new self($this->m, $this->n);
$newMatrix->setMatrix($newMatrixArr);
return $newMatrix;
}
/**
* Upper triangulize matrix.
*
* @return Matrix
*
* @since 1.0.0
*/
public function upperTriangular() : self
{
$matrix = new self($this->n, $this->n);
$matrixArr = $this->matrix;
$this->upperTrianglize($matrixArr);
$matrix->setMatrix($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.
*
* @return Matrix
*
* @throws InvalidDimensionException
*
* @since 1.0.0
*/
public function inverse() : self
{
return $this->solve(new IdentityMatrix($this->m));
}
/**
* Solve matrix
*
* @param Matrix $B Matrix/Vector b
*
* @return Matrix|Vector
*
* @since 1.0.0
*/
public function solve(self $B) : self
{
$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() : int
{
$row = (int) ($this->position / $this->m);
return $this->matrix[$row][$this->position - $row * $this->n];
}
/**
* {@inheritdoc}
*/
public function offsetGet($offset)
{
$row = (int) ($offset / $this->m);
return $this->matrix[$row][$offset - $row * $this->n];
}
/**
* {@inheritdoc}
*/
public function next() : void
{
++$this->position;
}
/**
* {@inheritdoc}
*/
public function key()
{
return $this->position;
}
/**
* {@inheritdoc}
*/
public function valid() : bool
{
return $this->offsetExists($this->position);
}
/**
* {@inheritdoc}
*/
public function offsetExists($offset) : bool
{
$row = (int) ($offset / $this->m);
return isset($this->matrix[$row][$offset - $row * $this->n]);
}
/**
* {@inheritdoc}
*/
public function rewind() : void
{
$this->position = 0;
}
/**
* {@inheritdoc}
*/
public function offsetSet($offset, $value) : void
{
$row = (int) ((int) $offset / $this->m);
$this->matrix[$row][$offset - $row * $this->n] = $value;
}
/**
* {@inheritdoc}
*/
public function offsetUnset($offset) : void
{
$row = (int) ($offset / $this->m);
unset($this->matrix[$row][$offset - $row * $this->n]);
}
}
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