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chegv_2stage.f
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*> \brief \b CHEGV_2STAGE
*
* @generated from zhegv_2stage.f, fortran z -> c, Sun Nov 6 13:09:52 2016
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CHEGV_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chegv_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chegv_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chegv_2stage.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CHEGV_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 ..
* REAL RWORK( * ), W( * )
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHEGV_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 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 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 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 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 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: CPOTRF or CHEEV returned an error code:
*> <= N: if INFO = i, CHEEV 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
*> principal minor of order i of B is not positive.
*> 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.
*
*> \ingroup complexHEeigen
*
*> \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 CHEGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
$ WORK, LWORK, RWORK, 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, ITYPE, LDA, LDB, LWORK, N
* ..
* .. Array Arguments ..
REAL RWORK( * ), W( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL LQUERY, UPPER, WANTZ
CHARACTER TRANS
INTEGER NEIG, LWMIN, LHTRD, LWTRD, KD, IB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV2STAGE
EXTERNAL LSAME, ILAENV2STAGE
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, CHEGST, CPOTRF, CTRMM, CTRSM,
$ CHEEV_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 = 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 )
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( 'CHEGV_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 CPOTRF( 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 CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
CALL CHEEV_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 CTRSM( '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 CTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
$ B, LDB, A, LDA )
END IF
END IF
*
WORK( 1 ) = LWMIN
*
RETURN
*
* End of CHEGV_2STAGE
*
END