elpa2.F90 324 KB
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!    This file is part of ELPA.
!
!    The ELPA library was originally created by the ELPA consortium,
!    consisting of the following organizations:
!
!    - Rechenzentrum Garching der Max-Planck-Gesellschaft (RZG),
!    - Bergische Universität Wuppertal, Lehrstuhl für angewandte
!      Informatik,
!    - Technische Universität München, Lehrstuhl für Informatik mit
!      Schwerpunkt Wissenschaftliches Rechnen ,
!    - Fritz-Haber-Institut, Berlin, Abt. Theorie,
!    - Max-Plack-Institut für Mathematik in den Naturwissenschaftrn,
!      Leipzig, Abt. Komplexe Strukutren in Biologie und Kognition,
!      and
!    - IBM Deutschland GmbH
!
!
!    More information can be found here:
!    http://elpa.rzg.mpg.de/
!
!    ELPA is free software: you can redistribute it and/or modify
!    it under the terms of the version 3 of the license of the
!    GNU Lesser General Public License as published by the Free
!    Software Foundation.
!
!    ELPA is distributed in the hope that it will be useful,
!    but WITHOUT ANY WARRANTY; without even the implied warranty of
!    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!    GNU Lesser General Public License for more details.
!
!    You should have received a copy of the GNU Lesser General Public License
!    along with ELPA.  If not, see <http://www.gnu.org/licenses/>
!
!    ELPA reflects a substantial effort on the part of the original
!    ELPA consortium, and we ask you to respect the spirit of the
!    license that we chose: i.e., please contribute any changes you
!    may have back to the original ELPA library distribution, and keep
!    any derivatives of ELPA under the same license that we chose for
!    the original distribution, the GNU Lesser General Public License.
!
!
! ELPA1 -- Faster replacements for ScaLAPACK symmetric eigenvalue routines
!
! Copyright of the original code rests with the authors inside the ELPA
! consortium. The copyright of any additional modifications shall rest
! with their original authors, but shall adhere to the licensing terms
! distributed along with the original code in the file "COPYING".



! ELPA2 -- 2-stage solver for ELPA
!
! Copyright of the original code rests with the authors inside the ELPA
! consortium. The copyright of any additional modifications shall rest
! with their original authors, but shall adhere to the licensing terms
! distributed along with the original code in the file "COPYING".


#include "config-f90.h"

module ELPA2

! Version 1.1.2, 2011-02-21

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  use elpa_utilities
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  USE ELPA1
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  use elpa2_utilities

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#ifdef HAVE_ISO_FORTRAN_ENV
  use iso_fortran_env, only : error_unit
#endif
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  use elpa_pdgeqrf

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#ifdef WITH_GPU_VERSION
  use cuda_routines
  use cuda_c_kernel
  use iso_c_binding
#endif
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  implicit none

  PRIVATE ! By default, all routines contained are private

  ! The following routines are public:

  public :: solve_evp_real_2stage
  public :: solve_evp_complex_2stage

  public :: bandred_real
  public :: tridiag_band_real
  public :: trans_ev_tridi_to_band_real
  public :: trans_ev_band_to_full_real

  public :: bandred_complex
  public :: tridiag_band_complex
  public :: trans_ev_tridi_to_band_complex
  public :: trans_ev_band_to_full_complex
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#ifndef HAVE_ISO_FORTRAN_ENV
  integer, parameter :: error_unit = 6
#endif

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  public :: band_band_real
  public :: divide_band

  integer, public :: which_qr_decomposition = 1     ! defines, which QR-decomposition algorithm will be used
                                                    ! 0 for unblocked
                                                    ! 1 for blocked (maxrank: nblk)
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!-------------------------------------------------------------------------------

  ! The following array contains the Householder vectors of the
  ! transformation band -> tridiagonal.
  ! It is allocated and set in tridiag_band_real and used in
  ! trans_ev_tridi_to_band_real.
  ! It must be deallocated by the user after trans_ev_tridi_to_band_real!

  real*8, allocatable :: hh_trans_real(:,:)
  complex*16, allocatable :: hh_trans_complex(:,:)

!-------------------------------------------------------------------------------

  include 'mpif.h'


!******
contains
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function solve_evp_real_2stage(na, nev, a, lda, ev, q, ldq, nblk, na_rows, matrixCols, &
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                                 mpi_comm_rows, mpi_comm_cols,             &
                                 mpi_comm_all, THIS_REAL_ELPA_KERNEL_API,  &
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                                 useQR) result(success)
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!-------------------------------------------------------------------------------
!  solve_evp_real_2stage: Solves the real eigenvalue problem with a 2 stage approach
!
!  Parameters
!
!  na          Order of matrix a
!
!  nev         Number of eigenvalues needed
!
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!  a(1:lda,:)    Distributed matrix for which eigenvalues are to be computed.
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!              Distribution is like in Scalapack.
!              The full matrix must be set (not only one half like in scalapack).
!              Destroyed on exit (upper and lower half).
!
!  lda         Leading dimension of a
!
!  ev(na)      On output: eigenvalues of a, every processor gets the complete set
!
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!  q(1:ldq,:)    On output: Eigenvectors of a
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!              Distribution is like in Scalapack.
!              Must be always dimensioned to the full size (corresponding to (na,na))
!              even if only a part of the eigenvalues is needed.
!
!  ldq         Leading dimension of q
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!  mpi_comm_all
!              MPI-Communicator for the total processor set
!
!-------------------------------------------------------------------------------
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#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
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   implicit none
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   logical, intent(in), optional :: useQR
   logical                       :: useQRActual, useQREnvironment
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   integer, intent(in), optional :: THIS_REAL_ELPA_KERNEL_API
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   integer                       :: THIS_REAL_ELPA_KERNEL
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   integer, intent(in)           :: na, nev, lda, ldq, na_rows, na_cols, mpi_comm_rows, &
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                                    mpi_comm_cols, mpi_comm_all
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   integer, intent(in)           :: nblk
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   real*8, intent(inout)         :: a(:,:), ev(na), q(:,:)
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   integer                       :: my_pe, n_pes, my_prow, my_pcol, np_rows, np_cols, mpierr
   integer                       :: nbw, num_blocks
   real*8, allocatable           :: tmat(:,:,:), e(:)
   real*8                        :: ttt0, ttt1, ttts
   integer                       :: i
   logical                       :: success
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   logical, save                 :: firstCall = .true.
   logical                       :: wantDebug
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#ifdef WITH_GPU_VERSION
   if (nblk .ne. 128) then
     print *,"At the moment GPU version needs blocksize 128"
     stop
   endif
#endif

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#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("solve_evp_real_2stage")
#endif
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   call mpi_comm_rank(mpi_comm_all,my_pe,mpierr)
   call mpi_comm_size(mpi_comm_all,n_pes,mpierr)

   call mpi_comm_rank(mpi_comm_rows,my_prow,mpierr)
   call mpi_comm_size(mpi_comm_rows,np_rows,mpierr)
   call mpi_comm_rank(mpi_comm_cols,my_pcol,mpierr)
   call mpi_comm_size(mpi_comm_cols,np_cols,mpierr)
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   wantDebug = .false.
   if (firstCall) then
     ! are debug messages desired?
     wantDebug = debug_messages_via_environment_variable()
     firstCall = .false.
   endif

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   success = .true.

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   useQRActual = .false.

   ! set usage of qr decomposition via API call
   if (present(useQR)) then
     if (useQR) useQRActual = .true.
     if (.not.(useQR)) useQRACtual = .false.
   endif

   ! overwrite this with environment variable settings
   if (qr_decomposition_via_environment_variable(useQREnvironment)) then
     useQRActual = useQREnvironment
   endif

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   if (useQRActual) then
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     if (mod(na,nblk) .ne. 0) then
       if (wantDebug) then
         write(error_unit,*) "solve_evp_real_2stage: QR-decomposition: blocksize does not fit with matrixsize"
       endif
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     print *, "Do not use QR-decomposition for this matrix and blocksize."
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     success = .false.
     return
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     endif
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   endif

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   if (present(THIS_REAL_ELPA_KERNEL_API)) then
     ! user defined kernel via the optional argument in the API call
     THIS_REAL_ELPA_KERNEL = THIS_REAL_ELPA_KERNEL_API
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   else
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     ! if kernel is not choosen via api
     ! check whether set by environment variable
     THIS_REAL_ELPA_KERNEL = get_actual_real_kernel()
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   endif

   ! check whether choosen kernel is allowed
   if (check_allowed_real_kernels(THIS_REAL_ELPA_KERNEL)) then
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     if (my_pe == 0) then
       write(error_unit,*) " "
       write(error_unit,*) "The choosen kernel ",REAL_ELPA_KERNEL_NAMES(THIS_REAL_ELPA_KERNEL)
       write(error_unit,*) "is not in the list of the allowed kernels!"
       write(error_unit,*) " "
       write(error_unit,*) "Allowed kernels are:"
       do i=1,size(REAL_ELPA_KERNEL_NAMES(:))
         if (AVAILABLE_REAL_ELPA_KERNELS(i) .ne. 0) then
           write(error_unit,*) REAL_ELPA_KERNEL_NAMES(i)
         endif
       enddo
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       write(error_unit,*) " "
       write(error_unit,*) "The defaul kernel REAL_ELPA_KERNEL_GENERIC will be used !"
     endif
     THIS_REAL_ELPA_KERNEL = REAL_ELPA_KERNEL_GENERIC
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   endif
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   ! Choose bandwidth, must be a multiple of nblk, set to a value >= 32

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#ifdef WITH_GPU_VERSION
   nbw = nblk
#else
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   nbw = (31/nblk+1)*nblk
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#endif
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   num_blocks = (na-1)/nbw + 1

   allocate(tmat(nbw,nbw,num_blocks))

   ! Reduction full -> band

   ttt0 = MPI_Wtime()
   ttts = ttt0
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   call bandred_real(na, a, lda, nblk, nbw, na_rows, na_cols, mpi_comm_rows, mpi_comm_cols, &
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                     tmat, wantDebug, success, useQRActual)
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   if (.not.(success)) return
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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time bandred_real               :',ttt1-ttt0
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   ! Reduction band -> tridiagonal

   allocate(e(na))

   ttt0 = MPI_Wtime()
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   call tridiag_band_real(na, nbw, nblk, a, lda, ev, e, mpi_comm_rows, &
                          mpi_comm_cols, mpi_comm_all)
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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time tridiag_band_real          :',ttt1-ttt0
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   call mpi_bcast(ev,na,MPI_REAL8,0,mpi_comm_all,mpierr)
   call mpi_bcast(e,na,MPI_REAL8,0,mpi_comm_all,mpierr)

   ttt1 = MPI_Wtime()
   time_evp_fwd = ttt1-ttts

   ! Solve tridiagonal system

   ttt0 = MPI_Wtime()
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   call solve_tridi(na, nev, ev, e, q, ldq, nblk, mpi_comm_rows,  &
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                    mpi_comm_cols, wantDebug, success)
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   if (.not.(success)) return

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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
     write(error_unit,*) 'Time solve_tridi                :',ttt1-ttt0
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   time_evp_solve = ttt1-ttt0
   ttts = ttt1

   deallocate(e)

   ! Backtransform stage 1

   ttt0 = MPI_Wtime()
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   call trans_ev_tridi_to_band_real(na, nev, nblk, nbw, q, ldq, mpi_comm_rows, &
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                                    mpi_comm_cols, wantDebug, success, THIS_REAL_ELPA_KERNEL)
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   if (.not.(success)) return
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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time trans_ev_tridi_to_band_real:',ttt1-ttt0
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   ! We can now deallocate the stored householder vectors
   deallocate(hh_trans_real)

   ! Backtransform stage 2

   ttt0 = MPI_Wtime()
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   call trans_ev_band_to_full_real(na, nev, nblk, nbw, a, lda, tmat, q, ldq, na_rows, na_cols, mpi_comm_rows, &
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                                   mpi_comm_cols, useQRActual)
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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time trans_ev_band_to_full_real :',ttt1-ttt0
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   time_evp_back = ttt1-ttts

   deallocate(tmat)
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#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("solve_evp_real_2stage")
#endif
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1  format(a,f10.3)

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end function solve_evp_real_2stage
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!-------------------------------------------------------------------------------

!-------------------------------------------------------------------------------

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function solve_evp_complex_2stage(na, nev, a, lda, ev, q, ldq, nblk, na_rows, na_cols, &
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                                    mpi_comm_rows, mpi_comm_cols,      &
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                                    mpi_comm_all, THIS_COMPLEX_ELPA_KERNEL_API) result(success)
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!-------------------------------------------------------------------------------
!  solve_evp_complex_2stage: Solves the complex eigenvalue problem with a 2 stage approach
!
!  Parameters
!
!  na          Order of matrix a
!
!  nev         Number of eigenvalues needed
!
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!  a(1:lda,:)    Distributed matrix for which eigenvalues are to be computed.
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!              Distribution is like in Scalapack.
!              The full matrix must be set (not only one half like in scalapack).
!              Destroyed on exit (upper and lower half).
!
!  lda         Leading dimension of a
!
!  ev(na)      On output: eigenvalues of a, every processor gets the complete set
!
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!  q(1:ldq,:)    On output: Eigenvectors of a
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!              Distribution is like in Scalapack.
!              Must be always dimensioned to the full size (corresponding to (na,na))
!              even if only a part of the eigenvalues is needed.
!
!  ldq         Leading dimension of q
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!  mpi_comm_all
!              MPI-Communicator for the total processor set
!
!-------------------------------------------------------------------------------
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#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
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   implicit none
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   integer, intent(in), optional :: THIS_COMPLEX_ELPA_KERNEL_API
   integer                       :: THIS_COMPLEX_ELPA_KERNEL
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   integer, intent(in)           :: na, nev, lda, ldq, nblk, na_rows, na_cols, mpi_comm_rows, mpi_comm_cols, mpi_comm_all
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   complex*16, intent(inout)     :: a(:,:), q(:,:)
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   real*8, intent(inout)         :: ev(na)

   integer                       :: my_prow, my_pcol, np_rows, np_cols, mpierr, my_pe, n_pes
   integer                       :: l_cols, l_rows, l_cols_nev, nbw, num_blocks
   complex*16, allocatable       :: tmat(:,:,:)
   real*8, allocatable           :: q_real(:,:), e(:)
   real*8                        :: ttt0, ttt1, ttts
   integer                       :: i
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   logical                       :: success, wantDebug
   logical, save                 :: firstCall = .true.

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#ifdef WITH_GPU_VERSION
   if (nblk .ne. 128) then
     print *,"At the moment GPU version needs blocksize 128"
     stop
   endif
#endif

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#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("solve_evp_complex_2stage")
#endif
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   call mpi_comm_rank(mpi_comm_all,my_pe,mpierr)
   call mpi_comm_size(mpi_comm_all,n_pes,mpierr)
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   call mpi_comm_rank(mpi_comm_rows,my_prow,mpierr)
   call mpi_comm_size(mpi_comm_rows,np_rows,mpierr)
   call mpi_comm_rank(mpi_comm_cols,my_pcol,mpierr)
   call mpi_comm_size(mpi_comm_cols,np_cols,mpierr)
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   wantDebug = .false.
   if (firstCall) then
     ! are debug messages desired?
     wantDebug = debug_messages_via_environment_variable()
     firstCall = .false.
   endif


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   success = .true.

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   if (present(THIS_COMPLEX_ELPA_KERNEL_API)) then
     ! user defined kernel via the optional argument in the API call
     THIS_COMPLEX_ELPA_KERNEL = THIS_COMPLEX_ELPA_KERNEL_API
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   else
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     ! if kernel is not choosen via api
     ! check whether set by environment variable
     THIS_COMPLEX_ELPA_KERNEL = get_actual_complex_kernel()
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   endif
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   ! check whether choosen kernel is allowed
   if (check_allowed_complex_kernels(THIS_COMPLEX_ELPA_KERNEL)) then
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     if (my_pe == 0) then
       write(error_unit,*) " "
       write(error_unit,*) "The choosen kernel ",COMPLEX_ELPA_KERNEL_NAMES(THIS_COMPLEX_ELPA_KERNEL)
       write(error_unit,*) "is not in the list of the allowed kernels!"
       write(error_unit,*) " "
       write(error_unit,*) "Allowed kernels are:"
       do i=1,size(COMPLEX_ELPA_KERNEL_NAMES(:))
         if (AVAILABLE_COMPLEX_ELPA_KERNELS(i) .ne. 0) then
           write(error_unit,*) COMPLEX_ELPA_KERNEL_NAMES(i)
         endif
       enddo
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       write(error_unit,*) " "
       write(error_unit,*) "The defaul kernel COMPLEX_ELPA_KERNEL_GENERIC will be used !"
     endif
     THIS_COMPLEX_ELPA_KERNEL = COMPLEX_ELPA_KERNEL_GENERIC
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   endif
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   ! Choose bandwidth, must be a multiple of nblk, set to a value >= 32

   nbw = (31/nblk+1)*nblk

   num_blocks = (na-1)/nbw + 1

   allocate(tmat(nbw,nbw,num_blocks))

   ! Reduction full -> band

   ttt0 = MPI_Wtime()
   ttts = ttt0
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   call bandred_complex(na, a, lda, nblk, nbw, na_rows, na_cols, mpi_comm_rows, mpi_comm_cols, &
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                        tmat, wantDebug, success)
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   if (.not.(success)) then
#ifdef HAVE_DETAILED_TIMINGS
     call timer%stop()
#endif
     return
   endif
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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time bandred_complex               :',ttt1-ttt0
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   ! Reduction band -> tridiagonal

   allocate(e(na))

   ttt0 = MPI_Wtime()
   call tridiag_band_complex(na, nbw, nblk, a, lda, ev, e, mpi_comm_rows, mpi_comm_cols, mpi_comm_all)
   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time tridiag_band_complex          :',ttt1-ttt0
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   call mpi_bcast(ev,na,MPI_REAL8,0,mpi_comm_all,mpierr)
   call mpi_bcast(e,na,MPI_REAL8,0,mpi_comm_all,mpierr)

   ttt1 = MPI_Wtime()
   time_evp_fwd = ttt1-ttts

   l_rows = local_index(na, my_prow, np_rows, nblk, -1) ! Local rows of a and q
   l_cols = local_index(na, my_pcol, np_cols, nblk, -1) ! Local columns of q
   l_cols_nev = local_index(nev, my_pcol, np_cols, nblk, -1) ! Local columns corresponding to nev

   allocate(q_real(l_rows,l_cols))

   ! Solve tridiagonal system

   ttt0 = MPI_Wtime()
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   call solve_tridi(na, nev, ev, e, q_real, ubound(q_real,1), nblk, &
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                    mpi_comm_rows, mpi_comm_cols, wantDebug, success)
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   if (.not.(success)) return

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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times)  &
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      write(error_unit,*) 'Time solve_tridi                   :',ttt1-ttt0
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   time_evp_solve = ttt1-ttt0
   ttts = ttt1

   q(1:l_rows,1:l_cols_nev) = q_real(1:l_rows,1:l_cols_nev)

   deallocate(e, q_real)

   ! Backtransform stage 1

   ttt0 = MPI_Wtime()
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   call trans_ev_tridi_to_band_complex(na, nev, nblk, nbw, q, ldq,  &
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                                       na_rows, na_cols, mpi_comm_rows, mpi_comm_cols,&
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                                       wantDebug, success,THIS_COMPLEX_ELPA_KERNEL)
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   if (.not.(success)) return
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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time trans_ev_tridi_to_band_complex:',ttt1-ttt0
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   ! We can now deallocate the stored householder vectors
   deallocate(hh_trans_complex)

   ! Backtransform stage 2

   ttt0 = MPI_Wtime()
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   call trans_ev_band_to_full_complex(na, nev, nblk, nbw, a, lda, tmat, q, ldq, na_rows, na_cols, mpi_comm_rows, mpi_comm_cols)
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   ttt1 = MPI_Wtime()
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   if (my_prow==0 .and. my_pcol==0 .and. elpa_print_times) &
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      write(error_unit,*) 'Time trans_ev_band_to_full_complex :',ttt1-ttt0
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   time_evp_back = ttt1-ttts

   deallocate(tmat)
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#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("solve_evp_complex_2stage")
#endif
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1  format(a,f10.3)

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end function solve_evp_complex_2stage
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!-------------------------------------------------------------------------------

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subroutine bandred_real(na, a, lda, nblk, nbw, na_rows, na_cols, mpi_comm_rows, mpi_comm_cols, &
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                        tmat, wantDebug, success, useQR)
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  !-------------------------------------------------------------------------------
  !  bandred_real: Reduces a distributed symmetric matrix to band form
  !
  !  Parameters
  !
  !  na          Order of matrix
  !
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  !  a(1:lda,:)    Distributed matrix which should be reduced.
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  !              Distribution is like in Scalapack.
  !              Opposed to Scalapack, a(:,:) must be set completely (upper and lower half)
  !              a(:,:) is overwritten on exit with the band and the Householder vectors
  !              in the upper half.
  !
  !  lda         Leading dimension of a
  !
  !  nblk        blocksize of cyclic distribution, must be the same in both directions!
  !
  !  nbw         semi bandwith of output matrix
  !
  !  mpi_comm_rows
  !  mpi_comm_cols
  !              MPI-Communicators for rows/columns
  !
  !  tmat(nbw,nbw,num_blocks)    where num_blocks = (na-1)/nbw + 1
  !              Factors for the Householder vectors (returned), needed for back transformation
  !
  !-------------------------------------------------------------------------------
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#ifdef HAVE_DETAILED_TIMINGS
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  use timings
#endif

#ifdef WITH_GPU_VERSION
  use cuda_routines
  use iso_c_binding
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#endif
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   implicit none
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   integer             :: na, lda, nblk, nbw, na_rows, na_cols, mpi_comm_rows, mpi_comm_cols
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   real*8              :: a(:,:), tmat(nbw,nbw,*) ! this assumed size should be changed once elpa_qr is cleaned up
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   integer             :: my_prow, my_pcol, np_rows, np_cols, mpierr
   integer             :: l_cols, l_rows
   integer             :: i, j, lcs, lce, lre, lc, lr, cur_pcol, n_cols, nrow
   integer             :: istep, ncol, lch, lcx, nlc
   integer             :: tile_size, l_rows_tile, l_cols_tile
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#ifdef WITH_GPU_VERSION
   real*8              :: eps
#endif

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   real*8              :: vnorm2, xf, aux1(nbw), aux2(nbw), vrl, tau, vav(nbw,nbw)
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#ifdef WITH_GPU_VERSION
   real*8, allocatable :: tmp(:), vr(:), vmr(:), umc(:)
#else

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   real*8, allocatable :: tmp(:,:), vr(:), vmr(:,:), umc(:,:)
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#endif
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   ! needed for blocked QR decomposition
   integer             :: PQRPARAM(11), work_size
   real*8              :: dwork_size(1)
   real*8, allocatable :: work_blocked(:), tauvector(:), blockheuristic(:)

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#ifdef WITH_GPU_VERSION
   integer(C_SIZE_T)   :: a_dev, vmr_dev, umc_dev, tmat_dev, vav_dev
   integer, external   :: numroc
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   integer             :: ierr
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   integer             :: cur_l_rows, cur_l_cols, vmr_size, umc_size
   integer(C_SIZE_T)   :: lc_start, lc_end
   integer             :: lr_end
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   integer             :: na_rows2, na_cols2
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#endif
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   logical, intent(in) :: wantDebug
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   logical, intent(out):: success

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   logical, intent(in) :: useQR
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   integer             :: istat
   character(200)      :: errorMessage
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#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("bandred_real")
#endif
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   call mpi_comm_rank(mpi_comm_rows,my_prow,mpierr)
   call mpi_comm_size(mpi_comm_rows,np_rows,mpierr)
   call mpi_comm_rank(mpi_comm_cols,my_pcol,mpierr)
   call mpi_comm_size(mpi_comm_cols,np_cols,mpierr)
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   success = .true.
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   ! Semibandwith nbw must be a multiple of blocksize nblk
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   if (mod(nbw,nblk)/=0) then
     if (my_prow==0 .and. my_pcol==0) then
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       if (wantDebug) then
         write(error_unit,*) 'ELPA2_bandred_real: ERROR: nbw=',nbw,', nblk=',nblk
         write(error_unit,*) 'ELPA2_bandred_real: ELPA2 works only for nbw==n*nblk'
       endif
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       success = .false.
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       return
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     endif
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   endif

   ! Matrix is split into tiles; work is done only for tiles on the diagonal or above

   tile_size = nblk*least_common_multiple(np_rows,np_cols) ! minimum global tile size
   tile_size = ((128*max(np_rows,np_cols)-1)/tile_size+1)*tile_size ! make local tiles at least 128 wide

   l_rows_tile = tile_size/np_rows ! local rows of a tile
   l_cols_tile = tile_size/np_cols ! local cols of a tile

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   if (useQR) then
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#ifdef WITH_GPU_VERSION
     print *,"qr decomposition at the moment not supported with GPU"
     stop
#else
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     if (which_qr_decomposition == 1) then
       call qr_pqrparam_init(pqrparam,    nblk,'M',0,   nblk,'M',0,   nblk,'M',1,'s')
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       allocate(tauvector(na), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when allocating tauvector "//errorMessage
         stop
       endif

       allocate(blockheuristic(nblk), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when allocating blockheuristic "//errorMessage
         stop
       endif

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       l_rows = local_index(na, my_prow, np_rows, nblk, -1)
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       allocate(vmr(max(l_rows,1),na), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when allocating vmr "//errorMessage
         stop
       endif
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       call qr_pdgeqrf_2dcomm(a, lda, vmr, max(l_rows,1), tauvector, tmat(1,1,1), nbw, dwork_size(1), -1, na, &
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                             nbw, nblk, nblk, na, na, 1, 0, PQRPARAM, mpi_comm_rows, mpi_comm_cols, blockheuristic)
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       work_size = dwork_size(1)
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       allocate(work_blocked(work_size), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when allocating work_blocked "//errorMessage
         stop
       endif
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       work_blocked = 0.0d0
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       deallocate(vmr, stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when deallocating vmr "//errorMessage
         stop
       endif

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     endif
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#endif
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   endif

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#ifdef WITH_GPU_VERSION
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   na_rows2 = numroc(na, nblk, my_prow, 0, np_rows)

   if (na_rows .ne. na_rows2) then
     print *,"why is na_rows not equal? ",na_rows,na_rows2
     stop
   endif
   na_cols2 = numroc(na, nblk, my_pcol, 0, np_cols)
   if (na_cols .ne. na_cols2) then
     print *,"why is na_cols not equal? ",na_cols,na_cols2
     stop
   endif
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   ! Here we convert the regular host array into a pinned host array
   istat = cuda_malloc(a_dev, lda*na_cols*8_8)
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   if (istat .ne. 0) then
     print *,"error in cudaMalloc"
     stop
   endif

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   istat = cuda_malloc(tmat_dev, nbw*nbw*8_8)
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   if (istat .ne. 0) then
     print *,"error in cudaMalloc"
     stop
   endif

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   istat = cuda_malloc(vav_dev, nbw*nbw*8_8)
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   if (istat .ne. 0) then
     print *,"error in cudaMalloc"
     stop
   endif
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   cur_l_rows = 0
   cur_l_cols = 0

   istat = cuda_memcpy(a_dev, loc(a(1,1)), (lda)*(na_cols)*8_8,cudaMemcpyHostToDevice)
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   if (istat .ne. 0) then
     print *,"error in cudaMemcpy"
     stop
   endif

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#endif

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   do istep = (na-1)/nbw, 1, -1

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     n_cols = MIN(na,(istep+1)*nbw) - istep*nbw ! Number of columns in current step
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     ! Number of local columns/rows of remaining matrix
     l_cols = local_index(istep*nbw, my_pcol, np_cols, nblk, -1)
     l_rows = local_index(istep*nbw, my_prow, np_rows, nblk, -1)
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#ifdef WITH_GPU_VERSION
     cur_l_rows = max(l_rows, 1)
     cur_l_cols = max(l_cols, 1)

     vmr_size = cur_l_rows * 2 * n_cols
     umc_size = cur_l_cols * 2 * n_cols

     ! Allocate vmr and umc only if the inew size exceeds their current capacity
     ! Added for FORTRAN CALLS
     if ((.not. allocated(vr)) .or. (l_rows + 1 .gt. ubound(vr, 1))) then
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       if (allocated(vr)) then
         deallocate(vr, stat=istat, errmsg=errorMessage)
         if (istat .ne. 0) then
           print *,"error when deallocating vr "//errorMessage
           stop
         endif
       endif
       allocate(vr(l_rows + 1), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when allocating vr "//errorMessage
         stop
       endif

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     endif

     if ((.not. allocated(vmr)) .or. (vmr_size .gt. ubound(vmr, 1))) then
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       if (allocated(vmr)) then
         deallocate(vmr, stat=istat, errmsg=errorMessage)
         if (istat .ne. 0) then
           print *,"error when allocating vmr "//errorMessage
           stop
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         endif
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         istat = cuda_free(vmr_dev)
         if (istat .ne. 0) then
           print *,"error in cuda_free"
           stop
         endif
       endif

       allocate(vmr(vmr_size), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when allocating vmr "//errorMessage
         stop
       endif

       istat = cuda_malloc(vmr_dev, vmr_size*8_8)
       if (istat .ne. 0) then
         print *,"error in cudaMalloc"
         stop
       endif

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     endif



     if ((.not. allocated(umc)) .or. (umc_size .gt. ubound(umc, 1))) then
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       if (allocated(umc)) then
         deallocate(umc, stat=istat, errmsg=errorMessage)
         if (istat .ne. 0) then
           print *,"error when deallocating umc "//errorMessage
           stop
         endif

         istat = cuda_free(umc_dev)
         if (istat .ne. 0) then
            print *,"error in cudaFree"
            stop
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         endif
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       endif

       allocate(umc(umc_size), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"error when deallocating umc "//errorMessage
         stop
       endif

       istat = cuda_malloc(umc_dev, umc_size*8_8)
       if (istat .ne. 0) then
         print *,"error in cudaMalloc"
         stop
       endif

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     endif
#else
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     ! Allocate vmr and umc to their exact sizes so that they can be used in bcasts and reduces
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     allocate(vmr(max(l_rows,1),2*n_cols), stat=istat, errmsg=errorMessage)
     if (istat .ne. 0) then
       print *,"error when allocating vmr "//errorMessage
       stop
     endif

     allocate(umc(max(l_cols,1),2*n_cols), stat=istat, errmsg=errorMessage)
     if (istat .ne. 0) then
       print *,"error when allocating umc "//errorMessage
       stop
     endif

     allocate(vr(l_rows+1), stat=istat, errmsg=errorMessage)
     if (istat .ne. 0) then
       print *,"error when allocating vr "//errorMessage
       stop
     endif
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#endif
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#ifdef WITH_GPU_VERSION
     vmr(1 : cur_l_rows * n_cols) = 0.
#else
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     vmr(1:l_rows,1:n_cols) = 0.
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#endif
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     vr(:) = 0
     tmat(:,:,istep) = 0
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#ifdef WITH_GPU_VERSION
     umc(1 : umc_size) = 0.

     lc_start = local_index(istep*nbw+1, my_pcol, np_cols, nblk, -1)
     lc_end   = local_index(istep*nbw+n_cols, my_pcol, np_cols, nblk, -1)
     lr_end   = local_index((istep-1)*nbw + n_cols, my_prow, np_rows, nblk, -1)

     if(lc_start .le. 0) lc_start = 1

     ! Here we assume that the processor grid and the block grid are aligned
     cur_pcol = pcol(istep*nbw+1, nblk, np_cols)

     if(my_pcol == cur_pcol) then

       istat = cuda_memcpy2d(loc(a(1, lc_start)), lda*8_8, (a_dev + ((lc_start-1) * lda*8_8)), lda*8_8, &
                            lr_end*8_8, (lc_end - lc_start+1), cudaMemcpyDeviceToHost)
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       if (istat .ne. 0) then
         print *,"error in cudaMemcpy2d"
         stop
       endif

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     endif
#endif

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     ! Reduce current block to lower triangular form
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     if (useQR) then
       if (which_qr_decomposition == 1) then
         call qr_pdgeqrf_2dcomm(a, lda, vmr, max(l_rows,1), tauvector(1), &
                                  tmat(1,1,istep), nbw, work_blocked,       &
                                  work_size, na, n_cols, nblk, nblk,        &
                                  istep*nbw+n_cols-nbw, istep*nbw+n_cols, 1,&
                                  0, PQRPARAM, mpi_comm_rows, mpi_comm_cols,&
                                  blockheuristic)
       endif
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     else
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       do lc = n_cols, 1, -1
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         ncol = istep*nbw + lc ! absolute column number of householder vector
         nrow = ncol - nbw ! Absolute number of pivot row
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         lr  = local_index(nrow, my_prow, np_rows, nblk, -1) ! current row length
         lch = local_index(ncol, my_pcol, np_cols, nblk, -1) ! HV local column number
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         tau = 0
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         if (nrow == 1) exit ! Nothing to do
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         cur_pcol = pcol(ncol, nblk, np_cols) ! Processor column owning current block
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         if (my_pcol==cur_pcol) then
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           ! Get vector to be transformed; distribute last element and norm of
           ! remaining elements to all procs in current column
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           vr(1:lr) = a(1:lr,lch) ! vector to be transformed
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           if (my_prow==prow(nrow, nblk, np_rows)) then
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             aux1(1) = dot_product(vr(1:lr-1),vr(1:lr-1))
             aux1(2) = vr(lr)
           else
             aux1(1) = dot_product(vr(1:lr),vr(1:lr))
             aux1(2) = 0.
           endif
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           call mpi_allreduce(aux1,aux2,2,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
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           vnorm2 = aux2(1)
           vrl    = aux2(2)
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           ! Householder transformation
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           call hh_transform_real(vrl, vnorm2, xf, tau)
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           ! Scale vr and store Householder vector for back transformation
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           vr(1:lr) = vr(1:lr) * xf
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           if (my_prow==prow(nrow, nblk, np_rows)) then
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             a(1:lr-1,lch) = vr(1:lr-1)
             a(lr,lch) = vrl
             vr(lr) = 1.
           else
             a(1:lr,lch) = vr(1:lr)
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           endif
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         endif
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         ! Broadcast Householder vector and tau along columns
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         vr(lr+1) = tau
         call MPI_Bcast(vr,lr+1,MPI_REAL8,cur_pcol,mpi_comm_cols,mpierr)
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#ifdef WITH_GPU_VERSION
         vmr(cur_l_rows * (lc - 1) + 1 : cur_l_rows * (lc - 1) + lr) = vr(1:lr)
#else
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         vmr(1:lr,lc) = vr(1:lr)
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#endif
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         tau = vr(lr+1)
         tmat(lc,lc,istep) = tau ! Store tau in diagonal of tmat
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         ! Transform remaining columns in current block with Householder vector
         ! Local dot product
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         aux1 = 0
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         nlc = 0 ! number of local columns
         do j=1,lc-1
           lcx = local_index(istep*nbw+j, my_pcol, np_cols, nblk, 0)
           if (lcx>0) then
             nlc = nlc+1
             if (lr>0) aux1(nlc) = dot_product(vr(1:lr),a(1:lr,lcx))
           endif
         enddo
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         ! Get global dot products
         if (nlc>0) call mpi_allreduce(aux1,aux2,nlc,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
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         ! Transform
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         nlc = 0
         do j=1,lc-1
           lcx = local_index(istep*nbw+j, my_pcol, np_cols, nblk, 0)
           if (lcx>0) then
             nlc = nlc+1
             a(1:lr,lcx) = a(1:lr,lcx) - tau*aux2(nlc)*vr(1:lr)
           endif
         enddo

       enddo
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#ifdef WITH_GPU_VERSION
      ! store column tiles back to GPU
      cur_pcol = pcol(istep*nbw+1, nblk, np_cols)
      if (my_pcol == cur_pcol) then
        istat = cuda_memcpy2d((a_dev+((lc_start-1)*lda*8_8)), lda*8_8, loc(a(1, lc_start)), lda*8_8,  lr_end*8_8, &
                                  (lc_end - lc_start+1),cudaMemcpyHostToDevice)
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        if (istat .ne. 0) then
          print *,"error in cudaMemcpy2d"
          stop
        endif
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      endif
#endif
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       ! Calculate scalar products of stored Householder vectors.
       ! This can be done in different ways, we use dsyrk
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       vav = 0
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#ifdef WITH_GPU_VERSION
       if (l_rows>0) &
1052
         call dsyrk('U','T',n_cols,l_rows,1.d0,vmr,cur_l_rows,0.d0,vav,ubound(vav,1))
1053
#else
1054
       if (l_rows>0) &
1055
         call dsyrk('U','T',n_cols,l_rows,1.d0,vmr,ubound(vmr,1),0.d0,vav,ubound(vav,1))
1056
#endif
1057
       call symm_matrix_allreduce(n_cols,vav,ubound(vav,1),mpi_comm_rows)
1058

1059
       ! Calculate triangular matrix T for block Householder Transformation
1060

1061
1062
1063
1064
1065
1066
1067
       do lc=n_cols,1,-1
         tau = tmat(lc,lc,istep)
         if (lc<n_cols) then
           call dtrmv('U','T','N',n_cols-lc,tmat(lc+1,lc+1,istep),ubound(tmat,1),vav(lc+1,lc),1)
           tmat(lc,lc+1:n_cols,istep) = -tau * vav(lc+1:n_cols,lc)
         endif
       enddo
1068
     endif
1069

1070
    ! Transpose vmr -> vmc (stored in umc, second half)
1071
1072
1073
1074
1075
#ifdef WITH_GPU_VERSION
    call elpa_transpose_vectors  (vmr, cur_l_rows, mpi_comm_rows, &
                                    umc(cur_l_cols * n_cols + 1), cur_l_cols, mpi_comm_cols, &
                                    1, istep*nbw, n_cols, nblk)
#else
1076
    call elpa_transpose_vectors  (vmr, ubound(vmr,1), mpi_comm_rows, &
1077
1078
                                    umc(1,n_cols+1), ubound(umc,1), mpi_comm_cols, &
                                    1, istep*nbw, n_cols, nblk)
1079
#endif
1080

1081
1082
1083
1084
    ! Calculate umc = A**T * vmr
    ! Note that the distributed A has to be transposed
    ! Opposed to direct tridiagonalization there is no need to use the cache locality
    ! of the tiles, so we can use strips of the matrix
1085
1086
1087
1088
#ifdef WITH_GPU_VERSION
    umc(1 : l_cols * n_cols) = 0.d0
    vmr(cur_l_rows * n_cols + 1 : cur_l_rows * n_cols * 2) = 0
#else
1089
1090
    umc(1:l_cols,1:n_cols) = 0.d0
    vmr(1:l_rows,n_cols+1:2*n_cols) = 0
1091
#endif
1092
    if (l_cols>0 .and. l_rows>0) then
1093
1094

#ifdef WITH_GPU_VERSION
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
      istat = cuda_memcpy(vmr_dev, loc(vmr(1)), vmr_size*8_8,cudaMemcpyHostToDevice)
      if (istat .ne. 0) then
        print *,"error in cudaMemcpy"
        stop
      endif

      istat = cuda_memcpy(umc_dev, loc(umc(1)), umc_size*8_8,cudaMemcpyHostToDevice)
      if (istat .ne. 0) then
        print *,"error in cudaMemcpy"
        stop
      endif

1107
#endif
1108
      do i=0,(istep*nbw-1)/tile_size
1109

1110
1111
1112
        lcs = i*l_cols_tile+1
        lce = min(l_cols,(i+1)*l_cols_tile)
        if (lce<lcs) cycle
1113