edu.mines.jtk.la
Class DMatrixEvd

java.lang.Object
  edu.mines.jtk.la.DMatrixEvd

public class DMatrixEvd
extends java.lang.Object

Eigenvalue and eigenvector decomposition of a square matrix A.

If A is symmetric, then A = V*D*V' where the matrix of eigenvalues D is diagonal and the matrix of eigenvectors V is orthogonal (V*V' = I).

If A is not symmetric, then the eigenvalue matrix D is block diagonal with real eigenvalues in 1-by-1 blocks and any complex eigenvalues lambda + i*mu in 2-by-2 block [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D. The matrix V may be badly conditioned or even singular, so the validity of the equation A = V*D*inverse(V) depends on the condition number of V.

This class was adapted from the package Jama, which was developed by Joe Hicklin, Cleve Moler, and Peter Webb of The MathWorks, Inc., and by Ronald Boisvert, Bruce Miller, Roldan Pozo, and Karin Remington of the National Institue of Standards and Technology.

Version:

2005.12.01

Author:

Dave Hale, Colorado School of Mines

Constructor Summary

DMatrixEvd(DMatrix a)
Constructs an eigenvalue decomposition for the specified square matrix.

Method Summary

DMatrix	getD() Gets the block diagonal matrix of eigenvalues D.
double[]	getImagEigenvalues() Gets the imaginary parts of the eigenvalues
double[]	getRealEigenvalues() Gets the real parts of the eigenvalues.
DMatrix	getV() Gets the matrix of eigenvectors V.

Methods inherited from class java.lang.Object

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

Constructor Detail

DMatrixEvd

public DMatrixEvd(DMatrix a)

Constructs an eigenvalue decomposition for the specified square matrix.

Parameters:

a - the square matrix

Method Detail

getV

public DMatrix getV()

Gets the matrix of eigenvectors V.

Returns:

the matrix V.

getD

public DMatrix getD()

Gets the block diagonal matrix of eigenvalues D.

Returns:

the matrix D.

getRealEigenvalues

public double[] getRealEigenvalues()

Gets the real parts of the eigenvalues.

Returns:

array of real parts = real(diag(D)).

getImagEigenvalues

public double[] getImagEigenvalues()

Gets the imaginary parts of the eigenvalues

Returns:

array of imaginary parts = imag(diag(D))