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

Class 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

    • 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.

    • Field Detail

      • 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 Detail

      • EigenvalueDecomposition

        public EigenvalueDecomposition​(double[][] Arg)

      • EigenvalueDecomposition

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

    • Method Detail

      • 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