      SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( LWORK )
*     ..
*
*  Purpose
*  =======
*
*  DORGRQ generates an M-by-N real matrix Q with orthonormal rows,
*  which is defined as the last M rows of a product of K elementary
*  reflectors of order N
*
*        Q  =  H(1) H(2) . . . H(k)
*
*  as returned by DGERQF.
*
*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. N >= M.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. M >= K >= 0.
*
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the (m-k+i)-th row must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by DGERQF in the last k rows of its array argument
*          A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) DOUBLE PRECISION array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by DGERQF.
*
*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,M).
*          For optimum performance LWORK >= M*NB, where NB is the
*          optimal blocksize.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IB, II, IINFO, IWS, J, KK, L, LDWORK, NB,
     $                   NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLARFB, DLARFT, DORGR2, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.M ) THEN
         INFO = -2
      ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LWORK.LT.MAX( 1, M ) ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DORGRQ', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.LE.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
*     Determine the block size.
*
      NB = ILAENV( 1, 'DORGRQ', ' ', M, N, K, -1 )
      NBMIN = 2
      NX = 0
      IWS = M
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
*
*        Determine when to cross over from blocked to unblocked code.
*
         NX = MAX( 0, ILAENV( 3, 'DORGRQ', ' ', M, N, K, -1 ) )
         IF( NX.LT.K ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = M
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  reduce NB and
*              determine the minimum value of NB.
*
               NB = LWORK / LDWORK
               NBMIN = MAX( 2, ILAENV( 2, 'DORGRQ', ' ', M, N, K, -1 ) )
            END IF
         END IF
      END IF
*
      IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
*
*        Use blocked code after the first block.
*        The last kk rows are handled by the block method.
*
         KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
*
*        Set A(1:m-kk,n-kk+1:n) to zero.
*
         DO 20 J = N - KK + 1, N
            DO 10 I = 1, M - KK
               A( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
      ELSE
         KK = 0
      END IF
*
*     Use unblocked code for the first or only block.
*
      CALL DORGR2( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
*
      IF( KK.GT.0 ) THEN
*
*        Use blocked code
*
         DO 50 I = K - KK + 1, K, NB
            IB = MIN( NB, K-I+1 )
            II = M - K + I
            IF( II.GT.1 ) THEN
*
*              Form the triangular factor of the block reflector
*              H = H(i+ib-1) . . . H(i+1) H(i)
*
               CALL DLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
     $                      A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )
*
*              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
*
               CALL DLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise',
     $                      II-1, N-K+I+IB-1, IB, A( II, 1 ), LDA, WORK,
     $                      LDWORK, A, LDA, WORK( IB+1 ), LDWORK )
            END IF
*
*           Apply H' to columns 1:n-k+i+ib-1 of current block
*
            CALL DORGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),
     $                   WORK, IINFO )
*
*           Set columns n-k+i+ib:n of current block to zero
*
            DO 40 L = N - K + I + IB, N
               DO 30 J = II, II + IB - 1
                  A( J, L ) = ZERO
   30          CONTINUE
   40       CONTINUE
   50    CONTINUE
      END IF
*
      WORK( 1 ) = IWS
      RETURN
*
*     End of DORGRQ
*
      END
