!>
!> 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.
!>
!> 

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
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  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).
!>