version 1.5, 2010/08/07 13:22:41
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version 1.11, 2012/08/22 09:48:37
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*> \brief \b ZLARZ |
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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 ZLARZ + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarz.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/zlarz.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/zlarz.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 ZLARZ( SIDE, M, N, L, 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, L, 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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*> ZLARZ applies a complex elementary reflector H to a complex |
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*> M-by-N matrix C, from either the left or the right. H is represented |
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*> in the 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 (the conjugate transpose of H), supply conjg(tau) instead |
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*> tau. |
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*> |
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*> H is a product of k elementary reflectors as returned by ZTZRZF. |
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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] L |
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*> \verbatim |
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*> L is INTEGER |
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*> The number of entries of the vector V containing |
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*> the meaningful part of the Householder vectors. |
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*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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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 (1+(L-1)*abs(INCV)) |
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*> The vector v in the representation of H as returned by |
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*> ZTZRZF. V is not used if 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 complex16OTHERcomputational |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) |
SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational 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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* ZLARZ applies a complex elementary reflector H to a complex |
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* M-by-N matrix C, from either the left or the right. H is represented |
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* in the 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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* H is a product of k elementary reflectors as returned by ZTZRZF. |
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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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* L (input) INTEGER |
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* The number of entries of the vector V containing |
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* the meaningful part of the Householder vectors. |
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* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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* |
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* V (input) COMPLEX*16 array, dimension (1+(L-1)*abs(INCV)) |
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* The vector v in the representation of H as returned by |
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* ZTZRZF. V is not used if 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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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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CALL ZCOPY( N, C, LDC, WORK, 1 ) |
CALL ZCOPY( N, C, LDC, WORK, 1 ) |
CALL ZLACGV( N, WORK, 1 ) |
CALL ZLACGV( N, WORK, 1 ) |
* |
* |
* w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l ) ) |
* w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) ) |
* |
* |
CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ), |
CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ), |
$ LDC, V, INCV, ONE, WORK, 1 ) |
$ LDC, V, INCV, ONE, WORK, 1 ) |
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CALL ZAXPY( N, -TAU, WORK, 1, C, LDC ) |
CALL ZAXPY( N, -TAU, WORK, 1, C, LDC ) |
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* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... |
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... |
* tau * v( 1:l ) * conjg( w( 1:n )' ) |
* tau * v( 1:l ) * w( 1:n )**H |
* |
* |
CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ), |
CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ), |
$ LDC ) |
$ LDC ) |
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CALL ZAXPY( M, -TAU, WORK, 1, C, 1 ) |
CALL ZAXPY( M, -TAU, WORK, 1, C, 1 ) |
* |
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* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... |
* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... |
* tau * w( 1:m ) * v( 1:l )' |
* tau * w( 1:m ) * v( 1:l )**H |
* |
* |
CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ), |
CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ), |
$ LDC ) |
$ LDC ) |