org.ejml.alg.block.decomposition.qr

Class QRDecompositionHouseholder_B64

java.lang.Object

org.ejml.alg.block.decomposition.qr.QRDecompositionHouseholder_B64

All Implemented Interfaces:

DecompositionInterface<BlockMatrix64F>, QRDecomposition<BlockMatrix64F>

public class QRDecompositionHouseholder_B64
extends java.lang.Object
implements QRDecomposition<BlockMatrix64F>

QR decomposition for BlockMatrix64F using householder reflectors. The decomposition is performed by computing a QR decomposition for each block column as is normally done, see QRDecompositionHouseholder_D64. The reflectors are then combined and applied to the remainder of the matrix. This process is repeated until all the block columns have been processed

The input matrix is modified and used to store the decomposition. Reflectors are stored in the lower triangle columns. The first element of the reflector is implicitly assumed to be one.

Each iteration can be sketched as follows:

 QR_Decomposition( A(:,i-r to i) )
 W=computeW( A(:,i-r to i) )
 A(:,i:n) = (I + W*YT)TA(:,i:n)
 

Where r is the block size, i is the submatrix being considered, A is the input matrix, Y is a matrix containing the reflectors just computed, and W is computed using BlockHouseHolder.computeW_Column(int, org.ejml.data.D1Submatrix64F, org.ejml.data.D1Submatrix64F, double[], double[], int).

Based upon "Block Householder QR Factorization" pg 255 in "Matrix Computations" 3rd Ed. 1996 by Gene H. Golub and Charles F. Van Loan.

Constructor Summary

Constructors

Constructor and Description
QRDecompositionHouseholder_B64()

Method Summary

Methods

Modifier and Type	Method and Description
void	applyQ(BlockMatrix64F B) Multiplies the provided matrix by Q using householder reflectors.
void	applyQ(BlockMatrix64F B, boolean isIdentity) Specialized version of applyQ() that allows the zeros in an identity matrix to be taken advantage of depending on if isIdentity is true or not.
void	applyQTran(BlockMatrix64F B) Multiplies the provided matrix by QT using householder reflectors.
boolean	decompose(BlockMatrix64F orig) Computes the decomposition of the input matrix.
BlockMatrix64F	getQ(BlockMatrix64F Q, boolean compact) Returns the Q matrix from the decomposition.
BlockMatrix64F	getQR() This is the input matrix after it has been overwritten with the decomposition.
BlockMatrix64F	getR(BlockMatrix64F R, boolean compact) Returns the R matrix from the decomposition.
static BlockMatrix64F	initializeQ(BlockMatrix64F Q, int numRows, int numCols, int blockLength, boolean compact) Sanity checks the input or declares a new matrix.
boolean	inputModified() The input matrix is always modified.
void	setSaveW(boolean saveW) Sets if it should internally save the W matrix before performing the decomposition.
protected void	updateA(D1Submatrix64F A) A = (I + W YT)TA A = A + Y (WTA) where A is a submatrix of the input matrix.

Methods inherited from class java.lang.Object

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

Constructor Detail

QRDecompositionHouseholder_B64

public QRDecompositionHouseholder_B64()

Method Detail

getQR

public BlockMatrix64F getQR()

This is the input matrix after it has been overwritten with the decomposition.

Returns:

Internal matrix used to store decomposition.

setSaveW

public void setSaveW(boolean saveW)

Sets if it should internally save the W matrix before performing the decomposition. Must be set before decomposition the matrix.

Saving W can result in about a 5% savings when solving systems around a height of 5k. The price is that it needs to save a matrix the size of the input matrix.

Parameters:

saveW - If the W matrix should be saved or not.

getQ

public BlockMatrix64F getQ(BlockMatrix64F Q,
                  boolean compact)

Description copied from interface: QRDecomposition

Returns the Q matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix64F) has been called.

If parameter Q is not null, then that matrix is used to store the Q matrix. Otherwise a new matrix is created.

Specified by:

getQ in interface QRDecomposition<BlockMatrix64F>

Parameters:

Q - If not null then the Q matrix is written to it. Modified.

compact - If true an m by n matrix is created, otherwise n by n.

Returns:

The Q matrix.

initializeQ

public static BlockMatrix64F initializeQ(BlockMatrix64F Q,
                         int numRows,
                         int numCols,
                         int blockLength,
                         boolean compact)

Sanity checks the input or declares a new matrix. Return matrix is an identity matrix.

applyQ

public void applyQ(BlockMatrix64F B)

Multiplies the provided matrix by Q using householder reflectors. This is more efficient that computing Q then applying it to the matrix.

B = Q * B

Parameters:

B - Matrix which Q is applied to. Modified.

applyQ

public void applyQ(BlockMatrix64F B,
          boolean isIdentity)

Specialized version of applyQ() that allows the zeros in an identity matrix to be taken advantage of depending on if isIdentity is true or not.

Parameters:

B -

isIdentity - If B is an identity matrix.

applyQTran

public void applyQTran(BlockMatrix64F B)

Multiplies the provided matrix by Q^T using householder reflectors. This is more efficient that computing Q then applying it to the matrix.

Q = Q*(I - γ W*Y^T)
QR = A => R = Q^T*A = (Q3^T * (Q2^T * (Q1^t * A)))

Parameters:

B - Matrix which Q is applied to. Modified.

getR

public BlockMatrix64F getR(BlockMatrix64F R,
                  boolean compact)

Description copied from interface: QRDecomposition

Returns the R matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix64F) has been.

If setZeros is true then an n × m matrix is required and all the elements are set. If setZeros is false then the matrix must be at least m × m and only the upper triangular elements are set.

If parameter R is not null, then that matrix is used to store the R matrix. Otherwise a new matrix is created.

Specified by:

getR in interface QRDecomposition<BlockMatrix64F>

Parameters:

R - If not null then the R matrix is written to it. Modified.

compact - If true only the upper triangular elements are set

Returns:

The R matrix.

decompose

public boolean decompose(BlockMatrix64F 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<BlockMatrix64F>

Parameters:

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

Returns:

Returns if it was able to decompose the matrix.

updateA

protected void updateA(D1Submatrix64F A)

A = (I + W Y^T)^TA
A = A + Y (W^TA)

where A is a submatrix of the input matrix.

inputModified

public boolean inputModified()

The input matrix is always modified.

Specified by:

inputModified in interface DecompositionInterface<BlockMatrix64F>

Returns:

Returns true since the input matrix is modified.