cusack.hcg.matrix

Class EigenvalueDecomposition

java.lang.Object

cusack.hcg.matrix.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

Constructors

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

Method Summary

Modifier and Type	Method and Description
Matrix	getD() Return the block diagonal eigenvalue matrix
double[]	getImagEigenvalues() Return the imaginary parts of the eigenvalues
double[]	getRealEigenvalues() Return the real parts of the eigenvalues
Matrix	getV() Return the eigenvector matrix

Methods inherited from class java.lang.Object

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

Constructor Detail

EigenvalueDecomposition

public EigenvalueDecomposition(Matrix Arg)

Check for symmetry, then construct the eigenvalue decomposition

Parameters:

A - Square matrix

Method Detail

getV

public Matrix getV()

Return the eigenvector matrix

Returns:

V

getRealEigenvalues

public double[] getRealEigenvalues()

Return the real parts of the eigenvalues

Returns:

real(diag(D))

getImagEigenvalues

public double[] getImagEigenvalues()

Return the imaginary parts of the eigenvalues

Returns:

imag(diag(D))

getD

public Matrix getD()

Return the block diagonal eigenvalue matrix

Returns:

D