*> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
* 
*       .. Scalar Arguments ..
*       INTEGER            INFO, K, LDA, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DORG2L generates an m by n real matrix Q with orthonormal columns,
*> which is defined as the last n columns of a product of k elementary
*> reflectors of order m
*>
*>       Q  =  H(k) . . . H(2) H(1)
*>
*> as returned by DGEQLF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix Q. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix Q. M >= N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines the
*>          matrix Q. N >= K >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          On entry, the (n-k+i)-th column must contain the vector which
*>          defines the elementary reflector H(i), for i = 1,2,...,k, as
*>          returned by DGEQLF in the last k columns of its array
*>          argument A.
*>          On exit, the m by n matrix Q.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The first dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (K)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by DGEQLF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE GAL_DORG2L(M,N,K,A,LDA,TAU,WORK,INFO)
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER INFO,K,LDA,M,N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),TAU(*),WORK(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
*     ..
*     .. Local Scalars ..
      INTEGER I,II,J,L
*     ..
*     .. External Subroutines ..
      EXTERNAL GAL_DLARF,GAL_DSCAL,GAL_XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO=0
      IF(M.LT.0)THEN
      INFO=-1
      ELSE IF(N.LT.0.OR.N.GT.M)THEN
      INFO=-2
      ELSE IF(K.LT.0.OR.K.GT.N)THEN
      INFO=-3
      ELSE IF(LDA.LT.MAX(1,M))THEN
      INFO=-5
      END IF
      IF(INFO.NE.0)THEN
      CALL GAL_XERBLA('GAL_DORG2L',-INFO)
      RETURN
      END IF
*
*     Quick return if possible
*
      IF(N.LE.0)
     $RETURN
*
*     Initialise columns 1:n-k to columns of the unit matrix
*
      DO 20J=1,N-K
      DO 10L=1,M
      A(L,J)=ZERO
   10 CONTINUE
      A(M-N+J,J)=ONE
   20 CONTINUE
*
      DO 40I=1,K
      II=N-K+I
*
*        Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
*
      A(M-N+II,II)=ONE
      CALL GAL_DLARF('LEFT',M-N+II,II-1,A(1,II),1,TAU(I),A,
     $LDA,WORK)
      CALL GAL_DSCAL(M-N+II-1,-TAU(I),A(1,II),1)
      A(M-N+II,II)=ONE-TAU(I)
*
*        Set A(m-k+i+1:m,n-k+i) to zero
*
      DO 30L=M-N+II+1,M
      A(L,II)=ZERO
   30 CONTINUE
   40 CONTINUE
      RETURN
*
*     End of DORG2L
*
      END 
