org.graffiti.plugins.algorithms.HighDimEmbed
Class EigenvalueDecomposition

java.lang.Object
  extended by org.graffiti.plugins.algorithms.HighDimEmbed.EigenvalueDecomposition
All Implemented Interfaces:
Serializable

public class EigenvalueDecomposition
extends Object
implements Serializable

Eigenvalues and eigenvectors of a real matrix.

If A is symmetric, then A = VDV' 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 + imu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that AV = VD, 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 = VDinverse(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
 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:
Arg - Square matrix
Method Detail

getD

public Matrix getD()
Return the block diagonal eigenvalue matrix

Returns:
D

getImagEigenvalues

public double[] getImagEigenvalues()
Return the imaginary parts of the eigenvalues

Returns:
imag(diag(D))

getRealEigenvalues

public double[] getRealEigenvalues()
Return the real parts of the eigenvalues

Returns:
real(diag(D))

getV

public Matrix getV()
Return the eigenvector matrix

Returns:
V


Generated at 2012-05-30 11:01:25 PM CEST