cern.colt.matrix.tfloat.algo.decomposition

Class DenseFloatEigenvalueDecomposition

java.lang.Object

cern.colt.matrix.tfloat.algo.decomposition.DenseFloatEigenvalueDecomposition

All Implemented Interfaces:

java.io.Serializable

public class DenseFloatEigenvalueDecomposition
extends java.lang.Object
implements java.io.Serializable

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).

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
DenseFloatEigenvalueDecomposition(FloatMatrix2D 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

Modifier and Type	Method and Description
FloatMatrix2D	getD() Returns the block diagonal eigenvalue matrix, D.
FloatMatrix1D	getImagEigenvalues() Returns the imaginary parts of the eigenvalues.
FloatMatrix1D	getRealEigenvalues() Returns the real parts of the eigenvalues.
FloatMatrix2D	getV() Returns the eigenvector matrix, V
java.lang.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

DenseFloatEigenvalueDecomposition

public DenseFloatEigenvalueDecomposition(FloatMatrix2D A)

Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object. Checks for symmetry, then constructs the eigenvalue decomposition.

Parameters:

A - A square matrix.

Throws:

java.lang.IllegalArgumentException - if A is not square.

Method Detail

getD

public FloatMatrix2D getD()

Returns the block diagonal eigenvalue matrix, D.

Returns:

D

getImagEigenvalues

public FloatMatrix1D getImagEigenvalues()

Returns the imaginary parts of the eigenvalues.

Returns:

imag(diag(D))

getRealEigenvalues

public FloatMatrix1D getRealEigenvalues()

Returns the real parts of the eigenvalues.

Returns:

real(diag(D))

getV

public FloatMatrix2D getV()

Returns the eigenvector matrix, V

Returns:

V

toString

public java.lang.String toString()

Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,

         rank          : 3
         trace         : 0
 
 

Overrides:

toString in class java.lang.Object