clarf.f

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*> \brief \b CLARF applies an elementary reflector to a general rectangular matrix.
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
* 
*       .. Scalar Arguments ..
*       CHARACTER          SIDE
*       INTEGER            INCV, LDC, M, N
*       COMPLEX            TAU
*       ..
*       .. Array Arguments ..
*       COMPLEX            C( LDC, * ), V( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CLARF applies a complex elementary reflector H to a complex M-by-N
*> matrix C, from either the left or the right. H is represented in the
*> form
*>
*>       H = I - tau * v * v**H
*>
*> where tau is a complex scalar and v is a complex vector.
*>
*> If tau = 0, then H is taken to be the unit matrix.
*>
*> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
*> tau.
*> \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 COMPLEX 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 COMPLEX
*>          The value tau in the representation of H.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*>          C is COMPLEX 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 COMPLEX 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. 
*
*> \date September 2012
*
*> \ingroup complexOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE clarf( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
*  -- LAPACK auxiliary 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
      INTEGER            incv, ldc, m, n
      COMPLEX            tau
*     ..
*     .. Array Arguments ..
      COMPLEX            c( ldc, * ), v( * ), work( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            one, zero
      parameter( one = ( 1.0e+0, 0.0e+0 ),
     $                   zero = ( 0.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            applyleft
      INTEGER            i, lastv, lastc
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgemv, cgerc
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      INTEGER            ilaclr, ilaclc
      EXTERNAL           lsame, ilaclr, ilaclc
*     ..
*     .. Executable Statements ..
*
      applyleft = lsame( side, 'L' )
      lastv = 0
      lastc = 0
      IF( tau.NE.zero ) THEN
!     Set up variables for scanning V.  LASTV begins pointing to the end
!     of V.
         IF( applyleft ) THEN
            lastv = m
         ELSE
            lastv = n
         END IF
         IF( incv.GT.0 ) THEN
            i = 1 + (lastv-1) * incv
         ELSE
            i = 1
         END IF
!     Look for the last non-zero row in V.
         DO WHILE( lastv.GT.0 .AND. v( i ).EQ.zero )
            lastv = lastv - 1
            i = i - incv
         END DO
         IF( applyleft ) THEN
!     Scan for the last non-zero column in C(1:lastv,:).
            lastc = ilaclc(lastv, n, c, ldc)
         ELSE
!     Scan for the last non-zero row in C(:,1:lastv).
            lastc = ilaclr(m, lastv, c, ldc)
         END IF
      END IF
!     Note that lastc.eq.0 renders the BLAS operations null; no special
!     case is needed at this level.
      IF( applyleft ) THEN
*
*        Form  H * C
*
         IF( lastv.GT.0 ) THEN
*
*           w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
*
            CALL cgemv( 'Conjugate transpose', lastv, lastc, one,
     $           c, ldc, v, incv, zero, work, 1 )
*
*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
*
            CALL cgerc( lastv, lastc, -tau, v, incv, work, 1, c, ldc )
         END IF
      ELSE
*
*        Form  C * H
*
         IF( lastv.GT.0 ) THEN
*
*           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
*
            CALL cgemv( 'No transpose', lastc, lastv, one, c, ldc,
     $           v, incv, zero, work, 1 )
*
*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
*
            CALL cgerc( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
         END IF
      END IF
      return
*
*     End of CLARF
*
      END