org.knime.base.util.math
Class EigenvalueDecomposition
java.lang.Object
org.knime.base.util.math.EigenvalueDecomposition
public class EigenvalueDecomposition
- extends Object
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().
Most of the code of this class is taken from the corresponding JMathTools
class and is under the BSD licence with the following required disclaimer:
Copyright (c) 2003, Yann RICHET All rights reserved.
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Constructor Summary |
EigenvalueDecomposition(double[][] arg)
Check for symmetry, then construct the eigenvalue decomposition. |
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
EigenvalueDecomposition
public EigenvalueDecomposition(double[][] arg)
- Check for symmetry, then construct the eigenvalue decomposition.
- Parameters:
arg
- Square matrix
isDReal
public boolean isDReal()
- Returns:
- the eigenvector matrix.
getV
public double[][] getV()
- Returns:
- the eigenvector matrix
getD
public double[][] getD()
- Returns:
- the block diagonal eigenvalue matrix
get1DRealD
public double[] get1DRealD()
- Returns:
- Real(D) the real diagonal eigenvalue matrix
get1DImagD
public double[] get1DImagD()
- Returns:
- Imag(D) the imaginary diagonal eigenvalue matrix
getRealD
public double[][] getRealD()
- Returns:
- Real(D) the real diagonal eigenvalue matrix
getImagD
public double[][] getImagD()
- Returns:
- Imag(D) the imaginary diagonal eigenvalue matrix
Copyright, 2003 - 2010. All rights reserved.
University of Konstanz, Germany.
Chair for Bioinformatics and Information Mining, Prof. Dr. Michael R. Berthold.
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