Package org.ejml.dense.row.decompose.hessenberg

Class HessenbergSimilarDecomposition_ZDRM

java.lang.Object

org.ejml.dense.row.decompose.hessenberg.HessenbergSimilarDecomposition_ZDRM

All Implemented Interfaces:

DecompositionInterface<ZMatrixRMaj>

public class HessenbergSimilarDecomposition_ZDRM
extends Object
implements DecompositionInterface<ZMatrixRMaj>

Complex Hessenberg decomposition. It find matrices O and P such that:

A = OPO^H

where A is an m by m matrix, O is an orthogonal matrix, and P 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.

Constructor Summary

Constructors

Constructor	Description
HessenbergSimilarDecomposition_ZDRM()
HessenbergSimilarDecomposition_ZDRM(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(ZMatrixRMaj A)	Computes the decomposition of the provided matrix.
double[]	getGammas()
ZMatrixRMaj	getH(@Nullable ZMatrixRMaj H)	An upper Hessenberg matrix from the decomposition.
ZMatrixRMaj	getQ(@Nullable ZMatrixRMaj Q)	An orthogonal matrix that has the following property: H = QTAQ
ZMatrixRMaj	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.

Methods inherited from class java.lang.Object

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

Constructor Details

HessenbergSimilarDecomposition_ZDRM

public HessenbergSimilarDecomposition_ZDRM(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_ZDRM

public HessenbergSimilarDecomposition_ZDRM()

Method Details

decompose

public boolean decompose(ZMatrixRMaj 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<ZMatrixRMaj>

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<ZMatrixRMaj>

Returns:

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

getQH

public ZMatrixRMaj getQH()

The raw QH matrix that is stored internally.

Returns:

QH matrix.

getH

public ZMatrixRMaj getH(@Nullable
 @Nullable ZMatrixRMaj 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 ZMatrixRMaj getQ(@Nullable
 @Nullable ZMatrixRMaj 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.

getGammas

public double[] getGammas()