*> \brief \b CHETRD_2STAGE
*
* @generated from zhetrd_2stage.f, fortran z -> c, Sun Nov 6 19:34:06 2016
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
* HOUS2, LHOUS2, WORK, LWORK, INFO )
*
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* CHARACTER VECT, UPLO
* INTEGER N, LDA, LWORK, LHOUS2, INFO
* ..
* .. Array Arguments ..
* REAL D( * ), E( * )
* COMPLEX A( LDA, * ), TAU( * ),
* HOUS2( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHETRD_2STAGE reduces a complex Hermitian matrix A to real symmetric
*> tridiagonal form T by a unitary similarity transformation:
*> Q1**H Q2**H* A * Q2 * Q1 = T.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] VECT
*> \verbatim
*> VECT is CHARACTER*1
*> = 'N': No need for the Housholder representation,
*> in particular for the second stage (Band to
*> tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
*> = 'V': the Householder representation is needed to
*> either generate Q1 Q2 or to apply Q1 Q2,
*> then LHOUS2 is to be queried and computed.
*> (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, and the strictly lower
*> triangular part of A is not referenced. If UPLO = 'L', the
*> leading N-by-N lower triangular part of A contains the lower
*> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced.
*> On exit, if UPLO = 'U', the band superdiagonal
*> of A are overwritten by the corresponding elements of the
*> internal band-diagonal matrix AB, and the elements above
*> the KD superdiagonal, with the array TAU, represent the unitary
*> matrix Q1 as a product of elementary reflectors; if UPLO
*> = 'L', the diagonal and band subdiagonal of A are over-
*> written by the corresponding elements of the internal band-diagonal
*> matrix AB, and the elements below the KD subdiagonal, with
*> the array TAU, represent the unitary matrix Q1 as a product
*> of elementary reflectors. See Further Details.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] D
*> \verbatim
*> D is REAL array, dimension (N)
*> The diagonal elements of the tridiagonal matrix T.
*> \endverbatim
*>
*> \param[out] E
*> \verbatim
*> E is REAL array, dimension (N-1)
*> The off-diagonal elements of the tridiagonal matrix T.
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (N-KD)
*> The scalar factors of the elementary reflectors of
*> the first stage (see Further Details).
*> \endverbatim
*>
*> \param[out] HOUS2
*> \verbatim
*> HOUS2 is COMPLEX array, dimension (LHOUS2)
*> Stores the Householder representation of the stage2
*> band to tridiagonal.
*> \endverbatim
*>
*> \param[in] LHOUS2
*> \verbatim
*> LHOUS2 is INTEGER
*> The dimension of the array HOUS2.
*> If LWORK = -1, or LHOUS2=-1,
*> then a query is assumed; the routine
*> only calculates the optimal size of the HOUS2 array, returns
*> this value as the first entry of the HOUS2 array, and no error
*> message related to LHOUS2 is issued by XERBLA.
*> If VECT='N', LHOUS2 = max(1, 4*n);
*> if VECT='V', option not yet available.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK. LWORK = MAX(1, dimension)
*> If LWORK = -1, or LHOUS2 = -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.
*> LWORK = MAX(1, dimension) where
*> dimension = max(stage1,stage2) + (KD+1)*N
*> = N*KD + N*max(KD+1,FACTOPTNB)
*> + max(2*KD*KD, KD*NTHREADS)
*> + (KD+1)*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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexHEcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Implemented by Azzam Haidar.
*>
*> All details are available on technical report, SC11, SC13 papers.
*>
*> 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 CHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
$ HOUS2, LHOUS2, WORK, LWORK, INFO )
*
IMPLICIT NONE
*
* -- LAPACK computational 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 VECT, UPLO
INTEGER N, LDA, LWORK, LHOUS2, INFO
* ..
* .. Array Arguments ..
REAL D( * ), E( * )
COMPLEX A( LDA, * ), TAU( * ),
$ HOUS2( * ), WORK( * )
* ..
*
* =====================================================================
* ..
* .. Local Scalars ..
LOGICAL LQUERY, UPPER, WANTQ
INTEGER KD, IB, LWMIN, LHMIN, LWRK, LDAB, WPOS, ABPOS
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, CHETRD_HE2HB, CHETRD_HB2ST
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV2STAGE
EXTERNAL LSAME, ILAENV2STAGE
* ..
* .. Executable Statements ..
*
* Test the input parameters
*
INFO = 0
WANTQ = LSAME( VECT, 'V' )
UPPER = LSAME( UPLO, 'U' )
LQUERY = ( LWORK.EQ.-1 ) .OR. ( LHOUS2.EQ.-1 )
*
* Determine the block size, the workspace size and the hous size.
*
KD = ILAENV2STAGE( 1, 'CHETRD_2STAGE', VECT, N, -1, -1, -1 )
IB = ILAENV2STAGE( 2, 'CHETRD_2STAGE', VECT, N, KD, -1, -1 )
LHMIN = ILAENV2STAGE( 3, 'CHETRD_2STAGE', VECT, N, KD, IB, -1 )
LWMIN = ILAENV2STAGE( 4, 'CHETRD_2STAGE', VECT, N, KD, IB, -1 )
* WRITE(*,*),'CHETRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
* $ LHMIN, LWMIN
*
IF( .NOT.LSAME( VECT, 'N' ) ) THEN
INFO = -1
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LHOUS2.LT.LHMIN .AND. .NOT.LQUERY ) THEN
INFO = -10
ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -12
END IF
*
IF( INFO.EQ.0 ) THEN
HOUS2( 1 ) = LHMIN
WORK( 1 ) = LWMIN
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHETRD_2STAGE', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
* Determine pointer position
*
LDAB = KD+1
LWRK = LWORK-LDAB*N
ABPOS = 1
WPOS = ABPOS + LDAB*N
CALL CHETRD_HE2HB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
$ TAU, WORK( WPOS ), LWRK, INFO )
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHETRD_HE2HB', -INFO )
RETURN
END IF
CALL CHETRD_HB2ST( 'Y', VECT, UPLO, N, KD,
$ WORK( ABPOS ), LDAB, D, E,
$ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHETRD_HB2ST', -INFO )
RETURN
END IF
*
*
HOUS2( 1 ) = LHMIN
WORK( 1 ) = LWMIN
RETURN
*
* End of CHETRD_2STAGE
*
END