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

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<?php
/**
 *	@package JAMA
 *
 *	For an m-by-n matrix A with m >= n, the singular value decomposition is
 *	an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
 *	an n-by-n orthogonal matrix V so that A = U*S*V'.
 *
 *	The singular values, sigma[$k] = S[$k][$k], are ordered so that
 *	sigma[0] >= sigma[1] >= ... >= sigma[n-1].
 *
 *	The singular value decompostion always exists, so the constructor will
 *	never fail.  The matrix condition number and the effective numerical
 *	rank can be computed from this decomposition.
 *
 *	@author  Paul Meagher
 *	@license PHP v3.0
 *	@version 1.1
 */
class SingularValueDecomposition  {

	/**
	 *	Internal storage of U.
	 *	@var array
	 */
	private $U = array();

	/**
	 *	Internal storage of V.
	 *	@var array
	 */
	private $V = array();

	/**
	 *	Internal storage of singular values.
	 *	@var array
	 */
	private $s = array();

	/**
	 *	Row dimension.
	 *	@var int
	 */
	private $m;

	/**
	 *	Column dimension.
	 *	@var int
	 */
	private $n;


	/**
	 *	Construct the singular value decomposition
	 *
	 *	Derived from LINPACK code.
	 *
	 *	@param $A Rectangular matrix
	 *	@return Structure to access U, S and V.
	 */