Package gov.nih.mipav.view.renderer.WildMagic.AAM

Class EigenvalueDecomposition

java.lang.Object

gov.nih.mipav.view.renderer.WildMagic.AAM.EigenvalueDecomposition

All Implemented Interfaces:

java.io.Serializable

public class EigenvalueDecomposition
extends java.lang.Object
implements java.io.Serializable

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().

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private double	cdivi
private double	cdivr
private double[]	d	Arrays for internal storage of eigenvalues.
private double[]	e	Arrays for internal storage of eigenvalues.
private double[][]	H	Array for internal storage of nonsymmetric Hessenberg form.
private boolean	issymmetric	Symmetry flag.
private int	n	Row and column dimension (square matrix).
private double[]	ort	Working storage for nonsymmetric algorithm.
private double[][]	V	Array for internal storage of eigenvectors.

Constructor Summary

Constructors

Constructor	Description
EigenvalueDecomposition(double[][] Arg)
EigenvalueDecomposition(CVisDMatrix Arg)	Check for symmetry, then construct the eigenvalue decomposition

Method Summary

Modifier and Type	Method	Description
private void	cdiv(double xr, double xi, double yr, double yi)
CVisDMatrix	getD()	Return the block diagonal eigenvalue matrix
CDVector	getImagEigenvalues()	Return the imaginary parts of the eigenvalues
CDVector	getRealEigenvalues()
CDMatrix	getV()	Return the eigenvector matrix
private void	hqr2()
private void	orthes()
private void	tql2()
private void	tred2()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

n

private int n

Row and column dimension (square matrix).

issymmetric

private boolean issymmetric

Symmetry flag.

d

private double[] d

Arrays for internal storage of eigenvalues.

e

private double[] e

Arrays for internal storage of eigenvalues.

V

private double[][] V

Array for internal storage of eigenvectors.

H

private double[][] H

Array for internal storage of nonsymmetric Hessenberg form.

ort

private double[] ort

Working storage for nonsymmetric algorithm.

cdivr

private transient double cdivr

cdivi

private transient double cdivi

Constructor Detail

EigenvalueDecomposition

public EigenvalueDecomposition(double[][] Arg)

EigenvalueDecomposition

public EigenvalueDecomposition(CVisDMatrix Arg)

Check for symmetry, then construct the eigenvalue decomposition

Parameters:

A - Square matrix

Method Detail

tred2

private void tred2()

tql2

private void tql2()

orthes

private void orthes()

cdiv

private void cdiv(double xr,
                  double xi,
                  double yr,
                  double yi)

hqr2

private void hqr2()

getV

public CDMatrix getV()

Return the eigenvector matrix

Returns:

V

getRealEigenvalues

public CDVector getRealEigenvalues()

getImagEigenvalues

public CDVector getImagEigenvalues()

Return the imaginary parts of the eigenvalues

Returns:

imag(diag(D))

getD

public CVisDMatrix getD()

Return the block diagonal eigenvalue matrix

Returns:

D