Jama
Class EigenvalueDecomposition

java.lang.Object
  |
  +--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(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
, 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:
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