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239 lines
6.2 KiB
239 lines
6.2 KiB
2 years ago
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*> \brief \b ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
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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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*> \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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* =====================================================================
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SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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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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*
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* .. Parameters ..
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COMPLEX*16 ONE, ZERO
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
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$ ZERO = ( 0.0D+0, 0.0D+0 ) )
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* ..
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* .. External Subroutines ..
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EXTERNAL ZAXPY, ZCOPY, ZGEMV, ZGERC, ZGERU, ZLACGV
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Executable Statements ..
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*
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IF( LSAME( SIDE, 'L' ) ) THEN
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*
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* Form H * C
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*
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IF( TAU.NE.ZERO ) THEN
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*
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* w( 1:n ) = conjg( C( 1, 1:n ) )
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*
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CALL ZCOPY( N, C, LDC, WORK, 1 )
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CALL ZLACGV( N, WORK, 1 )
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*
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* w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
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*
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CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
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$ LDC, V, INCV, ONE, WORK, 1 )
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CALL ZLACGV( N, WORK, 1 )
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*
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* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
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*
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CALL ZAXPY( N, -TAU, WORK, 1, C, LDC )
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*
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* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
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* tau * v( 1:l ) * w( 1:n )**H
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*
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CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
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$ LDC )
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END IF
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*
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ELSE
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*
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* Form C * H
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*
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IF( TAU.NE.ZERO ) THEN
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*
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* w( 1:m ) = C( 1:m, 1 )
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*
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CALL ZCOPY( M, C, 1, WORK, 1 )
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*
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* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
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*
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CALL ZGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
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$ V, INCV, ONE, WORK, 1 )
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*
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* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
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*
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CALL ZAXPY( M, -TAU, WORK, 1, C, 1 )
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*
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* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
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* tau * w( 1:m ) * v( 1:l )**H
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*
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CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
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$ LDC )
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*
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END IF
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*
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END IF
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*
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RETURN
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*
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* End of ZLARZ
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*
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END
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