xal.tools.math.r3

Class R3x3EigenDecomposition

java.lang.Object

xal.tools.math.r3.R3x3EigenDecomposition

public class R3x3EigenDecomposition
extends java.lang.Object

Essentially this class is just a wrapper over the Jama matrix package class EigenvalueDecomposition. Thus, XAL can present a consistent interface in the event that Jama gets removed/replaced in the future.

If the matrix A is invertible it can be decomposed as

A = VDV^-1

where V is an invertible matrix in the special linear group SL(3) ⊂ R^3×3 and D is the the real matrix with 2×2 blocks consisting of the real and imaginary parts of the eigenvalues on the diagonal. (Each eigenvalue of matrix A is the diagonal of the Jacobi block.)

The columns of V are the eigenvectors of A in the sense that AV = VD. Note that the matrix V may be badly conditioned, or even singular, so that the above equation may not be valid.

Constructor Summary

Constructors

Constructor and Description
R3x3EigenDecomposition(R3x3 matTarget) Package constructor for R3x3JacobiDecomposition objects.

Method Summary

Modifier and Type	Method and Description
R3x3	getEigenvalueMatrix() Return the matrix D of eigenvalues in the decomposition.
R3x3	getEigenvectorMatrix() Get the matrix V of eigenvectors (columns) for the decomposition.
double[]	getImagEigenvalues() Get the imaginary parts of the eigenvalues.
double[]	getRealEigenvalues() Get the real part of the eigenvalues.

Methods inherited from class java.lang.Object

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

Constructor Detail

R3x3EigenDecomposition

public R3x3EigenDecomposition(R3x3 matTarget)
                       throws java.lang.IllegalArgumentException

Package constructor for R3x3JacobiDecomposition objects.

Parameters:

matTarget - target matrix to factorize

Throws:

java.lang.IllegalArgumentException - matrix is not symmetric or zero eigenvalue

Method Detail

getRealEigenvalues

public double[] getRealEigenvalues()

Get the real part of the eigenvalues.

getImagEigenvalues

public double[] getImagEigenvalues()

Get the imaginary parts of the eigenvalues.

getEigenvectorMatrix

public R3x3 getEigenvectorMatrix()

Get the matrix V of eigenvectors (columns) for the decomposition. Note that this matrix is the diagonalizing (in the Jacaobi sense) matrix for the target matrix A. If the target matrix A is symmetric then the returned matrix V will be in the special orthogonal group SO(3). Note that, in general, this matrix may be ill conditioned.

Returns:

diagonalizing matrix of A

getEigenvalueMatrix

public R3x3 getEigenvalueMatrix()

Return the matrix D of eigenvalues in the decomposition. Note that if target matrix A is symmetric then this matrix will be diagonal. Otherwise it will be block diagonal in general where the 2x2 blocks are composed of the real and imaginary parts of the eigenvalues as described in the class documentation.

Returns:

block diagonal matrix D of eigenvalues of A