!>
!> DGERQF computes an RQ factorization of a real M-by-N matrix A:
!> A = R * Q.
!> 

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 DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A.
!>          On exit,
!>          if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the M-by-N upper trapezoidal matrix R;
!>          the remaining elements, 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 DOUBLE PRECISION array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!> 

WORK

!>          WORK is DOUBLE PRECISION 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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
!>          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
!> 

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!>
!>  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**T
!>
!>  where tau is a real scalar, and v is a real vector with
!>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
!>  A(m-k+i,1:n-k+i-1), and tau in TAU(i).
!>