222 lines
5.9 KiB
Fortran
222 lines
5.9 KiB
Fortran
*> \brief \b DLATZM
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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 DLATZM + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatzm.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/dlatzm.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/dlatzm.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 DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, 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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* DOUBLE PRECISION TAU
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION C1( LDC, * ), C2( 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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*> This routine is deprecated and has been replaced by routine DORMRZ.
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*>
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*> DLATZM applies a Householder matrix generated by DTZRQF to a matrix.
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*>
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*> Let P = I - tau*u*u**T, u = ( 1 ),
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*> ( v )
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*> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
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*> SIDE = 'R'.
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*>
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*> If SIDE equals 'L', let
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*> C = [ C1 ] 1
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*> [ C2 ] m-1
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*> n
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*> Then C is overwritten by P*C.
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*>
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*> If SIDE equals 'R', let
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*> C = [ C1, C2 ] m
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*> 1 n-1
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*> Then C is overwritten by C*P.
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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 P * C
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*> = 'R': form C * P
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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 DOUBLE PRECISION array, dimension
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*> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
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*> (1 + (N-1)*abs(INCV)) if SIDE = 'R'
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*> The vector v in the representation of P. V is not used
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*> 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 DOUBLE PRECISION
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*> The value tau in the representation of P.
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*> \endverbatim
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*>
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*> \param[in,out] C1
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*> \verbatim
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*> C1 is DOUBLE PRECISION array, dimension
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*> (LDC,N) if SIDE = 'L'
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*> (M,1) if SIDE = 'R'
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*> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
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*> if SIDE = 'R'.
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*>
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*> On exit, the first row of P*C if SIDE = 'L', or the first
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*> column of C*P if SIDE = 'R'.
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*> \endverbatim
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*>
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*> \param[in,out] C2
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*> \verbatim
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*> C2 is DOUBLE PRECISION array, dimension
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*> (LDC, N) if SIDE = 'L'
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*> (LDC, N-1) if SIDE = 'R'
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*> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
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*> m x (n - 1) matrix C2 if SIDE = 'R'.
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*>
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*> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
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*> 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 arrays C1 and C2. LDC >= (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 DOUBLE PRECISION array, dimension
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*> (N) if SIDE = 'L'
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*> (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 doubleOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
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*
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* -- LAPACK computational routine (version 3.4.0) --
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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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* November 2011
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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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DOUBLE PRECISION TAU
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION C1( LDC, * ), C2( 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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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. External Subroutines ..
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EXTERNAL DAXPY, DCOPY, DGEMV, DGER
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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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* .. Intrinsic Functions ..
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INTRINSIC MIN
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* ..
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* .. Executable Statements ..
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*
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IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) )
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$ RETURN
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*
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IF( LSAME( SIDE, 'L' ) ) THEN
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*
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* w := (C1 + v**T * C2)**T
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*
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CALL DCOPY( N, C1, LDC, WORK, 1 )
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CALL DGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE,
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$ WORK, 1 )
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*
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* [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
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* [ C2 ] [ C2 ] [ v ]
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*
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CALL DAXPY( N, -TAU, WORK, 1, C1, LDC )
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CALL DGER( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC )
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*
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ELSE IF( LSAME( SIDE, 'R' ) ) THEN
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*
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* w := C1 + C2 * v
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*
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CALL DCOPY( M, C1, 1, WORK, 1 )
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CALL DGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
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$ WORK, 1 )
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*
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* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
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*
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CALL DAXPY( M, -TAU, WORK, 1, C1, 1 )
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CALL DGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
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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 DLATZM
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*
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END
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