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diff --git a/SRC/dsyevd_2stage.f b/SRC/dsyevd_2stage.f new file mode 100644 index 00000000..161f0e9e --- /dev/null +++ b/SRC/dsyevd_2stage.f @@ -0,0 +1,406 @@ +*> \brief <b> DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b> +* +* @precisions fortran d -> s +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DSYEVD_2STAGE + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevd_2stage.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevd_2stage.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevd_2stage.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DSYEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, +* IWORK, LIWORK, INFO ) +* +* IMPLICIT NONE +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, UPLO +* INTEGER INFO, LDA, LIWORK, LWORK, N +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a +*> real symmetric matrix A using the 2stage technique for +*> the reduction to tridiagonal. If eigenvectors are desired, it uses a +*> divide and conquer algorithm. +*> +*> The divide and conquer algorithm makes very mild assumptions about +*> floating point arithmetic. It will work on machines with a guard +*> digit in add/subtract, or on those binary machines without guard +*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or +*> Cray-2. It could conceivably fail on hexadecimal or decimal machines +*> without guard digits, but we know of none. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOBZ +*> \verbatim +*> JOBZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only; +*> = 'V': Compute eigenvalues and eigenvectors. +*> 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 DOUBLE PRECISION 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. If UPLO = 'L', +*> the leading N-by-N lower triangular part of A contains +*> the lower triangular part of the matrix A. +*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the +*> orthonormal eigenvectors of the matrix A. +*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') +*> or the upper triangle (if UPLO='U') of A, including the +*> diagonal, is destroyed. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> If INFO = 0, the eigenvalues in ascending order. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, +*> dimension (LWORK) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. +*> If N <= 1, LWORK must be at least 1. +*> If JOBZ = 'N' and N > 1, LWORK must be queried. +*> LWORK = MAX(1, dimension) where +*> dimension = max(stage1,stage2) + (KD+1)*N + 2*N+1 +*> = N*KD + N*max(KD+1,FACTOPTNB) +*> + max(2*KD*KD, KD*NTHREADS) +*> + (KD+1)*N + 2*N+1 +*> 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. +*> If JOBZ = 'V' and N > 1, LWORK must be at least +*> 1 + 6*N + 2*N**2. +*> +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal sizes of the WORK and IWORK +*> arrays, returns these values as the first entries of the WORK +*> and IWORK arrays, and no error message related to LWORK or +*> LIWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) +*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. +*> \endverbatim +*> +*> \param[in] LIWORK +*> \verbatim +*> LIWORK is INTEGER +*> The dimension of the array IWORK. +*> If N <= 1, LIWORK must be at least 1. +*> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. +*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. +*> +*> If LIWORK = -1, then a workspace query is assumed; the +*> routine only calculates the optimal sizes of the WORK and +*> IWORK arrays, returns these values as the first entries of +*> the WORK and IWORK arrays, and no error message related to +*> LWORK or LIWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed +*> to converge; i off-diagonal elements of an intermediate +*> tridiagonal form did not converge to zero; +*> if INFO = i and JOBZ = 'V', then the algorithm failed +*> to compute an eigenvalue while working on the submatrix +*> lying in rows and columns INFO/(N+1) through +*> mod(INFO,N+1). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date September 2012 +* +*> \ingroup doubleSYeigen +* +*> \par Contributors: +* ================== +*> +*> Jeff Rutter, Computer Science Division, University of California +*> at Berkeley, USA \n +*> Modified by Francoise Tisseur, University of Tennessee \n +*> Modified description of INFO. Sven, 16 Feb 05. \n +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> All details about the 2stage techniques are available in: +*> +*> 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 DSYEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, + $ IWORK, LIWORK, INFO ) +* + IMPLICIT NONE +* +* -- LAPACK driver 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 JOBZ, UPLO + INTEGER INFO, LDA, LIWORK, LWORK, N +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. +* + LOGICAL LOWER, LQUERY, WANTZ + INTEGER IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE, + $ LIWMIN, LLWORK, LLWRK2, LWMIN, + $ LHTRD, LWTRD, KD, IB, INDHOUS + DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, + $ SMLNUM +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + DOUBLE PRECISION DLAMCH, DLANSY + EXTERNAL LSAME, DLAMCH, DLANSY, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL DLACPY, DLASCL, DORMTR, DSCAL, DSTEDC, DSTERF, + $ DSYTRD_2STAGE, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + LOWER = LSAME( UPLO, 'L' ) + LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) +* + INFO = 0 + IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + END IF +* + IF( INFO.EQ.0 ) THEN + IF( N.LE.1 ) THEN + LIWMIN = 1 + LWMIN = 1 + ELSE + KD = ILAENV( 17, 'DSYTRD_2STAGE', JOBZ, N, -1, -1, -1 ) + IB = ILAENV( 18, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1 ) + LHTRD = ILAENV( 19, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 ) + LWTRD = ILAENV( 20, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 ) + IF( WANTZ ) THEN + LIWMIN = 3 + 5*N + LWMIN = 1 + 6*N + 2*N**2 + ELSE + LIWMIN = 1 + LWMIN = 2*N + 1 + LHTRD + LWTRD + END IF + END IF + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN +* + IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -8 + ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN + INFO = -10 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSYEVD_2STAGE', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( N.EQ.1 ) THEN + W( 1 ) = A( 1, 1 ) + IF( WANTZ ) + $ A( 1, 1 ) = ONE + RETURN + END IF +* +* Get machine constants. +* + SAFMIN = DLAMCH( 'Safe minimum' ) + EPS = DLAMCH( 'Precision' ) + SMLNUM = SAFMIN / EPS + BIGNUM = ONE / SMLNUM + RMIN = SQRT( SMLNUM ) + RMAX = SQRT( BIGNUM ) +* +* Scale matrix to allowable range, if necessary. +* + ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) + ISCALE = 0 + IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN + ISCALE = 1 + SIGMA = RMIN / ANRM + ELSE IF( ANRM.GT.RMAX ) THEN + ISCALE = 1 + SIGMA = RMAX / ANRM + END IF + IF( ISCALE.EQ.1 ) + $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) +* +* Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form. +* + INDE = 1 + INDTAU = INDE + N + INDHOUS = INDTAU + N + INDWRK = INDHOUS + LHTRD + LLWORK = LWORK - INDWRK + 1 + INDWK2 = INDWRK + N*N + LLWRK2 = LWORK - INDWK2 + 1 +* + CALL DSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK( INDE ), + $ WORK( INDTAU ), WORK( INDHOUS ), LHTRD, + $ WORK( INDWRK ), LLWORK, IINFO ) +* +* For eigenvalues only, call DSTERF. For eigenvectors, first call +* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the +* tridiagonal matrix, then call DORMTR to multiply it by the +* Householder transformations stored in A. +* + IF( .NOT.WANTZ ) THEN + CALL DSTERF( N, W, WORK( INDE ), INFO ) + ELSE +* Not available in this release, and agrument checking should not +* let it getting here + RETURN + CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N, + $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO ) + CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), + $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) + CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) + END IF +* +* If matrix was scaled, then rescale eigenvalues appropriately. +* + IF( ISCALE.EQ.1 ) + $ CALL DSCAL( N, ONE / SIGMA, W, 1 ) +* + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN +* + RETURN +* +* End of DSYEVD_2STAGE +* + END |