dorm2l.f

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*> \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
*                          WORK, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          SIDE, TRANS
*       INTEGER            INFO, K, LDA, LDC, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DORM2L overwrites the general real m by n matrix C with
*>
*>       Q * C  if SIDE = 'L' and TRANS = 'N', or
*>
*>       Q**T * C  if SIDE = 'L' and TRANS = 'T', or
*>
*>       C * Q  if SIDE = 'R' and TRANS = 'N', or
*>
*>       C * Q**T if SIDE = 'R' and TRANS = 'T',
*>
*> where Q is a real orthogonal matrix defined as the product of k
*> elementary reflectors
*>
*>       Q = H(k) . . . H(2) H(1)
*>
*> as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] SIDE
*> \verbatim
*>          SIDE is CHARACTER*1
*>          = 'L': apply Q or Q**T from the Left
*>          = 'R': apply Q or Q**T from the Right
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          = 'N': apply Q  (No transpose)
*>          = 'T': apply Q**T (Transpose)
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix C. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines
*>          the matrix Q.
*>          If SIDE = 'L', M >= K >= 0;
*>          if SIDE = 'R', N >= K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,K)
*>          The 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.
*>          A is modified by the routine but restored on exit.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          If SIDE = 'L', LDA >= max(1,M);
*>          if SIDE = 'R', LDA >= max(1,N).
*> \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[in,out] C
*> \verbatim
*>          C is DOUBLE PRECISION array, dimension (LDC,N)
*>          On entry, the m by n matrix C.
*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*>          LDC is INTEGER
*>          The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension
*>                                   (N) if SIDE = 'L',
*>                                   (M) if SIDE = 'R'
*> \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 September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE dorm2l( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   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 ..
      CHARACTER          side, trans
      INTEGER            info, k, lda, ldc, m, n
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   a( lda, * ), c( ldc, * ), tau( * ), work( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   one
      parameter( one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            left, notran
      INTEGER            i, i1, i2, i3, mi, ni, nq
      DOUBLE PRECISION   aii
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarf, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      left = lsame( side, 'L' )
      notran = lsame( trans, 'N' )
*
*     NQ is the order of Q
*
      IF( left ) THEN
         nq = m
      ELSE
         nq = n
      END IF
      IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
         info = -1
      ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
         info = -2
      ELSE IF( m.LT.0 ) THEN
         info = -3
      ELSE IF( n.LT.0 ) THEN
         info = -4
      ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
         info = -5
      ELSE IF( lda.LT.max( 1, nq ) ) THEN
         info = -7
      ELSE IF( ldc.LT.max( 1, m ) ) THEN
         info = -10
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORM2L', -info )
         return
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
     $   return
*
      IF( ( left .AND. notran ) .OR. ( .NOT.left .AND. .NOT.notran ) )
     $     THEN
         i1 = 1
         i2 = k
         i3 = 1
      ELSE
         i1 = k
         i2 = 1
         i3 = -1
      END IF
*
      IF( left ) THEN
         ni = n
      ELSE
         mi = m
      END IF
*
      DO 10 i = i1, i2, i3
         IF( left ) THEN
*
*           H(i) is applied to C(1:m-k+i,1:n)
*
            mi = m - k + i
         ELSE
*
*           H(i) is applied to C(1:m,1:n-k+i)
*
            ni = n - k + i
         END IF
*
*        Apply H(i)
*
         aii = a( nq-k+i, i )
         a( nq-k+i, i ) = one
         CALL dlarf( side, mi, ni, a( 1, i ), 1, tau( i ), c, ldc,
     $               work )
         a( nq-k+i, i ) = aii
   10 continue
      return
*
*     End of DORM2L
*
      END