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

Class QRDecompositionHouseholder_DDRM

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

This variation of QR decomposition uses reflections to compute the Q matrix. Each reflection uses a householder operations, hence its name. To provide a meaningful solution the original matrix must have full rank. This is intended for processing of small to medium matrices.

Both Q and R are stored in the same m by n matrix. Q is not stored directly, instead the u from Qk=(I-γ*u*uT) is stored. Decomposition requires about 2n*m2-2m2/3 flops.

See the QR reflections algorithm described in:
David S. Watkins, "Fundamentals of Matrix Computations" 2nd Edition, 2002

For the most part this is a straight forward implementation. To improve performance on large matrices a column is writen to an array and the order of some of the loops has been changed. This will degrade performance noticeably on small matrices. Since it is unlikely that the QR decomposition would be a bottle neck when small matrices are involved only one implementation is provided.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected double[]
    dataQR
     
    protected boolean
    error
     
    protected double
    gamma
     
    protected double[]
    gammas
     
    protected int
    minLength
     
    protected int
    numCols
     
    protected int
    numRows
     
    protected org.ejml.data.DMatrixRMaj
    QR
    Where the Q and R matrices are stored.
    protected double
    tau
     
    protected double[]
    u
     
    protected double[]
    v
     

  • Constructor Summary

    Constructors
    Constructor
    Description
    QRDecompositionHouseholder_DDRM()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    protected void
    commonSetup(org.ejml.data.DMatrixRMaj A)
    This function performs sanity check on the input for decompose and sets up the QR matrix.
    boolean
    decompose(org.ejml.data.DMatrixRMaj A)
    In order to decompose the matrix 'A' it must have full rank.
    double[]
    getGammas()
     
    org.ejml.data.DMatrixRMaj
    getQ(@Nullable org.ejml.data.DMatrixRMaj Q, boolean compact)
    Computes the Q matrix from the imformation stored in the QR matrix.
    org.ejml.data.DMatrixRMaj
    getQR()
    Returns a single matrix which contains the combined values of Q and R.
    org.ejml.data.DMatrixRMaj
    getR(@Nullable org.ejml.data.DMatrixRMaj R, boolean compact)
    Returns an upper triangular matrix which is the R in the QR decomposition.
    protected void
    householder(int j)
    Computes the householder vector "u" for the first column of submatrix j.
    boolean
    inputModified()
     
    void
    setExpectedMaxSize(int numRows, int numCols)
     
    protected void
    updateA(int w)
    Takes the results from the householder computation and updates the 'A' matrix.

    A = (I - γ*u*uT)A

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • QR

      protected org.ejml.data.DMatrixRMaj QR
      Where the Q and R matrices are stored. R is stored in the upper triangular portion and Q on the lower bit. Lower columns are where u is stored. Q_k = (I - gamma_k*u_k*u_k^T).

    • u

      protected double[] u

    • v

      protected double[] v

    • numCols

      protected int numCols

    • numRows

      protected int numRows

    • minLength

      protected int minLength

    • dataQR

      protected double[] dataQR

    • gammas

      protected double[] gammas

    • gamma

      protected double gamma

    • tau

      protected double tau

    • error

      protected boolean error

  • Constructor Details

    • QRDecompositionHouseholder_DDRM

      public QRDecompositionHouseholder_DDRM()

  • Method Details

    • setExpectedMaxSize

      public void setExpectedMaxSize(int numRows, int numCols)

    • getQR

      public org.ejml.data.DMatrixRMaj getQR()
      Returns a single matrix which contains the combined values of Q and R. This is possible since Q is symmetric and R is upper triangular.
      Returns:
      The combined Q R matrix.

    • getQ

      public org.ejml.data.DMatrixRMaj getQ(@Nullable @Nullable org.ejml.data.DMatrixRMaj Q, boolean compact)
      Computes the Q matrix from the imformation 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>
      Parameters:
      Q - The orthogonal Q matrix.

    • getR

      public org.ejml.data.DMatrixRMaj getR(@Nullable @Nullable org.ejml.data.DMatrixRMaj R, boolean compact)
      Returns an upper triangular matrix which is the R in the QR decomposition.
      Specified by:
      getR in interface org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DMatrixRMaj>
      Parameters:
      R - An upper triangular matrix.

    • decompose

      public boolean decompose(org.ejml.data.DMatrixRMaj A)

      In order 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>

    • inputModified

      public boolean inputModified()
      Specified by:
      inputModified in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>

    • householder

      protected void householder(int j)

      Computes the householder vector "u" for the first column of submatrix j. Note this is a specialized householder for this problem. There is some protection against overflow and underflow.

      Q = I - γuuT

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

      Parameters:
      j - Which submatrix to work off of.

    • updateA

      protected void updateA(int w)

      Takes the results from the householder computation and updates the 'A' matrix.

      A = (I - γ*u*uT)A

      Parameters:
      w - The submatrix.

    • commonSetup

      protected void commonSetup(org.ejml.data.DMatrixRMaj A)
      This function performs sanity check on the input for decompose and sets up the QR matrix.

    • getGammas

      public double[] getGammas()