Package org.ejml.dense.block.decomposition.hessenberg

Class TridiagonalDecompositionHouseholder_DDRB

java.lang.Object

org.ejml.dense.block.decomposition.hessenberg.TridiagonalDecompositionHouseholder_DDRB

All Implemented Interfaces:

DecompositionInterface<DMatrixRBlock>, TridiagonalSimilarDecomposition<DMatrixRBlock>, TridiagonalSimilarDecomposition_F64<DMatrixRBlock>

public class TridiagonalDecompositionHouseholder_DDRB
extends Object
implements TridiagonalSimilarDecomposition_F64<DMatrixRBlock>

Tridiagonal similar decomposition for block matrices. Orthogonal matrices are computed using householder vectors.

Based off algorithm in section 2 of J. J. Dongarra, D. C. Sorensen, S. J. Hammarling, "Block Reduction of Matrices to Condensed Forms for Eigenvalue Computations" Journal of Computations and Applied Mathematics 27 (1989) 215-227

Computations of Householder reflectors has been modified from what is presented in that paper to how it is performed in "Fundamentals of Matrix Computations" 2nd ed. by David S. Watkins.

Field Summary

Fields

Modifier and Type	Field	Description
protected DMatrixRBlock	A
protected double[]	gammas
protected DMatrixRBlock	tmp
protected DMatrixRBlock	V
protected DMatrixRMaj	zerosM

Constructor Summary

Constructors

Constructor	Description
TridiagonalDecompositionHouseholder_DDRB()

Method Summary

Modifier and Type	Method	Description
boolean	decompose(DMatrixRBlock orig)	Computes the decomposition of the input matrix.
void	getDiagonal(double[] diag, double[] off)	Extracts the diagonal and off diagonal elements of the decomposed tridiagonal matrix.
DMatrixRBlock	getQ(@Nullable DMatrixRBlock Q, boolean transposed)	An orthogonal matrix that has the following property: T = QHAQ
DMatrixRBlock	getT(@Nullable DMatrixRBlock T)	Extracts the tridiagonal matrix found in the decomposition.
boolean	inputModified()	Checks if the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix) is modified during the decomposition process.
static void	multPlusTransA(int blockLength, DSubmatrixD1 A, DSubmatrixD1 B, DSubmatrixD1 C)	C = C + A^T*B

Methods inherited from class java.lang.Object

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

Field Details

A

protected DMatrixRBlock A

V

protected DMatrixRBlock V

tmp

protected DMatrixRBlock tmp

gammas

protected double[] gammas

zerosM

protected DMatrixRMaj zerosM

Constructor Details

TridiagonalDecompositionHouseholder_DDRB

public TridiagonalDecompositionHouseholder_DDRB()

Method Details

getT

public DMatrixRBlock getT(@Nullable
 @Nullable DMatrixRBlock T)

Description copied from interface: TridiagonalSimilarDecomposition

Extracts the tridiagonal matrix found in the decomposition.

Specified by:

getT in interface TridiagonalSimilarDecomposition<DMatrixRBlock>

Parameters:

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

Returns:

The extracted T matrix.

getQ

public DMatrixRBlock getQ(@Nullable
 @Nullable DMatrixRBlock Q,
 boolean transposed)

Description copied from interface: TridiagonalSimilarDecomposition

An orthogonal matrix that has the following property: T = Q^HAQ

Specified by:

getQ in interface TridiagonalSimilarDecomposition<DMatrixRBlock>

Parameters:

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

transposed - If true then the transpose (real) or conjugate transpose (complex) of Q is returned.

Returns:

The extracted Q matrix.

getDiagonal

public void getDiagonal(double[] diag,
 double[] off)

Description copied from interface: TridiagonalSimilarDecomposition_F64

Extracts the diagonal and off diagonal elements of the decomposed tridiagonal matrix. Since it is symmetric only one off diagonal array is returned.

Specified by:

getDiagonal in interface TridiagonalSimilarDecomposition_F64<DMatrixRBlock>

Parameters:

diag - Diagonal elements. Modified.

off - off diagonal elements. Modified.

decompose

public boolean decompose(DMatrixRBlock orig)

Description copied from interface: DecompositionInterface

Computes the decomposition of the input matrix. Depending on the implementation the input matrix might be stored internally or modified. If it is modified then the function DecompositionInterface.inputModified() will return true and the matrix should not be modified until the decomposition is no longer needed.

Specified by:

decompose in interface DecompositionInterface<DMatrixRBlock>

Parameters:

orig - The matrix which is being decomposed. Modification is implementation dependent.

Returns:

Returns if it was able to decompose the matrix.

multPlusTransA

public static void multPlusTransA(int blockLength,
 DSubmatrixD1 A,
 DSubmatrixD1 B,
 DSubmatrixD1 C)

C = C + A^T*B

Parameters:

A - row block vector

B - row block vector

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<DMatrixRBlock>

Returns:

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