SRC/sgelqf.f(3)

NAME
SRC/sgelqf.f

SYNOPSIS

  Functions/Subroutines
subroutine sgelqf (m, n, a, lda, tau, work, lwork, info)
SGELQF

Function/Subroutine Documentation

  subroutine sgelqf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SGELQF

Purpose:

     SGELQF computes an LQ factorization of a real M-by-N matrix A:
        A = ( L 0 ) *  Q
     where:
        Q is a N-by-N orthogonal matrix;
        L is a lower-triangular M-by-M matrix;
        0 is a M-by-(N-M) zero matrix, if M < N.

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 REAL array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and below the diagonal of the array
              contain the m-by-min(m,n) lower trapezoidal matrix L (L is
              lower triangular if m <= n); the elements above the diagonal,
              with the array TAU, represent the orthogonal matrix Q as a
              product of elementary reflectors (see Further Details).

    LDA

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

    TAU

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

    WORK

              WORK is REAL 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.  LWORK >= max(1,M).
              For optimum performance LWORK >= M*NB, where NB is the
              optimal blocksize.
              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.

Further Details:

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

Definition at line 142 of file sgelqf.f.

Author

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