OpenBLAS/lapack-netlib/SRC/dlarz.f

*> \brief \b DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          SIDE
*       INTEGER            INCV, L, LDC, M, N
*       DOUBLE PRECISION   TAU
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLARZ 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.
*>
*>
*> H is a product of k elementary reflectors as returned by DTZRZF.
*> \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] L
*> \verbatim
*>          L is INTEGER
*>          The number of entries of the vector V containing
*>          the meaningful part of the Householder vectors.
*>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*>          V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
*>          The vector v in the representation of H as returned by
*>          DTZRZF. 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 doubleOTHERcomputational
*
*> \par Contributors:
*  ==================
*>
*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE
      INTEGER            INCV, L, LDC, M, N
      DOUBLE PRECISION   TAU
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           DAXPY, DCOPY, DGEMV, DGER
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. Executable Statements ..
*
      IF( LSAME( SIDE, 'L' ) ) THEN
*
*        Form  H * C
*
         IF( TAU.NE.ZERO ) THEN
*
*           w( 1:n ) = C( 1, 1:n )
*
            CALL DCOPY( N, C, LDC, WORK, 1 )
*
*           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
*
            CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
     $                  INCV, ONE, WORK, 1 )
*
*           C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
*
            CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
*
*           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
*                               tau * v( 1:l ) * w( 1:n )**T
*
            CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
     $                 LDC )
         END IF
*
      ELSE
*
*        Form  C * H
*
         IF( TAU.NE.ZERO ) THEN
*
*           w( 1:m ) = C( 1:m, 1 )
*
            CALL DCOPY( M, C, 1, WORK, 1 )
*
*           w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
*
            CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
     $                  V, INCV, ONE, WORK, 1 )
*
*           C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
*
            CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
*
*           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
*                               tau * w( 1:m ) * v( 1:l )**T
*
            CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
     $                 LDC )
*
         END IF
*
      END IF
*
      RETURN
*
*     End of DLARZ
*
      END