1203 lines
36 KiB
PHP
1203 lines
36 KiB
PHP
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<?php
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namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
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use PhpOffice\PhpSpreadsheet\Calculation\Exception as CalculationException;
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use PhpOffice\PhpSpreadsheet\Calculation\Functions;
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use PhpOffice\PhpSpreadsheet\Shared\StringHelper;
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/**
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* Matrix class.
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*
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* @author Paul Meagher
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* @author Michael Bommarito
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* @author Lukasz Karapuda
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* @author Bartek Matosiuk
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*
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* @version 1.8
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*
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* @see https://math.nist.gov/javanumerics/jama/
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*/
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class Matrix
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{
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const POLYMORPHIC_ARGUMENT_EXCEPTION = 'Invalid argument pattern for polymorphic function.';
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const ARGUMENT_TYPE_EXCEPTION = 'Invalid argument type.';
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const ARGUMENT_BOUNDS_EXCEPTION = 'Invalid argument range.';
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const MATRIX_DIMENSION_EXCEPTION = 'Matrix dimensions are not equal.';
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const ARRAY_LENGTH_EXCEPTION = 'Array length must be a multiple of m.';
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const MATRIX_SPD_EXCEPTION = 'Can only perform operation on symmetric positive definite matrix.';
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/**
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* Matrix storage.
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*
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* @var array
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*/
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public $A = [];
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/**
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* Matrix row dimension.
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*
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* @var int
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*/
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private $m;
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/**
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* Matrix column dimension.
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*
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* @var int
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*/
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private $n;
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/**
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* Polymorphic constructor.
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*
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* As PHP has no support for polymorphic constructors, we use tricks to make our own sort of polymorphism using func_num_args, func_get_arg, and gettype. In essence, we're just implementing a simple RTTI filter and calling the appropriate constructor.
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*/
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public function __construct(...$args)
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{
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if (count($args) > 0) {
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$match = implode(',', array_map('gettype', $args));
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switch ($match) {
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//Rectangular matrix - m x n initialized from 2D array
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case 'array':
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$this->m = count($args[0]);
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$this->n = count($args[0][0]);
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$this->A = $args[0];
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break;
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//Square matrix - n x n
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case 'integer':
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$this->m = $args[0];
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$this->n = $args[0];
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$this->A = array_fill(0, $this->m, array_fill(0, $this->n, 0));
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break;
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//Rectangular matrix - m x n
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case 'integer,integer':
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$this->m = $args[0];
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$this->n = $args[1];
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$this->A = array_fill(0, $this->m, array_fill(0, $this->n, 0));
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break;
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//Rectangular matrix - m x n initialized from packed array
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case 'array,integer':
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$this->m = $args[1];
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if ($this->m != 0) {
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$this->n = count($args[0]) / $this->m;
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} else {
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$this->n = 0;
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}
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if (($this->m * $this->n) == count($args[0])) {
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for ($i = 0; $i < $this->m; ++$i) {
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for ($j = 0; $j < $this->n; ++$j) {
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$this->A[$i][$j] = $args[0][$i + $j * $this->m];
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}
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}
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} else {
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throw new CalculationException(self::ARRAY_LENGTH_EXCEPTION);
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}
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break;
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default:
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throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
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break;
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}
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} else {
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throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
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}
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}
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/**
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* getArray.
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*
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* @return array Matrix array
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*/
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public function getArray()
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{
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return $this->A;
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}
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/**
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* getRowDimension.
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*
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* @return int Row dimension
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*/
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public function getRowDimension()
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{
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return $this->m;
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}
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/**
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* getColumnDimension.
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*
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* @return int Column dimension
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*/
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public function getColumnDimension()
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{
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return $this->n;
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}
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/**
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* get.
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*
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* Get the i,j-th element of the matrix.
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*
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* @param int $i Row position
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* @param int $j Column position
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*
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* @return mixed Element (int/float/double)
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*/
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public function get($i = null, $j = null)
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{
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return $this->A[$i][$j];
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}
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/**
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* getMatrix.
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*
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* Get a submatrix
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*
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* @return Matrix Submatrix
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*/
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public function getMatrix(...$args)
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{
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if (count($args) > 0) {
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$match = implode(',', array_map('gettype', $args));
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switch ($match) {
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//A($i0...; $j0...)
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case 'integer,integer':
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[$i0, $j0] = $args;
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if ($i0 >= 0) {
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$m = $this->m - $i0;
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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if ($j0 >= 0) {
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$n = $this->n - $j0;
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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$R = new self($m, $n);
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for ($i = $i0; $i < $this->m; ++$i) {
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for ($j = $j0; $j < $this->n; ++$j) {
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$R->set($i, $j, $this->A[$i][$j]);
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}
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}
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return $R;
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break;
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//A($i0...$iF; $j0...$jF)
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case 'integer,integer,integer,integer':
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[$i0, $iF, $j0, $jF] = $args;
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if (($iF > $i0) && ($this->m >= $iF) && ($i0 >= 0)) {
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$m = $iF - $i0;
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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if (($jF > $j0) && ($this->n >= $jF) && ($j0 >= 0)) {
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$n = $jF - $j0;
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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$R = new self($m + 1, $n + 1);
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for ($i = $i0; $i <= $iF; ++$i) {
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for ($j = $j0; $j <= $jF; ++$j) {
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$R->set($i - $i0, $j - $j0, $this->A[$i][$j]);
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}
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}
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return $R;
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break;
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//$R = array of row indices; $C = array of column indices
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case 'array,array':
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[$RL, $CL] = $args;
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if (count($RL) > 0) {
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$m = count($RL);
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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if (count($CL) > 0) {
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$n = count($CL);
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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$R = new self($m, $n);
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for ($i = 0; $i < $m; ++$i) {
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for ($j = 0; $j < $n; ++$j) {
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$R->set($i, $j, $this->A[$RL[$i]][$CL[$j]]);
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}
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}
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return $R;
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break;
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//A($i0...$iF); $CL = array of column indices
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case 'integer,integer,array':
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[$i0, $iF, $CL] = $args;
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if (($iF > $i0) && ($this->m >= $iF) && ($i0 >= 0)) {
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$m = $iF - $i0;
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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if (count($CL) > 0) {
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$n = count($CL);
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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$R = new self($m, $n);
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for ($i = $i0; $i < $iF; ++$i) {
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for ($j = 0; $j < $n; ++$j) {
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$R->set($i - $i0, $j, $this->A[$i][$CL[$j]]);
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}
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}
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return $R;
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break;
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//$RL = array of row indices
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case 'array,integer,integer':
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[$RL, $j0, $jF] = $args;
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if (count($RL) > 0) {
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$m = count($RL);
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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if (($jF >= $j0) && ($this->n >= $jF) && ($j0 >= 0)) {
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$n = $jF - $j0;
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} else {
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throw new CalculationException(self::ARGUMENT_BOUNDS_EXCEPTION);
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}
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$R = new self($m, $n + 1);
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for ($i = 0; $i < $m; ++$i) {
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for ($j = $j0; $j <= $jF; ++$j) {
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$R->set($i, $j - $j0, $this->A[$RL[$i]][$j]);
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}
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}
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return $R;
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break;
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default:
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throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
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break;
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}
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} else {
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throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
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}
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}
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/**
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* checkMatrixDimensions.
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*
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* Is matrix B the same size?
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*
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* @param Matrix $B Matrix B
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*
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* @return bool
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*/
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public function checkMatrixDimensions($B = null)
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{
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if ($B instanceof self) {
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if (($this->m == $B->getRowDimension()) && ($this->n == $B->getColumnDimension())) {
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return true;
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}
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throw new CalculationException(self::MATRIX_DIMENSION_EXCEPTION);
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}
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throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
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}
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// function checkMatrixDimensions()
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/**
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* set.
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*
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* Set the i,j-th element of the matrix.
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*
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* @param int $i Row position
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* @param int $j Column position
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* @param mixed $c Int/float/double value
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*
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* @return mixed Element (int/float/double)
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*/
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public function set($i = null, $j = null, $c = null)
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{
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// Optimized set version just has this
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$this->A[$i][$j] = $c;
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}
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// function set()
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/**
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* identity.
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*
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* Generate an identity matrix.
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*
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* @param int $m Row dimension
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* @param int $n Column dimension
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*
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* @return Matrix Identity matrix
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*/
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public function identity($m = null, $n = null)
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{
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return $this->diagonal($m, $n, 1);
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}
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/**
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* diagonal.
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*
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* Generate a diagonal matrix
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*
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* @param int $m Row dimension
|
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* @param int $n Column dimension
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* @param mixed $c Diagonal value
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*
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* @return Matrix Diagonal matrix
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*/
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public function diagonal($m = null, $n = null, $c = 1)
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{
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$R = new self($m, $n);
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for ($i = 0; $i < $m; ++$i) {
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$R->set($i, $i, $c);
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}
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return $R;
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}
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/**
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* getMatrixByRow.
|
||
|
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*
|
||
|
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* Get a submatrix by row index/range
|
||
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*
|
||
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* @param int $i0 Initial row index
|
||
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* @param int $iF Final row index
|
||
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*
|
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* @return Matrix Submatrix
|
||
|
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*/
|
||
|
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public function getMatrixByRow($i0 = null, $iF = null)
|
||
|
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{
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||
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if (is_int($i0)) {
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if (is_int($iF)) {
|
||
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return $this->getMatrix($i0, 0, $iF + 1, $this->n);
|
||
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}
|
||
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||
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return $this->getMatrix($i0, 0, $i0 + 1, $this->n);
|
||
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}
|
||
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|
||
|
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throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* getMatrixByCol.
|
||
|
|
*
|
||
|
|
* Get a submatrix by column index/range
|
||
|
|
*
|
||
|
|
* @param int $j0 Initial column index
|
||
|
|
* @param int $jF Final column index
|
||
|
|
*
|
||
|
|
* @return Matrix Submatrix
|
||
|
|
*/
|
||
|
|
public function getMatrixByCol($j0 = null, $jF = null)
|
||
|
|
{
|
||
|
|
if (is_int($j0)) {
|
||
|
|
if (is_int($jF)) {
|
||
|
|
return $this->getMatrix(0, $j0, $this->m, $jF + 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
return $this->getMatrix(0, $j0, $this->m, $j0 + 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* transpose.
|
||
|
|
*
|
||
|
|
* Tranpose matrix
|
||
|
|
*
|
||
|
|
* @return Matrix Transposed matrix
|
||
|
|
*/
|
||
|
|
public function transpose()
|
||
|
|
{
|
||
|
|
$R = new self($this->n, $this->m);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$R->set($j, $i, $this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $R;
|
||
|
|
}
|
||
|
|
|
||
|
|
// function transpose()
|
||
|
|
|
||
|
|
/**
|
||
|
|
* trace.
|
||
|
|
*
|
||
|
|
* Sum of diagonal elements
|
||
|
|
*
|
||
|
|
* @return float Sum of diagonal elements
|
||
|
|
*/
|
||
|
|
public function trace()
|
||
|
|
{
|
||
|
|
$s = 0;
|
||
|
|
$n = min($this->m, $this->n);
|
||
|
|
for ($i = 0; $i < $n; ++$i) {
|
||
|
|
$s += $this->A[$i][$i];
|
||
|
|
}
|
||
|
|
|
||
|
|
return $s;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* uminus.
|
||
|
|
*
|
||
|
|
* Unary minus matrix -A
|
||
|
|
*
|
||
|
|
* @return Matrix Unary minus matrix
|
||
|
|
*/
|
||
|
|
public function uminus()
|
||
|
|
{
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* plus.
|
||
|
|
*
|
||
|
|
* A + B
|
||
|
|
*
|
||
|
|
* @return Matrix Sum
|
||
|
|
*/
|
||
|
|
public function plus(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$M->set($i, $j, $M->get($i, $j) + $this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $M;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* plusEquals.
|
||
|
|
*
|
||
|
|
* A = A + B
|
||
|
|
*
|
||
|
|
* @return $this
|
||
|
|
*/
|
||
|
|
public function plusEquals(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$validValues = true;
|
||
|
|
$value = $M->get($i, $j);
|
||
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
||
|
|
$this->A[$i][$j] = trim($this->A[$i][$j], '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
||
|
|
$value = trim($value, '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($value);
|
||
|
|
}
|
||
|
|
if ($validValues) {
|
||
|
|
$this->A[$i][$j] += $value;
|
||
|
|
} else {
|
||
|
|
$this->A[$i][$j] = Functions::NAN();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $this;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* minus.
|
||
|
|
*
|
||
|
|
* A - B
|
||
|
|
*
|
||
|
|
* @return Matrix Sum
|
||
|
|
*/
|
||
|
|
public function minus(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$M->set($i, $j, $M->get($i, $j) - $this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $M;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* minusEquals.
|
||
|
|
*
|
||
|
|
* A = A - B
|
||
|
|
*
|
||
|
|
* @return $this
|
||
|
|
*/
|
||
|
|
public function minusEquals(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$validValues = true;
|
||
|
|
$value = $M->get($i, $j);
|
||
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
||
|
|
$this->A[$i][$j] = trim($this->A[$i][$j], '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
||
|
|
$value = trim($value, '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($value);
|
||
|
|
}
|
||
|
|
if ($validValues) {
|
||
|
|
$this->A[$i][$j] -= $value;
|
||
|
|
} else {
|
||
|
|
$this->A[$i][$j] = Functions::NAN();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $this;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* arrayTimes.
|
||
|
|
*
|
||
|
|
* Element-by-element multiplication
|
||
|
|
* Cij = Aij * Bij
|
||
|
|
*
|
||
|
|
* @return Matrix Matrix Cij
|
||
|
|
*/
|
||
|
|
public function arrayTimes(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$M->set($i, $j, $M->get($i, $j) * $this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $M;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* arrayTimesEquals.
|
||
|
|
*
|
||
|
|
* Element-by-element multiplication
|
||
|
|
* Aij = Aij * Bij
|
||
|
|
*
|
||
|
|
* @return $this
|
||
|
|
*/
|
||
|
|
public function arrayTimesEquals(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$validValues = true;
|
||
|
|
$value = $M->get($i, $j);
|
||
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
||
|
|
$this->A[$i][$j] = trim($this->A[$i][$j], '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
||
|
|
$value = trim($value, '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($value);
|
||
|
|
}
|
||
|
|
if ($validValues) {
|
||
|
|
$this->A[$i][$j] *= $value;
|
||
|
|
} else {
|
||
|
|
$this->A[$i][$j] = Functions::NAN();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $this;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* arrayRightDivide.
|
||
|
|
*
|
||
|
|
* Element-by-element right division
|
||
|
|
* A / B
|
||
|
|
*
|
||
|
|
* @return Matrix Division result
|
||
|
|
*/
|
||
|
|
public function arrayRightDivide(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$validValues = true;
|
||
|
|
$value = $M->get($i, $j);
|
||
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
||
|
|
$this->A[$i][$j] = trim($this->A[$i][$j], '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
||
|
|
$value = trim($value, '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($value);
|
||
|
|
}
|
||
|
|
if ($validValues) {
|
||
|
|
if ($value == 0) {
|
||
|
|
// Trap for Divide by Zero error
|
||
|
|
$M->set($i, $j, '#DIV/0!');
|
||
|
|
} else {
|
||
|
|
$M->set($i, $j, $this->A[$i][$j] / $value);
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
$M->set($i, $j, Functions::NAN());
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $M;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* arrayRightDivideEquals.
|
||
|
|
*
|
||
|
|
* Element-by-element right division
|
||
|
|
* Aij = Aij / Bij
|
||
|
|
*
|
||
|
|
* @return Matrix Matrix Aij
|
||
|
|
*/
|
||
|
|
public function arrayRightDivideEquals(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$this->A[$i][$j] = $this->A[$i][$j] / $M->get($i, $j);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $M;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* arrayLeftDivide.
|
||
|
|
*
|
||
|
|
* Element-by-element Left division
|
||
|
|
* A / B
|
||
|
|
*
|
||
|
|
* @return Matrix Division result
|
||
|
|
*/
|
||
|
|
public function arrayLeftDivide(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$M->set($i, $j, $M->get($i, $j) / $this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $M;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* arrayLeftDivideEquals.
|
||
|
|
*
|
||
|
|
* Element-by-element Left division
|
||
|
|
* Aij = Aij / Bij
|
||
|
|
*
|
||
|
|
* @return Matrix Matrix Aij
|
||
|
|
*/
|
||
|
|
public function arrayLeftDivideEquals(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$this->A[$i][$j] = $M->get($i, $j) / $this->A[$i][$j];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $M;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* times.
|
||
|
|
*
|
||
|
|
* Matrix multiplication
|
||
|
|
*
|
||
|
|
* @return Matrix Product
|
||
|
|
*/
|
||
|
|
public function times(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$B = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
if ($this->n == $B->m) {
|
||
|
|
$C = new self($this->m, $B->n);
|
||
|
|
for ($j = 0; $j < $B->n; ++$j) {
|
||
|
|
$Bcolj = [];
|
||
|
|
for ($k = 0; $k < $this->n; ++$k) {
|
||
|
|
$Bcolj[$k] = $B->A[$k][$j];
|
||
|
|
}
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
$Arowi = $this->A[$i];
|
||
|
|
$s = 0;
|
||
|
|
for ($k = 0; $k < $this->n; ++$k) {
|
||
|
|
$s += $Arowi[$k] * $Bcolj[$k];
|
||
|
|
}
|
||
|
|
$C->A[$i][$j] = $s;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $C;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::MATRIX_DIMENSION_EXCEPTION);
|
||
|
|
case 'array':
|
||
|
|
$B = new self($args[0]);
|
||
|
|
if ($this->n == $B->m) {
|
||
|
|
$C = new self($this->m, $B->n);
|
||
|
|
for ($i = 0; $i < $C->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $C->n; ++$j) {
|
||
|
|
$s = '0';
|
||
|
|
for ($k = 0; $k < $C->n; ++$k) {
|
||
|
|
$s += $this->A[$i][$k] * $B->A[$k][$j];
|
||
|
|
}
|
||
|
|
$C->A[$i][$j] = $s;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $C;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::MATRIX_DIMENSION_EXCEPTION);
|
||
|
|
case 'integer':
|
||
|
|
$C = new self($this->A);
|
||
|
|
for ($i = 0; $i < $C->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $C->n; ++$j) {
|
||
|
|
$C->A[$i][$j] *= $args[0];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $C;
|
||
|
|
case 'double':
|
||
|
|
$C = new self($this->m, $this->n);
|
||
|
|
for ($i = 0; $i < $C->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $C->n; ++$j) {
|
||
|
|
$C->A[$i][$j] = $args[0] * $this->A[$i][$j];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $C;
|
||
|
|
case 'float':
|
||
|
|
$C = new self($this->A);
|
||
|
|
for ($i = 0; $i < $C->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $C->n; ++$j) {
|
||
|
|
$C->A[$i][$j] *= $args[0];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $C;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* power.
|
||
|
|
*
|
||
|
|
* A = A ^ B
|
||
|
|
*
|
||
|
|
* @return $this
|
||
|
|
*/
|
||
|
|
public function power(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$validValues = true;
|
||
|
|
$value = $M->get($i, $j);
|
||
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
||
|
|
$this->A[$i][$j] = trim($this->A[$i][$j], '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($this->A[$i][$j]);
|
||
|
|
}
|
||
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
||
|
|
$value = trim($value, '"');
|
||
|
|
$validValues &= StringHelper::convertToNumberIfFraction($value);
|
||
|
|
}
|
||
|
|
if ($validValues) {
|
||
|
|
$this->A[$i][$j] = $this->A[$i][$j] ** $value;
|
||
|
|
} else {
|
||
|
|
$this->A[$i][$j] = Functions::NAN();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $this;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* concat.
|
||
|
|
*
|
||
|
|
* A = A & B
|
||
|
|
*
|
||
|
|
* @return $this
|
||
|
|
*/
|
||
|
|
public function concat(...$args)
|
||
|
|
{
|
||
|
|
if (count($args) > 0) {
|
||
|
|
$match = implode(',', array_map('gettype', $args));
|
||
|
|
|
||
|
|
switch ($match) {
|
||
|
|
case 'object':
|
||
|
|
if ($args[0] instanceof self) {
|
||
|
|
$M = $args[0];
|
||
|
|
} else {
|
||
|
|
throw new CalculationException(self::ARGUMENT_TYPE_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
break;
|
||
|
|
case 'array':
|
||
|
|
$M = new self($args[0]);
|
||
|
|
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
$this->checkMatrixDimensions($M);
|
||
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
||
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
||
|
|
$this->A[$i][$j] = trim($this->A[$i][$j], '"') . trim($M->get($i, $j), '"');
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return $this;
|
||
|
|
}
|
||
|
|
|
||
|
|
throw new CalculationException(self::POLYMORPHIC_ARGUMENT_EXCEPTION);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Solve A*X = B.
|
||
|
|
*
|
||
|
|
* @param Matrix $B Right hand side
|
||
|
|
*
|
||
|
|
* @return Matrix ... Solution if A is square, least squares solution otherwise
|
||
|
|
*/
|
||
|
|
public function solve($B)
|
||
|
|
{
|
||
|
|
if ($this->m == $this->n) {
|
||
|
|
$LU = new LUDecomposition($this);
|
||
|
|
|
||
|
|
return $LU->solve($B);
|
||
|
|
}
|
||
|
|
$QR = new QRDecomposition($this);
|
||
|
|
|
||
|
|
return $QR->solve($B);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Matrix inverse or pseudoinverse.
|
||
|
|
*
|
||
|
|
* @return Matrix ... Inverse(A) if A is square, pseudoinverse otherwise.
|
||
|
|
*/
|
||
|
|
public function inverse()
|
||
|
|
{
|
||
|
|
return $this->solve($this->identity($this->m, $this->m));
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* det.
|
||
|
|
*
|
||
|
|
* Calculate determinant
|
||
|
|
*
|
||
|
|
* @return float Determinant
|
||
|
|
*/
|
||
|
|
public function det()
|
||
|
|
{
|
||
|
|
$L = new LUDecomposition($this);
|
||
|
|
|
||
|
|
return $L->det();
|
||
|
|
}
|
||
|
|
}
|