Class QRDecompositionHouseholderColumn_ZDRM

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

public class QRDecompositionHouseholderColumn_ZDRM extends Object implements QRDecomposition<ZMatrixRMaj>

Householder QR decomposition is rich in operations along the columns of the matrix. This can be taken advantage of by solving for the Q matrix in a column major format to reduce the number of CPU cache misses and the number of copies that are performed.

See Also:
  • Field Details

    • dataQR

      protected double[][] dataQR
      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).
    • v

      protected double[] v
    • numCols

      protected int numCols
    • numRows

      protected int numRows
    • minLength

      protected int minLength
    • gammas

      protected double[] gammas
    • gamma

      protected double gamma
    • tau

      protected Complex_F64 tau
    • error

      protected boolean error
  • Constructor Details

    • QRDecompositionHouseholderColumn_ZDRM

      public QRDecompositionHouseholderColumn_ZDRM()
  • Method Details

    • setExpectedMaxSize

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

      public double[][] getQR()
      Returns the combined QR matrix in a 2D array format that is column major.
      The QR matrix in a 2D matrix column major format. [ column ][ row ]
    • getQ

      public ZMatrixRMaj getQ(@Nullable @Nullable ZMatrixRMaj 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 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. If compact then the input expected to be size = [min(rows,cols) , numCols] otherwise size = [numRows,numCols].
      Specified by:
      getR in interface QRDecomposition<ZMatrixRMaj>
      R - Storage for upper triangular matrix.
      compact - If true then a compact matrix is expected.
      The R matrix.
    • decompose

      public boolean decompose(ZMatrixRMaj 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 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.
    • convertToColumnMajor

      protected void convertToColumnMajor(ZMatrixRMaj A)
      Converts the standard row-major matrix into a column-major vector that is advantageous for this problem.
      A - original matrix that is to be decomposed.
    • 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 overfloaw and underflow.

      Q = I - γuuT

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

      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*uH)A

      w - The submatrix.
    • getGammas

      public double[] getGammas()