mikera.matrixx.decompose.impl.hessenberg

Class TridiagonalDecompositionHouseholder

java.lang.Object

mikera.matrixx.decompose.impl.hessenberg.TridiagonalDecompositionHouseholder

public class TridiagonalDecompositionHouseholder
extends Object

Performs a TridiagonalSimilarDecomposition similar tridiagonal decomposition on a square symmetric input matrix. Householder vectors perform the similar operation and the symmetry is taken advantage of for good performance.

Finds the decomposition of a matrix in the form of:

A = O*T*O^T

where A is a symmetric m by m matrix, O is an orthogonal matrix, and T is a tridiagonal matrix.

This implementation is based off of the algorithm described in:

David S. Watkins, "Fundamentals of Matrix Computations," Second Edition. Page 349-355

Author:

Peter Abeles

Constructor Summary

Constructors

Constructor and Description
TridiagonalDecompositionHouseholder()

Method Summary

Modifier and Type	Method and Description
boolean	decompose(AMatrix A) Decomposes the provided symmetric matrix.
void	getDiagonal(double[] diag, double[] off)
AMatrix	getQ(boolean transposed) An orthogonal matrix that has the following property: T = QTAQ
AMatrix	getQT() Returns the internal matrix where the decomposed results are stored.
AMatrix	getT() Extracts the tridiagonal matrix found in the decomposition.
void	householderSymmetric(int row, double gamma) Performs the householder operations on left and right and side of the matrix.
void	init(AMatrix A) If needed declares and sets up internal data structures.

Methods inherited from class java.lang.Object

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

Constructor Detail

TridiagonalDecompositionHouseholder

public TridiagonalDecompositionHouseholder()

Method Detail

getQT

public AMatrix getQT()

Returns the internal matrix where the decomposed results are stored.

Returns:

getDiagonal

public void getDiagonal(double[] diag,
                        double[] off)

getT

public AMatrix getT()

Extracts the tridiagonal matrix found in the decomposition.

Returns:

The extracted T matrix.

getQ

public AMatrix getQ(boolean transposed)

An orthogonal matrix that has the following property: T = Q^TAQ

Returns:

The extracted Q matrix.

decompose

public boolean decompose(AMatrix A)

Decomposes the provided symmetric matrix.

Parameters:

A - Symmetric matrix that is going to be decomposed. Not modified.

householderSymmetric

public void householderSymmetric(int row,
                                 double gamma)

Performs the householder operations on left and right and side of the matrix. Q^TAQ

Parameters:

row - Specifies the submatrix.

gamma - The gamma for the householder operation

init

public void init(AMatrix A)

If needed declares and sets up internal data structures.

Parameters:

A - Matrix being decomposed.