Package org.biojava.nbio.structure.jama

Class EigenvalueDecomposition

java.lang.Object
org.biojava.nbio.structure.jama.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:

  • Constructor Details

    • EigenvalueDecomposition

      public EigenvalueDecomposition(Matrix Arg)
      Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.
      Parameters:
      Arg - Square matrix

  • Method Details

    • 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