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java.lang.Object mpv2.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.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 | |
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EigenvalueDecomposition(JamaMatrix Arg)
Check for symmetry, then construct the eigenvalue decomposition Constructor returns a structure to access D and V. |
Method Summary | |
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JamaMatrix |
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 |
JamaMatrix |
getV()
Return the eigenvector matrix |
Methods inherited from class java.lang.Object |
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public EigenvalueDecomposition(JamaMatrix Arg)
Arg
- Square matrixMethod Detail |
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public JamaMatrix getV()
public double[] getRealEigenvalues()
public double[] getImagEigenvalues()
public JamaMatrix getD()
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