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

Class TridiagonalDecompositionHouseholder_FDRM

java.lang.Object

org.ejml.dense.row.decomposition.hessenberg.TridiagonalDecompositionHouseholder_FDRM

All Implemented Interfaces:

DecompositionInterface<FMatrixRMaj>, TridiagonalSimilarDecomposition<FMatrixRMaj>, TridiagonalSimilarDecomposition_F32<FMatrixRMaj>

Direct Known Subclasses:

TridiagonalDecompositionHouseholder_MT_FDRM

@Generated("org.ejml.dense.row.decomposition.hessenberg.TridiagonalDecompositionHouseholder_DDRM")
public class TridiagonalDecompositionHouseholder_FDRM
extends Object
implements TridiagonalSimilarDecomposition_F32<FMatrixRMaj>

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 float[]	b
protected float[]	gammas
protected int	N
protected FMatrixRMaj	QT	Only the upper right triangle is used.
protected float[]	w

Constructor Summary

Constructors

Constructor	Description
TridiagonalDecompositionHouseholder_FDRM()

Method Summary

Modifier and Type	Method	Description
boolean	decompose(FMatrixRMaj A)	Decomposes the provided symmetric matrix.
void	getDiagonal(float[] diag, float[] off)	Extracts the diagonal and off diagonal elements of the decomposed tridiagonal matrix.
FMatrixRMaj	getQ(@Nullable FMatrixRMaj Q, boolean transposed)	An orthogonal matrix that has the following property: T = QTAQ
FMatrixRMaj	getQT()	Returns the internal matrix where the decomposed results are stored.
FMatrixRMaj	getT(@Nullable FMatrixRMaj T)	Extracts the tridiagonal matrix found in the decomposition.
void	householderSymmetric(int row, float gamma)	Performs the householder operations on left and right and side of the matrix.
void	init(FMatrixRMaj 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(FMatrixRMaj A, float gamma, int colA0, int w0, int w1)
protected void	rank1UpdateMultR(FMatrixRMaj A, float 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 FMatrixRMaj 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 float[] w

gammas

protected float[] gammas

b

protected float[] b

Constructor Details

TridiagonalDecompositionHouseholder_FDRM

public TridiagonalDecompositionHouseholder_FDRM()

Method Details

getQT

public FMatrixRMaj getQT()

Returns the internal matrix where the decomposed results are stored.

getDiagonal

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

Description copied from interface: TridiagonalSimilarDecomposition_F32

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_F32<FMatrixRMaj>

Parameters:

diag - Diagonal elements. Modified.

off - off diagonal elements. Modified.

getT

public FMatrixRMaj getT(@Nullable
 @Nullable FMatrixRMaj T)

Extracts the tridiagonal matrix found in the decomposition.

Specified by:

getT in interface TridiagonalSimilarDecomposition<FMatrixRMaj>

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

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

Specified by:

getQ in interface TridiagonalSimilarDecomposition<FMatrixRMaj>

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(FMatrixRMaj A)

Decomposes the provided symmetric matrix.

Specified by:

decompose in interface DecompositionInterface<FMatrixRMaj>

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,
 float 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(FMatrixRMaj A)

If needed declares and sets up internal data structures.

Parameters:

A - Matrix being decomposed.

rank1UpdateMultL

protected void rank1UpdateMultL(FMatrixRMaj A,
 float gamma,
 int colA0,
 int w0,
 int w1)

rank1UpdateMultR

protected void rank1UpdateMultR(FMatrixRMaj A,
 float 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<FMatrixRMaj>

Returns:

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