Class QRDecompositionHouseholder_MT_DDRB
 All Implemented Interfaces:
DecompositionInterface<DMatrixRBlock>
,QRDecomposition<DMatrixRBlock>
QR decomposition for DMatrixRBlock
using householder reflectors. The decomposition is
performed by computing a QR decomposition for each block column as is normally done, see QRDecompositionHouseholder_DDRM
.
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(:,ir to i) ) W=computeW( A(:,ir to i) ) A(:,i:n) = (I + W*Y^T)^T*A(:,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_MT_DDRB.computeW_Column(int, org.ejml.data.DSubmatrixD1, org.ejml.data.DSubmatrixD1, pabeles.concurrency.GrowArray<org.ejml.data.DGrowArray>, 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

Method Summary
Modifier and TypeMethodDescriptionvoid
Multiplies the provided matrix by Q using householder reflectors.void
applyQ
(DMatrixRBlock 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
Multiplies the provided matrix by Q^{T} using householder reflectors.boolean
decompose
(DMatrixRBlock orig) Computes the decomposition of the input matrix.getQ
(@Nullable DMatrixRBlock Q, boolean compact) Returns the Q matrix from the decomposition.getQR()
This is the input matrix after it has been overwritten with the decomposition.getR
(@Nullable DMatrixRBlock R, boolean compact) Returns the R matrix from the decomposition.static DMatrixRBlock
initializeQ
(@Nullable DMatrixRBlock Q, int numRows, int numCols, int blockLength, boolean compact) Sanity checks the input or declares a new matrix.boolean
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
A = (I + W Y^{T})^{T}A
A = A + Y (W^{T}A)
where A is a submatrix of the input matrix.

Constructor Details

QRDecompositionHouseholder_MT_DDRB
public QRDecompositionHouseholder_MT_DDRB()


Method Details

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
Description copied from interface:QRDecomposition
Returns the Q matrix from the decomposition. Should only be called after
DecompositionInterface.decompose(org.ejml.data.Matrix)
has been called. Specified by:
getQ
in interfaceQRDecomposition<DMatrixRBlock>
 Parameters:
Q
 (Input) Storage for Q. Reshaped to correct size automatically. If null a new matrix is created.compact
 If true an m by n matrix is created, otherwise n by n. Returns:
 The Q matrix.

initializeQ
public static DMatrixRBlock initializeQ(@Nullable @Nullable DMatrixRBlock 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
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
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:
isIdentity
 If B is an identity matrix.

applyQTran
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
Description copied from interface:QRDecomposition
Returns the R matrix from the decomposition. Should only be called after
DecompositionInterface.decompose(org.ejml.data.Matrix)
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.
 Specified by:
getR
in interfaceQRDecomposition<DMatrixRBlock>
 Parameters:
R
 (Input) Storage for R. Reshaped to correct size automatically. If null a new matrix is created.compact
 If true only the upper triangular elements are set Returns:
 The R matrix.

decompose
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 functionDecompositionInterface.inputModified()
will return true and the matrix should not be modified until the decomposition is no longer needed. Specified by:
decompose
in interfaceDecompositionInterface<DMatrixRBlock>
 Parameters:
orig
 The matrix which is being decomposed. Modification is implementation dependent. Returns:
 Returns if it was able to decompose the matrix.

updateA
A = (I + W Y^{T})^{T}A
A = A + Y (W^{T}A)
where A is a submatrix of the input matrix. 
inputModified
public boolean inputModified()The input matrix is always modified. Specified by:
inputModified
in interfaceDecompositionInterface<DMatrixRBlock>
 Returns:
 Returns true since the input matrix is modified.
