org.ejml.alg.dense.decomposition.hessenberg

Class TridiagonalDecompositionHouseholder_D64

java.lang.Object

org.ejml.alg.dense.decomposition.hessenberg.TridiagonalDecompositionHouseholder_D64

All Implemented Interfaces:

org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DenseMatrix64F>, org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.DenseMatrix64F>

public class TridiagonalDecompositionHouseholder_D64
extends java.lang.Object
implements org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.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

Constructor Summary

Constructors

Constructor and Description
TridiagonalDecompositionHouseholder_D64()

Method Summary

Modifier and Type	Method and Description
boolean	decompose(org.ejml.data.DenseMatrix64F A) Decomposes the provided symmetric matrix.
void	getDiagonal(double[] diag, double[] off)
org.ejml.data.DenseMatrix64F	getQ(org.ejml.data.DenseMatrix64F Q, boolean transposed) An orthogonal matrix that has the following property: T = QTAQ
org.ejml.data.DenseMatrix64F	getQT() Returns the internal matrix where the decomposed results are stored.
org.ejml.data.DenseMatrix64F	getT(org.ejml.data.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(org.ejml.data.DenseMatrix64F A) If needed declares and sets up internal data structures.
boolean	inputModified()

Methods inherited from class java.lang.Object

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

Constructor Detail

TridiagonalDecompositionHouseholder_D64

public TridiagonalDecompositionHouseholder_D64()

Method Detail

getQT

public org.ejml.data.DenseMatrix64F getQT()

Returns the internal matrix where the decomposed results are stored.

Returns:

getDiagonal

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

Specified by:

getDiagonal in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.DenseMatrix64F>

getT

public org.ejml.data.DenseMatrix64F getT(org.ejml.data.DenseMatrix64F T)

Extracts the tridiagonal matrix found in the decomposition.

Specified by:

getT in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.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 org.ejml.data.DenseMatrix64F getQ(org.ejml.data.DenseMatrix64F Q,
                                         boolean transposed)

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

Specified by:

getQ in interface org.ejml.interfaces.decomposition.TridiagonalSimilarDecomposition<org.ejml.data.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(org.ejml.data.DenseMatrix64F A)

Decomposes the provided symmetric matrix.

Specified by:

decompose in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DenseMatrix64F>

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(org.ejml.data.DenseMatrix64F A)

If needed declares and sets up internal data structures.

Parameters:

A - Matrix being decomposed.

inputModified

public boolean inputModified()

Specified by:

inputModified in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DenseMatrix64F>