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:

Serialized Form

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.

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