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jmat.data.matrixDecompositions
Class EigenvalueDecomposition  

java.lang.Object
  jmat.data.matrixDecompositions.EigenvalueDecomposition

All Implemented Interfaces:

java.io.Serializable

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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().

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Field Summary
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

EigenvalueDecomposition(jmat.data.Matrix Arg)           Check for symmetry, then construct the eigenvalue decomposition

 

Method Summary
private  void	cdiv(double xr, double xi, double yr, double yi)
jmat.data.Matrix	getD_Imag()           Return the imaginary diagonal eigenvalue matrix
jmat.data.Matrix	getD_Real()           Return the real diagonal eigenvalue matrix
jmat.data.Matrix	getD()           Return the block diagonal eigenvalue matrix
double[]	getRealEigenvalues()
jmat.data.Matrix	getV()           Return the eigenvector matrix
private  void	hqr2()
boolean	isDReal()           Return the eigenvector matrix
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

H

private double[][] H

Array for internal storage of nonsymmetric Hessenberg form.

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V

private double[][] V

Array for internal storage of eigenvectors.

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d

private double[] d

Arrays for internal storage of eigenvalues.

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e

private double[] e

Arrays for internal storage of eigenvalues.

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ort

private double[] ort

Working storage for nonsymmetric algorithm.

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issymmetric

private boolean issymmetric

Symmetry flag.

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cdivi

private transient double cdivi

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cdivr

private transient double cdivr

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n

private int n

Row and column dimension (square matrix).

Constructor Detail

EigenvalueDecomposition

public EigenvalueDecomposition(jmat.data.Matrix Arg)

Check for symmetry, then construct the eigenvalue decomposition

Method Detail

getD

public jmat.data.Matrix getD()

Return the block diagonal eigenvalue matrix

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isDReal

public boolean isDReal()

Return the eigenvector matrix

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getD_Imag

public jmat.data.Matrix getD_Imag()

Return the imaginary diagonal eigenvalue matrix

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getD_Real

public jmat.data.Matrix getD_Real()

Return the real diagonal eigenvalue matrix

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getRealEigenvalues

public double[] getRealEigenvalues()

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getV

public jmat.data.Matrix getV()

Return the eigenvector matrix

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cdiv

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

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hqr2

private void hqr2()

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orthes

private void orthes()

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tql2

private void tql2()

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tred2

private void tred2()

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