\EigenvalueDecomposition

Summary

Methods

Properties

Constants

__construct()
getV()
getRealEigenvalues()
getImagEigenvalues()
getD()

No public properties found

No constants found

No protected methods found

No protected properties found

N/A

tred2()
tql2()
orthes()
cdiv()
hqr2()

$n
$issymmetric
$d
$e
$V
$H
$ort
$cdivr
$cdivi

N/A

File: vendor/Execl/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(). @author Paul Meagher @license PHP v3.0 @version 1.1
Class hierarchy: \EigenvalueDecomposition

Properties

$n

$n :

Row and column dimension (square matrix).

@var int

Type

$issymmetric

$issymmetric :

Internal symmetry flag.

@var int

Type

$d

$d :

Arrays for internal storage of eigenvalues.

@var array

Type

$e

$e :

Type

$V

$V :

Array for internal storage of eigenvectors.

@var array

Type

$H

$H :

Array for internal storage of nonsymmetric Hessenberg form.

@var array

Type

$ort

$ort :

Working storage for nonsymmetric algorithm.

@var array

Type

$cdivr

$cdivr :

Used for complex scalar division.

@var float

Type

$cdivi

$cdivi :

Type

Methods

__construct()

__construct(  $Arg)

Constructor: Check for symmetry, then construct the eigenvalue decomposition

@access public

Parameters

$Arg

getV()

getV() : \V

Return the eigenvector matrix

@access public

Returns

getRealEigenvalues()

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

Return the real parts of the eigenvalues

@access public

Returns

\real(diag(D))

getImagEigenvalues()

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

Return the imaginary parts of the eigenvalues

@access public

Returns

\imag(diag(D))

getD()

getD() : \D

Return the block diagonal eigenvalue matrix

@access public

Returns

tred2()

tred2()

Symmetric Householder reduction to tridiagonal form.

@access private

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.

@access private

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.