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version 1.3, 2010/08/06 15:28:41 version 1.19, 2023/08/07 08:38:57
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   *> \brief \b DLARF applies an elementary reflector to a general rectangular matrix.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DLARF + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarf.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarf.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarf.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          SIDE
   *       INTEGER            INCV, LDC, M, N
   *       DOUBLE PRECISION   TAU
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLARF applies a real elementary reflector H to a real m by n matrix
   *> C, from either the left or the right. H is represented in the form
   *>
   *>       H = I - tau * v * v**T
   *>
   *> where tau is a real scalar and v is a real vector.
   *>
   *> If tau = 0, then H is taken to be the unit matrix.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] SIDE
   *> \verbatim
   *>          SIDE is CHARACTER*1
   *>          = 'L': form  H * C
   *>          = 'R': form  C * H
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix C.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix C.
   *> \endverbatim
   *>
   *> \param[in] V
   *> \verbatim
   *>          V is DOUBLE PRECISION array, dimension
   *>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
   *>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
   *>          The vector v in the representation of H. V is not used if
   *>          TAU = 0.
   *> \endverbatim
   *>
   *> \param[in] INCV
   *> \verbatim
   *>          INCV is INTEGER
   *>          The increment between elements of v. INCV <> 0.
   *> \endverbatim
   *>
   *> \param[in] TAU
   *> \verbatim
   *>          TAU is DOUBLE PRECISION
   *>          The value tau in the representation of H.
   *> \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 the matrix H * C if SIDE = 'L',
   *>          or C * H if SIDE = 'R'.
   *> \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'
   *>                      or (M) if SIDE = 'R'
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup doubleOTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )        SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
       IMPLICIT NONE  
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          SIDE        CHARACTER          SIDE
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       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )        DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLARF applies a real elementary reflector H to a real m by n matrix  
 *  C, from either the left or the right. H is represented in the form  
 *  
 *        H = I - tau * v * v'  
 *  
 *  where tau is a real scalar and v is a real vector.  
 *  
 *  If tau = 0, then H is taken to be the unit matrix.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  SIDE    (input) CHARACTER*1  
 *          = 'L': form  H * C  
 *          = 'R': form  C * H  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix C.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix C.  
 *  
 *  V       (input) DOUBLE PRECISION array, dimension  
 *                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'  
 *                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'  
 *          The vector v in the representation of H. V is not used if  
 *          TAU = 0.  
 *  
 *  INCV    (input) INTEGER  
 *          The increment between elements of v. INCV <> 0.  
 *  
 *  TAU     (input) DOUBLE PRECISION  
 *          The value tau in the representation of H.  
 *  
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)  
 *          On entry, the m by n matrix C.  
 *          On exit, C is overwritten by the matrix H * C if SIDE = 'L',  
 *          or C * H if SIDE = 'R'.  
 *  
 *  LDC     (input) INTEGER  
 *          The leading dimension of the array C. LDC >= max(1,M).  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension  
 *                         (N) if SIDE = 'L'  
 *                      or (M) if SIDE = 'R'  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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 *  *
          IF( LASTV.GT.0 ) THEN           IF( LASTV.GT.0 ) THEN
 *  *
 *           w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1)  *           w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
 *  *
             CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,              CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,
      $           ZERO, WORK, 1 )       $           ZERO, WORK, 1 )
 *  *
 *           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)'  *           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
 *  *
             CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )              CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
          END IF           END IF
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             CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,              CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
      $           V, INCV, ZERO, WORK, 1 )       $           V, INCV, ZERO, WORK, 1 )
 *  *
 *           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)'  *           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
 *  *
             CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )              CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
          END IF           END IF
Removed from v.1.3  
changed lines
  Added in v.1.19

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