elpa2_bandred_template.X90 75 KB
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#if 0
!    This file is part of ELPA.
!
!    The ELPA library was originally created by the ELPA consortium,
!    consisting of the following organizations:
!
!    - Max Planck Computing and Data Facility (MPCDF), fomerly known as
!      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 Naturwissenschaften,
!      Leipzig, Abt. Komplexe Strukutren in Biologie und Kognition,
!      and
!    - IBM Deutschland GmbH
!
!    This particular source code file contains additions, changes and
!    enhancements authored by Intel Corporation which is not part of
!    the ELPA consortium.
!
!    More information can be found here:
!    http://elpa.mpcdf.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".
#endif
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    subroutine bandred_&
    &MATH_DATATYPE&
    &_&
    &PRECISION &
    (na, a, &
#if REALCASE == 1
     a_dev, &
#endif
     lda, nblk, nbw, matrixCols, numBlocks, mpi_comm_rows, mpi_comm_cols, tmat, &
#if REALCASE == 1
     tmat_dev, &
#endif
     wantDebug, useGPU, success &
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#if REALCASE == 1
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     , useQR)
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#endif
#if COMPLEXCASE == 1
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     )
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#endif
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  !-------------------------------------------------------------------------------
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  !  bandred_real/complex: Reduces a distributed symmetric matrix to band form
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  !
  !  Parameters
  !
  !  na          Order of matrix
  !
  !  a(lda,matrixCols)    Distributed matrix which should be reduced.
  !              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
  !  matrixCols  local columns of matrix 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,numBlocks)    where numBlocks = (na-1)/nbw + 1
  !              Factors for the Householder vectors (returned), needed for back transformation
  !
  !-------------------------------------------------------------------------------

      use cuda_functions
      use iso_c_binding
      use elpa1_compute
#ifdef HAVE_DETAILED_TIMINGS
      use timings
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#else
      use timings_dummy
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#endif
#ifdef WITH_OPENMP
      use omp_lib
#endif
      use precision
      implicit none

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      integer(kind=ik)                            :: na, lda, nblk, nbw, matrixCols, numBlocks, mpi_comm_rows, mpi_comm_cols

#if REALCASE == 1
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#ifdef USE_ASSUMED_SIZE
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      real(kind=REAL_DATATYPE)                    :: a(lda,*), tmat(nbw,nbw,*)
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#else
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      real(kind=REAL_DATATYPE)                    :: a(lda,matrixCols), tmat(nbw,nbw,numBlocks)
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#endif
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#endif
#if COMPLEXCASE == 1
#ifdef USE_ASSUMED_SIZE
      complex(kind=COMPLEX_DATATYPE)              :: a(lda,*), tmat(nbw,nbw,*)
#else
      complex(kind=COMPLEX_DATATYPE)              :: a(lda,matrixCols), tmat(nbw,nbw,numBlocks)
#endif
#ifdef DOUBLE_PRECISION_COMPLEX
      complex(kind=COMPLEX_DATATYPE), parameter   :: CZERO = (0.0_rk8, 0.0_rk8), CONE = (1.0_rk8, 0.0_rk8)
#else
      complex(kind=COMPLEX_DATATYPE), parameter   :: CZERO = (0.0_rk4, 0.0_rk4), CONE = (1.0_rk4, 0.0_rk4)
#endif
#endif /* COMPLEXCASE == 1 */
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#if REALCASE == 1
      real(kind=REAL_DATATYPE)                    :: eps
#endif
      logical, intent(in)                         :: useGPU
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      integer(kind=ik)                            :: my_prow, my_pcol, np_rows, np_cols, mpierr
      integer(kind=ik)                            :: l_cols, l_rows
#if REALCASE == 1
      integer(kind=ik)                            :: vmrCols, mynlc
#endif
      integer(kind=ik)                            :: i, j, lcs, lce, lrs, lre, lc, lr, cur_pcol, n_cols, nrow
      integer(kind=ik)                            :: istep, ncol, lch, lcx, nlc
      integer(kind=ik)                            :: tile_size, l_rows_tile, l_cols_tile
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      real(kind=REAL_DATATYPE)                    :: vnorm2
#if REALCASE == 1
      real(kind=REAL_DATATYPE)                    :: xf, aux1(nbw), aux2(nbw), vrl, tau, vav(nbw,nbw)
#endif
#if COMPLEXCASE == 1
      complex(kind=COMPLEX_DATATYPE)              :: xf, aux1(nbw), aux2(nbw), vrl, tau, vav(nbw,nbw)

      complex(kind=COMPLEX_DATATYPE), allocatable :: tmp(:,:), vr(:), vmrCPU(:,:), umcCPU(:,:)
#endif
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#if REALCASE == 1
      real(kind=REAL_DATATYPE), allocatable       :: tmpCUDA(:),  vmrCUDA(:),  umcCUDA(:)
      real(kind=REAL_DATATYPE), allocatable       :: tmpCPU(:,:), vmrCPU(:,:), umcCPU(:,:)
      real(kind=REAL_DATATYPE), allocatable       :: vr(:)
#endif

#if REALCASE == 1
      ! needed for blocked QR decomposition
      integer(kind=ik)                            :: PQRPARAM(11), work_size
      real(kind=REAL_DATATYPE)                    :: dwork_size(1)
      real(kind=REAL_DATATYPE), allocatable       :: work_blocked(:), tauvector(:), blockheuristic(:)
#endif
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      ! a_dev is passed from bandred_real to trans_ev_band
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      integer(kind=C_intptr_T)                    :: a_dev, vmr_dev, umc_dev, tmat_dev, vav_dev
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#ifdef WITH_MPI
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      integer(kind=ik), external                  :: numroc
#endif
      integer(kind=ik)                            :: ierr
      integer(kind=ik)                            :: cur_l_rows, cur_l_cols, vmr_size, umc_size
      integer(kind=c_size_t)                      :: lc_start, lc_end
#if COMPLEXCASE == 1
      integer(kind=c_size_t)                      :: lce_1, lcs_1, lre_1
#endif
      integer(kind=ik)                            :: lr_end
      integer(kind=ik)                            :: na_cols
#if COMPLEXCASE == 1
      integer(kind=ik)                            :: na_rows
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#endif

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      logical, intent(in)                         :: wantDebug
      logical, intent(out)                        :: success
      logical                                     :: successCUDA
      integer(kind=ik)                            :: istat
      character(200)                              :: errorMessage
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#if REALCASE == 1
      logical, intent(in)                         :: useQR
#endif
#if REALCASE == 1
      integer(kind=ik)                            :: mystart, myend, m_way, n_way, work_per_thread, m_id, n_id, n_threads, &
                                                    ii, pp, transformChunkSize
#endif
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#if REALCASE == 1
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      call timer%start("bandred_real" // PRECISION_SUFFIX)
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#endif
#if COMPLEXCASE == 1
      call timer%start("bandred_complex" // PRECISION_SUFFIX)
#endif
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      call timer%start("mpi_communication")

      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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      call timer%stop("mpi_communication")
      success = .true.


      ! Semibandwith nbw must be a multiple of blocksize nblk
      if (mod(nbw,nblk)/=0) then
        if (my_prow==0 .and. my_pcol==0) then
          if (wantDebug) then
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#if REALCASE == 1
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            write(error_unit,*) 'ELPA2_bandred_real: ERROR: nbw=',nbw,', nblk=',nblk
            write(error_unit,*) 'ELPA2_bandred_real: ELPA2 works only for nbw==n*nblk'
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#endif
#if COMPLEXCASE == 1
            write(error_unit,*) 'ELPA2_bandred_complex: ERROR: nbw=',nbw,', nblk=',nblk
            write(error_unit,*) 'ELPA2_bandred_complex: ELPA2 works only for nbw==n*nblk'
#endif
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          endif
          success = .false.
          return
        endif
      endif

! na_rows in used nowhere; only na_cols
      if (useGPU) then
#ifdef WITH_MPI
!        na_rows = numroc(na, nblk, my_prow, 0, np_rows)
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#if COMPLEXCASE == 1
         na_rows = numroc(na, nblk, my_prow, 0, np_rows)
#endif
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        na_cols = numroc(na, nblk, my_pcol, 0, np_cols)
#else
!        na_rows = na
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#if COMPLEXCASE == 1
         na_rows = na
#endif
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        na_cols = na
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#endif

#if REALCASE == 1
        ! Here we convert the regular host array into a pinned host array
        successCUDA = cuda_malloc(a_dev, lda*na_cols*size_of_PRECISION_real)
        if (.not.(successCUDA)) then
          print *,"bandred_real: error in cudaMalloc"
          stop
        endif
#endif
#if COMPLEXCASE == 1
        successCUDA = cuda_malloc(a_dev, lda*na_cols*size_of_PRECISION_complex)
        if (.not.(successCUDA)) then
          print *, "bandred_complex:  cuda malloc failed a_dev ", istat
          stop
        endif
#endif

#if REALCASE == 1
        successCUDA = cuda_malloc(tmat_dev, nbw*nbw*size_of_PRECISION_real)
        if (.not.(successCUDA)) then
          print *,"bandred_real: error in cudaMalloc"
          stop
        endif
#endif
#if COMPLEXCASE == 1
        successCUDA = cuda_malloc(tmat_dev, nbw*nbw*size_of_PRECISION_complex)
        if (.not.(successCUDA)) then
          print *, " bandred_complex: cuda malloc failed tmat_dev ", istat
          stop
        endif

#endif

#if REALCASE == 1
        successCUDA = cuda_malloc(vav_dev, nbw*nbw*size_of_PRECISION_real)
        if (.not.(successCUDA)) then
          print *,"bandred_real: error in cudaMalloc"
          stop
        endif
#endif
#if COMPLEXCASE == 1
        successCUDA = cuda_malloc(vav_dev, nbw*nbw*size_of_PRECISION_complex)
        if (.not.(successCUDA)) then
          print *, "bandred_complex:  cuda malloc failed vav_dev ", istat
          stop
        endif

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#endif
      endif ! useGPU

      ! 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 REALCASE == 1
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      if (useQR) then

        if (useGPU) then
          print *,"qr decomposition at the moment not supported with GPU"
          stop
        endif

        if (which_qr_decomposition == 1) then
          call qr_pqrparam_init(pqrparam(1:11),    nblk,'M',0,   nblk,'M',0,   nblk,'M',1,'s')
          allocate(tauvector(na), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_real: error when allocating tauvector "//errorMessage
            stop
          endif

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

          l_rows = local_index(na, my_prow, np_rows, nblk, -1)
          allocate(vmrCPU(max(l_rows,1),na), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_real: error when allocating vmrCPU "//errorMessage
            stop
          endif

          vmrCols = na

#ifdef USE_ASSUMED_SIZE_QR
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          call qr_pdgeqrf_2dcomm_PRECISION(a, lda, matrixCols, vmrCPU, max(l_rows,1), vmrCols, tauvector(1), na, tmat(1,1,1), &
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                                 nbw, nbw, dwork_size, 1, -1, na, nbw, nblk, nblk, na, na, 1, 0, PQRPARAM(1:11), &
                                 mpi_comm_rows, mpi_comm_cols, blockheuristic)

#else
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          call qr_pdgeqrf_2dcomm_PRECISION(a(1:lda,1:matrixCols), matrixCols, lda, vmrCPU(1:max(l_rows,1),1:vmrCols), max(l_rows,1), &
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                                 vmrCols, tauvector(1:na), na, tmat(1:nbw,1:nbw,1), nbw, &
                                 nbw, dwork_size(1:1), 1, -1, na, nbw, nblk, nblk, na, na, 1, 0, PQRPARAM(1:11), &
                                 mpi_comm_rows, mpi_comm_cols, blockheuristic)
#endif

          work_size = dwork_size(1)
          allocate(work_blocked(work_size), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_real: error when allocating work_blocked "//errorMessage
            stop
          endif
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          work_blocked = CONST_0_0
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          deallocate(vmrCPU, stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_real: error when deallocating vmrCPU "//errorMessage
            stop
          endif

        endif ! which_qr_decomposition

      endif ! useQr
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#endif /* useQr */
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      if (useGPU) then
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!#if !defined(USE_ASSUMED_SIZE)
!        if (size(a,dim=1) .ne. lda .or. size(a,dim=2) .ne. na_cols) then
!          print *,"bandred_complex: sizes of a wrong ? ",lda,size(a,dim=1),na_cols,size(a,dim=2)
!        endif
!#endif
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        cur_l_rows = 0
        cur_l_cols = 0
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#if REALCASE == 1
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        successCUDA = cuda_memcpy(a_dev, loc(a(1,1)), (lda)*(na_cols)*size_of_PRECISION_real, cudaMemcpyHostToDevice)
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        if (.not.(successCUDA)) then
          print *,"bandred_real: error in cudaMemcpy"
          stop
        endif
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#endif
#if COMPLEXCASE == 1
        successCUDA = cuda_memcpy(a_dev, loc(a(1,1)),(lda)*(na_cols)*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
        if (.not.(successCUDA)) then
          print *, "bandred_complex:  cuda memcpy faild a_dev ", istat
          stop
        endif
#endif
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      endif ! useGPU


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

        n_cols = MIN(na,(istep+1)*nbw) - istep*nbw ! Number of columns in current step

        ! 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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        ! Allocate vmr and umc to their exact sizes so that they can be used in bcasts and reduces

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        if (useGPU) then
          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, dim=1))) then
            if (allocated(vr)) then
              deallocate(vr, stat=istat, errmsg=errorMessage)
              if (istat .ne. 0) then
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#if REALCASE == 1
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                print *,"bandred_real: error when deallocating vr "//errorMessage
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#endif
#if COMPLEXCASE == 1
                print *,"bandred_complex: error when deallocating vr "//errorMessage
#endif
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                stop
              endif
            endif
            allocate(vr(l_rows + 1), stat=istat, errmsg=errorMessage)
            if (istat .ne. 0) then
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              print *,"bandred_real: error when allocating vr "//errorMessage
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#endif
#if COMPLEXCASE == 1
              print *,"bandred_complex: error when allocating vr "//errorMessage
#endif
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              stop
            endif

          endif

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#if REALCASE == 1
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          if ((.not. allocated(vmrCUDA)) .or. (vmr_size .gt. ubound(vmrCUDA, dim=1))) then
            if (allocated(vmrCUDA)) then
              deallocate(vmrCUDA, stat=istat, errmsg=errorMessage)
              if (istat .ne. 0) then
                print *,"bandred_real: error when allocating vmrCUDA "//errorMessage
                stop
              endif

              successCUDA = cuda_free(vmr_dev)
              if (.not.(successCUDA)) then
                print *,"bandred_real: error in cuda_free"
                stop
              endif
            endif

            allocate(vmrCUDA(vmr_size), stat=istat, errmsg=errorMessage)
            if (istat .ne. 0) then
              print *,"bandred_real: error when allocating vmrCUDA "//errorMessage
              stop
            endif
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            successCUDA = cuda_malloc(vmr_dev, vmr_size*size_of_PRECISION_real)
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            if (.not.(successCUDA)) then
              print *,"bandred_real: error in cudaMalloc"
              stop
            endif

          endif
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#endif

#if COMPLEXCASE == 1
          if ((.not. allocated(vmrCPU)) .or. (vmr_size .gt. ubound(vmrCPU, dim=1))) then
            if (allocated(vmrCPU)) then
              deallocate(vmrCPU, stat=istat, errmsg=errorMessage)
              if (istat .ne. 0) then
                print *,"bandred_complex: error when deallocating vmrCPU "//errorMessage
                stop
              endif

              successCUDA = cuda_free(vmr_dev)
              if (.not.(successCUDA))then
                print *,"bandred_complex: error in cudaFree"
                stop
              endif
            endif

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

            if (max(l_rows,1) * 2*n_cols .gt. vmr_size) then
              print *,"bandred_complex: vmc_size ",max(l_rows,1) * 2*n_cols,vmr_size
            endif

            successCUDA = cuda_malloc(vmr_dev, vmr_size*size_of_PRECISION_complex)
            if (.not.(successCUDA)) then
              print *, "bandred_complex:  cuda malloc failed vmr_dev ", istat
              stop
            endif

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

              successCUDA = cuda_free(umc_dev)
              if (.not.(successCUDA)) then
                 print *,"bandred_real: error in cudaFree"
                 stop
              endif

            endif
            allocate(umcCUDA(umc_size), stat=istat, errmsg=errorMessage)
            if (istat .ne. 0) then
              print *,"bandred_real: error when deallocating umcCUDA "//errorMessage
              stop
            endif
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            successCUDA = cuda_malloc(umc_dev, umc_size*size_of_PRECISION_real)
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            if (.not.(successCUDA)) then
              print *,"bandred_real: error in cudaMalloc"
              stop
            endif

          endif
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#endif /* REALCASE == 1 */

#if COMPLEXCASE == 1
          if ((.not. allocated(umcCPU)) .or. (umc_size .gt. ubound(umcCPU, dim=1))) then
            if (allocated(umcCPU)) then
              deallocate(umcCPU, stat=istat, errmsg=errorMessage)


              if (istat .ne. 0) then
                print *,"bandred_complex: error when allocating umcCPU "//errorMessage
                stop
              endif
              successCUDA = cuda_free(umc_dev)
              if (.not.(successCUDA))then
                print *,"bandred_complex: error in cudaFree"
                stop
              endif
            endif

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

            if (max(l_cols,1) * 2*n_cols .gt. umc_size) then
              print *,"bandred_complex: umc_size ",max(l_cols,1) * 2*n_cols,umc_size
            endif
            successCUDA = cuda_malloc(umc_dev, umc_size*size_of_PRECISION_complex)
            if (.not.(successCUDA)) then
              print *, "bandred_complex:  cuda malloc failed umc_dev ", istat
              stop
            endif
          endif
#endif
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        else ! GPU not used

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          ! unify the the name vmr and vmrCPU, as well as vmrGPU
          ! the same for umcCPU and umcGPU
#if REALCASE == 1
          ! Allocate vmr and umcCPU to their exact sizes so that they can be used in bcasts and reduces
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          allocate(vmrCPU(max(l_rows,1),2*n_cols), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_real: error when allocating vmrCPU "//errorMessage
            stop
          endif
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#endif
#if COMPLEXCASE == 1
          allocate(vmrCPU(max(l_rows,1),2*n_cols), stat=istat, errmsg=errorMessage)

          if (istat .ne. 0) then
            print *,"bandred_complex: error when allocating vmrCPU "//errorMessage
            stop
          endif
#endif
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          allocate(umcCPU(max(l_cols,1),2*n_cols), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_real: error when allocating umcCPU "//errorMessage
            stop
          endif
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#endif
#if COMPLEXCASE == 1
          allocate(umcCPU(max(l_cols,1),2*n_cols), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_complex: error when allocating umcCPU "//errorMessage
            stop
          endif
#endif
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          allocate(vr(l_rows+1), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
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            print *,"bandred_real: error when allocating vr "//errorMessage
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#endif
#if COMPLEXCASE == 1
            print *,"bandred_complex: error when allocating vr "//errorMessage
#endif
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            stop
          endif

        endif ! use GPU

        if (useGPU) then
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#if REALCASE == 1
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          vmrCUDA(1 : cur_l_rows * n_cols) = CONST_0_0
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#endif
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        else
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#if REALCASE == 1
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          vmrCPU(1:l_rows,1:n_cols) = CONST_0_0
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#endif
#if COMPLEXCASE == 1
          vmrCPU(1:l_rows,1:n_cols) = CONST_COMPLEX_0_0
#endif
        endif ! useGPU

#if REALCASE == 1
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        vr(:) = CONST_0_0
        tmat(:,:,istep) = CONST_0_0
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#endif
#if COMPLEXCASE == 1
        vr(:) = CONST_COMPLEX_0_0
        tmat(:,:,istep) = CONST_COMPLEX_0_0
#endif
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        if (useGPU) then
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#if REALCASE == 1
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          umcCUDA(1 : umc_size) = CONST_0_0
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#endif
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          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)

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          if (lc_start .le. 0) lc_start = 1
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          ! 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
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#if REALCASE == 1
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            successCUDA = cuda_memcpy2d(loc(a(1, lc_start)), lda*size_of_PRECISION_real,         &
                                       (a_dev + ((lc_start-1) * lda*size_of_PRECISION_real)),    &
                                       lda*size_of_PRECISION_real, lr_end*size_of_PRECISION_real, &
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                                       (lc_end - lc_start+1), cudaMemcpyDeviceToHost)
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#endif
#if COMPLEXCASE == 1
            successCUDA = cuda_memcpy2d(loc(a(1, lc_start)), int(lda*size_of_PRECISION_complex,kind=c_size_t),            &
                                        (a_dev + int( ( (lc_start-1) * lda*size_of_PRECISION_complex),kind=c_size_t )),      &
                                        int(lda*size_of_PRECISION_complex,kind=c_size_t),              &
                                    int(lr_end*size_of_PRECISION_complex,kind=c_size_t),               &
                                      int((lc_end - lc_start+1),kind=c_size_t),int(cudaMemcpyDeviceToHost,kind=c_int))
#endif
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            if (.not.(successCUDA)) then
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#if REALCASE == 1
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              print *,"bandred_real: error in cudaMemcpy2d"
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#endif
#if COMPLEXCASE == 1
              print *, "bandred_complex: error in cudaMemcpy2"
#endif
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              stop
            endif

          endif
        endif ! useGPU

        ! Reduce current block to lower triangular form
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#if REALCASE == 1
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        if (useQR) then
          if (which_qr_decomposition == 1) then
            vmrCols = 2*n_cols
#ifdef USE_ASSUMED_SIZE_QR
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            call qr_pdgeqrf_2dcomm_PRECISION(a, lda, matrixCols, vmrCPU, max(l_rows,1), vmrCols, tauvector(1), &
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                                   na, tmat(1,1,istep), nbw, nbw, work_blocked, work_size,        &
                                     work_size, na, n_cols, nblk, nblk,        &
                                     istep*nbw+n_cols-nbw, istep*nbw+n_cols, 1,&
                                     0, PQRPARAM(1:11), mpi_comm_rows, mpi_comm_cols,&
                                     blockheuristic)

#else
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            call qr_pdgeqrf_2dcomm_PRECISION(a(1:lda,1:matrixCols), lda, matrixCols, vmrCPU(1:max(l_rows,1),1:vmrCols) ,   &
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                                    max(l_rows,1), vmrCols, tauvector(1:na), na, &
                                     tmat(1:nbw,1:nbw,istep), nbw, nbw, work_blocked(1:work_size), work_size, &
                                     work_size, na, n_cols, nblk, nblk,        &
                                     istep*nbw+n_cols-nbw, istep*nbw+n_cols, 1,&
                                     0, PQRPARAM(1:11), mpi_comm_rows, mpi_comm_cols,&
                                     blockheuristic)
#endif
          endif

       else !useQR
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#endif /* REALCASE == 1 */
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         do lc = n_cols, 1, -1

           ncol = istep*nbw + lc ! absolute column number of householder vector
           nrow = ncol - nbw ! Absolute number of pivot row

           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

           tau = 0

           if (nrow == 1) exit ! Nothing to do

           cur_pcol = pcol(ncol, nblk, np_cols) ! Processor column owning current block

           if (my_pcol==cur_pcol) then

             ! Get vector to be transformed; distribute last element and norm of
             ! remaining elements to all procs in current column

             vr(1:lr) = a(1:lr,lch) ! vector to be transformed

             if (my_prow==prow(nrow, nblk, np_rows)) then
               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))
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               aux1(2) = CONST_0_0
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#endif
#if COMPLEXCASE == 1
               aux1(2) = CONST_COMPLEX_0_0
#endif
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             endif

#ifdef WITH_MPI
             call timer%start("mpi_communication")
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#if REALCASE == 1
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             call mpi_allreduce(aux1, aux2, 2, MPI_REAL_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)
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#endif
#if COMPLEXCASE == 1
             call mpi_allreduce(aux1, aux2, 2, MPI_COMPLEX_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)
#endif
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             call timer%stop("mpi_communication")

#else /* WITH_MPI */
              aux2 = aux1 ! this should be optimized
Andreas Marek's avatar
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#endif
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             vnorm2 = aux2(1)
             vrl    = aux2(2)

             ! Householder transformation
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#if REALCASE == 1
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             call hh_transform_real_PRECISION(vrl, vnorm2, xf, tau)
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#endif
#if COMPLEXCASE == 1
             call hh_transform_complex_PRECISION(vrl, vnorm2, xf, tau)
#endif
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             ! Scale vr and store Householder vector for back transformation

             vr(1:lr) = vr(1:lr) * xf
             if (my_prow==prow(nrow, nblk, np_rows)) then
               a(1:lr-1,lch) = vr(1:lr-1)
               a(lr,lch) = vrl
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               vr(lr) = CONST_1_0
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#endif
#if COMPLEXCASE == 1
               vr(lr) = CONST_COMPLEX_1_0
#endif
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             else
               a(1:lr,lch) = vr(1:lr)
             endif

           endif

           ! Broadcast Householder vector and tau along columns

           vr(lr+1) = tau
#ifdef WITH_MPI
           call timer%start("mpi_communication")
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           call MPI_Bcast(vr, lr+1, MPI_REAL_PRECISION, cur_pcol, mpi_comm_cols, mpierr)
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#endif
#if COMPLEXCASE == 1
           call MPI_Bcast(vr, lr+1, MPI_COMPLEX_PRECISION, cur_pcol, mpi_comm_cols, mpierr)
#endif
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           call timer%stop("mpi_communication")

#endif /* WITH_MPI */
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#if REALCASE == 1
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           if (useGPU) then
             vmrCUDA(cur_l_rows * (lc - 1) + 1 : cur_l_rows * (lc - 1) + lr) = vr(1:lr)
           else
             vmrCPU(1:lr,lc) = vr(1:lr)
           endif
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#endif
#if COMPLEXCASE == 1
           vmrCPU(1:lr,lc) = vr(1:lr)
#endif
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           tau = vr(lr+1)

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#if REALCASE == 1
           tmat(lc,lc,istep) = tau ! Store tau in diagonal of tmat
#endif
#if COMPLEXCASE == 1
           tmat(lc,lc,istep) = conjg(tau) ! Store tau in diagonal of tmat
#endif
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           ! Transform remaining columns in current block with Householder vector
           ! Local dot product

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#if REALCASE == 1
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           aux1 = 0
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#endif
#if COMPLEXCASE == 1
          aux1 = CONST_COMPLEX_0_0
#endif
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#if REALCASE == 1
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#ifdef WITH_OPENMP
           !Open up one omp region to avoid paying openmp overhead.
           !This does not help performance due to the addition of two openmp barriers around the MPI call,
           !But in the future this may be beneficial if these barriers are replaced with a faster implementation

           !$omp parallel private(mynlc, j, lcx, ii, pp ) shared(aux1)
           mynlc = 0 ! number of local columns

           !This loop does not have independent iterations,
           !'mynlc' is incremented each iteration, and it is difficult to remove this dependency
           !Thus each thread executes every iteration of the loop, except it only does the work if it 'owns' that iteration
           !That is, a thread only executes the work associated with an iteration if its thread id is congruent to
           !the iteration number modulo the number of threads
           do j=1,lc-1
             lcx = local_index(istep*nbw+j, my_pcol, np_cols, nblk, 0)
             if (lcx>0 ) then
               mynlc = mynlc+1
               if ( mod((j-1), omp_get_num_threads()) .eq. omp_get_thread_num() ) then
                   if (lr>0) aux1(mynlc) = dot_product(vr(1:lr),a(1:lr,lcx))
               endif
             endif
           enddo

           ! Get global dot products

           !$omp barrier
           !$omp single
#ifdef WITH_MPI
           call timer%start("mpi_communication")
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           if (mynlc>0) call mpi_allreduce(aux1, aux2, mynlc, MPI_REAL_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)
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           call timer%stop("mpi_communication")
#else /* WITH_MPI */
           if (mynlc>0) aux2 = aux1
#endif /* WITH_MPI */
           !$omp end single
           !$omp barrier

           ! Transform
           transformChunkSize=32
           mynlc = 0
           do j=1,lc-1
             lcx = local_index(istep*nbw+j, my_pcol, np_cols, nblk, 0)
             if (lcx>0) then
               mynlc = mynlc+1
               !This loop could be parallelized with an openmp pragma with static scheduling and chunk size 32
               !However, for some reason this is slower than doing it manually, so it is parallelized as below.
               do ii=omp_get_thread_num()*transformChunkSize,lr,omp_get_num_threads()*transformChunkSize
                  do pp = 1,transformChunkSize
                      if (pp + ii > lr) exit
                          a(ii+pp,lcx) = a(ii+pp,lcx) - tau*aux2(mynlc)*vr(ii+pp)
                  enddo
               enddo
             endif
           enddo
           !$omp end parallel
#else /* WITH_OPENMP */

           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

           ! Get global dot products
#ifdef WITH_MPI
           call timer%start("mpi_communication")
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           if (nlc>0) call mpi_allreduce(aux1, aux2, nlc, MPI_REAL_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)
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           call timer%stop("mpi_communication")
#else /* WITH_MPI */
           if (nlc>0) aux2=aux1
#endif /* WITH_MPI */
           ! Transform

           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
#endif /* WITH_OPENMP */
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#endif /* REALCASE == 1 */

#if COMPLEXCASE == 1
           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
               aux1(nlc) = dot_product(vr(1:lr),a(1:lr,lcx))
             endif
           enddo

           ! Get global dot products
#ifdef WITH_MPI
           call timer%start("mpi_communication")
           if (nlc>0) call mpi_allreduce(aux1, aux2, nlc, MPI_COMPLEX_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)

           ! Transform

           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) - conjg(tau)*aux2(nlc)*vr(1:lr)
             endif
           enddo

           call timer%stop("mpi_communication")

#else /* WITH_MPI */
!          if (nlc>0) aux2=aux1

           ! Transform

           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) - conjg(tau)*aux1(nlc)*vr(1:lr)
             endif
           enddo

#endif /* WITH_MPI */
!
!           ! Transform
!
!           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) - conjg(tau)*aux2(nlc)*vr(1:lr)
!             endif
!           enddo
#endif
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         enddo ! lc

         if (useGPU) then
           ! store column tiles back to GPU
           cur_pcol = pcol(istep*nbw+1, nblk, np_cols)
           if (my_pcol == cur_pcol) then
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#if REALCASE == 1
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             successCUDA = cuda_memcpy2d((a_dev+((lc_start-1)*lda*size_of_PRECISION_real)),          &
                                          lda*size_of_PRECISION_real, loc(a(1, lc_start)),           &
                                          lda*size_of_PRECISION_real,  lr_end*size_of_PRECISION_real, &
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                                          (lc_end - lc_start+1),cudaMemcpyHostToDevice)
             if (.not.(successCUDA)) then
               print *,"bandred_real: error in cudaMemcpy2d"
               stop
             endif
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#endif
#if COMPLEXCASE == 1
             successCUDA = cuda_memcpy2d((a_dev+int(((lc_start-1)*lda*size_of_PRECISION_complex),kind=c_size_t)),    &
                                        int(lda*size_of_PRECISION_complex,kind=c_size_t), loc(a(1,lc_start)),       &
                                        int(lda*size_of_PRECISION_complex,kind=c_size_t),                           &
                                        int(lr_end*size_of_PRECISION_complex,kind=c_size_t),                        &
                                        int((lc_end - lc_start+1),kind=c_size_t) &
                                        ,int(cudaMemcpyHostToDevice,kind=c_int))
             if (.not.(successCUDA)) then
               print *, "bandred_complex: cuda memcpy a_dev  failed ", istat
               stop
             endif
#endif
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           endif
         endif

         ! Calculate scalar products of stored Householder vectors.
         ! This can be done in different ways, we use dsyrk

         vav = 0
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	 call timer%start("blas")
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#if REALCASE == 1
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         if (useGPU) then
           if (l_rows>0) &
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             call PRECISION_SYRK('U', 'T', n_cols, l_rows, CONST_1_0, vmrCUDA, cur_l_rows, CONST_0_0, vav, ubound(vav,dim=1))
1023
1024
         else
           if (l_rows>0) &
1025
             call PRECISION_SYRK('U', 'T', n_cols, l_rows, CONST_1_0, vmrCPU, ubound(vmrCPU,dim=1), CONST_0_0, vav, ubound(vav,dim=1))
1026
         endif
1027
1028
1029
1030
1031
1032
1033
1034
#endif
#if COMPLEXCASE == 1
        if (l_rows>0) then
          call timer%start("blas")
          call PRECISION_HERK('U', 'C', n_cols, l_rows, CONE, vmrCPU, ubound(vmrCPU,dim=1), CZERO, vav, ubound(vav,dim=1))
          call timer%stop("blas")
        endif
#endif
1035
	 call timer%stop("blas")
1036
#if REALCASE == 1
1037
         call symm_matrix_allreduce_PRECISION(n_cols,vav, nbw, nbw,mpi_comm_rows)
1038
1039
1040
1041
#endif
#if COMPLEXCASE == 1
         call herm_matrix_allreduce_PRECISION(n_cols,vav, nbw,nbw,mpi_comm_rows)
#endif
1042
         ! Calculate triangular matrix T for block Householder Transformation
1043
	 call timer%start("blas")
1044
1045
1046
         do lc=n_cols,1,-1
           tau = tmat(lc,lc,istep)
           if (lc<n_cols) then
1047
#if REALCASE == 1
1048
             call PRECISION_TRMV('U', 'T', 'N', n_cols-lc, tmat(lc+1,lc+1,istep), ubound(tmat,dim=1), vav(lc+1,lc), 1)
1049
1050
1051
1052
1053
1054
#endif
#if COMPLEXCASE == 1
             call PRECISION_TRMV('U', 'C', 'N', n_cols-lc, tmat(lc+1,lc+1,istep), ubound(tmat,dim=1), vav(lc+1,lc), 1)
#endif

#if REALCASE == 1
1055
             tmat(lc,lc+1:n_cols,istep) = -tau * vav(lc+1:n_cols,lc)
1056
1057
1058
1059
#endif
#if COMPLEXCASE == 1
             tmat(lc,lc+1:n_cols,istep) = -tau * conjg(vav(lc+1:n_cols,lc))
#endif
1060
1061
           endif
         enddo
1062
 	 call timer%stop("blas")
1063
1064
1065
#if REALCASE == 1
       endif !useQR
#endif
1066
       ! Transpose vmr -> vmc (stored in umc, second half)
1067
#if REALCASE == 1
1068
       if (useGPU) then
1069
         call elpa_transpose_vectors_real_PRECISION  (vmrCUDA, cur_l_rows, mpi_comm_rows, &
1070
1071
1072
                                            umcCUDA(cur_l_cols * n_cols + 1), cur_l_cols, mpi_comm_cols, &
                                            1, istep*nbw, n_cols, nblk)
       else
1073
         call elpa_transpose_vectors_real_PRECISION  (vmrCPU, ubound(vmrCPU,dim=1), mpi_comm_rows, &
1074
1075
1076
                                            umcCPU(1,n_cols+1), ubound(umcCPU,dim=1), mpi_comm_cols, &
                                            1, istep*nbw, n_cols, nblk)
       endif
1077
1078
1079
1080
1081
1082
#endif
#if COMPLEXCASE == 1
       call elpa_transpose_vectors_complex_PRECISION  (vmrCPU, ubound(vmrCPU,dim=1), mpi_comm_rows, &
                                      umcCPU(1,n_cols+1), ubound(umcCPU,dim=1), mpi_comm_cols, &
                                      1, istep*nbw, n_cols, nblk)
#endif
1083
1084
1085
1086
1087

       ! 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
1088
#if REALCASE == 1
1089
1090
1091
       ! here the GPU version and CPU version diverged substantially, due to the newest
       ! optimizations due to Intel. The GPU version has to be re-written
       if (useGPU) then
1092
1093
         umcCUDA(1 : l_cols * n_cols) = CONST_0_0
         vmrCUDA(cur_l_rows * n_cols + 1 : cur_l_rows * n_cols * 2) = CONST_0_0
1094
1095

         if (l_cols>0 .and. l_rows>0) then
1096
           successCUDA = cuda_memcpy(vmr_dev, loc(vmrCUDA(1)), vmr_size*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1097
1098
1099
1100
           if (.not.(successCUDA)) then
             print *,"bandred_real: error in cudaMemcpy"
             stop
           endif
1101
           successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
           if (.not.(successCUDA)) then
             print *,"bandred_real: error in cudaMemcpy"
             stop
           endif

           do i=0,(istep*nbw-1)/tile_size

             lcs = i*l_cols_tile+1
             lce = min(l_cols,(i+1)*l_cols_tile)
             if (lce<lcs) cycle
1112
             call timer%start("cublas")
1113
             lre = min(l_rows,(i+1)*l_rows_tile)
1114
             call cublas_PRECISION_GEMM('T', 'N', lce-lcs+1, n_cols, lre, &
1115
1116
                               CONST_1_0, (a_dev + ((lcs-1)*lda*size_of_PRECISION_real)), lda, vmr_dev,cur_l_rows, &
                               CONST_1_0, (umc_dev+ (lcs-1)*size_of_PRECISION_real), cur_l_cols)
1117
1118
             if(i==0) cycle
             lre = min(l_rows,i*l_rows_tile)
1119
             call cublas_PRECISION_GEMM('N', 'N', lre,n_cols, lce-lcs+1,&
1120
1121
1122
                               CONST_1_0, (a_dev+ ((lcs-1)*lda*size_of_PRECISION_real)), lda,                  &
                               (umc_dev+(cur_l_cols * n_cols+lcs-1)*size_of_PRECISION_real), cur_l_cols, &
                               CONST_1_0, (vmr_dev+(cur_l_rows * n_cols)*size_of_PRECISION_real), cur_l_rows)
1123
             call timer%stop("cublas")
1124
           enddo
1125
           successCUDA = cuda_memcpy(loc(vmrCUDA(1)), vmr_dev,vmr_size*size_of_PRECISION_real,cudaMemcpyDeviceToHost)
1126
1127
1128
1129
           if (.not.(successCUDA)) then
             print *,"bandred_real: error in cudaMemcpy"
             stop
           endif
1130
           successCUDA = cuda_memcpy(loc(umcCUDA(1)), umc_dev, umc_size*size_of_PRECISION_real,cudaMemcpyDeviceToHost)
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
           if (.not.(successCUDA)) then
             print *,"bandred_real: error in cudaMemcpy"
             stop
           endif

         endif ! l_cols>0 .and. l_rows>0

       else ! do not useGPU version

         !Code for Algorithm 4

         n_way = 1
#ifdef WITH_OPENMP
         n_way = omp_get_max_threads()
#endif
1146
1147
         !umcCPU(1:l_cols,1:n_cols) = 0.d0
         !vmrCPU(1:l_rows,n_cols+1:2*n_cols) = 0
1148
1149
1150
1151
1152
1153
#ifdef WITH_OPENMP
         !$omp parallel private( i,lcs,lce,lrs,lre)
#endif
         if (n_way > 1) then
           !$omp do
           do i=1,min(l_cols_tile, l_cols)
1154
             umcCPU(i,1:n_cols) = CONST_0_0
1155
1156
1157
1158
           enddo

           !$omp do
           do i=1,l_rows
1159
             vmrCPU(i,n_cols+1:2*n_cols) = CONST_0_0
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
           enddo
           if (l_cols>0 .and. l_rows>0) then

             !SYMM variant 4
             !Partitioned Matrix Expression:
             ! Ct = Atl Bt + Atr Bb
             ! Cb = Atr' Bt + Abl Bb
             !
             !Loop invariant:
             ! Ct = Atl Bt + Atr Bb
             !
             !Update:
             ! C1 = A10'B0 + A11B1 + A21 B2
             !
             !This algorithm chosen because in this algoirhtm, the loop around the dgemm calls
             !is easily parallelized, and regardless of choise of algorithm,
             !the startup cost for parallelizing the dgemms inside the loop is too great

             !$omp do schedule(static,1)
             do i=0,(istep*nbw-1)/tile_size
               lcs = i*l_cols_tile+1                   ! local column start
               lce = min(l_cols, (i+1)*l_cols_tile)    ! local column end

               lrs = i*l_rows_tile+1                   ! local row start
               lre = min(l_rows, (i+1)*l_rows_tile)    ! local row end

               !C1 += [A11 A12] [B1
               !                 B2]
               if ( lre > lrs .and. l_cols > lcs ) then
1189
	         call timer%start("blas")
1190
1191
                 call PRECISION_GEMM('N', 'N', lre-lrs+1, n_cols, l_cols-lcs+1,          &
                            CONST_1_0, a(lrs,lcs), ubound(a,dim=1),                 &
1192
                                  umcCPU(lcs,n_cols+1), ubound(umcCPU,dim=1),  &
1193
                            CONST_0_0, vmrCPU(lrs,n_cols+1), ubound(vmrCPU,dim=1))
1194
	         call timer%stop("blas")
1195
1196
1197
1198
               endif

               ! C1 += A10' B0
               if ( lce > lcs .and. i > 0 ) then
1199
	       	 call timer%start("blas")
1200
1201
                 call PRECISION_GEMM('T', 'N', lce-lcs+1, n_cols, lrs-1,           &
                            CONST_1_0, a(1,lcs),   ubound(a,dim=1),           &
1202
                                  vmrCPU(1,1),   ubound(vmrCPU,dim=1),   &
1203
                            CONST_0_0, umcCPU(lcs,1), ubound(umcCPU,dim=1))
1204
	       	 call timer%stop("blas")
1205
1206
1207
1208
               endif
             enddo
           endif ! l_cols>0 .and. l_rows>0
         else ! n_way > 1
1209
1210
           umcCPU(1:l_cols,1:n_cols) = CONST_0_0
           vmrCPU(1:l_rows,n_cols+1:2*n_cols) = CONST_0_0
1211
1212
1213
1214
1215
1216
           if (l_cols>0 .and. l_rows>0) then
             do i=0,(istep*nbw-1)/tile_size

               lcs = i*l_cols_tile+1
               lce = min(l_cols,(i+1)*l_cols_tile)
               if (lce<lcs) cycle
1217
	       call timer%start("blas")
1218
               lre = min(l_rows,(i+1)*l_rows_tile)
1219
1220
               call PRECISION_GEMM('T', 'N', lce-lcs+1, n_cols, lre, CONST_1_0, a(1,lcs), ubound(a,dim=1), &
                            vmrCPU, ubound(vmrCPU,dim=1), CONST_1_0, umcCPU(lcs,1), ubound(umcCPU,dim=1))
1221
	       call timer%stop("blas")
1222
1223
               if (i==0) cycle
                 lre = min(l_rows,i*l_rows_tile)
1224
	       	 call timer%start("blas")
1225
1226
                 call PRECISION_GEMM('N', 'N', lre, n_cols, lce-lcs+1, CONST_1_0, a(1,lcs), lda, &
                            umcCPU(lcs,n_cols+1), ubound(umcCPU,dim=1), CONST_1_0, vmrCPU(1,n_cols+1), ubound(vmrCPU,dim=1))
1227
	       	 call timer%stop("blas")
1228
1229
1230
1231
1232
1233
1234
             enddo
           endif
         endif ! n_way > 1
#ifdef WITH_OPENMP
        !$omp end parallel
#endif
       endif ! do not useGPU version
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
#endif /* REALCASE == 1 */

#if COMPLEXCASE == 1
        umcCPU(1:l_cols,1:n_cols) = CONST_COMPLEX_0_0
        vmrCPU(1:l_rows,n_cols+1:2*n_cols) = CONST_COMPLEX_0_0
        if (l_cols>0 .and. l_rows>0) then
          if (useGPU) then
            if (size(vmrCPU,dim=1)*size(vmrCPU,dim=2) .gt. vmr_size) then
              print *,"bandred_complex: vmr size 2 :",size(vmrCPU,dim=1)*size(vmrCPU,dim=2),vmr_size
              stop
            endif
            successCUDA = cuda_memcpy(vmr_dev, loc(vmrCPU(1,1)),vmr_size*size_of_PRECISION_complex,cudaMemcpyHostToDevice)

            if (.not.(successCUDA)) then
              print *, "bandred_complex:  cuda memcpy vmr_dev failed ", istat
              stop
            endif
            if (size(umcCPU,dim=1)*size(umcCPU,dim=2) .gt. umc_size) then
              print *,"bandred_complex: umc size 2 :",size(umcCPU,dim=1)*size(umcCPU,dim=2),umc_size
              stop
            endif
            successCUDA = cuda_memcpy(umc_dev, loc(umcCPU(1,1)),umc_size*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
            if (.not.(successCUDA)) then
              print *, "bandred_complex:  cuda memcpy umc_dev failed  ", istat
              stop
            endif
          endif
          do i=0,(istep*nbw-1)/tile_size

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

            lre = min(l_rows,(i+1)*l_rows_tile)

            if (useGPU) then
              call timer%start("cublas")
              call cublas_PRECISION_GEMM('C', 'N', lce-lcs+1, n_cols, lre, CONE, (a_dev + ((lcs-1)*lda* &
                        size_of_PRECISION_complex)), lda, &
                        vmr_dev, cur_l_rows, CONE, (umc_dev +(lcs-1)*size_of_PRECISION_complex), cur_l_cols)
              call timer%stop("cublas")
            else
              call timer%start("blas")
              call PRECISION_GEMM('C', 'N', lce-lcs+1, n_cols, lre, CONE, a(1,lcs), ubound(a,dim=1), &
                         vmrCPU, ubound(vmrCPU,dim=1), CONE, umcCPU(lcs,1), ubound(umcCPU,dim=1))
              call timer%stop("blas")
            endif

            if (i==0) cycle
            lre = min(l_rows,i*l_rows_tile)
            if (useGPU) then
              call timer%start("cublas")
              call cublas_PRECISION_GEMM('N', 'N', lre, n_cols, lce-lcs+1, CONE, (a_dev+((lcs-1)*lda* &
                        size_of_PRECISION_complex)),lda,  &
                        (umc_dev+(cur_l_cols * n_cols+lcs-1)*size_of_PRECISION_complex), cur_l_cols,CONE,  &
                        (vmr_dev+(cur_l_rows * n_cols)*size_of_PRECISION_complex), cur_l_rows)
              call timer%stop("cublas")
            else
              call timer%start("blas")
              call PRECISION_GEMM('N', 'N', lre, n_cols, lce-lcs+1, CONE, a(1,lcs), lda, &
                         umcCPU(lcs,n_cols+1), ubound(umcCPU,dim=1), CONE, vmrCPU(1,n_cols+1), ubound(vmrCPU,dim=1))
              call timer%stop("blas")
            endif
          enddo

          if (useGPU) then
            if (size(vmrCPU,dim=1)*size(vmrCPU,dim=2) .gt. vmr_size) then
              print *,"bandred_complex: vmr size 3 :",size(vmrCPU,dim=1)*size(vmrCPU,dim=2),vmr_size
              stop
            endif
            successCUDA = cuda_memcpy(loc(vmrCPU(1,1)),vmr_dev,vmr_size*size_of_PRECISION_complex,cudaMemcpyDeviceToHost)
            if (.not.(successCUDA)) then
              print *, "bandred_complex:  cuad memcpy failed vmrCPU ", istat
              stop
            endif
            if (size(umcCPU,dim=1)*size(umcCPU,dim=2) .gt. umc_size) then
              print *,"bandred_complex: umc size 3 :",size(umcCPU,dim=1)*size(umcCPU,dim=2),umc_size
              stop
            endif
            successCUDA = cuda_memcpy(loc(umcCPU(1,1)), umc_dev,umc_size*size_of_PRECISION_complex,cudaMemcpyDeviceToHost)
            if (.not.(successCUDA)) then
              print *, "bandred_complex:  cuad memcpy failed umcCPU ", istat
              stop
            endif
          endif ! useGPU
        endif ! (l_cols>0 .and. l_rows>0) 
#endif /* COMPLEXCASE == 1 */
1322
1323
1324
1325
1326
1327

       ! Sum up all ur(:) parts along rows and add them to the uc(:) parts
       ! on the processors containing the diagonal
       ! This is only necessary if ur has been calculated, i.e. if the
       ! global tile size is smaller than the global remaining matrix

1328
#if REALCASE == 1
1329
1330
1331
1332
       if (useGPU) then
         ! here the GPU version and CPU version divereged due to the same reasons as above

         if (tile_size < istep*nbw) then
1333
           call elpa_reduce_add_vectors_real_PRECISION  (vmrCUDA(cur_l_rows * n_cols + 1),cur_l_rows,mpi_comm_rows, &
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
                                               umcCUDA, cur_l_cols, mpi_comm_cols, &
                                               istep*nbw, n_cols, nblk)
         endif

         if (l_cols>0) then
           allocate(tmpCUDA(l_cols * n_cols), stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
             print *,"bandred_real: error when allocating tmpCUDA "//errorMessage
             stop
           endif

#ifdef WITH_MPI
           call timer%start("mpi_communication")

1348
           call mpi_allreduce(umcCUDA, tmpCUDA, l_cols*n_cols, MPI_REAL_PRECISION, MPI_SUM, mpi_comm_rows, ierr)
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
           umcCUDA(1 : l_cols * n_cols) = tmpCUDA(1 : l_cols * n_cols)
           call timer%stop("mpi_communication")
#else /* WITH_MPI */

!           tmpCUDA(1 : l_cols * n_cols) = umcCUDA(1 : l_cols * n_cols)

#endif /* WITH_MPI */

           if (allocated(tmpCUDA)) then
             deallocate(tmpCUDA, stat=istat, errmsg=errorMessage)
             if (istat .ne. 0) then
               print *,"bandred_real: error when deallocating tmpCUDA "//errorMessage
               stop
             endif
           endif
         endif ! l_cols

         ! U = U * Tmat**T
1367
         successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_PRECISION_real, cudaMemcpyHostToDevice)
1368
1369
1370
1371
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif
1372
         successCUDA = cuda_memcpy(tmat_dev,loc(tmat(1,1,istep)),nbw*nbw*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1373
1374
1375
1376
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif
1377
	 call timer%start("cublas")
1378
         call cublas_PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', l_cols, n_cols, &
1379
                           CONST_1_0, tmat_dev, nbw, umc_dev, cur_l_cols)
1380
1381
	 call timer%start("cublas")

1382
         ! VAV = Tmat * V**T * A * V * Tmat**T = (U*Tmat**T)**T * V * Tmat**T
1383
         successCUDA = cuda_memcpy(vav_dev,loc(vav(1,1)), nbw*nbw*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1384
1385
1386
1387
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif
1388
1389
	 call timer%start("cublas")

1390
         call cublas_PRECISION_GEMM('T', 'N', n_cols, n_cols, l_cols, &
1391
1392
                           CONST_1_0, umc_dev, cur_l_cols, (umc_dev+(cur_l_cols * n_cols )*size_of_PRECISION_real),cur_l_cols, &
                           CONST_0_0, vav_dev, nbw)
1393

1394
         call cublas_PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', n_cols, n_cols, &
1395
                           CONST_1_0, tmat_dev, nbw, vav_dev, nbw)
1396
	 call timer%stop("cublas")
1397

1398
         successCUDA = cuda_memcpy(loc(vav(1,1)), vav_dev, nbw*nbw*size_of_PRECISION_real, cudaMemcpyDeviceToHost)
1399
1400
1401
1402
1403
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

1404
         call symm_matrix_allreduce_PRECISION(n_cols,vav, nbw,nbw,mpi_comm_cols)
1405

1406
         successCUDA = cuda_memcpy(vav_dev, loc(vav(1,1)), nbw*nbw*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1407
1408
1409
1410
1411
1412
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

         ! U = U - 0.5 * V * VAV
1413
1414
 	 call timer%start("cublas")

1415
         call cublas_PRECISION_GEMM('N', 'N', l_cols, n_cols, n_cols,&
1416
1417
                           -CONST_0_5, (umc_dev+(cur_l_cols * n_cols )*size_of_PRECISION_real),cur_l_cols, vav_dev,nbw,&
                           CONST_1_0, umc_dev, cur_l_cols)
1418
	 call timer%stop("cublas")
1419

1420
         successCUDA = cuda_memcpy(loc(umcCUDA(1)), umc_dev, umc_size*size_of_PRECISION_real, cudaMemcpyDeviceToHost)
1421
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         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

         ! Transpose umc -> umr (stored in vmr, second half)
1428
         call elpa_transpose_vectors_real_PRECISION  (umcCUDA, cur_l_cols, mpi_comm_cols, &
1429
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                                            vmrCUDA(cur_l_rows * n_cols + 1), cur_l_rows, mpi_comm_rows, &
                                            1, istep*nbw, n_cols, nblk)

1432
         successCUDA = cuda_memcpy(vmr_dev, loc(vmrCUDA(1)), vmr_size*size_of_PRECISION_real, cudaMemcpyHostToDevice)
1433
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1437
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

1438
         successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_PRECISION_real, cudaMemcpyHostToDevice)
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         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

         ! A = A - V*U**T - U*V**T
         do i=0,(istep*nbw-1)/tile_size
           lcs = i*l_cols_tile+1
           lce = min(l_cols,(i+1)*l_cols_tile)
           lre = min(l_rows,(i+1)*l_rows_tile)
           if (lce<lcs .or. lre<1) cycle
1450
1451
	   call timer%start("cublas")

1452
           call cublas_PRECISION_GEMM('N', 'T', lre, lce-lcs+1, 2*n_cols, -CONST_1_0, &
1453
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                             vmr_dev, cur_l_rows, (umc_dev +(lcs-1)*size_of_PRECISION_real), cur_l_cols, &
                             CONST_1_0, (a_dev+(lcs-1)*lda*size_of_PRECISION_real), lda)
1455
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	   call timer%stop("cublas")

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         enddo

       else ! do not useGPU

         ! Or if we used the Algorithm 4
         if (tile_size < istep*nbw .or. n_way > 1) then
1463
           call elpa_reduce_add_vectors_real_PRECISION  (vmrCPU(1,n_cols+1),ubound(vmrCPU,dim=1),mpi_comm_rows, &
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                                             umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
                                             istep*nbw, n_cols, nblk)
         endif

         if (l_cols>0) then
           allocate(tmpCPU(l_cols,n_cols), stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
             print *,"bandred_real: error when allocating tmpCPU "//errorMessage
             stop
           endif

#ifdef WITH_MPI
           call timer%start("mpi_communication")
1477
           call mpi_allreduce(umcCPU, tmpCPU, l_cols*n_cols, MPI_REAL_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)
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           umcCPU(1:l_cols,1:n_cols) = tmpCPU(1:l_cols,1:n_cols)
           call timer%stop("mpi_communication")
#else /* WITH_MPI */
!           tmpCPU(1:l_cols,1:n_cols) = umcCPU(1:l_cols,1:n_cols)
#endif /* WITH_MPI */

           deallocate(tmpCPU, stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
             print *,"bandred_real: error when deallocating tmpCPU "//errorMessage
             stop
           endif
         endif

         ! U = U * Tmat**T
1492
1493
	 call timer%start("blas")

1494
         call PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', l_cols,n_cols, CONST_1_0, tmat(1,1,istep), ubound(tmat,dim=1), &
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                    umcCPU, ubound(umcCPU,dim=1))

         ! VAV = Tmat * V**T * A * V * Tmat**T = (U*Tmat**T)**T * V * Tmat**T

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         call PRECISION_GEMM('T', 'N', n_cols, n_cols, l_cols, CONST_1_0, umcCPU, ubound(umcCPU,dim=1), umcCPU(1,n_cols+1), &
                    ubound(umcCPU,dim=1), CONST_0_0, vav, ubound(vav,dim=1))
1501

1502
         call PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', n_cols, n_cols, CONST_1_0, tmat(1,1,istep),    &
1503
                    ubound(tmat,dim=1), vav, ubound(vav,dim=1))
1504
	 call timer%stop("blas")
1505
         call symm_matrix_allreduce_PRECISION(n_cols,vav, nbw, nbw ,mpi_comm_cols)
1506
1507

         ! U = U - 0.5 * V * VAV
1508
	 call timer%start("blas")
1509
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         call PRECISION_GEMM('N', 'N', l_cols, n_cols, n_cols, -CONST_0_5, umcCPU(1,n_cols+1), ubound(umcCPU,dim=1), vav, &
                     ubound(vav,dim=1), CONST_1_0, umcCPU, ubound(umcCPU,dim=1))
1511
	 call timer%stop("blas")
1512
         ! Transpose umc -> umr (stored in vmr, second half)
1513
         call elpa_transpose_vectors_real_PRECISION(umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
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                                         vmrCPU(1,n_cols+1), ubound(vmrCPU,dim=1), mpi_comm_rows, &
                                         1, istep*nbw, n_cols, nblk)

         ! A = A - V*U**T - U*V**T

#ifdef WITH_OPENMP
         !$omp parallel private( ii, i, lcs, lce, lre, n_way, m_way, m_id, n_id, work_per_thread, mystart, myend  )
         n_threads = omp_get_num_threads()
         if (mod(n_threads, 2) == 0) then
           n_way = 2
         else
           n_way = 1
         endif

         m_way = n_threads / n_way

         m_id = mod(omp_get_thread_num(),  m_way)
         n_id = omp_get_thread_num() / m_way

         do ii=n_id*tile_size,(istep*nbw-1),tile_size*n_way
           i = ii / tile_size
           lcs = i*l_cols_tile+1
           lce = min(l_cols,(i+1)*l_cols_tile)
           lre = min(l_rows,(i+1)*l_rows_tile)
           if (lce<lcs .or. lre<1) cycle

           !Figure out this thread's range
           work_per_thread = lre / m_way
           if (work_per_thread * m_way < lre) work_per_thread = work_per_thread + 1
           mystart = m_id * work_per_thread + 1
           myend   = mystart + work_per_thread - 1
           if ( myend > lre ) myend = lre
           if ( myend-mystart+1 < 1) cycle
1547
	   call timer%start("blas")
1548
           call PRECISION_GEMM('N', 'T', myend-mystart+1, lce-lcs+1, 2*n_cols, -CONST_1_0, &
1549
                      vmrCPU(mystart, 1), ubound(vmrCPU,1), umcCPU(lcs,1), ubound(umcCPU,1), &
1550
                       CONST_1_0, a(mystart,lcs), ubound(a,1))
1551
       	   call timer%stop("blas")
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         enddo
         !$omp end parallel

#else /* WITH_OPENMP */

         do i=0,(istep*nbw-1)/tile_size
           lcs = i*l_cols_tile+1
           lce = min(l_cols,(i+1)*l_cols_tile)
           lre = min(l_rows,(i+1)*l_rows_tile)
           if (lce<lcs .or. lre<1) cycle
1562
	   call timer%start("blas")
1563
           call PRECISION_GEMM('N', 'T', lre,lce-lcs+1, 2*n_cols, -CONST_1_0, &
1564
                       vmrCPU, ubound(vmrCPU,dim=1), umcCPU(lcs,1), ubound(umcCPU,dim=1), &
1565
                       CONST_1_0, a(1,lcs), lda)
1566
	   call timer%stop("blas")
1567
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1570
         enddo
#endif /* WITH_OPENMP */

       endif ! useGPU
1571
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#endif /* REALCASE == 1 */

#if COMPLEXCASE == 1
        if (tile_size < istep*nbw) then
          call elpa_reduce_add_vectors_complex_PRECISION  (vmrCPU(1,n_cols+1),ubound(vmrCPU,dim=1),mpi_comm_rows, &
                                          umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
                                          istep*nbw, n_cols, nblk)
        endif
#ifdef WITH_MPI
        if (l_cols>0) then
          allocate(tmp(l_cols,n_cols), stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_complex: error when allocating tmp "//errorMessage
            stop
          endif
          call timer%start("mpi_communication")
          call mpi_allreduce(umcCPU, tmp, l_cols*n_cols, MPI_COMPLEX_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)
          call timer%stop("mpi_communication")
1589

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1757
          umcCPU(1:l_cols,1:n_cols) = tmp(1:l_cols,1:n_cols)
          deallocate(tmp, stat=istat, errmsg=errorMessage)
          if (istat .ne. 0) then
            print *,"bandred_complex: error when deallocating tmp "//errorMessage
            stop
          endif
        endif

#else /* WITH_MPI */

!        if (l_cols>0) then
!          allocate(tmp(l_cols,n_cols), stat=istat, errmsg=errorMessage)
!          if (istat .ne. 0) then
!            print *,"bandred_complex: error when allocating tmp "//errorMessage
!            stop
!          endif
!          tmp(1:l_cols,1:n_cols) = umcCPU(1:l_cols,1:n_cols)
!
!          umcCPU(1:l_cols,1:n_cols) = tmp(1:l_cols,1:n_cols)
!          deallocate(tmp, stat=istat, errmsg=errorMessage)
!          if (istat .ne. 0) then
!            print *,"bandred_complex: error when deallocating tmp "//errorMessage
!            stop
!          endif
!        endif

#endif /* WITH_MPI */




        ! U = U * Tmat**T
        if (useGPU) then
          if (size(umcCPU,dim=1)*size(umcCPU,dim=2) .gt. umc_size) then
            print *,"bandred_complex: umcCPU size 4 :",size(umcCPU,dim=1)*size(umcCPU,dim=2),umc_size
            stop
          endif
          successCUDA = cuda_memcpy(umc_dev, loc(umcCPU(1,1)),umc_size*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuad memcpy failed umc_dev ", istat
            stop
          endif
          successCUDA = cuda_memcpy(tmat_dev,loc(tmat(1,1,istep)),nbw*nbw*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuad memcpy failed tmat_dev ", istat
            stop
          endif
          call timer%start("cublas")
          call  cublas_PRECISION_TRMM('Right', 'Upper', 'C', 'Nonunit', l_cols, n_cols, CONE, tmat_dev, nbw, umc_dev, cur_l_cols)
          call timer%stop("cublas")
        else ! not useGPU
          call timer%start("blas")
          call PRECISION_TRMM('Right', 'Upper', 'C', 'Nonunit', l_cols, n_cols, CONE, tmat(1,1,istep), ubound(tmat,dim=1), &
                     umcCPU, ubound(umcCPU,dim=1))
          call timer%stop("blas")
        endif

        ! VAV = Tmat * V**T * A * V * Tmat**T = (U*Tmat**T)**T * V * Tmat**T
        if (useGPU) then
          successCUDA = cuda_memcpy(vav_dev,loc(vav(1,1)), nbw*nbw*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuad memcpy failed vav_dev ", istat
            stop
          endif
          call timer%start("cublas")
          call cublas_PRECISION_GEMM('C', 'N', n_cols, n_cols, l_cols, CONE, umc_dev, cur_l_cols, (umc_dev +( cur_l_cols *n_cols) &
                            *size_of_PRECISION_complex ), cur_l_cols, CZERO, vav_dev, nbw)

          call cublas_PRECISION_TRMM('Right', 'Upper', 'C', 'Nonunit', n_cols, n_cols, CONE, tmat_dev, nbw, vav_dev, nbw)
          call timer%stop("cublas")
          successCUDA = cuda_memcpy(loc(vav(1,1)), vav_dev,nbw*nbw*size_of_PRECISION_complex,cudaMemcpyDeviceToHost)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuad memcpy failed vav ", istat
            stop
          endif

          call herm_matrix_allreduce_PRECISION(n_cols,vav, nbw, nbw,mpi_comm_cols)

          successCUDA = cuda_memcpy(vav_dev,loc(vav(1,1)),nbw*nbw*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuad memcpy failed vav_dev ", istat
            stop
          endif
        else ! useGPU
          call timer%start("blas")
          call PRECISION_GEMM('C', 'N', n_cols, n_cols, l_cols, CONE, umcCPU, ubound(umcCPU,dim=1), umcCPU(1,n_cols+1), &
                     ubound(umcCPU,dim=1), CZERO, vav, ubound(vav,dim=1))
          call PRECISION_TRMM('Right', 'Upper', 'C', 'Nonunit', n_cols, n_cols, CONE, tmat(1,1,istep), &
                     ubound(tmat,dim=1), vav, ubound(vav,dim=1))
          call timer%stop("blas")
          call herm_matrix_allreduce_PRECISION(n_cols,vav,nbw,nbw,mpi_comm_cols)
        endif

        ! U = U - 0.5 * V * VAV

        if (useGPU) then
          call timer%start("cublas")
          call cublas_PRECISION_GEMM('N', 'N', l_cols, n_cols, n_cols, CONST_COMPLEX_PAIR_NEGATIVE_0_5, (umc_dev +  &
                            (cur_l_cols * n_cols )*size_of_PRECISION_complex), &
                            cur_l_cols, vav_dev, nbw, CONE, umc_dev, cur_l_cols)
          call timer%stop("cublas")
          ! Transpose umc -> umr (stored in vmr, second half)

          if (size(umcCPU,dim=1)*size(umcCPU,dim=2) .gt. umc_size) then
            print *,"bandred_complex: umcCPU size 5 :",size(umcCPU,dim=1)*size(umcCPU,dim=2),umc_size
            stop
          endif
          successCUDA = cuda_memcpy(loc(umcCPU(1,1)),umc_dev,umc_size*size_of_PRECISION_complex,cudaMemcpyDeviceToHost)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuda memcpy failed umcCPU ", istat
            stop
          endif
          call elpa_transpose_vectors_complex_PRECISION  (umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
                                                vmrCPU(1,n_cols+1), ubound(vmrCPU,dim=1), mpi_comm_rows, &
                                                1, istep*nbw, n_cols, nblk)
          if (size(vmrCPU,dim=1)*size(vmrCPU,dim=2) .gt. vmr_size) then
            print *,"bandred_complex: vmr size 4 :",size(vmrCPU,dim=1)*size(vmrCPU,dim=2),vmr_size
            stop
          endif
          successCUDA = cuda_memcpy(vmr_dev,loc(vmrCPU(1,1)),vmr_size*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuda memcpy failed vav_dev", istat
            stop
          endif

          if (size(umcCPU,dim=1)*size(umcCPU,dim=2) .gt. umc_size) then
            print *,"bandred_complex: umcCPU size 6 :",size(umcCPU,dim=1)*size(umcCPU,dim=2),umc_size
            stop
          endif
          successCUDA = cuda_memcpy(umc_dev,loc(umcCPU(1,1)),umc_size*size_of_PRECISION_complex,cudaMemcpyHostToDevice)
          if (.not.(successCUDA)) then
            print *, "bandred_complex:  cuda memcpy failed umc_dev ", istat
            stop
          endif
        else ! not useGPU
          call timer%start("blas")
          call PRECISION_GEMM('N', 'N', l_cols, n_cols, n_cols, CONST_COMPLEX_PAIR_NEGATIVE_0_5, umcCPU(1,n_cols+1), ubound(umcCPU,dim=1), &
                     vav, ubound(vav,dim=1), CONE, umcCPU, ubound(umcCPU,dim=1))
          call timer%stop("blas")
          ! Transpose umc -> umr (stored in vmr, second half)

          call elpa_transpose_vectors_complex_PRECISION  (umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
                                                vmrCPU(1,n_cols+1), ubound(vmrCPU,dim=1), mpi_comm_rows, &
                                                1, istep*nbw, n_cols, nblk)
        endif
        ! A = A - V*U**T - U*V**T

        do i=0,(istep*nbw-1)/tile_size
          lcs = i*l_cols_tile+1
          lce = min(l_cols,(i+1)*l_cols_tile)
          lre = min(l_rows,(i+1)*l_rows_tile)
          if (lce<lcs .or. lre<1) cycle
            if (useGPU) then
              call timer%start("cublas")
              call cublas_PRECISION_GEMM('N', 'C', lre, lce-lcs+1, 2*n_cols, -CONE, &
                                vmr_dev ,cur_l_rows, (umc_dev +(lcs-1)*size_of_PRECISION_complex),cur_l_cols, &
                                CONE, (a_dev + (lcs-1)*lda*size_of_PRECISION_complex),lda)
              call timer%stop("cublas")
            else
              call timer%start("blas")
              call PRECISION_GEMM('N', 'C', lre,lce-lcs+1, 2*n_cols, -CONE, &
                         vmrCPU, ubound(vmrCPU,dim=1), umcCPU(lcs,1), ubound(umcCPU,dim=1), &
                         CONE, a(1,lcs), lda)
              call timer%stop("blas")
            endif
          enddo
#endif
 
1758
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1760
1761
       if (.not.(useGPU)) then
         if (allocated(vr)) then
           deallocate(vr, stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
1762
#if REALCASE == 1
1763
             print *,"bandred_real: error when deallocating vr "//errorMessage
1764
1765
1766
1767
#endif
#if COMPLEXCASE == 1
             print *,"bandred_complex: error when deallocating vr "//errorMessage
#endif
1768
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1770
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1774
             stop
           endif
         endif

         if (allocated(umcCPU)) then
           deallocate(umcCPU, stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
1775
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1779
1780
#if REALCASE == 1
             print *,"bandred_real: error when deallocating umcCPU "//errorMessage
#endif
#if COMPLEXCASE == 1
             print *,"bandred_complex: error when deallocating umcCPU "//errorMessage
#endif
1781
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1784
             stop
           endif
         endif

1785
#if REALCASE == 1
1786
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1792
         if (allocated(vmrCPU)) then
           deallocate(vmrCPU, stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
             print *,"bandred_real: error when deallocating vmrCPU "//errorMessage
             stop
           endif
         endif
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#endif
#if COMPLEXCASE == 1
         if (allocated(vmrCPU)) then
           deallocate(vmrCPU, stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
             print *,"bandred_complex: error when deallocating vmrCPU "//errorMessage
             stop
           endif
         endif
#endif
1803
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       endif !useGPU

     enddo ! istep

     if (useGPU) then
1808
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1812
!#if !(defined(USE_ASSUMED_SIZE))
!       if (size(a,dim=1)*size(a,dim=2) .ne. lda*na_cols) then
!         print *,"bandred_complex: size a ",size(a,dim=1)*size(a,dim=2) , lda*na_cols
!       endif
!#endif
1813
       ! this is not needed since a_dev is passed along from one subroutine to the other
1814
#if REALCASE == 1
1815
       successCUDA = cuda_memcpy ( loc (a), a_dev, lda*na_cols*size_of_PRECISION_real,cudaMemcpyDeviceToHost)
1816
1817
1818
1819
#endif
#if COMPLEXCASE == 1
       successCUDA = cuda_memcpy ( loc(a(1,1)), a_dev, lda*na_cols*size_of_PRECISION_complex,cudaMemcpyDeviceToHost)
#endif
1820
       if (.not.(successCUDA)) then
1821
#if REALCASE == 1
1822
         print *,"bandred_real: error in cudaMemcpy"
1823
1824
1825
1826
#endif
#if COMPLEXCASE == 1
         print *, "bandred_complex:  cuad memcpy failed a ", istat
#endif
1827
1828
1829
1830
1831
         stop
       endif

       successCUDA = cuda_free(a_dev)
       if (.not.(successCUDA)) then
1832
#if REALCASE == 1
1833
         print *,"bandred_real: error in cudaFree"
1834
1835
1836
1837