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

Class HessenbergSimilarDecomposition_DDRM

java.lang.Object

org.ejml.dense.row.decomposition.hessenberg.HessenbergSimilarDecomposition_DDRM

All Implemented Interfaces:

DecompositionInterface<DMatrixRMaj>

Direct Known Subclasses:

HessenbergSimilarDecomposition_MT_DDRM

public class HessenbergSimilarDecomposition_DDRM
extends Object
implements DecompositionInterface<DMatrixRMaj>

Finds the decomposition of a matrix in the form of:

A = OHO^T

where A is an m by m matrix, O is an orthogonal matrix, and H is an upper Hessenberg matrix.

A matrix is upper Hessenberg if a^ij = 0 for all i > j+1. For example, the following matrix is upper Hessenberg.

WRITE IT OUT USING A TABLE

This decomposition is primarily used as a step for computing the eigenvalue decomposition of a matrix. The basic algorithm comes from David S. Watkins, "Fundamentals of MatrixComputations" Second Edition.

Field Summary

Fields

Modifier and Type	Field	Description
protected double[]	b
protected double[]	u

Constructor Summary

Constructors

Constructor	Description
HessenbergSimilarDecomposition_DDRM()
HessenbergSimilarDecomposition_DDRM(int initialSize)	Creates a decomposition that won't need to allocate new memory if it is passed matrices up to the specified size.

Method Summary

Modifier and Type	Method	Description
boolean	decompose(DMatrixRMaj A)	Computes the decomposition of the provided matrix.
double[]	getGammas()
DMatrixRMaj	getH(@Nullable DMatrixRMaj H)	An upper Hessenberg matrix from the decomposition.
DMatrixRMaj	getQ(@Nullable DMatrixRMaj Q)	An orthogonal matrix that has the following property: H = QTAQ
DMatrixRMaj	getQH()	The raw QH matrix that is stored internally.
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

b

protected double[] b

u

protected double[] u

Constructor Details

HessenbergSimilarDecomposition_DDRM

public HessenbergSimilarDecomposition_DDRM(int initialSize)

Creates a decomposition that won't need to allocate new memory if it is passed matrices up to the specified size.

Parameters:

initialSize - Expected size of the matrices it will decompose.

HessenbergSimilarDecomposition_DDRM

public HessenbergSimilarDecomposition_DDRM()

Method Details

decompose

public boolean decompose(DMatrixRMaj A)

Computes the decomposition of the provided matrix. If no errors are detected then true is returned, false otherwise.

Specified by:

decompose in interface DecompositionInterface<DMatrixRMaj>

Parameters:

A - The matrix that is being decomposed. Not modified.

Returns:

If it detects any errors or not.

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.

getQH

public DMatrixRMaj getQH()

The raw QH matrix that is stored internally.

Returns:

QH matrix.

getH

public DMatrixRMaj getH(@Nullable
 @Nullable DMatrixRMaj H)

An upper Hessenberg matrix from the decomposition.

Parameters:

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

Returns:

The extracted H matrix.

getQ

public DMatrixRMaj getQ(@Nullable
 @Nullable DMatrixRMaj Q)

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

Parameters:

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

Returns:

The extracted Q matrix.

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)

getGammas

public double[] getGammas()