SGERQF 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 REAL 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 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 >= 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).