zhetrd_2stage.f

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*> \brief \b ZHETRD_2STAGE
*
*  @precisions fortran z -> s d c
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZHETRD_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 ..
*       DOUBLE PRECISION   D( * ), E( * )
*       COMPLEX*16         A( LDA, * ), TAU( * ),
*                          HOUS2( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZHETRD_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*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, 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 DOUBLE PRECISION array, dimension (N)
*>          The diagonal elements of the tridiagonal matrix T.
*> \endverbatim
*>
*> \param[out] E
*> \verbatim
*>          E is DOUBLE PRECISION array, dimension (N-1)
*>          The off-diagonal elements of the tridiagonal matrix T.
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*>          TAU is COMPLEX*16 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*16 array, dimension LHOUS2, that
*>          store the Householder representation of the stage2
*>          band to tridiagonal.
*> \endverbatim
*>
*> \param[in] LHOUS2
*> \verbatim
*>          LHOUS2 is INTEGER
*>          The dimension of the array HOUS2. LHOUS2 = MAX(1, dimension)
*>          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.
*>          LHOUS2 = MAX(1, dimension) where
*>          dimension = 4*N if VECT='N'
*>          not available now if VECT='H'
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 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. 
*
*> \date December 2016
*
*> \ingroup complex16HEcomputational
*
*> \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 zhetrd_2stage( VECT, UPLO, N, A, LDA, D, E, TAU, 
     $                          hous2, lhous2, work, lwork, info )
*
      IMPLICIT NONE
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          VECT, UPLO
      INTEGER            N, LDA, LWORK, LHOUS2, INFO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   D( * ), E( * )
      COMPLEX*16         A( lda, * ), TAU( * ),
     $                   hous2( * ), work( * )
*     ..
*
*  =====================================================================
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER, WANTQ
      INTEGER            KD, IB, LWMIN, LHMIN, LWRK, LDAB, WPOS, ABPOS
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zhetrd_he2hb, zhetrd_hb2st
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. 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     = ilaenv( 17, 'ZHETRD_2STAGE', vect, n, -1, -1, -1 )
      ib     = ilaenv( 18, 'ZHETRD_2STAGE', vect, n, kd, -1, -1 )
      lhmin  = ilaenv( 19, 'ZHETRD_2STAGE', vect, n, kd, ib, -1 )
      lwmin  = ilaenv( 20, 'ZHETRD_2STAGE', vect, n, kd, ib, -1 )
*      WRITE(*,*),'ZHETRD_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( 'ZHETRD_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 zhetrd_he2hb( uplo, n, kd, a, lda, work( abpos ), ldab, 
     $                   tau, work( wpos ), lwrk, info )
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZHETRD_HE2HB', -info )
         RETURN
      END IF
      CALL zhetrd_hb2st( 'Y', vect, uplo, n, kd, 
     $                   work( abpos ), ldab, d, e, 
     $                   hous2, lhous2, work( wpos ), lwrk, info )
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZHETRD_HB2ST', -info )
         RETURN
      END IF
*
*
      hous2( 1 ) = lhmin
      work( 1 )  = lwmin
      RETURN
*
*     End of ZHETRD_2STAGE
*
      END