Package etomica.eigenstuff

Class MyEigenvalueDecomposition

java.lang.Object

etomica.eigenstuff.MyEigenvalueDecomposition

All Implemented Interfaces:

java.io.Serializable

public class MyEigenvalueDecomposition
extends java.lang.Object
implements java.io.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:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
MyEigenvalueDecomposition(int n, double[][] input)	Check for symmetry, then construct the eigenvalue decomposition

Method Summary

Modifier and Type	Method	Description
double[][]	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
double[][]	getV()	Return the eigenvector matrix
protected void	setArray(double[][] input)

Methods inherited from class java.lang.Object

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

Constructor Detail

MyEigenvalueDecomposition

public MyEigenvalueDecomposition(int n,
                                 double[][] input)

Check for symmetry, then construct the eigenvalue decomposition

Parameters:

A - Square matrix

Method Detail

setArray

protected void setArray(double[][] input)

getV

public double[][] 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 double[][] getD()

Return the block diagonal eigenvalue matrix

Returns:

D