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diff --git a/SRC/zhegv_2stage.f b/SRC/zhegv_2stage.f new file mode 100644 index 00000000..5079d240 --- /dev/null +++ b/SRC/zhegv_2stage.f @@ -0,0 +1,379 @@ +*> \brief \b ZHEGV_2STAGE +* +* @precisions fortran z -> c +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZHEGV_2STAGE + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegv_2stage.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegv_2stage.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegv_2stage.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZHEGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, +* WORK, LWORK, RWORK, INFO ) +* +* IMPLICIT NONE +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, UPLO +* INTEGER INFO, ITYPE, LDA, LDB, LWORK, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION RWORK( * ), W( * ) +* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors +*> of a complex generalized Hermitian-definite eigenproblem, of the form +*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. +*> Here A and B are assumed to be Hermitian and B is also +*> positive definite. +*> This routine use the 2stage technique for the reduction to tridiagonal +*> which showed higher performance on recent architecture and for large +* sizes N>2000. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] ITYPE +*> \verbatim +*> ITYPE is INTEGER +*> Specifies the problem type to be solved: +*> = 1: A*x = (lambda)*B*x +*> = 2: A*B*x = (lambda)*x +*> = 3: B*A*x = (lambda)*x +*> \endverbatim +*> +*> \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 triangles of A and B are stored; +*> = 'L': Lower triangles of A and B are stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrices A and B. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA, N) +*> On entry, the Hermitian 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 +*> matrix Z of eigenvectors. The eigenvectors are normalized +*> as follows: +*> if ITYPE = 1 or 2, Z**H*B*Z = I; +*> if ITYPE = 3, Z**H*inv(B)*Z = I. +*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') +*> or the lower triangle (if UPLO='L') 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[in,out] B +*> \verbatim +*> B is COMPLEX*16 array, dimension (LDB, N) +*> On entry, the Hermitian positive definite matrix B. +*> If UPLO = 'U', the leading N-by-N upper triangular part of B +*> contains the upper triangular part of the matrix B. +*> If UPLO = 'L', the leading N-by-N lower triangular part of B +*> contains the lower triangular part of the matrix B. +*> +*> On exit, if INFO <= N, the part of B containing the matrix is +*> overwritten by the triangular factor U or L from the Cholesky +*> factorization B = U**H*U or B = L*L**H. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= 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 COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The length of the array WORK. LWORK >= 1, when N <= 1; +*> otherwise +*> If JOBZ = 'N' and N > 1, LWORK must be queried. +*> LWORK = MAX(1, dimension) where +*> dimension = max(stage1,stage2) + (KD+1)*N + N +*> = N*KD + N*max(KD+1,FACTOPTNB) +*> + max(2*KD*KD, KD*NTHREADS) +*> + (KD+1)*N + 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. +*> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available +*> +*> If LWORK = -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. +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: ZPOTRF or ZHEEV returned an error code: +*> <= N: if INFO = i, ZHEEV failed to converge; +*> i off-diagonal elements of an intermediate +*> tridiagonal form did not converge to zero; +*> > N: if INFO = N + i, for 1 <= i <= N, then the leading +*> minor of order i of B is not positive definite. +*> The factorization of B could not be completed and +*> no eigenvalues or eigenvectors were computed. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2016 +* +*> \ingroup complex16HEeigen +* +*> \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 ZHEGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, + $ WORK, LWORK, RWORK, INFO ) +* + IMPLICIT NONE +* +* -- LAPACK driver routine (version 3.6.0) -- +* -- 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 JOBZ, UPLO + INTEGER INFO, ITYPE, LDA, LDB, LWORK, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION RWORK( * ), W( * ) + COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER NEIG, LWMIN, LHTRD, LWTRD, KD, IB +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZHEGST, ZPOTRF, ZTRMM, ZTRSM, + $ ZHEEV_2STAGE +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ.-1 ) +* + INFO = 0 + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -6 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF +* + IF( INFO.EQ.0 ) THEN + KD = ILAENV( 17, 'ZHETRD_2STAGE', JOBZ, N, -1, -1, -1 ) + IB = ILAENV( 18, 'ZHETRD_2STAGE', JOBZ, N, KD, -1, -1 ) + LHTRD = ILAENV( 19, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) + LWTRD = ILAENV( 20, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) + LWMIN = N + LHTRD + LWTRD + WORK( 1 ) = LWMIN +* + IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -11 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZHEGV_2STAGE ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a Cholesky factorization of B. +* + CALL ZPOTRF( UPLO, N, B, LDB, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem and solve. +* + CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + CALL ZHEEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, + $ WORK, LWORK, RWORK, INFO ) +* + IF( WANTZ ) THEN +* +* Backtransform eigenvectors to the original problem. +* + NEIG = N + IF( INFO.GT.0 ) + $ NEIG = INFO - 1 + IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN +* +* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; +* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y +* + IF( UPPER ) THEN + TRANS = 'N' + ELSE + TRANS = 'C' + END IF +* + CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) +* + ELSE IF( ITYPE.EQ.3 ) THEN +* +* For B*A*x=(lambda)*x; +* backtransform eigenvectors: x = L*y or U**H *y +* + IF( UPPER ) THEN + TRANS = 'C' + ELSE + TRANS = 'N' + END IF +* + CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) + END IF + END IF +* + WORK( 1 ) = LWMIN +* + RETURN +* +* End of ZHEGV_2STAGE +* + END |