org.jmat.data.matrixDecompositions
Class EigenvalueDecomposition

java.lang.Object
  |
  +--org.jmat.data.matrixDecompositions.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

Constructor Summary

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

Method Summary

Matrix	getD() Return the block diagonal eigenvalue matrix
Matrix	getImagD() Return the imaginary diagonal eigenvalue matrix
Matrix	getRealD() Return the real diagonal eigenvalue matrix
Matrix	getV() Return the eigenvector matrix
boolean	isDReal() Return the eigenvector matrix
void	toCommandLine(java.lang.String title)

Methods inherited from class java.lang.Object

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

Constructor Detail

EigenvalueDecomposition

public EigenvalueDecomposition(Matrix Arg)

Check for symmetry, then construct the eigenvalue decomposition

Parameters:

Arg - Square matrix

Method Detail

isDReal

public boolean isDReal()

Return the eigenvector matrix

Returns:

V

getV

public Matrix getV()

Return the eigenvector matrix

Returns:

V

getD

public Matrix getD()

Return the block diagonal eigenvalue matrix

Returns:

D

getRealD

public Matrix getRealD()

Return the real diagonal eigenvalue matrix

Returns:

Real(D)

getImagD

public Matrix getImagD()

Return the imaginary diagonal eigenvalue matrix

Returns:

Imag(D)

toCommandLine

public void toCommandLine(java.lang.String title)