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*> \brief \b SSB2ST_KERNELS
*
* @generated from zhb2st_kernels.f, fortran z -> s, Wed Dec 7 08:22:40 2016
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SSB2ST_KERNELS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssb2st_kernels.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssb2st_kernels.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssb2st_kernels.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SSB2ST_KERNELS( UPLO, WANTZ, TTYPE,
* ST, ED, SWEEP, N, NB, IB,
* A, LDA, V, TAU, LDVT, WORK)
*
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* LOGICAL WANTZ
* INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), V( * ),
* TAU( * ), WORK( * )
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SSB2ST_KERNELS is an internal routine used by the SSYTRD_SB2ST
*> subroutine.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> \endverbatim
*>
*> \param[in] WANTZ
*> \verbatim
*> WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
*> Eigenvalue/Eigenvectors.
*> \endverbatim
*>
*> \param[in] TTYPE
*> \verbatim
*> TTYPE is INTEGER
*> \endverbatim
*>
*> \param[in] ST
*> \verbatim
*> ST is INTEGER
*> internal parameter for indices.
*> \endverbatim
*>
*> \param[in] ED
*> \verbatim
*> ED is INTEGER
*> internal parameter for indices.
*> \endverbatim
*>
*> \param[in] SWEEP
*> \verbatim
*> SWEEP is INTEGER
*> internal parameter for indices.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER. The order of the matrix A.
*> \endverbatim
*>
*> \param[in] NB
*> \verbatim
*> NB is INTEGER. The size of the band.
*> \endverbatim
*>
*> \param[in] IB
*> \verbatim
*> IB is INTEGER.
*> \endverbatim
*>
*> \param[in, out] A
*> \verbatim
*> A is REAL array. A pointer to the matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER. The leading dimension of the matrix A.
*> \endverbatim
*>
*> \param[out] V
*> \verbatim
*> V is REAL array, dimension 2*n if eigenvalues only are
*> requested or to be queried for vectors.
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is REAL array, dimension (2*n).
*> The scalar factors of the Householder reflectors are stored
*> in this array.
*> \endverbatim
*>
*> \param[in] LDVT
*> \verbatim
*> LDVT is INTEGER.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array. Workspace of size nb.
*> \endverbatim
*> @param[in] n
*> The order of the matrix A.
*>
*>
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Implemented by Azzam Haidar.
*>
*> All details are available on technical report, SC11, SC13 papers.
*>
*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
*> Parallel reduction to condensed forms for symmetric eigenvalue problems
*> using aggregated fine-grained and memory-aware kernels. In Proceedings
*> of 2011 International Conference for High Performance Computing,
*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
*> Article 8 , 11 pages.
*> http://doi.acm.org/10.1145/2063384.2063394
*>
*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
*> An improved parallel singular value algorithm and its implementation
*> for multicore hardware, In Proceedings of 2013 International Conference
*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
*> Denver, Colorado, USA, 2013.
*> Article 90, 12 pages.
*> http://doi.acm.org/10.1145/2503210.2503292
*>
*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
*> calculations based on fine-grained memory aware tasks.
*> International Journal of High Performance Computing Applications.
*> Volume 28 Issue 2, Pages 196-209, May 2014.
*> http://hpc.sagepub.com/content/28/2/196
*>
*> \endverbatim
*>
* =====================================================================
SUBROUTINE SSB2ST_KERNELS( UPLO, WANTZ, TTYPE,
$ ST, ED, SWEEP, N, NB, IB,
$ A, LDA, V, TAU, LDVT, WORK)
*
IMPLICIT NONE
*
* -- LAPACK computational routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2017
*
* .. Scalar Arguments ..
CHARACTER UPLO
LOGICAL WANTZ
INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
* ..
* .. Array Arguments ..
REAL A( LDA, * ), V( * ),
$ TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0,
$ ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, J1, J2, LM, LN, VPOS, TAUPOS,
$ DPOS, OFDPOS, AJETER
REAL CTMP
* ..
* .. External Subroutines ..
EXTERNAL SLARFG, SLARFX, SLARFY
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* ..
* .. Executable Statements ..
*
AJETER = IB + LDVT
UPPER = LSAME( UPLO, 'U' )
IF( UPPER ) THEN
DPOS = 2 * NB + 1
OFDPOS = 2 * NB
ELSE
DPOS = 1
OFDPOS = 2
ENDIF
*
* Upper case
*
IF( UPPER ) THEN
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ENDIF
*
IF( TTYPE.EQ.1 ) THEN
LM = ED - ST + 1
*
V( VPOS ) = ONE
DO 10 I = 1, LM-1
V( VPOS+I ) = ( A( OFDPOS-I, ST+I ) )
A( OFDPOS-I, ST+I ) = ZERO
10 CONTINUE
CTMP = ( A( OFDPOS, ST ) )
CALL SLARFG( LM, CTMP, V( VPOS+1 ), 1,
$ TAU( TAUPOS ) )
A( OFDPOS, ST ) = CTMP
*
LM = ED - ST + 1
CALL SLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.3 ) THEN
*
LM = ED - ST + 1
CALL SLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.2 ) THEN
J1 = ED+1
J2 = MIN( ED+NB, N )
LN = ED-ST+1
LM = J2-J1+1
IF( LM.GT.0) THEN
CALL SLARFX( 'Left', LN, LM, V( VPOS ),
$ ( TAU( TAUPOS ) ),
$ A( DPOS-NB, J1 ), LDA-1, WORK)
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ENDIF
*
V( VPOS ) = ONE
DO 30 I = 1, LM-1
V( VPOS+I ) =
$ ( A( DPOS-NB-I, J1+I ) )
A( DPOS-NB-I, J1+I ) = ZERO
30 CONTINUE
CTMP = ( A( DPOS-NB, J1 ) )
CALL SLARFG( LM, CTMP, V( VPOS+1 ), 1, TAU( TAUPOS ) )
A( DPOS-NB, J1 ) = CTMP
*
CALL SLARFX( 'Right', LN-1, LM, V( VPOS ),
$ TAU( TAUPOS ),
$ A( DPOS-NB+1, J1 ), LDA-1, WORK)
ENDIF
ENDIF
*
* Lower case
*
ELSE
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ENDIF
*
IF( TTYPE.EQ.1 ) THEN
LM = ED - ST + 1
*
V( VPOS ) = ONE
DO 20 I = 1, LM-1
V( VPOS+I ) = A( OFDPOS+I, ST-1 )
A( OFDPOS+I, ST-1 ) = ZERO
20 CONTINUE
CALL SLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1,
$ TAU( TAUPOS ) )
*
LM = ED - ST + 1
*
CALL SLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.3 ) THEN
LM = ED - ST + 1
*
CALL SLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.2 ) THEN
J1 = ED+1
J2 = MIN( ED+NB, N )
LN = ED-ST+1
LM = J2-J1+1
*
IF( LM.GT.0) THEN
CALL SLARFX( 'Right', LM, LN, V( VPOS ),
$ TAU( TAUPOS ), A( DPOS+NB, ST ),
$ LDA-1, WORK)
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ENDIF
*
V( VPOS ) = ONE
DO 40 I = 1, LM-1
V( VPOS+I ) = A( DPOS+NB+I, ST )
A( DPOS+NB+I, ST ) = ZERO
40 CONTINUE
CALL SLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1,
$ TAU( TAUPOS ) )
*
CALL SLARFX( 'Left', LM, LN-1, V( VPOS ),
$ ( TAU( TAUPOS ) ),
$ A( DPOS+NB-1, ST+1 ), LDA-1, WORK)
ENDIF
ENDIF
ENDIF
*
RETURN
*
* END OF SSB2ST_KERNELS
*
END
|
