Package gov.nih.mipav.view.renderer.WildMagic.AAM

Class EigenvalueDecomposition

java.lang.Object
gov.nih.mipav.view.renderer.WildMagic.AAM.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 = 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:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private double
    cdivi
     
    private double
    cdivr
     
    private double[]
    d
    Arrays for internal storage of eigenvalues.
    private double[]
    e
    Arrays for internal storage of eigenvalues.
    private double[][]
    H
    Array for internal storage of nonsymmetric Hessenberg form.
    private boolean
    issymmetric
    Symmetry flag.
    private int
    n
    Row and column dimension (square matrix).
    private double[]
    ort
    Working storage for nonsymmetric algorithm.
    private double[][]
    V
    Array for internal storage of eigenvectors.

  • Constructor Summary

    Constructors
    Constructor
    Description
    EigenvalueDecomposition(double[][] Arg)
     
    EigenvalueDecomposition(CVisDMatrix Arg)
    Check for symmetry, then construct the eigenvalue decomposition

  • Method Summary

    Modifier and Type
    Method
    Description
    private void
    cdiv(double xr, double xi, double yr, double yi)
     
    CVisDMatrix
    getD()
    Return the block diagonal eigenvalue matrix
    CDVector
    getImagEigenvalues()
    Return the imaginary parts of the eigenvalues
    CDVector
    getRealEigenvalues()
     
    CDMatrix
    getV()
    Return the eigenvector matrix
    private void
    hqr2()
     
    private void
    orthes()
     
    private void
    tql2()
     
    private void
    tred2()
     

    Methods inherited from class java.lang.Object

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

  • Field Details

    • n

      private int n
      Row and column dimension (square matrix).

    • issymmetric

      private boolean issymmetric
      Symmetry flag.

    • d

      private double[] d
      Arrays for internal storage of eigenvalues.

    • e

      private double[] e
      Arrays for internal storage of eigenvalues.

    • V

      private double[][] V
      Array for internal storage of eigenvectors.

    • H

      private double[][] H
      Array for internal storage of nonsymmetric Hessenberg form.

    • ort

      private double[] ort
      Working storage for nonsymmetric algorithm.

    • cdivr

      private transient double cdivr

    • cdivi

      private transient double cdivi

  • Constructor Details

    • EigenvalueDecomposition

      public EigenvalueDecomposition(double[][] Arg)

    • EigenvalueDecomposition

      public EigenvalueDecomposition(CVisDMatrix Arg)
      Check for symmetry, then construct the eigenvalue decomposition
      Parameters:
      A - Square matrix

  • Method Details

    • tred2

      private void tred2()

    • tql2

      private void tql2()

    • orthes

      private void orthes()

    • cdiv

      private void cdiv(double xr, double xi, double yr, double yi)

    • hqr2

      private void hqr2()

    • getV

      public CDMatrix getV()
      Return the eigenvector matrix
      Returns:
      V

    • getRealEigenvalues

      public CDVector getRealEigenvalues()

    • getImagEigenvalues

      public CDVector getImagEigenvalues()
      Return the imaginary parts of the eigenvalues
      Returns:
      imag(diag(D))

    • getD

      public CVisDMatrix getD()
      Return the block diagonal eigenvalue matrix
      Returns:
      D