vendor/phpoffice/phpexcel/Classes/PHPExcel/Shared/JAMA/CholeskyDecomposition.php

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<?php
/**
 *	@package JAMA
 *
 *	Cholesky decomposition class
 *
 *	For a symmetric, positive definite matrix A, the Cholesky decomposition
 *	is an lower triangular matrix L so that A = L*L'.
 *
 *	If the matrix is not symmetric or positive definite, the constructor
 *	returns a partial decomposition and sets an internal flag that may
 *	be queried by the isSPD() method.
 *
 *	@author Paul Meagher
 *	@author Michael Bommarito
 *	@version 1.2
 */
class CholeskyDecomposition {

	/**
	 *	Decomposition storage
	 *	@var array
	 *	@access private
	 */
	private $L = array();

	/**
	 *	Matrix row and column dimension
	 *	@var int
	 *	@access private
	 */
	private $m;

	/**
	 *	Symmetric positive definite flag
	 *	@var boolean
	 *	@access private
	 */
	private $isspd = true;


	/**
	 *	CholeskyDecomposition
	 *
	 *	Class constructor - decomposes symmetric positive definite matrix
	 *	@param mixed Matrix square symmetric positive definite matrix
	 */
	public function __construct($A = null) {
		if ($A instanceof Matrix) {
			$this->L = $A->getArray();
			$this->m = $A->getRowDimension();

			for($i = 0; $i < $this->m; ++$i) {
				for($j = $i; $j < $this->m; ++$j) {
					for($sum = $this->L[$i][$j], $k = $i - 1; $k >= 0; --$k) {
						$sum -= $this->L[$i][$k] * $this->L[$j][$k];
					}
					if ($i == $j) {
						if ($sum >= 0) {
							$this->L[$i][$i] = sqrt($sum);