Package org.flag4j.linalg.decompositions.hess

Class ComplexHess

java.lang.Object

org.flag4j.linalg.decompositions.unitary.UnitaryDecomposition<CMatrix,CNumber[]>

org.flag4j.linalg.decompositions.unitary.ComplexUnitaryDecomposition

org.flag4j.linalg.decompositions.hess.ComplexHess

All Implemented Interfaces:

Decomposition<CMatrix>

public class ComplexHess
extends ComplexUnitaryDecomposition

Computes the Hessenburg decomposition of a complex dense square matrix. That is, for a square matrix A, computes the decomposition A=QHQ^H where Q is an orthogonal matrix and H is a matrix in upper Hessenburg form which is similar to A (i.e. has the same eigenvalues).

A matrix H is in upper Hessenburg form if it is nearly upper triangular. Specifically, if H has all zeros below the first sub-diagonal.

For example, the following matrix is in upper Hessenburg form where each x is a placeholder which may hold a different value:

     [[ x x x x x ]
      [ x x x x x ]
      [ 0 x x x x ]
      [ 0 0 x x x ]
      [ 0 0 0 x x ]]

Field Summary

Fields inherited from class org.flag4j.linalg.decompositions.unitary.ComplexUnitaryDecomposition

norm, normRe

Fields inherited from class org.flag4j.linalg.decompositions.unitary.UnitaryDecomposition

applyUpdate, householderVector, minAxisSize, numCols, numRows, qFactors, storeReflectors, subDiagonal, transformData, transformMatrix, workArray

Constructor Summary

Constructors

Constructor	Description
ComplexHess()	Creates a Hessenburg decomposer.
ComplexHess(boolean computeQ)	Creates a real unitary decomposer which will reduce the matrix to an upper quasi-triangular matrix which is has zeros below the specified sub-diagonal.

Method Summary

Modifier and Type	Method	Description
ComplexHess	decompose(CMatrix src)	Computes the QR decomposition of a real dense matrix.
CMatrix	getH()	Gets the upper Hessenburg matrix H from the Hessenburg decomposition.
CMatrix	getUpper()	Gets the upper Hessenburg matrix from the last decomposition.
protected CMatrix	initQ()	Creates and initializes Q to the appropriately sized identity matrix.

Methods inherited from class org.flag4j.linalg.decompositions.unitary.ComplexUnitaryDecomposition

computeHouseholder, computePhasedNorm, findMaxAndInit, getQ, getUpper, initWorkArrays, updateData

Methods inherited from class org.flag4j.linalg.decompositions.unitary.UnitaryDecomposition

decomposeBase, setUp

Methods inherited from class java.lang.Object

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

Constructor Details

ComplexHess

public ComplexHess()

Creates a Hessenburg decomposer. This decomposer will compute the Hessenburg decomposition for complex dense matrices.

ComplexHess

public ComplexHess(boolean computeQ)

Creates a real unitary decomposer which will reduce the matrix to an upper quasi-triangular matrix which is has zeros below the specified sub-diagonal.

Method Details

decompose

public ComplexHess decompose(CMatrix src)

Computes the QR decomposition of a real dense matrix.

Parameters:

src - The source matrix to decompose.

Returns:

A reference to this decomposer.

initQ

protected CMatrix initQ()

Creates and initializes Q to the appropriately sized identity matrix.

Specified by:

initQ in class UnitaryDecomposition<CMatrix,CNumber[]>

Returns:

An identity matrix with the appropriate size.

getUpper

public CMatrix getUpper()

Gets the upper Hessenburg matrix from the last decomposition. Same as getH()

Specified by:

getUpper in class UnitaryDecomposition<CMatrix,CNumber[]>

Returns:

The upper Hessenburg matrix from the last decomposition.

getH

public CMatrix getH()

Gets the upper Hessenburg matrix H from the Hessenburg decomposition.

Returns:

The upper Hessenburg matrix H from the Hessenburg decomposition.