Module flag4j

Package org.flag4j.linalg.decompositions.hess

Class RealHess

java.lang.Object

org.flag4j.linalg.decompositions.unitary.UnitaryDecomposition<Matrix,double[]>

org.flag4j.linalg.decompositions.unitary.RealUnitaryDecomposition

org.flag4j.linalg.decompositions.hess.RealHess

All Implemented Interfaces:

Decomposition<Matrix>

Direct Known Subclasses:

SymmHess

public class RealHess
extends RealUnitaryDecomposition

Computes the Hessenburg decomposition of a real dense square matrix. That is, for a square matrix A, computes the decomposition A=QHQ^T 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' 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.RealUnitaryDecomposition

currentFactor, norm, shift

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
RealHess()	Creates a real Hessenburg decomposer which will reduce the matrix to an upper quasi-triangular matrix which is has zeros below the first sub-diagonal.
RealHess(boolean computeQ)	Creates a real Hessenburg decomposer which will reduce the matrix to an upper quasi-triangular matrix which is has zeros below the first sub-diagonal.

Method Summary

Modifier and Type	Method	Description
RealHess	decompose(Matrix src)	Applies decomposition to the source matrix.
Matrix	getH()	Gets the upper Hessenburg matrix H from the Hessenburg decomposition.
Matrix	getUpper()	Gets the upper Hessenburg matrix from the last decomposition.
protected Matrix	initQ()	Creates and initializes Q to the appropriately sized identity matrix.

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

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

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

decomposeUnitary, setUp

Methods inherited from class java.lang.Object

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

Constructor Details

RealHess

public RealHess()

Creates a real Hessenburg decomposer which will reduce the matrix to an upper quasi-triangular matrix which is has zeros below the first sub-diagonal. That is, reduce to an upper Hessenburg matrix.

By default, the orthogonal matrix will be computed. To specify if the orthogonal matrix should be computed, use RealHess(boolean).

See Also:

• RealHess(boolean)

RealHess

public RealHess(boolean computeQ)

Creates a real Hessenburg decomposer which will reduce the matrix to an upper quasi-triangular matrix which is has zeros below the first sub-diagonal. That is, reduce to an upper Hessenburg matrix.

Parameters:

computeQ - Flag indicating if the orthogonal matrix in the Hessenburg decomposition should be computed. If it is not needed, setting this to false may yield a slight increase in efficiency.

See Also:

• RealHess()

Method Details

decompose

public RealHess decompose(Matrix src)

Applies decomposition to the source matrix. Note, the computation of the orthogonal matrix Q in the decomposition is deferred until RealUnitaryDecomposition.getQ() is explicitly called. This allows for efficient decompositions when Q is not needed.

Parameters:

src - The source matrix to decompose.

Returns:

A reference to this decomposer.

Throws:

LinearAlgebraException - If src is not a square matrix.

initQ

protected Matrix initQ()

Creates and initializes Q to the appropriately sized identity matrix.

Specified by:

initQ in class UnitaryDecomposition<Matrix,double[]>

Returns:

An identity matrix with the appropriate size.

getUpper

public Matrix getUpper()

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

Specified by:

getUpper in class UnitaryDecomposition<Matrix,double[]>

Returns:

The upper Hessenburg matrix from the last decomposition.

getH

public Matrix getH()

Gets the upper Hessenburg matrix H from the Hessenburg decomposition.

Returns:

The upper Hessenburg matrix H from the Hessenburg decomposition.