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*> \brief \b DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLARZ + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarz.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarz.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarz.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* .. Scalar Arguments ..
* CHARACTER SIDE
* INTEGER INCV, L, LDC, M, N
* DOUBLE PRECISION TAU
* ..
* .. Array Arguments ..
* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLARZ applies a real elementary reflector H to a real M-by-N
*> matrix C, from either the left or the right. H is represented in the
*> form
*>
*> H = I - tau * v * v**T
*>
*> where tau is a real scalar and v is a real vector.
*>
*> If tau = 0, then H is taken to be the unit matrix.
*>
*>
*> H is a product of k elementary reflectors as returned by DTZRZF.
*> \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] L
*> \verbatim
*> L is INTEGER
*> The number of entries of the vector V containing
*> the meaningful part of the Householder vectors.
*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
*> The vector v in the representation of H as returned by
*> DTZRZF. 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 DOUBLE PRECISION
*> The value tau in the representation of H.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE PRECISION 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 DOUBLE PRECISION 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 August 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
* ==================
*>
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* August 2012
*
* .. Scalar Arguments ..
CHARACTER SIDE
INTEGER INCV, L, LDC, M, N
DOUBLE PRECISION TAU
* ..
* .. Array Arguments ..
DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DCOPY, DGEMV, DGER
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form H * C
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:n ) = C( 1, 1:n )
*
CALL DCOPY( N, C, LDC, WORK, 1 )
*
* w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
*
CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
$ INCV, ONE, WORK, 1 )
*
* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
*
CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
*
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
* tau * v( 1:l ) * w( 1:n )**T
*
CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
$ LDC )
END IF
*
ELSE
*
* Form C * H
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:m ) = C( 1:m, 1 )
*
CALL DCOPY( M, C, 1, WORK, 1 )
*
* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
*
CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
$ V, INCV, ONE, WORK, 1 )
*
* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
*
CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
*
* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
* tau * w( 1:m ) * v( 1:l )**T
*
CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
$ LDC )
*
END IF
*
END IF
*
RETURN
*
* End of DLARZ
*
END
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