elpa2_bandred_template.X90 75.7 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
Andreas Marek committed
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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_&
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#endif
#if COMPLEXCASE == 1
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	     call hh_transform_complex_&
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#endif
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&PRECISION &
                              (vrl, vnorm2, xf, tau)
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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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#if REALCASE == 1
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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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           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) &
1024
             call PRECISION_SYRK('U', 'T', n_cols, l_rows, CONST_1_0, vmrCUDA, cur_l_rows, CONST_0_0, vav, ubound(vav,dim=1))
1025
1026
         else
           if (l_rows>0) &
1027
             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))
1028
         endif
1029
1030
1031
1032
1033
1034
1035
1036
#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
1037
	 call timer%stop("blas")
1038
#if REALCASE == 1
1039
	 call symm_matrix_allreduce_&
1040
1041
#endif
#if COMPLEXCASE == 1
1042
         call herm_matrix_allreduce_&
1043
#endif
1044
1045
&PRECISION &
                         (n_cols,vav, nbw, nbw,mpi_comm_rows)
1046
         ! Calculate triangular matrix T for block Householder Transformation
1047
	 call timer%start("blas")
1048
1049
1050
         do lc=n_cols,1,-1
           tau = tmat(lc,lc,istep)
           if (lc<n_cols) then
1051
#if REALCASE == 1
1052
             call PRECISION_TRMV('U', 'T', 'N', n_cols-lc, tmat(lc+1,lc+1,istep), ubound(tmat,dim=1), vav(lc+1,lc), 1)
1053
1054
1055
1056
1057
1058
#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
1059
             tmat(lc,lc+1:n_cols,istep) = -tau * vav(lc+1:n_cols,lc)
1060
1061
1062
1063
#endif
#if COMPLEXCASE == 1
             tmat(lc,lc+1:n_cols,istep) = -tau * conjg(vav(lc+1:n_cols,lc))
#endif
1064
1065
           endif
         enddo
1066
 	 call timer%stop("blas")
1067
1068
1069
#if REALCASE == 1
       endif !useQR
#endif
1070
       ! Transpose vmr -> vmc (stored in umc, second half)
1071
#if REALCASE == 1
1072
       if (useGPU) then
1073
1074
1075
1076
1077
         call elpa_transpose_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
	                                   (vmrCUDA, cur_l_rows, mpi_comm_rows, &
1078
1079
1080
                                            umcCUDA(cur_l_cols * n_cols + 1), cur_l_cols, mpi_comm_cols, &
                                            1, istep*nbw, n_cols, nblk)
       else
1081
1082
1083
1084
1085
         call elpa_transpose_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
                                           (vmrCPU, ubound(vmrCPU,dim=1), mpi_comm_rows, &
1086
1087
1088
                                            umcCPU(1,n_cols+1), ubound(umcCPU,dim=1), mpi_comm_cols, &
                                            1, istep*nbw, n_cols, nblk)
       endif
1089
1090
#endif
#if COMPLEXCASE == 1
1091
1092
1093
1094
1095
         call elpa_transpose_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
                                      (vmrCPU, ubound(vmrCPU,dim=1), mpi_comm_rows, &
1096
1097
1098
                                      umcCPU(1,n_cols+1), ubound(umcCPU,dim=1), mpi_comm_cols, &
                                      1, istep*nbw, n_cols, nblk)
#endif
1099
1100
1101
1102
1103

       ! 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
1104
#if REALCASE == 1
1105
1106
1107
       ! 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
1108
1109
         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
1110
1111

         if (l_cols>0 .and. l_rows>0) then
1112
           successCUDA = cuda_memcpy(vmr_dev, loc(vmrCUDA(1)), vmr_size*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1113
1114
1115
1116
           if (.not.(successCUDA)) then
             print *,"bandred_real: error in cudaMemcpy"
             stop
           endif
1117
           successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
           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
1128
             call timer%start("cublas")
1129
             lre = min(l_rows,(i+1)*l_rows_tile)
1130
             call cublas_PRECISION_GEMM('T', 'N', lce-lcs+1, n_cols, lre, &
1131
1132
                               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)
1133
1134
             if(i==0) cycle
             lre = min(l_rows,i*l_rows_tile)
1135
             call cublas_PRECISION_GEMM('N', 'N', lre,n_cols, lce-lcs+1,&
1136
1137
1138
                               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)
1139
             call timer%stop("cublas")
1140
           enddo
1141
           successCUDA = cuda_memcpy(loc(vmrCUDA(1)), vmr_dev,vmr_size*size_of_PRECISION_real,cudaMemcpyDeviceToHost)
1142
1143
1144
1145
           if (.not.(successCUDA)) then
             print *,"bandred_real: error in cudaMemcpy"
             stop
           endif
1146
           successCUDA = cuda_memcpy(loc(umcCUDA(1)), umc_dev, umc_size*size_of_PRECISION_real,cudaMemcpyDeviceToHost)
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
           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
1162
1163
         !umcCPU(1:l_cols,1:n_cols) = 0.d0
         !vmrCPU(1:l_rows,n_cols+1:2*n_cols) = 0
1164
1165
1166
1167
1168
1169
#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)
1170
             umcCPU(i,1:n_cols) = CONST_0_0
1171
1172
1173
1174
           enddo

           !$omp do
           do i=1,l_rows
1175
             vmrCPU(i,n_cols+1:2*n_cols) = CONST_0_0
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
           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
1205
	         call timer%start("blas")
1206
1207
                 call PRECISION_GEMM('N', 'N', lre-lrs+1, n_cols, l_cols-lcs+1,          &
                            CONST_1_0, a(lrs,lcs), ubound(a,dim=1),                 &
1208
                                  umcCPU(lcs,n_cols+1), ubound(umcCPU,dim=1),  &
1209
                            CONST_0_0, vmrCPU(lrs,n_cols+1), ubound(vmrCPU,dim=1))
1210
	         call timer%stop("blas")
1211
1212
1213
1214
               endif

               ! C1 += A10' B0
               if ( lce > lcs .and. i > 0 ) then
1215
	       	 call timer%start("blas")
1216
1217
                 call PRECISION_GEMM('T', 'N', lce-lcs+1, n_cols, lrs-1,           &
                            CONST_1_0, a(1,lcs),   ubound(a,dim=1),           &
1218
                                  vmrCPU(1,1),   ubound(vmrCPU,dim=1),   &
1219
                            CONST_0_0, umcCPU(lcs,1), ubound(umcCPU,dim=1))
1220
	       	 call timer%stop("blas")
1221
1222
1223
1224
               endif
             enddo
           endif ! l_cols>0 .and. l_rows>0
         else ! n_way > 1
1225
1226
           umcCPU(1:l_cols,1:n_cols) = CONST_0_0
           vmrCPU(1:l_rows,n_cols+1:2*n_cols) = CONST_0_0
1227
1228
1229
1230
1231
1232
           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
1233
	       call timer%start("blas")
1234
               lre = min(l_rows,(i+1)*l_rows_tile)
1235
1236
               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))
1237
	       call timer%stop("blas")
1238
1239
               if (i==0) cycle
                 lre = min(l_rows,i*l_rows_tile)
1240
	       	 call timer%start("blas")
1241
1242
                 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))
1243
	       	 call timer%stop("blas")
1244
1245
1246
1247
1248
1249
1250
             enddo
           endif
         endif ! n_way > 1
#ifdef WITH_OPENMP
        !$omp end parallel
#endif
       endif ! do not useGPU version
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
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
#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
1336
        endif ! (l_cols>0 .and. l_rows>0)
1337
#endif /* COMPLEXCASE == 1 */
1338
1339
1340
1341
1342
1343

       ! 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

1344
#if REALCASE == 1
1345
1346
1347
1348
       if (useGPU) then
         ! here the GPU version and CPU version divereged due to the same reasons as above

         if (tile_size < istep*nbw) then
1349
1350
1351
1352
1353
           call elpa_reduce_add_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
                                               (vmrCUDA(cur_l_rows * n_cols + 1),cur_l_rows,mpi_comm_rows, &
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
                                               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")

1368
           call mpi_allreduce(umcCUDA, tmpCUDA, l_cols*n_cols, MPI_REAL_PRECISION, MPI_SUM, mpi_comm_rows, ierr)
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
           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
1387
         successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_PRECISION_real, cudaMemcpyHostToDevice)
1388
1389
1390
1391
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif
1392
         successCUDA = cuda_memcpy(tmat_dev,loc(tmat(1,1,istep)),nbw*nbw*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1393
1394
1395
1396
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif
1397
	 call timer%start("cublas")
1398
         call cublas_PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', l_cols, n_cols, &
1399
                           CONST_1_0, tmat_dev, nbw, umc_dev, cur_l_cols)
1400
1401
	 call timer%start("cublas")

1402
         ! VAV = Tmat * V**T * A * V * Tmat**T = (U*Tmat**T)**T * V * Tmat**T
1403
         successCUDA = cuda_memcpy(vav_dev,loc(vav(1,1)), nbw*nbw*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1404
1405
1406
1407
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif
1408
1409
	 call timer%start("cublas")

1410
         call cublas_PRECISION_GEMM('T', 'N', n_cols, n_cols, l_cols, &
1411
1412
                           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)
1413

1414
         call cublas_PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', n_cols, n_cols, &
1415
                           CONST_1_0, tmat_dev, nbw, vav_dev, nbw)
1416
	 call timer%stop("cublas")
1417

1418
         successCUDA = cuda_memcpy(loc(vav(1,1)), vav_dev, nbw*nbw*size_of_PRECISION_real, cudaMemcpyDeviceToHost)
1419
1420
1421
1422
1423
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

1424
1425
1426
         call symm_matrix_allreduce_&
&PRECISION &
	                          (n_cols,vav, nbw,nbw,mpi_comm_cols)
1427

1428
         successCUDA = cuda_memcpy(vav_dev, loc(vav(1,1)), nbw*nbw*size_of_PRECISION_real,cudaMemcpyHostToDevice)
1429
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1431
1432
1433
1434
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

         ! U = U - 0.5 * V * VAV
1435
1436
 	 call timer%start("cublas")

1437
         call cublas_PRECISION_GEMM('N', 'N', l_cols, n_cols, n_cols,&
1438
1439
                           -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)
1440
	 call timer%stop("cublas")
1441

1442
         successCUDA = cuda_memcpy(loc(umcCUDA(1)), umc_dev, umc_size*size_of_PRECISION_real, cudaMemcpyDeviceToHost)
1443
1444
1445
1446
1447
1448
1449

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

         ! Transpose umc -> umr (stored in vmr, second half)
1450
1451
1452
1453
1454
         call elpa_transpose_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
                                           (umcCUDA, cur_l_cols, mpi_comm_cols, &
1455
1456
1457
                                            vmrCUDA(cur_l_rows * n_cols + 1), cur_l_rows, mpi_comm_rows, &
                                            1, istep*nbw, n_cols, nblk)

1458
         successCUDA = cuda_memcpy(vmr_dev, loc(vmrCUDA(1)), vmr_size*size_of_PRECISION_real, cudaMemcpyHostToDevice)
1459
1460
1461
1462
1463
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy"
           stop
         endif

1464
         successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_PRECISION_real, cudaMemcpyHostToDevice)
1465
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1471
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1473
1474
1475
         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
1476
1477
	   call timer%start("cublas")

1478
           call cublas_PRECISION_GEMM('N', 'T', lre, lce-lcs+1, 2*n_cols, -CONST_1_0, &
1479
1480
                             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)
1481
1482
	   call timer%stop("cublas")

1483
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1485
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1488
         enddo

       else ! do not useGPU

         ! Or if we used the Algorithm 4
         if (tile_size < istep*nbw .or. n_way > 1) then
1489
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1493
           call elpa_reduce_add_vectors_&
&MATH_DATATYPE&
&_&
&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")
1507
           call mpi_allreduce(umcCPU, tmpCPU, l_cols*n_cols, MPI_REAL_PRECISION, MPI_SUM, mpi_comm_rows, mpierr)
1508
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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
1522
1523
	 call timer%start("blas")

1524
         call PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', l_cols,n_cols, CONST_1_0, tmat(1,1,istep), ubound(tmat,dim=1), &
1525
1526
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1528
                    umcCPU, ubound(umcCPU,dim=1))

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

1529
1530
         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))
1531

1532
         call PRECISION_TRMM('Right', 'Upper', 'Trans', 'Nonunit', n_cols, n_cols, CONST_1_0, tmat(1,1,istep),    &
1533
                    ubound(tmat,dim=1), vav, ubound(vav,dim=1))
1534
	 call timer%stop("blas")
1535
1536
1537
         call symm_matrix_allreduce_&
&PRECISION &
	                            (n_cols,vav, nbw, nbw ,mpi_comm_cols)
1538
1539

         ! U = U - 0.5 * V * VAV
1540
	 call timer%start("blas")
1541
1542
         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))
1543
	 call timer%stop("blas")
1544
         ! Transpose umc -> umr (stored in vmr, second half)
1545
1546
1547
1548
1549
         call elpa_transpose_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
	                                (umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
1550
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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
1583
	   call timer%start("blas")
1584
           call PRECISION_GEMM('N', 'T', myend-mystart+1, lce-lcs+1, 2*n_cols, -CONST_1_0, &
1585
                      vmrCPU(mystart, 1), ubound(vmrCPU,1), umcCPU(lcs,1), ubound(umcCPU,1), &
1586
                       CONST_1_0, a(mystart,lcs), ubound(a,1))
1587
       	   call timer%stop("blas")
1588
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1592
1593
1594
1595
1596
1597
         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
1598
	   call timer%start("blas")
1599
           call PRECISION_GEMM('N', 'T', lre,lce-lcs+1, 2*n_cols, -CONST_1_0, &
1600
                       vmrCPU, ubound(vmrCPU,dim=1), umcCPU(lcs,1), ubound(umcCPU,dim=1), &
1601
                       CONST_1_0, a(1,lcs), lda)
1602
	   call timer%stop("blas")
1603
1604
1605
1606
         enddo
#endif /* WITH_OPENMP */

       endif ! useGPU
1607
1608
1609
1610
#endif /* REALCASE == 1 */

#if COMPLEXCASE == 1
        if (tile_size < istep*nbw) then
1611
1612
1613
1614
1615
          call elpa_reduce_add_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
                                          (vmrCPU(1,n_cols+1),ubound(vmrCPU,dim=1),mpi_comm_rows, &
1616
1617
1618
1619
1620
1621
1622
1623
1624
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1627
1628
                                          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")
1629

1630
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1698
1699
1700
1701
1702
1703
1704
1705
          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

1706
1707
1708
          call herm_matrix_allreduce_&
&PRECISION &
                                    (n_cols,vav, nbw, nbw,mpi_comm_cols)
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721

          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")
1722
1723
1724
          call herm_matrix_allreduce_&
&PRECISION &
                                    (n_cols,vav,nbw,nbw,mpi_comm_cols)
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
        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
1746
1747
1748
1749
1750
          call elpa_transpose_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
	                                       (umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
                                                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)
1778
1779
1780
1781
1782
          call elpa_transpose_vectors_&
&MATH_DATATYPE&
&_&
&PRECISION &
	                                       (umcCPU, ubound(umcCPU,dim=1), mpi_comm_cols, &
1783
1784
1785
1786
1787
1788
1789
1790
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1800
1801
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1803
1804
1805
1806
1807
1808
                                                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
 
1809
1810
1811
1812
       if (.not.(useGPU)) then
         if (allocated(vr)) then
           deallocate(vr, stat=istat, errmsg=errorMessage)
           if (istat .ne. 0) then
1813
#if REALCASE == 1
1814
             print *,"bandred_real: error when deallocating vr "//errorMessage
1815
1816
1817
1818
#endif
#if COMPLEXCASE == 1
             print *,"bandred_complex: error when deallocating vr "//errorMessage
#endif
1819
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1823