EigenvalueDecomposition (original) (raw)

• java.lang.Object

• • weka.core.matrix.EigenvalueDecomposition

• All Implemented Interfaces:
  java.io.Serializable, RevisionHandler

public class EigenvalueDecomposition
extends java.lang.Object
implements java.io.Serializable, RevisionHandler
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().
Adapted from the JAMA package.
Version: Revision:1.4Revision: 1.4 Revision:1.4
Author:
The Mathworks and NIST, Fracpete (fracpete at waikato dot ac dot nz)
See Also:
Serialized Form

• • Constructor Summary

  Constructors

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

  • Method Summary

  All Methods Instance Methods Concrete Methods

  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
  java.lang.String	getRevision() Returns the revision string.
  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](../../../weka/core/matrix/Matrix.html "class in weka.core.matrix") Arg)  
     Check for symmetry, then construct the eigenvalue decomposition  
     Parameters:  
     `Arg` \- Square matrix  

  • Method Detail

    * #### getV  
    public [Matrix](../../../weka/core/matrix/Matrix.html "class in weka.core.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](../../../weka/core/matrix/Matrix.html "class in weka.core.matrix") getD()  
    Return the block diagonal eigenvalue matrix  
    Returns:  
    D  
    * #### getRevision  
    public java.lang.String getRevision()  
    Returns the revision string.  
    Specified by:  
    `[getRevision](../../../weka/core/RevisionHandler.html#getRevision--)` in interface `[RevisionHandler](../../../weka/core/RevisionHandler.html "interface in weka.core")`  
    Returns:  
    the revision