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diff --git a/SRC/ssytrd_2stage.f b/SRC/ssytrd_2stage.f new file mode 100644 index 00000000..fba3dd45 --- /dev/null +++ b/SRC/ssytrd_2stage.f @@ -0,0 +1,337 @@ +*> \brief \b SSYTRD_2STAGE +* +* @generated from zhetrd_2stage.f, fortran z -> s, Sun Nov 6 19:34:06 2016 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SSYTRD_2STAGE + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrd_2stage.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssytrd_2stage.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrd_2stage.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, +* HOUS2, LHOUS2, WORK, LWORK, INFO ) +* +* IMPLICIT NONE +* +* .. Scalar Arguments .. +* CHARACTER VECT, UPLO +* INTEGER N, LDA, LWORK, LHOUS2, INFO +* .. +* .. Array Arguments .. +* REAL D( * ), E( * ) +* REAL A( LDA, * ), TAU( * ), +* HOUS2( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric +*> tridiagonal form T by a orthogonal similarity transformation: +*> Q1**T Q2**T* A * Q2 * Q1 = T. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] VECT +*> \verbatim +*> VECT is CHARACTER*1 +*> = 'N': No need for the Housholder representation, +*> in particular for the second stage (Band to +*> tridiagonal) and thus LHOUS2 is of size max(1, 4*N); +*> = 'V': the Householder representation is needed to +*> either generate Q1 Q2 or to apply Q1 Q2, +*> then LHOUS2 is to be queried and computed. +*> (NOT AVAILABLE IN THIS RELEASE). +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> On entry, the symmetric matrix A. If UPLO = 'U', the leading +*> N-by-N upper triangular part of A contains the upper +*> triangular part of the matrix A, and the strictly lower +*> triangular part of A is not referenced. If UPLO = 'L', the +*> leading N-by-N lower triangular part of A contains the lower +*> triangular part of the matrix A, and the strictly upper +*> triangular part of A is not referenced. +*> On exit, if UPLO = 'U', the band superdiagonal +*> of A are overwritten by the corresponding elements of the +*> internal band-diagonal matrix AB, and the elements above +*> the KD superdiagonal, with the array TAU, represent the orthogonal +*> matrix Q1 as a product of elementary reflectors; if UPLO +*> = 'L', the diagonal and band subdiagonal of A are over- +*> written by the corresponding elements of the internal band-diagonal +*> matrix AB, and the elements below the KD subdiagonal, with +*> the array TAU, represent the orthogonal matrix Q1 as a product +*> of elementary reflectors. See Further Details. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] D +*> \verbatim +*> D is REAL array, dimension (N) +*> The diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[out] E +*> \verbatim +*> E is REAL array, dimension (N-1) +*> The off-diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is REAL array, dimension (N-KD) +*> The scalar factors of the elementary reflectors of +*> the first stage (see Further Details). +*> \endverbatim +*> +*> \param[out] HOUS2 +*> \verbatim +*> HOUS2 is REAL array, dimension LHOUS2, that +*> store the Householder representation of the stage2 +*> band to tridiagonal. +*> \endverbatim +*> +*> \param[in] LHOUS2 +*> \verbatim +*> LHOUS2 is INTEGER +*> The dimension of the array HOUS2. LHOUS2 = MAX(1, dimension) +*> If LWORK = -1, or LHOUS2=-1, +*> then a query is assumed; the routine +*> only calculates the optimal size of the HOUS2 array, returns +*> this value as the first entry of the HOUS2 array, and no error +*> message related to LHOUS2 is issued by XERBLA. +*> LHOUS2 = MAX(1, dimension) where +*> dimension = 4*N if VECT='N' +*> not available now if VECT='H' +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. LWORK = MAX(1, dimension) +*> If LWORK = -1, or LHOUS2=-1, +*> then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> LWORK = MAX(1, dimension) where +*> dimension = max(stage1,stage2) + (KD+1)*N +*> = N*KD + N*max(KD+1,FACTOPTNB) +*> + max(2*KD*KD, KD*NTHREADS) +*> + (KD+1)*N +*> where KD is the blocking size of the reduction, +*> FACTOPTNB is the blocking used by the QR or LQ +*> algorithm, usually FACTOPTNB=128 is a good choice +*> NTHREADS is the number of threads used when +*> openMP compilation is enabled, otherwise =1. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2016 +* +*> \ingroup realSYcomputational +* +*> \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 SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, + $ HOUS2, LHOUS2, WORK, LWORK, INFO ) +* + IMPLICIT NONE +* +* -- 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 2016 +* +* .. Scalar Arguments .. + CHARACTER VECT, UPLO + INTEGER N, LDA, LWORK, LHOUS2, INFO +* .. +* .. Array Arguments .. + REAL D( * ), E( * ) + REAL A( LDA, * ), TAU( * ), + $ HOUS2( * ), WORK( * ) +* .. +* +* ===================================================================== +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTQ + INTEGER KD, IB, LWMIN, LHMIN, LWRK, LDAB, WPOS, ABPOS +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, SSYTRD_SY2SB, SSYTRD_SB2ST +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. Executable Statements .. +* +* Test the input parameters +* + INFO = 0 + WANTQ = LSAME( VECT, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ.-1 ) .OR. ( LHOUS2.EQ.-1 ) +* +* Determine the block size, the workspace size and the hous size. +* + KD = ILAENV( 17, 'SSYTRD_2STAGE', VECT, N, -1, -1, -1 ) + IB = ILAENV( 18, 'SSYTRD_2STAGE', VECT, N, KD, -1, -1 ) + LHMIN = ILAENV( 19, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 ) + LWMIN = ILAENV( 20, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 ) +* WRITE(*,*),'SSYTRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO, +* $ LHMIN, LWMIN +* + IF( .NOT.LSAME( VECT, 'N' ) ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LHOUS2.LT.LHMIN .AND. .NOT.LQUERY ) THEN + INFO = -10 + ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -12 + END IF +* + IF( INFO.EQ.0 ) THEN + HOUS2( 1 ) = LHMIN + WORK( 1 ) = LWMIN + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSYTRD_2STAGE', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) THEN + WORK( 1 ) = 1 + RETURN + END IF +* +* Determine pointer position +* + LDAB = KD+1 + LWRK = LWORK-LDAB*N + ABPOS = 1 + WPOS = ABPOS + LDAB*N + CALL SSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB, + $ TAU, WORK( WPOS ), LWRK, INFO ) + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSYTRD_SY2SB', -INFO ) + RETURN + END IF + CALL SSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD, + $ WORK( ABPOS ), LDAB, D, E, + $ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO ) + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSYTRD_SB2ST', -INFO ) + RETURN + END IF +* +* + HOUS2( 1 ) = LHMIN + WORK( 1 ) = LWMIN + RETURN +* +* End of SSYTRD_2STAGE +* + END |