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lapack/SRC/cheevd_2stage.f
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*> \brief <b> CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
*
* @generated from zheevd_2stage.f, fortran z -> c, Sat Nov 5 23:18:14 2016
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CHEEVD_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheevd_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheevd_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheevd_2stage.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CHEEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
* RWORK, LRWORK, IWORK, LIWORK, INFO )
*
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, UPLO
* INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* REAL RWORK( * ), W( * )
* COMPLEX A( LDA, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian 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 COMPLEX 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
*> 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 REAL array, dimension (N)
*> If INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX 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 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 + N+1
*> = N*KD + N*max(KD+1,FACTOPTNB)
*> + max(2*KD*KD, KD*NTHREADS)
*> + (KD+1)*N + 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 2*N + N**2
*>
*> 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 (LRWORK)
*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
*> \endverbatim
*>
*> \param[in] LRWORK
*> \verbatim
*> LRWORK is INTEGER
*> The dimension of the array RWORK.
*> If N <= 1, LRWORK must be at least 1.
*> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
*> If JOBZ = 'V' and N > 1, LRWORK must be at least
*> 1 + 5*N + 2*N**2.
*>
*> If LRWORK = -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] 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, 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] 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.
*
*> \ingroup complexHEeigen
*
*> \par Further Details:
* =====================
*>
*> Modified description of INFO. Sven, 16 Feb 05.
*
*> \par Contributors:
* ==================
*>
*> Jeff Rutter, Computer Science Division, University of California
*> at Berkeley, USA
*>
*> \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 CHEEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
$ RWORK, LRWORK, IWORK, LIWORK, INFO )
*
IMPLICIT NONE
*
* -- LAPACK driver routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E0, 0.0E0 ) )
* ..
* .. Local Scalars ..
LOGICAL LOWER, LQUERY, WANTZ
INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2,
$ INDWRK, ISCALE, LIWMIN, LLRWK, LLWORK,
$ LLWRK2, LRWMIN, LWMIN,
$ LHTRD, LWTRD, KD, IB, INDHOUS
REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV2STAGE
REAL SLAMCH, CLANHE
EXTERNAL LSAME, SLAMCH, CLANHE, ILAENV2STAGE
* ..
* .. External Subroutines ..
EXTERNAL SSCAL, SSTERF, XERBLA, CLACPY, CLASCL,
$ CSTEDC, CUNMTR, CHETRD_2STAGE
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL, MAX, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
LOWER = LSAME( UPLO, 'L' )
LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.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
LWMIN = 1
LRWMIN = 1
LIWMIN = 1
ELSE
KD = ILAENV2STAGE( 1, 'CHETRD_2STAGE', JOBZ,
$ N, -1, -1, -1 )
IB = ILAENV2STAGE( 2, 'CHETRD_2STAGE', JOBZ,
$ N, KD, -1, -1 )
LHTRD = ILAENV2STAGE( 3, 'CHETRD_2STAGE', JOBZ,
$ N, KD, IB, -1 )
LWTRD = ILAENV2STAGE( 4, 'CHETRD_2STAGE', JOBZ,
$ N, KD, IB, -1 )
IF( WANTZ ) THEN
LWMIN = 2*N + N*N
LRWMIN = 1 + 5*N + 2*N**2
LIWMIN = 3 + 5*N
ELSE
LWMIN = N + 1 + LHTRD + LWTRD
LRWMIN = N
LIWMIN = 1
END IF
END IF
WORK( 1 ) = LWMIN
RWORK( 1 ) = LRWMIN
IWORK( 1 ) = LIWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -8
ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
INFO = -10
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -12
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHEEVD_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 ) = REAL( A( 1, 1 ) )
IF( WANTZ )
$ A( 1, 1 ) = CONE
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 = CLANHE( 'M', UPLO, N, A, LDA, 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 )
$ CALL CLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
*
* Call CHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form.
*
INDE = 1
INDRWK = INDE + N
LLRWK = LRWORK - INDRWK + 1
INDTAU = 1
INDHOUS = INDTAU + N
INDWRK = INDHOUS + LHTRD
LLWORK = LWORK - INDWRK + 1
INDWK2 = INDWRK + N*N
LLWRK2 = LWORK - INDWK2 + 1
*
CALL CHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, W, RWORK( INDE ),
$ WORK( INDTAU ), WORK( INDHOUS ), LHTRD,
$ WORK( INDWRK ), LLWORK, IINFO )
*
* For eigenvalues only, call SSTERF. For eigenvectors, first call
* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
* tridiagonal matrix, then call CUNMTR to multiply it to the
* Householder transformations represented as Householder vectors in
* A.
*
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, W, RWORK( INDE ), INFO )
ELSE
CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N,
$ WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK,
$ IWORK, LIWORK, INFO )
CALL CUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
$ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
CALL CLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
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
*
WORK( 1 ) = LWMIN
RWORK( 1 ) = LRWMIN
IWORK( 1 ) = LIWMIN
*
RETURN
*
* End of CHEEVD_2STAGE
*
END
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