Package org.jmol.util

Class Eigen

java.lang.Object

org.jmol.util.Eigen

public class Eigen
extends java.lang.Object

Eigenvalues and eigenvectors of a real matrix. adapted by Bob Hanson from http://math.nist.gov/javanumerics/jama/ (public domain) output is as a set of double[n] columns, but for Jmol we use getEigenvectorsFloatTransformed to return them as a set of rows for easier use as A[0], A[1], etc.

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().

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
protected static class	Eigen.EigenSort	sort from smallest to largest

Constructor Summary

Constructors

Constructor	Description
Eigen(int n)

Method Summary

Modifier and Type	Method	Description
void	calc(double[][] A)	Check for symmetry, then construct the eigenvalue decomposition
double[]	getEigenvalues()
Vector3f[]	getEigenVectors3()
float[][]	getEigenvectorsFloatTransposed()	transpose V and turn into floats
static Quadric	getEllipsoid(Vector3f[] vectors, float[] lengths, boolean isThermal)
static Quadric	getEllipsoidDD(double[][] a)
double[]	getImagEigenvalues()	Return the imaginary parts of the eigenvalues
double[]	getRealEigenvalues()	Return the real parts of the eigenvalues
static void	getUnitVectors(double[][] m, Vector3f[] unitVectors, float[] lengths)
static Eigen	newM(double[][] m)

Methods inherited from class java.lang.Object

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

Constructor Detail

Eigen

public Eigen(int n)

Method Detail

newM

public static Eigen newM(double[][] m)

getUnitVectors

public static void getUnitVectors(double[][] m,
                                  Vector3f[] unitVectors,
                                  float[] lengths)

calc

public void calc(double[][] A)

Check for symmetry, then construct the eigenvalue decomposition

Parameters:

A - Square matrix

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))

getEigenvalues

public double[] getEigenvalues()

getEigenvectorsFloatTransposed

public float[][] getEigenvectorsFloatTransposed()

transpose V and turn into floats

Returns:

ROWS of eigenvectors f[0], f[1], f[2], etc.

getEigenVectors3

public Vector3f[] getEigenVectors3()

getEllipsoidDD

public static Quadric getEllipsoidDD(double[][] a)

getEllipsoid

public static Quadric getEllipsoid(Vector3f[] vectors,
                                   float[] lengths,
                                   boolean isThermal)