Package org.ejml.dense.block.decomposition.qr

Class QRDecompositionHouseholder_DDRB

java.lang.Object
org.ejml.dense.block.decomposition.qr.QRDecompositionHouseholder_DDRB
All Implemented Interfaces:
DecompositionInterface<DMatrixRBlock>, QRDecomposition<DMatrixRBlock>
public class QRDecompositionHouseholder_DDRB extends Object implements 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(:,i-r to i) )
 W=computeW( A(:,i-r 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_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 Details

    • QRDecompositionHouseholder_DDRB

      public QRDecompositionHouseholder_DDRB()

  • Method Details

    • getQR

      public DMatrixRBlock 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 DMatrixRBlock getQ(@Nullable @Nullable DMatrixRBlock 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.Matrix) has been called.

      Specified by:
      getQ in interface QRDecomposition<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

      public void applyQ(DMatrixRBlock 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(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.
      Parameters:
      isIdentity - If B is an identity matrix.

    • applyQTran

      public void applyQTran(DMatrixRBlock B)

      Multiplies the provided matrix by QT 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 DMatrixRBlock getR(@Nullable @Nullable DMatrixRBlock 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.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 interface QRDecomposition<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

      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.

    • updateA

      protected void updateA(DSubmatrixD1 A)

      A = (I + W YT)TA
      A = A + Y (WTA)

      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<DMatrixRBlock>
      Returns:
      Returns true since the input matrix is modified.