Package com.macrofocus.high_d.mds.pca

Class EigenvalueDecomposition

  • public class EigenvalueDecomposition
extends java.lang.Object
    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().

    • Constructor Summary

      Constructors 
      Constructor Description
      EigenvalueDecomposition​(PCAMatrix Arg)
      Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      PCAMatrix 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
      PCAMatrix 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​(PCAMatrix Arg)
        Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.
        Parameters:
        Arg - Square matrix

    • Method Detail

      • getV

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