org.ejml.alg.dense.decompose.hessenberg

Class HessenbergSimilarDecomposition_CD64

java.lang.Object

org.ejml.alg.dense.decompose.hessenberg.HessenbergSimilarDecomposition_CD64

All Implemented Interfaces:

org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.CDenseMatrix64F>

public class HessenbergSimilarDecomposition_CD64
extends java.lang.Object
implements org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.CDenseMatrix64F>

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 and Description
HessenbergSimilarDecomposition_CD64()
HessenbergSimilarDecomposition_CD64(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 and Description
boolean	decompose(org.ejml.data.CDenseMatrix64F A) Computes the decomposition of the provided matrix.
double[]	getGammas()
org.ejml.data.CDenseMatrix64F	getH(org.ejml.data.CDenseMatrix64F H) An upper Hessenberg matrix from the decomposition.
org.ejml.data.CDenseMatrix64F	getQ(org.ejml.data.CDenseMatrix64F Q) An orthogonal matrix that has the following property: H = QTAQ
org.ejml.data.CDenseMatrix64F	getQH() The raw QH matrix that is stored internally.
boolean	inputModified()

Methods inherited from class java.lang.Object

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

Constructor Detail

HessenbergSimilarDecomposition_CD64

public HessenbergSimilarDecomposition_CD64(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_CD64

public HessenbergSimilarDecomposition_CD64()

Method Detail

decompose

public boolean decompose(org.ejml.data.CDenseMatrix64F A)

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

Specified by:

decompose in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.CDenseMatrix64F>

Parameters:

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

Returns:

If it detects any errors or not.

inputModified

public boolean inputModified()

Specified by:

inputModified in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.CDenseMatrix64F>

getQH

public org.ejml.data.CDenseMatrix64F getQH()

The raw QH matrix that is stored internally.

Returns:

QH matrix.

getH

public org.ejml.data.CDenseMatrix64F getH(org.ejml.data.CDenseMatrix64F 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 org.ejml.data.CDenseMatrix64F getQ(org.ejml.data.CDenseMatrix64F 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()