--- rpl/lapack/lapack/zlarf.f 2010/01/26 15:22:45 1.1.1.1 +++ rpl/lapack/lapack/zlarf.f 2012/08/22 09:48:37 1.11 @@ -1,10 +1,137 @@ +*> \brief \b ZLARF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \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 ) - IMPLICIT NONE * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- 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 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER SIDE @@ -15,59 +142,6 @@ COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) * .. * -* 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' -* -* 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' (the conjugate transpose of H), supply conjg(tau) instead -* tau. -* -* 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) 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. -* -* INCV (input) INTEGER -* The increment between elements of v. INCV <> 0. -* -* TAU (input) COMPLEX*16 -* The value tau in the representation of H. -* -* C (input/output) 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'. -* -* LDC (input) INTEGER -* The leading dimension of the array C. LDC >= max(1,M). -* -* WORK (workspace) COMPLEX*16 array, dimension -* (N) if SIDE = 'L' -* or (M) if SIDE = 'R' -* * ===================================================================== * * .. Parameters .. @@ -93,8 +167,8 @@ LASTV = 0 LASTC = 0 IF( TAU.NE.ZERO ) THEN -! Set up variables for scanning V. LASTV begins pointing to the end -! of V. +* Set up variables for scanning V. LASTV begins pointing to the end +* of V. IF( APPLYLEFT ) THEN LASTV = M ELSE @@ -105,33 +179,33 @@ ELSE I = 1 END IF -! Look for the last non-zero row in V. +* 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,:). +* 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). +* 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. +* 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)' * v(1:lastv,1) +* 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)' +* 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 @@ -146,7 +220,7 @@ 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)' +* 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