# \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

## Properties

### \$n

`\$n : integer`

Row and column dimension (square matrix).

integer

### \$issymmetric

`\$issymmetric : integer`

Internal symmetry flag.

integer

### \$d

`\$d : array`

Arrays for internal storage of eigenvalues.

array

`\$e : `

### \$V

`\$V : array`

Array for internal storage of eigenvectors.

array

### \$H

`\$H : array`

Array for internal storage of nonsymmetric Hessenberg form.

array

### \$ort

`\$ort : array`

Working storage for nonsymmetric algorithm.

array

### \$cdivr

`\$cdivr : float`

Used for complex scalar division.

float

### \$cdivi

`\$cdivi : `

## Methods

### __construct()

`__construct(  \$Arg) : \Structure`

Constructor: Check for symmetry, then construct the eigenvalue decomposition

 \$Arg

#### Returns

\Structure —

to access D and V.

### getV()

`getV() : \V`

Return the eigenvector matrix

\V

### getRealEigenvalues()

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

Return the real parts of the eigenvalues

\real(diag(D))

### getImagEigenvalues()

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

Return the imaginary parts of the eigenvalues

\imag(diag(D))

### getD()

`getD() : \D`

Return the block diagonal eigenvalue matrix

\D

### 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.