File: vendor/phpoffice/phpexcel/Classes/PHPExcel/Shared/JAMA/EigenvalueDecomposition.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().
Class hierarchy: \EigenvalueDecomposition

Properties

$n

$n : integer

Row and column dimension (square matrix).

Type

integer

$issymmetric

$issymmetric : integer

Internal symmetry flag.

Type

integer

$d

$d : array

Arrays for internal storage of eigenvalues.

Type

array

$e

$e :

Type

$V

$V : array

Array for internal storage of eigenvectors.

Type

array

$H

$H : array

Array for internal storage of nonsymmetric Hessenberg form.

Type

array

$ort

$ort : array

Working storage for nonsymmetric algorithm.

Type

array

$cdivr

$cdivr : float

Used for complex scalar division.

Type

float

$cdivi

$cdivi :

Type

Methods

__construct()

__construct(  $Arg) : \Structure

Constructor: Check for symmetry, then construct the eigenvalue decomposition

Parameters

$Arg

Returns

\Structure —

to access D and V.

getV()

getV() : \V

Return the eigenvector matrix

Returns

getRealEigenvalues()

getRealEigenvalues() : \real(diag(D))

Return the real parts of the eigenvalues

Returns

\real(diag(D))

getImagEigenvalues()

getImagEigenvalues() : \imag(diag(D))

Return the imaginary parts of the eigenvalues

Returns

\imag(diag(D))

getD()

getD() : \D

Return the block diagonal eigenvalue matrix

Returns

tred2()

tred2()

Symmetric Householder reduction to tridiagonal form.

tql2()

tql2()

Symmetric tridiagonal QL algorithm.

This is derived from the Algol procedures tql2, by Bowdler, Martin, Reinsch, and Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.

orthes()

orthes()

Nonsymmetric reduction to Hessenberg form.

This is derived from the Algol procedures orthes and ortran, by Martin and Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutines in EISPACK.

cdiv()

cdiv(  $xr,   $xi,   $yr,   $yi)

Performs complex division.

Parameters

	$xr
	$xi
	$yr
	$yi

hqr2()

hqr2()

Nonsymmetric reduction from Hessenberg to real Schur form.

Code is derived from the Algol procedure hqr2, by Martin and Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.

author	Paul Meagher
license	PHP v3.0
version	1.1