Package org.ejml.dense.row.decomposition.qr

Class QRColPivDecompositionHouseholderColumn_FDRM

  • All Implemented Interfaces:
    org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.FMatrixRMaj>, org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.FMatrixRMaj>, org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.FMatrixRMaj>, org.ejml.interfaces.decomposition.QRPDecomposition_F32<org.ejml.data.FMatrixRMaj>
    public class QRColPivDecompositionHouseholderColumn_FDRM
extends QRDecompositionHouseholderColumn_FDRM
implements org.ejml.interfaces.decomposition.QRPDecomposition_F32<org.ejml.data.FMatrixRMaj>

    Performs QR decomposition with column pivoting. To prevent overflow/underflow the whole matrix is normalized by the max value, but columns are not normalized individually any more. To enable code reuse it extends QRDecompositionHouseholderColumn_FDRM and functions from that class are used whenever possible. Columns are transposed into single arrays, which allow for fast pivots.

    Decomposition: A*P = Q*R

    Based off the description in "Fundamentals of Matrix Computations", 2nd by David S. Watkins.

    • Field Detail

      • pivots

        protected int[] pivots

      • normsCol

        protected float[] normsCol

      • singularThreshold

        protected float singularThreshold

      • rank

        protected int rank

    • Constructor Detail

      • QRColPivDecompositionHouseholderColumn_FDRM

        public QRColPivDecompositionHouseholderColumn_FDRM​(float singularThreshold)
        Configure parameters.
        Parameters:
        singularThreshold - The singular threshold.

      • QRColPivDecompositionHouseholderColumn_FDRM

        public QRColPivDecompositionHouseholderColumn_FDRM()

    • Method Detail

      • setSingularThreshold

        public void setSingularThreshold​(float threshold)
        Specified by:
        setSingularThreshold in interface org.ejml.interfaces.decomposition.QRPDecomposition_F32<org.ejml.data.FMatrixRMaj>

      • getQ

        public org.ejml.data.FMatrixRMaj getQ​(org.ejml.data.FMatrixRMaj Q,
                                      boolean compact)
        Computes the Q matrix from the information stored in the QR matrix. This operation requires about 4(m2n-mn2+n3/3) flops.
        Specified by:
        getQ in interface org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.FMatrixRMaj>
        Overrides:
        getQ in class QRDecompositionHouseholderColumn_FDRM
        Parameters:
        Q - The orthogonal Q matrix.

      • decompose

        public boolean decompose​(org.ejml.data.FMatrixRMaj A)

        To decompose the matrix 'A' it must have full rank. 'A' is a 'm' by 'n' matrix. It requires about 2n*m2-2m2/3 flops.

        The matrix provided here can be of different dimension than the one specified in the constructor. It just has to be smaller than or equal to it.

        Specified by:
        decompose in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.FMatrixRMaj>
        Overrides:
        decompose in class QRDecompositionHouseholderColumn_FDRM

      • setupPivotInfo

        protected void setupPivotInfo()
        Sets the initial pivot ordering and compute the F-norm squared for each column

      • updateNorms

        protected void updateNorms​(int j)
        Performs an efficient update of each columns' norm

      • swapColumns

        protected void swapColumns​(int j)
        Finds the column with the largest normal and makes that the first column
        Parameters:
        j - Current column being inspected

      • householderPivot

        protected boolean householderPivot​(int j)

        Computes the householder vector "u" for the first column of submatrix j. The already computed norm is used and checks to see if the matrix is singular at this point.

        Q = I - γuuT

        This function finds the values of 'u' and 'γ'.

        Parameters:
        j - Which submatrix to work off of.
        Returns:
        false if it is degenerate

      • getRank

        public int getRank()
        Specified by:
        getRank in interface org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.FMatrixRMaj>

      • getColPivots

        public int[] getColPivots()
        Specified by:
        getColPivots in interface org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.FMatrixRMaj>

      • getColPivotMatrix

        public org.ejml.data.FMatrixRMaj getColPivotMatrix​(org.ejml.data.FMatrixRMaj P)
        Specified by:
        getColPivotMatrix in interface org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.FMatrixRMaj>