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*> \brief \b ZLARF** =========== DOCUMENTATION ===========** Online html documentation available at * http://www.netlib.org/lapack/explore-html/ **> \htmlonly*> Download ZLARF + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarf.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarf.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarf.f"> *> [TXT]</a>*> \endhtmlonly ** Definition:* ===========** SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )* * .. Scalar Arguments ..* CHARACTER SIDE* INTEGER INCV, LDC, M, N* COMPLEX*16 TAU* ..* .. Array Arguments ..* COMPLEX*16 C( LDC, * ), V( * ), WORK( * )* ..* **> \par Purpose:* =============*>*> \verbatim*>*> 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.*> \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*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.*> \endverbatim*>*> \param[in] INCV*> \verbatim*> INCV is INTEGER*> The increment between elements of v. INCV <> 0.*> \endverbatim*>*> \param[in] TAU*> \verbatim*> TAU is COMPLEX*16*> The value tau in the representation of H.*> \endverbatim*>*> \param[in,out] C*> \verbatim*> 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'.*> \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*16 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 November 2011**> \ingroup complex16OTHERauxiliary** ===================================================================== SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )** -- LAPACK auxiliary routine (version 3.4.0) --* -- LAPACK is a software package provided by Univ. of Tennessee, --* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--* November 2011** .. 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* END
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