org.ejml.alg.dense.decomposition.hessenberg
Class TridiagonalDecompositionHouseholder

java.lang.Object
  org.ejml.alg.dense.decomposition.hessenberg.TridiagonalDecompositionHouseholder

All Implemented Interfaces:

DecompositionInterface<DenseMatrix64F>, TridiagonalSimilarDecomposition<DenseMatrix64F>

public class TridiagonalDecompositionHouseholder
extends Object
implements TridiagonalSimilarDecomposition<DenseMatrix64F>

Performs a 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

TridiagonalDecompositionHouseholder()

Method Summary

boolean	decompose(DenseMatrix64F A) Decomposes the provided symmetric matrix.
void	getDiagonal(double[] diag, double[] off) Extracts the diagonal and off diagonal elements of the decomposed tridiagonal matrix.
DenseMatrix64F	getQ(DenseMatrix64F Q, boolean transposed) An orthogonal matrix that has the following property: T = QTAQ
DenseMatrix64F	getQT() Returns the internal matrix where the decomposed results are stored.
DenseMatrix64F	getT(DenseMatrix64F T) 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(DenseMatrix64F A) If needed declares and sets up internal data structures.
boolean	inputModified() Is the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix64F) is modified during the decomposition process.

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 DenseMatrix64F getQT()

Returns the internal matrix where the decomposed results are stored.

Returns:

getDiagonal

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

Description copied from interface: TridiagonalSimilarDecomposition

Extracts the diagonal and off diagonal elements of the decomposed tridiagonal matrix. Since it is symmetric only one off diagonal array is returned.

Specified by:

getDiagonal in interface TridiagonalSimilarDecomposition<DenseMatrix64F>

Parameters:

diag - Diagonal elements. Modified.

off - off diagonal elements. Modified.

getT

public DenseMatrix64F getT(DenseMatrix64F T)

Extracts the tridiagonal matrix found in the decomposition.

Specified by:

getT in interface TridiagonalSimilarDecomposition<DenseMatrix64F>

Parameters:

T - If not null then the results will be stored here. Otherwise a new matrix will be created.

Returns:

The extracted T matrix.

getQ

public DenseMatrix64F getQ(DenseMatrix64F Q,
                           boolean transposed)

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

Specified by:

getQ in interface TridiagonalSimilarDecomposition<DenseMatrix64F>

Parameters:

Q - If not null then the results will be stored here. Otherwise a new matrix will be created.

Returns:

The extracted Q matrix.

decompose

public boolean decompose(DenseMatrix64F A)

Decomposes the provided symmetric matrix.

Specified by:

decompose in interface DecompositionInterface<DenseMatrix64F>

Parameters:

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

Returns:

Returns if it was able to decompose the matrix.

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(DenseMatrix64F A)

If needed declares and sets up internal data structures.

Parameters:

A - Matrix being decomposed.

inputModified

public boolean inputModified()

Description copied from interface: DecompositionInterface

Is the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix64F) is modified during the decomposition process.

Specified by:

inputModified in interface DecompositionInterface<DenseMatrix64F>

Returns:

true if the input matrix to decompose() is modified.