dgeqrt.f(3)

NAME
dgeqrt.f -

SYNOPSIS

  Functions/Subroutines
subroutine dgeqrt (M, N, NB, A, LDA, T, LDT, WORK, INFO)
DGEQRT

Function/Subroutine Documentation

  subroutine dgeqrt (integerM, integerN, integerNB, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( * )WORK, integerINFO)

DGEQRT

Purpose:

     DGEQRT computes a blocked QR factorization of a real M-by-N matrix A
     using the compact WY representation of Q.

Parameters:
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix A.  N >= 0.

    NB

              NB is INTEGER
              The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal of the array
              contain the min(M,N)-by-N upper trapezoidal matrix R (R is
              upper triangular if M >= N); the elements below the diagonal
              are the columns of V.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,M).

    T

              T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
              The upper triangular block reflectors stored in compact form
              as a sequence of upper triangular blocks.  See below
              for further details.

    LDT

              LDT is INTEGER
              The leading dimension of the array T.  LDT >= NB.

    WORK

              WORK is DOUBLE PRECISION array, dimension (NB*N)

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Further Details:

      The matrix V stores the elementary reflectors H(i) in the i-th column
      below the diagonal. For example, if M=5 and N=3, the matrix V is
                   V = (  1       )
                       ( v1  1    )
                       ( v1 v2  1 )
                       ( v1 v2 v3 )
                       ( v1 v2 v3 )
      where the vi's represent the vectors which define H(i), which are returned
      in the matrix A.  The 1's along the diagonal of V are not stored in A.
      Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
      block is of order NB except for the last block, which is of order
      IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
      reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
      for the last block) T's are stored in the NB-by-N matrix T as
                   T = (T1 T2 ... TB).

Definition at line 142 of file dgeqrt.f.

Author

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