\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 :

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.