You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
227 lines
6.0 KiB
227 lines
6.0 KiB
*> \brief \b DLARF
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download DLARF + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarf.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarf.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarf.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER SIDE
|
|
* INTEGER INCV, LDC, M, N
|
|
* DOUBLE PRECISION TAU
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DLARF 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.
|
|
*> \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] V
|
|
*> \verbatim
|
|
*> V is DOUBLE PRECISION array, dimension
|
|
*> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
|
|
*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
|
|
*> The vector v in the representation of H. 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 November 2011
|
|
*
|
|
*> \ingroup doubleOTHERauxiliary
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
|
|
*
|
|
* -- LAPACK auxiliary routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER SIDE
|
|
INTEGER INCV, 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 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL APPLYLEFT
|
|
INTEGER I, LASTV, LASTC
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DGEMV, DGER
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
INTEGER ILADLR, ILADLC
|
|
EXTERNAL LSAME, ILADLR, ILADLC
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
APPLYLEFT = LSAME( SIDE, 'L' )
|
|
LASTV = 0
|
|
LASTC = 0
|
|
IF( TAU.NE.ZERO ) THEN
|
|
! Set up variables for scanning V. LASTV begins pointing to the end
|
|
! of V.
|
|
IF( APPLYLEFT ) THEN
|
|
LASTV = M
|
|
ELSE
|
|
LASTV = N
|
|
END IF
|
|
IF( INCV.GT.0 ) THEN
|
|
I = 1 + (LASTV-1) * INCV
|
|
ELSE
|
|
I = 1
|
|
END IF
|
|
! Look for the last non-zero row in V.
|
|
DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
|
|
LASTV = LASTV - 1
|
|
I = I - INCV
|
|
END DO
|
|
IF( APPLYLEFT ) THEN
|
|
! Scan for the last non-zero column in C(1:lastv,:).
|
|
LASTC = ILADLC(LASTV, N, C, LDC)
|
|
ELSE
|
|
! Scan for the last non-zero row in C(:,1:lastv).
|
|
LASTC = ILADLR(M, LASTV, C, LDC)
|
|
END IF
|
|
END IF
|
|
! Note that lastc.eq.0 renders the BLAS operations null; no special
|
|
! case is needed at this level.
|
|
IF( APPLYLEFT ) THEN
|
|
*
|
|
* Form H * C
|
|
*
|
|
IF( LASTV.GT.0 ) THEN
|
|
*
|
|
* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
|
|
*
|
|
CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,
|
|
$ ZERO, WORK, 1 )
|
|
*
|
|
* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
|
|
*
|
|
CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
|
|
END IF
|
|
ELSE
|
|
*
|
|
* Form C * H
|
|
*
|
|
IF( LASTV.GT.0 ) THEN
|
|
*
|
|
* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
|
|
*
|
|
CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
|
|
$ V, INCV, ZERO, WORK, 1 )
|
|
*
|
|
* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
|
|
*
|
|
CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
|
|
END IF
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of DLARF
|
|
*
|
|
END
|