Class QRDecompositionHouseholder_ZDRM

All Implemented Interfaces:
DecompositionInterface<ZMatrixRMaj>, QRDecomposition<ZMatrixRMaj>

public class QRDecompositionHouseholder_ZDRM extends Object implements QRDecomposition<ZMatrixRMaj>

This variation of complex 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*uH) 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 written 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 Details

    • QR

      protected ZMatrixRMaj 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^H).
    • 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
    • tau

      protected Complex_F64 tau
    • error

      protected boolean error
  • Constructor Details

    • QRDecompositionHouseholder_ZDRM

      public QRDecompositionHouseholder_ZDRM()
  • Method Details

    • setExpectedMaxSize

      public void setExpectedMaxSize(int numRows, int numCols)
    • getQR

      public ZMatrixRMaj 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.
      The combined Q R matrix.
    • getQ

      public ZMatrixRMaj getQ(@Nullable @Nullable ZMatrixRMaj 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 QRDecomposition<ZMatrixRMaj>
      Q - The orthogonal Q matrix.
      compact - If true an m by n matrix is created, otherwise n by n.
      The Q matrix.
    • getR

      public ZMatrixRMaj getR(@Nullable @Nullable ZMatrixRMaj R, boolean compact)
      Returns an upper triangular matrix which is the R in the QR decomposition.
      Specified by:
      getR in interface QRDecomposition<ZMatrixRMaj>
      R - An upper triangular matrix.
      compact - If true only the upper triangular elements are set
      The R matrix.
    • decompose

      public boolean decompose(ZMatrixRMaj 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 DecompositionInterface<ZMatrixRMaj>
      A - The matrix which is being decomposed. Modification is implementation dependent.
      Returns if it was able to decompose the matrix.
    • inputModified

      public boolean inputModified()
      Description copied from interface: DecompositionInterface
      Checks if the input matrix to DecompositionInterface.decompose( is modified during the decomposition process.
      Specified by:
      inputModified in interface DecompositionInterface<ZMatrixRMaj>
      true if the input matrix to decompose() is modified.
    • 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 - γuuH

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

      j - Which submatrix to work off of.
    • commonSetup

      protected void commonSetup(ZMatrixRMaj A)
      This function performs sanity check on the input for decompose and sets up the QR matrix.
    • getGammas

      public double[] getGammas()