org.mathIT.algebra

Class EigenvalueDecomposition

java.lang.Object

org.mathIT.algebra.EigenvalueDecomposition

public class EigenvalueDecomposition
extends Object

This class computes the eigenvalues and eigenvectors of a real square 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.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 (1×1) blocks and any complex eigenvalues, λ + i⋅μ, in (2×2) blocks, [λ, μ; -μ, λ]. 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⋅V^-1 depends upon V.cond().

This class is a slight modification of the Java class by the JAMA Java Matrix Package by NIST, see http://math.nist.gov/javanumerics/jama/

Author:

JAMA, Andreas de Vries

Constructor Summary

Constructors

Constructor and Description
EigenvalueDecomposition(Matrix A) Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.

Method Summary

Modifier and Type	Method and Description
Matrix	getD() Returns the block diagonal eigenvalue matrix
double[]	getImagEigenvalues() Return the imaginary parts of the eigenvalues
double[]	getRealEigenvalues() Return the real parts of the eigenvalues
Matrix	getV() Return a matrix with the real parts of the eigenvectors as columns

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

EigenvalueDecomposition

public EigenvalueDecomposition(Matrix A)

Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.

Parameters:

A - square matrix

Throws:

IllegalArgumentException - if the matrix M is not square

Method Detail

getV

public Matrix getV()

Return a matrix with the real parts of the eigenvectors as columns

Returns:

the eigenvector matrix

getRealEigenvalues

public double[] getRealEigenvalues()

Return the real parts of the eigenvalues

Returns:

the real parts of the eigenvalues

getImagEigenvalues

public double[] getImagEigenvalues()

Return the imaginary parts of the eigenvalues

Returns:

the imaginary parts of the eigenvalues

getD

public Matrix getD()

Returns the block diagonal eigenvalue matrix

Returns:

the block diagonal eigenvalue matrix D