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

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<?php
/**
 *	@package JAMA
 *
 *	Class to obtain eigenvalues and eigenvectors of a real matrix.
 *
 *	If A is symmetric, then A = V*D*V' where the eigenvalue matrix D
 *	is diagonal and the eigenvector matrix V is orthogonal (i.e.
 *	A = V.times(D.times(V.transpose())) and V.times(V.transpose())
 *	equals the identity matrix).
 *
 *	If A is not symmetric, then the eigenvalue matrix D is block diagonal
 *	with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
 *	lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].  The
 *	columns of V represent the eigenvectors in the sense that A*V = V*D,
 *	i.e. A.times(V) equals V.times(D).  The matrix V may be badly
 *	conditioned, or even singular, so the validity of the equation
 *	A = V*D*inverse(V) depends upon V.cond().
 *
 *	@author  Paul Meagher
 *	@license PHP v3.0
 *	@version 1.1
 */
class EigenvalueDecomposition {

	/**
	 *	Row and column dimension (square matrix).
	 *	@var int
	 */
	private $n;

	/**
	 *	Internal symmetry flag.
	 *	@var int
	 */
	private $issymmetric;

	/**
	 *	Arrays for internal storage of eigenvalues.
	 *	@var array
	 */
	private $d = array();
	private $e = array();

	/**
	 *	Array for internal storage of eigenvectors.
	 *	@var array
	 */
	private $V = array();

	/**
	*	Array for internal storage of nonsymmetric Hessenberg form.
	*	@var array
	*/
	private $H = array();

	/**
	*	Working storage for nonsymmetric algorithm.
	*	@var array
	*/