Package cern.colt.matrix.linalg

Class EigenvalueDecomposition

java.lang.Object
cern.colt.matrix.linalg.EigenvalueDecomposition
All Implemented Interfaces:
Serializable
public class EigenvalueDecomposition extends Object implements Serializable
Eigenvalues and eigenvectors of a real matrix A.

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.mult(D.mult(transpose(V))) and V.mult(transpose(V)) 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.mult(V) equals V.mult(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon Algebra.cond(V).

See Also:

  • Constructor Details

    • EigenvalueDecomposition

      public EigenvalueDecomposition(DoubleMatrix2D A)
      Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object. Checks for symmetry, then constructs the eigenvalue decomposition.
      Parameters:
      A - A square matrix.
      Throws:
      IllegalArgumentException - if A is not square.

  • Method Details

    • getD

      public DoubleMatrix2D getD()
      Returns the block diagonal eigenvalue matrix, D.
      Returns:
      D

    • getImagEigenvalues

      public DoubleMatrix1D getImagEigenvalues()
      Returns the imaginary parts of the eigenvalues.
      Returns:
      imag(diag(D))

    • getRealEigenvalues

      public DoubleMatrix1D getRealEigenvalues()
      Returns the real parts of the eigenvalues.
      Returns:
      real(diag(D))

    • getV

      public DoubleMatrix2D getV()
      Returns the eigenvector matrix, V
      Returns:
      V

    • toString

      public String toString()
      Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example, 
      rank          : 3
trace         : 0
      Overrides:
      toString in class Object