zlarf()

subroutine zlarf	(	character	side,
		integer	m,
		integer	n,
		complex*16, dimension( * )	v,
		integer	incv,
		complex*16	tau,
		complex*16, dimension( ldc, * )	c,
		integer	ldc,
		complex*16, dimension( * )	work )

ZLARF applies an elementary reflector to a general rectangular matrix.

Download ZLARF + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZLARF 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, supply conjg(tau) instead
!> tau.
!> 

Parameters

[in]	SIDE	!> SIDE is CHARACTER*1 !> = 'L': form H * C !> = 'R': form C * H !>
[in]	M	!> M is INTEGER !> The number of rows of the matrix C. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix C. !>
[in]	V	!> V is COMPLEX*16 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. !>
[in]	INCV	!> INCV is INTEGER !> The increment between elements of v. INCV <> 0. !>
[in]	TAU	!> TAU is COMPLEX*16 !> The value tau in the representation of H. !>
[in,out]	C	!> C is COMPLEX*16 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'. !>
[in]	LDC	!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension !> (N) if SIDE = 'L' !> or (M) if SIDE = 'R' !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 125 of file zlarf.f.

*
*  -- LAPACK auxiliary 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, LDC, M, N
      COMPLEX*16         TAU
*     ..
*     .. Array Arguments ..
      COMPLEX*16         C( LDC, * ), V( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE, ZERO
      parameter( one = ( 1.0d+0, 0.0d+0 ),
     $                   zero = ( 0.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            APPLYLEFT
      INTEGER            I, LASTV, LASTC
*     ..
*     .. External Subroutines ..
      EXTERNAL           zgemv, zgerc
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAZLR, ILAZLC
      EXTERNAL           lsame, ilazlr, ilazlc
*     ..
*     .. 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 = ilazlc(lastv, n, c, ldc)
         ELSE
*     Scan for the last non-zero row in C(:,1:lastv).
            lastc = ilazlr(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 zgemv( '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 zgerc( 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 zgemv( '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 zgerc( lastc, lastv, -tau, work, 1, v, incv, c,
     $                  ldc )
         END IF
      END IF
      RETURN
*
*     End of ZLARF
*

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