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java.lang.Objectcern.colt.matrix.linalg.EigenvalueDecomposition
Eigenvalues and eigenvectors of a real matrix A.
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.mult(D.mult(transpose(V))) and V.mult(transpose(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.mult(V) equals V.mult(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon Algebra.cond(V).
| Constructor Summary | |
| EigenvalueDecomposition(DoubleMatrix2D A)Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object. | |
| Method Summary | |
|  DoubleMatrix2D | getD()Returns the block diagonal eigenvalue matrix, D. | 
|  DoubleMatrix1D | getImagEigenvalues()Returns the imaginary parts of the eigenvalues. | 
|  DoubleMatrix1D | getRealEigenvalues()Returns the real parts of the eigenvalues. | 
|  DoubleMatrix2D | getV()Returns the eigenvector matrix, V | 
|  String | toString()Returns a String with (propertyName, propertyValue) pairs. | 
| Methods inherited from class java.lang.Object | 
| equals, getClass, hashCode, notify, notifyAll, wait, wait, wait | 
| Constructor Detail | 
public EigenvalueDecomposition(DoubleMatrix2D A)
A - A square matrix.
IllegalArgumentException - if A is not square.| Method Detail | 
public DoubleMatrix2D getD()
public DoubleMatrix1D getImagEigenvalues()
public DoubleMatrix1D getRealEigenvalues()
public DoubleMatrix2D getV()
public String toString()
rank : 3 trace : 0
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