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

Class QRColPivDecompositionHouseholderColumn_FDRM

java.lang.Object
org.ejml.dense.row.decomposition.qr.QRDecompositionHouseholderColumn_FDRM
org.ejml.dense.row.decomposition.qr.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>
@Generated("org.ejml.dense.row.decomposition.qr.QRColPivDecompositionHouseholderColumn_DDRM") 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 Details

    • pivots

      protected int[] pivots

    • normsCol

      protected float[] normsCol

    • singularThreshold

      protected float singularThreshold

    • rank

      protected int rank

  • Constructor Details

    • QRColPivDecompositionHouseholderColumn_FDRM

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

    • QRColPivDecompositionHouseholderColumn_FDRM

      public QRColPivDecompositionHouseholderColumn_FDRM()

  • Method Details

    • setSingularThreshold

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

    • setExpectedMaxSize

      public void setExpectedMaxSize(int numRows, int numCols)
      Overrides:
      setExpectedMaxSize in class QRDecompositionHouseholderColumn_FDRM

    • getQ

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