javax.robotics.vecmath.jama
Class EigenvalueDecomposition

java.lang.Object
  javax.robotics.vecmath.jama.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(double[][] Arg, int dim)
Check for symmetry, then construct the eigenvalue decomposition

Method Summary

double[][]	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
double[][]	getV() Return the eigenvector matrix

Methods inherited from class java.lang.Object

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

Constructor Detail

EigenvalueDecomposition

public EigenvalueDecomposition(double[][] Arg,
                               int dim)

Check for symmetry, then construct the eigenvalue decomposition

Parameters:

dim - number rows or columns of matrix

Arg - Square matrix

Method Detail

getV

public final double[][] getV()

Return the eigenvector matrix

Returns:

V

getRealEigenvalues

public final double[] getRealEigenvalues()

Return the real parts of the eigenvalues

Returns:

real(diag(D))

getImagEigenvalues

public final double[] getImagEigenvalues()

Return the imaginary parts of the eigenvalues

Returns:

imag(diag(D))

getD

public double[][] getD()

Return the block diagonal eigenvalue matrix

Returns:

D