mikera.matrixx.decompose.impl.eigen

Class SymmetricQRAlgorithmDecomposition

java.lang.Object

mikera.matrixx.decompose.impl.eigen.SymmetricQRAlgorithmDecomposition

public class SymmetricQRAlgorithmDecomposition
extends Object

Computes the eigenvalues and eigenvectors of a real symmetric matrix using the symmetric implicit QR algorithm. Inside each iteration a QR decomposition of A_i-p_iI is implicitly computed.

This implementation is based on the algorithm is sketched out in:
David S. Watkins, "Fundamentals of Matrix Computations," Second Edition. page 377-385

Author:

Peter Abeles

Constructor Summary

Constructors

Constructor and Description
SymmetricQRAlgorithmDecomposition(boolean computeVectors)
SymmetricQRAlgorithmDecomposition(TridiagonalDecompositionHouseholder decomp, boolean computeVectors)

Method Summary

Modifier and Type	Method and Description
EigenResult	decompose(AMatrix orig) Decomposes the matrix using the QR algorithm.
Vector2	getEigenvalue(int index)
AVector	getEigenVector(int index)
int	getNumberOfEigenvalues()
void	setComputeVectorsWithValues(boolean computeVectorsWithValues)
void	setMaxIterations(int max) Used to limit the number of internal QR iterations that the QR algorithm performs.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SymmetricQRAlgorithmDecomposition

public SymmetricQRAlgorithmDecomposition(TridiagonalDecompositionHouseholder decomp,
                                         boolean computeVectors)

SymmetricQRAlgorithmDecomposition

public SymmetricQRAlgorithmDecomposition(boolean computeVectors)

Method Detail

setComputeVectorsWithValues

public void setComputeVectorsWithValues(boolean computeVectorsWithValues)

setMaxIterations

public void setMaxIterations(int max)

Used to limit the number of internal QR iterations that the QR algorithm performs. 20 should be enough for most applications.

Parameters:

max - The maximum number of QR iterations it will perform.

getNumberOfEigenvalues

public int getNumberOfEigenvalues()

getEigenvalue

public Vector2 getEigenvalue(int index)

getEigenVector

public AVector getEigenVector(int index)

decompose

public EigenResult decompose(AMatrix orig)

Decomposes the matrix using the QR algorithm. Care was taken to minimize unnecessary memory copying and cache skipping.

Parameters:

orig - The matrix which is being decomposed. Not modified.

Returns:

true if it decomposed the matrix or false if an error was detected. This will not catch all errors.