|
||||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Objectorg.apache.mahout.math.solver.EigenDecomposition
public class EigenDecomposition
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().
Constructor Summary | |
---|---|
EigenDecomposition(Matrix x)
|
|
EigenDecomposition(Matrix x,
boolean isSymmetric)
|
Method Summary | |
---|---|
Matrix |
getD()
Return the block diagonal eigenvalue matrix |
Vector |
getImagEigenvalues()
Return the imaginary parts of the eigenvalues |
Vector |
getRealEigenvalues()
Return the real parts of the eigenvalues |
Matrix |
getV()
Return the eigenvector matrix |
Methods inherited from class java.lang.Object |
---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
---|
public EigenDecomposition(Matrix x)
public EigenDecomposition(Matrix x, boolean isSymmetric)
Method Detail |
---|
public Matrix getV()
public Vector getRealEigenvalues()
public Vector getImagEigenvalues()
public Matrix getD()
|
||||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |