*> \brief CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices * * @generated from zhbev_2stage.f, fortran z -> c, Sat Nov 5 23:18:20 2016 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CHBEV_2STAGE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CHBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, * WORK, LWORK, RWORK, INFO ) * * IMPLICIT NONE * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, KD, LDAB, LDZ, N, LWORK * .. * .. Array Arguments .. * REAL RWORK( * ), W( * ) * COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of *> a complex Hermitian band matrix A using the 2stage technique for *> the reduction to tridiagonal. *> \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] KD *> \verbatim *> KD is INTEGER *> The number of superdiagonals of the matrix A if UPLO = 'U', *> or the number of subdiagonals if UPLO = 'L'. KD >= 0. *> \endverbatim *> *> \param[in,out] AB *> \verbatim *> AB is COMPLEX array, dimension (LDAB, N) *> On entry, the upper or lower triangle of the Hermitian band *> matrix A, stored in the first KD+1 rows of the array. The *> j-th column of A is stored in the j-th column of the array AB *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). *> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L', *> the diagonal and first subdiagonal of T are returned in the *> first two rows of AB. *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> The leading dimension of the array AB. LDAB >= KD + 1. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is REAL array, dimension (N) *> If INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is COMPLEX array, dimension (LDZ, N) *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal *> eigenvectors of the matrix A, with the i-th column of Z *> holding the eigenvector associated with W(i). *> If JOBZ = 'N', then Z is not referenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension 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 = (2KD+1)*N + KD*NTHREADS *> where KD is the size of the band. *> 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 sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of *> the WORK, RWORK and IWORK arrays, and no error message *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL 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: if INFO = i, the algorithm failed to converge; i *> off-diagonal elements of an intermediate tridiagonal *> form did not converge to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complexOTHEReigen * *> \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 CHBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, \$ WORK, LWORK, RWORK, INFO ) * IMPLICIT NONE * * -- LAPACK driver 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 JOBZ, UPLO INTEGER INFO, KD, LDAB, LDZ, N, LWORK * .. * .. Array Arguments .. REAL RWORK( * ), W( * ) COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. LOGICAL LOWER, WANTZ, LQUERY INTEGER IINFO, IMAX, INDE, INDWRK, INDRWK, ISCALE, \$ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, \$ SMLNUM * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV REAL SLAMCH, CLANHB EXTERNAL LSAME, SLAMCH, CLANHB, ILAENV * .. * .. External Subroutines .. EXTERNAL SSCAL, SSTERF, XERBLA, CLASCL, CSTEQR, \$ CHETRD_2STAGE * .. * .. Intrinsic Functions .. INTRINSIC REAL, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) LQUERY = ( LWORK.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( KD.LT.0 ) THEN INFO = -4 ELSE IF( LDAB.LT.KD+1 ) THEN INFO = -6 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -9 END IF * IF( INFO.EQ.0 ) THEN IF( N.LE.1 ) THEN LWMIN = 1 WORK( 1 ) = LWMIN ELSE IB = ILAENV( 18, 'CHETRD_HB2ST', JOBZ, N, KD, -1, -1 ) LHTRD = ILAENV( 19, 'CHETRD_HB2ST', JOBZ, N, KD, IB, -1 ) LWTRD = ILAENV( 20, 'CHETRD_HB2ST', JOBZ, N, KD, IB, -1 ) LWMIN = LHTRD + LWTRD WORK( 1 ) = LWMIN ENDIF * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) \$ INFO = -11 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHBEV_2STAGE ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( N.EQ.1 ) THEN IF( LOWER ) THEN W( 1 ) = REAL( AB( 1, 1 ) ) ELSE W( 1 ) = REAL( AB( KD+1, 1 ) ) END IF IF( WANTZ ) \$ Z( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * SAFMIN = SLAMCH( 'Safe minimum' ) EPS = SLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = CLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK ) 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 ) THEN IF( LOWER ) THEN CALL CLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO ) ELSE CALL CLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO ) END IF END IF * * Call CHBTRD_HB2ST to reduce Hermitian band matrix to tridiagonal form. * INDE = 1 INDHOUS = 1 INDWRK = INDHOUS + LHTRD LLWORK = LWORK - INDWRK + 1 * CALL CHETRD_HB2ST( "N", JOBZ, UPLO, N, KD, AB, LDAB, W, \$ RWORK( INDE ), WORK( INDHOUS ), LHTRD, \$ WORK( INDWRK ), LLWORK, IINFO ) * * For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, W, RWORK( INDE ), INFO ) ELSE INDRWK = INDE + N CALL CSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ, \$ RWORK( INDRWK ), INFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = N ELSE IMAX = INFO - 1 END IF CALL SSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * Set WORK(1) to optimal workspace size. * WORK( 1 ) = LWMIN * RETURN * * End of CHBEV_2STAGE * END