237 lines
6.0 KiB
Fortran
237 lines
6.0 KiB
Fortran
*> \brief \b SLARZ 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 SLARZ + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarz.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarz.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarz.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER SIDE
|
|
* INTEGER INCV, L, LDC, M, N
|
|
* REAL TAU
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL C( LDC, * ), V( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SLARZ 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 STZRZF.
|
|
*> \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 REAL array, dimension (1+(L-1)*abs(INCV))
|
|
*> The vector v in the representation of H as returned by
|
|
*> STZRZF. 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 REAL
|
|
*> The value tau in the representation of H.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] C
|
|
*> \verbatim
|
|
*> C is REAL 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 REAL 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 September 2012
|
|
*
|
|
*> \ingroup realOTHERcomputational
|
|
*
|
|
*> \par Contributors:
|
|
* ==================
|
|
*>
|
|
*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
|
|
*
|
|
*> \par Further Details:
|
|
* =====================
|
|
*>
|
|
*> \verbatim
|
|
*> \endverbatim
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE SLARZ( 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..--
|
|
* September 2012
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER SIDE
|
|
INTEGER INCV, L, LDC, M, N
|
|
REAL TAU
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL C( LDC, * ), V( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ONE, ZERO
|
|
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SAXPY, SCOPY, SGEMV, SGER
|
|
* ..
|
|
* .. 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 SCOPY( N, C, LDC, WORK, 1 )
|
|
*
|
|
* w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
|
|
*
|
|
CALL SGEMV( '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 SAXPY( 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 SGER( 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 SCOPY( M, C, 1, WORK, 1 )
|
|
*
|
|
* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
|
|
*
|
|
CALL SGEMV( '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 SAXPY( 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 SGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
|
|
$ LDC )
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SLARZ
|
|
*
|
|
END
|