|
||||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Object de.lmu.ifi.dbs.elki.math.linearalgebra.EigenvalueDecomposition
public class EigenvalueDecomposition
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.timesTranspose(V)) and V.timesTranspose(V) 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().
Field Summary | |
---|---|
private double |
cdivi
|
private double |
cdivr
|
private double[] |
d
Arrays for internal storage of eigenvalues. |
private double[] |
e
Arrays for internal storage of eigenvalues. |
private double[][] |
H
Array for internal storage of nonsymmetric Hessenberg form. |
private boolean |
issymmetric
Symmetry flag. |
private int |
n
Row and column dimension (square matrix). |
private double[] |
ort
Working storage for nonsymmetric algorithm. |
private static long |
serialVersionUID
Serial version |
private double[][] |
V
Array for internal storage of eigenvectors. |
Constructor Summary | |
---|---|
EigenvalueDecomposition(Matrix Arg)
Check for symmetry, then construct the eigenvalue decomposition |
Method Summary | |
---|---|
private void |
cdiv(double xr,
double xi,
double yr,
double yi)
|
Matrix |
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 |
Matrix |
getV()
Return the eigenvector matrix |
private void |
hqr2()
|
private void |
orthes()
|
private void |
tql2()
|
private void |
tred2()
|
Methods inherited from class java.lang.Object |
---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
---|
private static final long serialVersionUID
private int n
private boolean issymmetric
private double[] d
private double[] e
private double[][] V
private double[][] H
private double[] ort
private transient double cdivr
private transient double cdivi
Constructor Detail |
---|
public EigenvalueDecomposition(Matrix Arg)
Arg
- Square matrixMethod Detail |
---|
private void tred2()
private void tql2()
private void orthes()
private void cdiv(double xr, double xi, double yr, double yi)
private void hqr2()
public Matrix getV()
public double[] getRealEigenvalues()
public double[] getImagEigenvalues()
public Matrix getD()
|
|
|||||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |