version 1.5, 2010/08/07 13:22:40
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version 1.11, 2012/08/22 09:48:37
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*> \brief \b ZLARF |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZLARF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarf.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarf.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarf.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER SIDE |
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* INTEGER INCV, LDC, M, N |
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* COMPLEX*16 TAU |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZLARF applies a complex elementary reflector H to a complex M-by-N |
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*> matrix C, from either the left or the right. H is represented in the |
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*> form |
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*> |
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*> H = I - tau * v * v**H |
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*> |
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*> where tau is a complex scalar and v is a complex vector. |
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*> |
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*> If tau = 0, then H is taken to be the unit matrix. |
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*> |
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*> To apply H**H, supply conjg(tau) instead |
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*> tau. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] SIDE |
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*> \verbatim |
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*> SIDE is CHARACTER*1 |
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*> = 'L': form H * C |
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*> = 'R': form C * H |
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*> \endverbatim |
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*> |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix C. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of columns of the matrix C. |
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*> \endverbatim |
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*> |
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*> \param[in] V |
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*> \verbatim |
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*> V is COMPLEX*16 array, dimension |
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*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' |
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*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' |
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*> The vector v in the representation of H. V is not used if |
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*> TAU = 0. |
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*> \endverbatim |
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*> |
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*> \param[in] INCV |
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*> \verbatim |
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*> INCV is INTEGER |
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*> The increment between elements of v. INCV <> 0. |
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*> \endverbatim |
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*> |
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*> \param[in] TAU |
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*> \verbatim |
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*> TAU is COMPLEX*16 |
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*> The value tau in the representation of H. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C |
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*> \verbatim |
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*> C is COMPLEX*16 array, dimension (LDC,N) |
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*> On entry, the M-by-N matrix C. |
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*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', |
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*> or C * H if SIDE = 'R'. |
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*> \endverbatim |
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*> |
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*> \param[in] LDC |
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*> \verbatim |
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*> LDC is INTEGER |
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*> The leading dimension of the array C. LDC >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension |
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*> (N) if SIDE = 'L' |
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*> or (M) if SIDE = 'R' |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup complex16OTHERauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) |
SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) |
IMPLICIT NONE |
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* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER SIDE |
CHARACTER SIDE |
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COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) |
COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLARF applies a complex elementary reflector H to a complex M-by-N |
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* matrix C, from either the left or the right. H is represented in the |
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* form |
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* |
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* H = I - tau * v * v' |
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* |
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* where tau is a complex scalar and v is a complex vector. |
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* |
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* If tau = 0, then H is taken to be the unit matrix. |
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* |
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* To apply H' (the conjugate transpose of H), supply conjg(tau) instead |
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* tau. |
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* |
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* Arguments |
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* ========= |
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* |
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* SIDE (input) CHARACTER*1 |
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* = 'L': form H * C |
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* = 'R': form C * H |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix C. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix C. |
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* |
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* V (input) COMPLEX*16 array, dimension |
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* (1 + (M-1)*abs(INCV)) if SIDE = 'L' |
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* or (1 + (N-1)*abs(INCV)) if SIDE = 'R' |
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* The vector v in the representation of H. V is not used if |
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* TAU = 0. |
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* |
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* INCV (input) INTEGER |
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* The increment between elements of v. INCV <> 0. |
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* |
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* TAU (input) COMPLEX*16 |
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* The value tau in the representation of H. |
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* |
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* C (input/output) COMPLEX*16 array, dimension (LDC,N) |
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* On entry, the M-by-N matrix C. |
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* On exit, C is overwritten by the matrix H * C if SIDE = 'L', |
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* or C * H if SIDE = 'R'. |
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* |
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* LDC (input) INTEGER |
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* The leading dimension of the array C. LDC >= max(1,M). |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension |
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* (N) if SIDE = 'L' |
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* or (M) if SIDE = 'R' |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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LASTV = 0 |
LASTV = 0 |
LASTC = 0 |
LASTC = 0 |
IF( TAU.NE.ZERO ) THEN |
IF( TAU.NE.ZERO ) THEN |
! Set up variables for scanning V. LASTV begins pointing to the end |
* Set up variables for scanning V. LASTV begins pointing to the end |
! of V. |
* of V. |
IF( APPLYLEFT ) THEN |
IF( APPLYLEFT ) THEN |
LASTV = M |
LASTV = M |
ELSE |
ELSE |
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ELSE |
ELSE |
I = 1 |
I = 1 |
END IF |
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 ) |
DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) |
LASTV = LASTV - 1 |
LASTV = LASTV - 1 |
I = I - INCV |
I = I - INCV |
END DO |
END DO |
IF( APPLYLEFT ) THEN |
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) |
LASTC = ILAZLC(LASTV, N, C, LDC) |
ELSE |
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) |
LASTC = ILAZLR(M, LASTV, C, LDC) |
END IF |
END IF |
END IF |
END IF |
! Note that lastc.eq.0 renders the BLAS operations null; no special |
* Note that lastc.eq.0 renders the BLAS operations null; no special |
! case is needed at this level. |
* case is needed at this level. |
IF( APPLYLEFT ) THEN |
IF( APPLYLEFT ) THEN |
* |
* |
* Form H * C |
* Form H * C |
* |
* |
IF( LASTV.GT.0 ) THEN |
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, |
CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE, |
$ C, LDC, V, INCV, ZERO, WORK, 1 ) |
$ 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 ) |
CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) |
END IF |
END IF |
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CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, |
CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, |
$ V, INCV, ZERO, WORK, 1 ) |
$ 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 ) |
CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) |
END IF |
END IF |