org.knime.base.util.math
Class EigenvalueDecomposition

java.lang.Object
  extended by 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. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of JMATHTOOLS nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.


Constructor Summary
EigenvalueDecomposition(double[][] arg)
          Check for symmetry, then construct the eigenvalue decomposition.
 
Method Summary
 double[] get1DImagD()
           
 double[] get1DRealD()
           
 double[][] getD()
           
 double[][] getImagD()
           
 double[][] getRealD()
           
 double[][] getV()
           
 boolean isDReal()
           
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

EigenvalueDecomposition

public EigenvalueDecomposition(double[][] arg)
Check for symmetry, then construct the eigenvalue decomposition.

Parameters:
arg - Square matrix
Method Detail

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


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University of Konstanz, Germany.
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