222 lines
5.9 KiB
Fortran
222 lines
5.9 KiB
Fortran
*> \brief \b SLATZM
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download SLATZM + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slatzm.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slatzm.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slatzm.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER SIDE
|
|
* INTEGER INCV, LDC, M, N
|
|
* REAL TAU
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> This routine is deprecated and has been replaced by routine SORMRZ.
|
|
*>
|
|
*> SLATZM applies a Householder matrix generated by STZRQF to a matrix.
|
|
*>
|
|
*> Let P = I - tau*u*u**T, u = ( 1 ),
|
|
*> ( v )
|
|
*> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
|
|
*> SIDE = 'R'.
|
|
*>
|
|
*> If SIDE equals 'L', let
|
|
*> C = [ C1 ] 1
|
|
*> [ C2 ] m-1
|
|
*> n
|
|
*> Then C is overwritten by P*C.
|
|
*>
|
|
*> If SIDE equals 'R', let
|
|
*> C = [ C1, C2 ] m
|
|
*> 1 n-1
|
|
*> Then C is overwritten by C*P.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] SIDE
|
|
*> \verbatim
|
|
*> SIDE is CHARACTER*1
|
|
*> = 'L': form P * C
|
|
*> = 'R': form C * P
|
|
*> \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 REAL array, dimension
|
|
*> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
|
|
*> (1 + (N-1)*abs(INCV)) if SIDE = 'R'
|
|
*> The vector v in the representation of P. 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 P.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] C1
|
|
*> \verbatim
|
|
*> C1 is REAL array, dimension
|
|
*> (LDC,N) if SIDE = 'L'
|
|
*> (M,1) if SIDE = 'R'
|
|
*> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
|
|
*> if SIDE = 'R'.
|
|
*>
|
|
*> On exit, the first row of P*C if SIDE = 'L', or the first
|
|
*> column of C*P if SIDE = 'R'.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] C2
|
|
*> \verbatim
|
|
*> C2 is REAL array, dimension
|
|
*> (LDC, N) if SIDE = 'L'
|
|
*> (LDC, N-1) if SIDE = 'R'
|
|
*> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
|
|
*> m x (n - 1) matrix C2 if SIDE = 'R'.
|
|
*>
|
|
*> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
|
|
*> if SIDE = 'R'.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDC
|
|
*> \verbatim
|
|
*> LDC is INTEGER
|
|
*> The leading dimension of the arrays C1 and C2. LDC >= (1,M).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is REAL array, dimension
|
|
*> (N) if SIDE = 'L'
|
|
*> (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 realOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
|
|
*
|
|
* -- LAPACK computational 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
|
|
REAL TAU
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL C1( LDC, * ), C2( 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
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MIN
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) )
|
|
$ RETURN
|
|
*
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
|
*
|
|
* w := (C1 + v**T * C2)**T
|
|
*
|
|
CALL SCOPY( N, C1, LDC, WORK, 1 )
|
|
CALL SGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE,
|
|
$ WORK, 1 )
|
|
*
|
|
* [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
|
|
* [ C2 ] [ C2 ] [ v ]
|
|
*
|
|
CALL SAXPY( N, -TAU, WORK, 1, C1, LDC )
|
|
CALL SGER( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC )
|
|
*
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
|
*
|
|
* w := C1 + C2 * v
|
|
*
|
|
CALL SCOPY( M, C1, 1, WORK, 1 )
|
|
CALL SGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
|
|
$ WORK, 1 )
|
|
*
|
|
* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
|
|
*
|
|
CALL SAXPY( M, -TAU, WORK, 1, C1, 1 )
|
|
CALL SGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SLATZM
|
|
*
|
|
END
|