Documentation of 'org.ejml.alg.block.decomposition.qr.QRDecompositionHouseholder_B64' Java class
QRDecompositionHouseholder_B64
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org.ejml.alg.block.decomposition.qr

Class 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 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.

      • 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 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 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.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.

        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.
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