Package org.ejml.dense.row.decomposition.bidiagonal

Class BidiagonalDecompositionTall_DDRM

java.lang.Object

org.ejml.dense.row.decomposition.bidiagonal.BidiagonalDecompositionTall_DDRM

All Implemented Interfaces:

BidiagonalDecomposition<DMatrixRMaj>, BidiagonalDecomposition_F64<DMatrixRMaj>, DecompositionInterface<DMatrixRMaj>

public class BidiagonalDecompositionTall_DDRM
extends Object
implements BidiagonalDecomposition_F64<DMatrixRMaj>

BidiagonalDecomposition_F64 specifically designed for tall matrices. First step is to perform QR decomposition on the input matrix. Then R is decomposed using a bidiagonal decomposition. By performing the bidiagonal decomposition on the smaller matrix computations can be saved if m/n > 5/3 and if U is NOT needed.

A = [Q₁ Q₂][U1 0; 0 I] [B1;0] V^T
U=[Q₁*U1 Q₂]
B=[B1;0]
A = U*B*V^T

A QRP decomposition is used internally. That decomposition relies an a fixed threshold for selecting singular values and is known to be less stable than SVD. There is the potential for a degregation of stability by using BidiagonalDecompositionTall instead of BidiagonalDecomposition_F64. A few simple tests have shown that loss in stability to be insignificant.

See page 404 in "Fundamentals of Matrix Computations", 2nd by David S. Watkins.

Constructor Summary

Constructors

Constructor	Description
BidiagonalDecompositionTall_DDRM()

Method Summary

Modifier and Type	Method	Description
boolean	decompose(DMatrixRMaj orig)	Computes the decomposition of the input matrix.
DMatrixRMaj	getB(@Nullable DMatrixRMaj B, boolean compact)	Returns the bidiagonal matrix.
void	getDiagonal(double[] diag, double[] off)	Extracts the diagonal and off diagonal elements from the decomposition.
DMatrixRMaj	getU(@Nullable DMatrixRMaj U, boolean transpose, boolean compact)	Returns the orthogonal U matrix.
DMatrixRMaj	getV(@Nullable DMatrixRMaj V, boolean transpose, boolean compact)	Returns the orthogonal V matrix.
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

BidiagonalDecompositionTall_DDRM

public BidiagonalDecompositionTall_DDRM()

Method Details

getDiagonal

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

Description copied from interface: BidiagonalDecomposition_F64

Extracts the diagonal and off diagonal elements from the decomposition.

Specified by:

getDiagonal in interface BidiagonalDecomposition_F64<DMatrixRMaj>

Parameters:

diag - diagonal elements from B.

off - off diagonal elements form B.

getB

public DMatrixRMaj getB(@Nullable
 @Nullable DMatrixRMaj B,
 boolean compact)

Description copied from interface: BidiagonalDecomposition

Returns the bidiagonal matrix.

Specified by:

getB in interface BidiagonalDecomposition<DMatrixRMaj>

Parameters:

B - If not null the results are stored here, if null a new matrix is created.

Returns:

The bidiagonal matrix.

getU

public DMatrixRMaj getU(@Nullable
 @Nullable DMatrixRMaj U,
 boolean transpose,
 boolean compact)

Description copied from interface: BidiagonalDecomposition

Returns the orthogonal U matrix.

Specified by:

getU in interface BidiagonalDecomposition<DMatrixRMaj>

Parameters:

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

Returns:

The extracted Q matrix.

getV

public DMatrixRMaj getV(@Nullable
 @Nullable DMatrixRMaj V,
 boolean transpose,
 boolean compact)

Description copied from interface: BidiagonalDecomposition

Returns the orthogonal V matrix.

Specified by:

getV in interface BidiagonalDecomposition<DMatrixRMaj>

Parameters:

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

Returns:

The extracted Q matrix.

decompose

public boolean decompose(DMatrixRMaj 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<DMatrixRMaj>

Parameters:

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

Returns:

Returns if it was able to decompose the matrix.

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<DMatrixRMaj>

Returns:

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