Package org.ejml.dense.row.decomposition.hessenberg

Class TridiagonalDecompositionHouseholder_DDRM

java.lang.Object

org.ejml.dense.row.decomposition.hessenberg.TridiagonalDecompositionHouseholder_DDRM

All Implemented Interfaces:

DecompositionInterface<DMatrixRMaj>, TridiagonalSimilarDecomposition<DMatrixRMaj>, TridiagonalSimilarDecomposition_F64<DMatrixRMaj>

Direct Known Subclasses:

TridiagonalDecompositionHouseholder_MT_DDRM

public class TridiagonalDecompositionHouseholder_DDRM
extends Object
implements TridiagonalSimilarDecomposition_F64<DMatrixRMaj>

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

Field Summary

Fields

Modifier and Type	Field	Description
protected double[]	b
protected double[]	gammas
protected int	N
protected DMatrixRMaj	QT	Only the upper right triangle is used.
protected double[]	w

Constructor Summary

Constructors

Constructor	Description
TridiagonalDecompositionHouseholder_DDRM()

Method Summary

Modifier and Type	Method	Description
boolean	decompose(DMatrixRMaj A)	Decomposes the provided symmetric matrix.
void	getDiagonal(double[] diag, double[] off)	Extracts the diagonal and off diagonal elements of the decomposed tridiagonal matrix.
DMatrixRMaj	getQ(@Nullable DMatrixRMaj Q, boolean transposed)	An orthogonal matrix that has the following property: T = QTAQ
DMatrixRMaj	getQT()	Returns the internal matrix where the decomposed results are stored.
DMatrixRMaj	getT(@Nullable DMatrixRMaj 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(DMatrixRMaj A)	If needed declares and sets up internal data structures.
boolean	inputModified()	Checks if the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix) is modified during the decomposition process.
protected void	rank1UpdateMultL(DMatrixRMaj A, double gamma, int colA0, int w0, int w1)
protected void	rank1UpdateMultR(DMatrixRMaj A, double gamma, int colA0, int w0, int w1)

Methods inherited from class java.lang.Object

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

Field Details

QT

protected DMatrixRMaj QT

Only the upper right triangle is used. The Tridiagonal portion stores the tridiagonal matrix. The rows store householder vectors.

N

protected int N

w

protected double[] w

gammas

protected double[] gammas

b

protected double[] b

Constructor Details

TridiagonalDecompositionHouseholder_DDRM

public TridiagonalDecompositionHouseholder_DDRM()

Method Details

getQT

public DMatrixRMaj getQT()

Returns the internal matrix where the decomposed results are stored.

getDiagonal

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

Description copied from interface: TridiagonalSimilarDecomposition_F64

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_F64<DMatrixRMaj>

Parameters:

diag - Diagonal elements. Modified.

off - off diagonal elements. Modified.

getT

public DMatrixRMaj getT(@Nullable
 @Nullable DMatrixRMaj T)

Extracts the tridiagonal matrix found in the decomposition.

Specified by:

getT in interface TridiagonalSimilarDecomposition<DMatrixRMaj>

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 DMatrixRMaj getQ(@Nullable
 @Nullable DMatrixRMaj Q,
 boolean transposed)

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

Specified by:

getQ in interface TridiagonalSimilarDecomposition<DMatrixRMaj>

Parameters:

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

transposed - If true then the transpose (real) or conjugate transpose (complex) of Q is returned.

Returns:

The extracted Q matrix.

decompose

public boolean decompose(DMatrixRMaj A)

Decomposes the provided symmetric matrix.

Specified by:

decompose in interface DecompositionInterface<DMatrixRMaj>

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(DMatrixRMaj A)

If needed declares and sets up internal data structures.

Parameters:

A - Matrix being decomposed.

rank1UpdateMultL

protected void rank1UpdateMultL(DMatrixRMaj A,
 double gamma,
 int colA0,
 int w0,
 int w1)

rank1UpdateMultR

protected void rank1UpdateMultR(DMatrixRMaj A,
 double gamma,
 int colA0,
 int w0,
 int w1)

inputModified

public boolean inputModified()

Description copied from interface: DecompositionInterface

Checks if the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix) is modified during the decomposition process.

Specified by:

inputModified in interface DecompositionInterface<DMatrixRMaj>

Returns:

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