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

Class QRColPivDecompositionHouseholderColumn_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.qr.QRDecompositionHouseholderColumn_DDRM
org.ejml.dense.row.decomposition.qr.QRColPivDecompositionHouseholderColumn_DDRM
All Implemented Interfaces:
org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj>
public class QRColPivDecompositionHouseholderColumn_DDRM
extends QRDecompositionHouseholderColumn_DDRM
implements org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj>

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_DDRM 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

  • Constructor Details

  • Method Details

    • setSingularThreshold

      public void setSingularThreshold​(double threshold)
      Specified by:
      setSingularThreshold in interface org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj>

    • setExpectedMaxSize

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

    • getQ

      public org.ejml.data.DMatrixRMaj getQ​(@Nullable @Nullable org.ejml.data.DMatrixRMaj 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.DMatrixRMaj>
      Overrides:
      getQ in class QRDecompositionHouseholderColumn_DDRM
      Parameters:
      Q - The orthogonal Q matrix.

    • decompose

      public boolean decompose​(org.ejml.data.DMatrixRMaj 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.DMatrixRMaj>
      Overrides:
      decompose in class QRDecompositionHouseholderColumn_DDRM

    • 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.DMatrixRMaj>

    • getColPivots

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

    • getColPivotMatrix

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