cgeqrf.f(3)

NAME
cgeqrf.f

SYNOPSIS

  Functions/Subroutines
subroutine cgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm.

Function/Subroutine Documentation

  subroutine cgeqrf (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer LWORK, integer INFO)

CGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm. Purpose:

 CGEQRF computes a QR factorization of a real M-by-N matrix A:
 A = Q * R.
 This is the left-looking Level 3 BLAS version of the algorithm.

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.

    A

              A is COMPLEX 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,
              with the array TAU, represent the orthogonal matrix Q as a
              product of min(m,n) elementary reflectors (see Further
              Details).

    LDA

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

    TAU

              TAU is COMPLEX array, dimension (min(M,N))
              The scalar factors of the elementary reflectors (see Further
              Details).

    WORK

              WORK is COMPLEX array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER

              The dimension of the array WORK. The dimension can be divided into three parts.

              1) The part for the triangular factor T. If the very last T is not bigger
                 than any of the rest, then this part is NB x ceiling(K/NB), otherwise,
                 NB x (K-NT), where K = min(M,N) and NT is the dimension of the very last T

              2) The part for the very last T when T is bigger than any of the rest T.
                 The size of this part is NT x NT, where NT = K - ceiling ((K-NX)/NB) x NB,
                 where K = min(M,N), NX is calculated by
                       NX = MAX( 0, ILAENV( 3, 'CGEQRF', ' ', M, N, -1, -1 ) )

              3) The part for dlarfb is of size max((N-M)*K, (N-M)*NB, K*NB, NB*NB)

              So LWORK = part1 + part2 + part3

              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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:
    December 2016

Further Details

  The matrix Q is represented as a product of elementary reflectors
     Q = H(1) H(2) . . . H(k), where k = min(m,n).
  Each H(i) has the form
     H(i) = I - tau * v * v'
  where tau is a real scalar, and v is a real vector with
  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
  and tau in TAU(i).

Definition at line 151 of file VARIANTS/qr/LL/cgeqrf.f.

Author

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