Parallel Colt 0.7.2

cern.colt.matrix.tfloat.algo.decomposition
Class FloatEigenvalueDecomposition

java.lang.Object
  extended by cern.colt.matrix.tfloat.algo.decomposition.FloatEigenvalueDecomposition
All Implemented Interfaces:
Serializable

public class FloatEigenvalueDecomposition
extends Object
implements 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
FloatEigenvalueDecomposition(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
 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
 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

FloatEigenvalueDecomposition

public FloatEigenvalueDecomposition(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:
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 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 Object

Parallel Colt 0.7.2

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