*> \brief \b SGERQS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
*                          INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), B( LDB, * ), TAU( * ),
*      $                   WORK( LWORK )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> Compute a minimum-norm solution
*>     min || A*X - B ||
*> using the RQ factorization
*>     A = R*Q
*> computed by SGERQF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= M >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of columns of B.  NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>          Details of the RQ factorization of the original matrix A as
*>          returned by SGERQF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is REAL array, dimension (M)
*>          Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is REAL array, dimension (LDB,NRHS)
*>          On entry, the right hand side vectors for the linear system.
*>          On exit, the solution vectors X.  Each solution vector
*>          is contained in rows 1:N of a column of B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The length of the array WORK.  LWORK must be at least NRHS,
*>          and should be at least NRHS*NB, where NB is the block size
*>          for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup single_lin
*
*  =====================================================================
      SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
     $                   INFO )
*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), B( LDB, * ), TAU( * ),
     $                   WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLASET, SORMRQ, STRSM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
     $          THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SGERQS', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
     $   RETURN
*
*     Solve R*X = B(n-m+1:n,:)
*
      CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS,
     $            ONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB )
*
*     Set B(1:n-m,:) to zero
*
      CALL SLASET( 'Full', N-M, NRHS, ZERO, ZERO, B, LDB )
*
*     B := Q' * B
*
      CALL SORMRQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB,
     $             WORK, LWORK, INFO )
*
      RETURN
*
*     End of SGERQS
*
      END
