mirror of
https://github.com/Karaka-Management/phpOMS.git
synced 2026-01-11 09:48:40 +00:00
762 lines
16 KiB
PHP
762 lines
16 KiB
PHP
<?php
|
|
/**
|
|
* Orange Management
|
|
*
|
|
* PHP Version 7.4
|
|
*
|
|
* @package phpOMS\Math\Matrix
|
|
* @copyright Dennis Eichhorn
|
|
* @license OMS License 1.0
|
|
* @version 1.0.0
|
|
* @link https://orange-management.org
|
|
*/
|
|
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://orange-management.org
|
|
* @since 1.0.0
|
|
*/
|
|
class Matrix implements \ArrayAccess, \Iterator
|
|
{
|
|
/**
|
|
* Matrix.
|
|
*
|
|
* @var array
|
|
* @since 1.0.0
|
|
*/
|
|
protected array $matrix = [];
|
|
|
|
/**
|
|
* Columns.
|
|
*
|
|
* @var int
|
|
* @since 1.0.0
|
|
*/
|
|
protected int $n = 0;
|
|
|
|
/**
|
|
* Rows.
|
|
*
|
|
* @var int
|
|
* @since 1.0.0
|
|
*/
|
|
protected int $m = 0;
|
|
|
|
/**
|
|
* Iterator position.
|
|
*
|
|
* @var int
|
|
* @since 1.0.0
|
|
*/
|
|
protected int $position = 0;
|
|
|
|
/**
|
|
* Constructor.
|
|
*
|
|
* @param int $m Rows
|
|
* @param int $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);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Set value.
|
|
*
|
|
* @param int $m Row
|
|
* @param int $n Column
|
|
* @param int $value Value
|
|
*
|
|
* @return void
|
|
*
|
|
* @throws InvalidDimensionException
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function set(int $m, int $n, $value) : void
|
|
{
|
|
if (!isset($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 $n = 0)
|
|
{
|
|
if (!isset($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, mixed>>
|
|
*
|
|
* @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][$i]) > 0.0001) {
|
|
break;
|
|
}
|
|
}
|
|
|
|
if ($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]) > 0.0001) {
|
|
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<float|int>> $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 mixed $value Value
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws \InvalidArgumentException
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function sub($value) : self
|
|
{
|
|
if ($value instanceof self) {
|
|
return $this->add($value->mult(-1));
|
|
} elseif (!\is_string($value) && \is_numeric($value)) {
|
|
return $this->add(-$value);
|
|
}
|
|
|
|
throw new \InvalidArgumentException('Type');
|
|
}
|
|
|
|
/**
|
|
* Add right.
|
|
*
|
|
* @param mixed $value Value
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws \InvalidArgumentException
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function add($value) : self
|
|
{
|
|
if ($value instanceof self) {
|
|
return $this->addMatrix($value);
|
|
} elseif (!\is_string($value) && \is_numeric($value)) {
|
|
return $this->addScalar($value);
|
|
}
|
|
|
|
throw new \InvalidArgumentException();
|
|
}
|
|
|
|
/**
|
|
* Add matrix.
|
|
*
|
|
* @param Matrix $matrix Matrix to add
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws \Exception
|
|
*
|
|
* @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
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function getM() : int
|
|
{
|
|
return $this->m;
|
|
}
|
|
|
|
/**
|
|
* Get matrix columns.
|
|
*
|
|
* @return int
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function getN() : int
|
|
{
|
|
return $this->n;
|
|
}
|
|
|
|
/**
|
|
* Add scalar.
|
|
*
|
|
* @param mixed $scalar Scalar
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws \Exception
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
private function addScalar($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 mixed $value Factor
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws \InvalidArgumentException
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
public function mult($value) : self
|
|
{
|
|
if ($value instanceof self) {
|
|
return $this->multMatrix($value);
|
|
} elseif (!\is_string($value) && \is_numeric($value)) {
|
|
return $this->multScalar($value);
|
|
}
|
|
|
|
throw new \InvalidArgumentException('Type');
|
|
}
|
|
|
|
/**
|
|
* Multiply matrix.
|
|
*
|
|
* @param Matrix $matrix Matrix to multiply with
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws \Exception
|
|
*
|
|
* @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 mixed $scalar Scalar value
|
|
*
|
|
* @return Matrix
|
|
*
|
|
* @throws \Exception
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
private function multScalar($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<float|int>> $arr Matrix to trianglize
|
|
*
|
|
* @return int Det sign
|
|
*
|
|
* @since 1.0.0
|
|
*/
|
|
private function upperTrianglize(array &$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()
|
|
{
|
|
return $this->offsetGet($this->position);
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function offsetGet($offset)
|
|
{
|
|
$row = (int) ($offset / $this->m);
|
|
|
|
return $this->matrix[$row][$offset - $row * $this->n];
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function next() : void
|
|
{
|
|
++$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() : void
|
|
{
|
|
$this->position = 0;
|
|
}
|
|
|
|
/**
|
|
* {@inheritdoc}
|
|
*/
|
|
public function offsetSet($offset, $value) : void
|
|
{
|
|
$row = (int) ($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]);
|
|
}
|
|
}
|