elpa2_compute.F90 325 KB
Newer Older
Andreas Marek's avatar
Andreas Marek committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
!    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 Naturwissenschaftrn,
!      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".


#include "config-f90.h"

module ELPA2_compute

! Version 1.1.2, 2011-02-21

  use elpa_utilities
  USE ELPA1_compute
  use elpa1, only : elpa_print_times, time_evp_back, time_evp_fwd, time_evp_solve
  use elpa2_utilities
  use elpa_pdgeqrf

  implicit none

  PRIVATE ! By default, all routines contained are private

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

  public :: bandred_complex
  public :: tridiag_band_complex
  public :: trans_ev_tridi_to_band_complex
  public :: trans_ev_band_to_full_complex

  public :: band_band_real
  public :: divide_band

  integer, public :: which_qr_decomposition = 1     ! defines, which QR-decomposition algorithm will be used
                                                    ! 0 for unblocked
                                                    ! 1 for blocked (maxrank: nblk)
  real*8, allocatable, public :: hh_trans_real(:,:)
  complex*16, allocatable, public :: hh_trans_complex(:,:)
  include 'mpif.h'

  contains


  subroutine bandred_real(na, a, lda, nblk, nbw, matrixCols, numBlocks, mpi_comm_rows, mpi_comm_cols, &
                        tmat, wantDebug, useGPU, success, useQR)

  !-------------------------------------------------------------------------------
  !  bandred_real: Reduces a distributed symmetric matrix to band form
  !
  !  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

#ifdef HAVE_DETAILED_TIMINGS
   use timings
#endif

   implicit none

   integer                  :: na, lda, nblk, nbw, matrixCols, numBlocks, mpi_comm_rows, mpi_comm_cols
   real*8                   :: a(lda,matrixCols), tmat(nbw,nbw,numBlocks)
   logical, intent(in)      :: useGPU

   integer                  :: my_prow, my_pcol, np_rows, np_cols, mpierr
   integer                  :: l_cols, l_rows
   integer                  :: i, j, lcs, lce, lre, lc, lr, cur_pcol, n_cols, nrow
   integer                  :: istep, ncol, lch, lcx, nlc
   integer                  :: tile_size, l_rows_tile, l_cols_tile

   real*8                   :: eps

   real*8                   :: vnorm2, xf, aux1(nbw), aux2(nbw), vrl, tau, vav(nbw,nbw)


   real*8, allocatable      :: tmpCUDA(:),  vmrCUDA(:),  umcCUDA(:)
   real*8, allocatable      :: tmpCPU(:,:), vmrCPU(:,:), umcCPU(:,:)
   real*8, allocatable      :: vr(:)


   ! needed for blocked QR decomposition
   integer                  :: PQRPARAM(11), work_size
   real*8                   :: dwork_size(1)
   real*8, allocatable      :: work_blocked(:), tauvector(:), blockheuristic(:)

   integer(kind=C_intptr_T) :: a_dev, vmr_dev, umc_dev, tmat_dev, vav_dev
   integer, external        :: numroc
   integer                  :: ierr
   integer                  :: cur_l_rows, cur_l_cols, vmr_size, umc_size
   integer(kind=c_size_t)   :: lc_start, lc_end
   integer                  :: lr_end
   integer                  :: na_rows, na_cols

   logical, intent(in)      :: wantDebug
   logical, intent(out)     :: success

   logical, intent(in)      :: useQR
   logical                  :: successCUDA
   integer                  :: istat
   character(200)           :: errorMessage

#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("bandred_real")
#endif
   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)
   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
         write(error_unit,*) 'ELPA2_bandred_real: ERROR: nbw=',nbw,', nblk=',nblk
         write(error_unit,*) 'ELPA2_bandred_real: ELPA2 works only for nbw==n*nblk'
       endif
       success = .false.
       return
     endif
   endif

   if (useGPU) then
     na_rows = numroc(na, nblk, my_prow, 0, np_rows)
     na_cols = numroc(na, nblk, my_pcol, 0, np_cols)
   endif

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

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

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

   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,    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

       call qr_pdgeqrf_2dcomm(a, lda, vmrCPU, max(l_rows,1), tauvector, tmat(1,1,1), nbw, dwork_size(1), -1, na, &
                             nbw, nblk, nblk, na, na, 1, 0, PQRPARAM, mpi_comm_rows, mpi_comm_cols, blockheuristic)
       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

       work_blocked = 0.0d0
       deallocate(vmrCPU, stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"bandred_real: error when deallocating vmrCPU "//errorMessage
         stop
       endif

     endif

   endif ! useQr

   if (useGPU) then
     ! Here we convert the regular host array into a pinned host array
     successCUDA = cuda_malloc(a_dev, lda*na_cols*size_of_real_datatype)
     if (.not.(successCUDA)) then
       print *,"bandred_real: error in cudaMalloc"
       stop
     endif

     successCUDA = cuda_malloc(tmat_dev, nbw*nbw*size_of_real_datatype)
     if (.not.(successCUDA)) then
       print *,"bandred_real: error in cudaMalloc"
       stop
     endif

     successCUDA = cuda_malloc(vav_dev, nbw*nbw*size_of_real_datatype)
     if (.not.(successCUDA)) then
       print *,"bandred_real: error in cudaMalloc"
       stop
     endif

     cur_l_rows = 0
     cur_l_cols = 0

     successCUDA = cuda_memcpy(a_dev, loc(a(1,1)), (lda)*(na_cols)*size_of_real_datatype,cudaMemcpyHostToDevice)
     if (.not.(successCUDA)) then
       print *,"bandred_real: error in cudaMemcpy"
       stop
     endif
   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)

     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
             print *,"bandred_real: error when deallocating vr "//errorMessage
             stop
           endif
         endif
         allocate(vr(l_rows + 1), stat=istat, errmsg=errorMessage)
         if (istat .ne. 0) then
           print *,"bandred_real: error when allocating vr "//errorMessage
           stop
         endif

       endif

       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

         successCUDA = cuda_malloc(vmr_dev, vmr_size*size_of_real_datatype)
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMalloc"
           stop
         endif

       endif

       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

         successCUDA = cuda_malloc(umc_dev, umc_size*size_of_real_datatype)
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMalloc"
           stop
         endif

       endif
     else ! GPU not used
       ! Allocate vmr and umc to their exact sizes so that they can be used in bcasts and reduces

       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

       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

       allocate(vr(l_rows+1), stat=istat, errmsg=errorMessage)
       if (istat .ne. 0) then
         print *,"bandred_real: error when allocating vr "//errorMessage
         stop
       endif
     endif ! use GPU

     if (useGPU) then
       vmrCUDA(1 : cur_l_rows * n_cols) = 0.
     else
       vmrCPU(1:l_rows,1:n_cols) = 0.
     endif

     vr(:) = 0
     tmat(:,:,istep) = 0

     if (useGPU) then
       umcCUDA(1 : umc_size) = 0.

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

       if(lc_start .le. 0) lc_start = 1

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

       if(my_pcol == cur_pcol) then

         successCUDA = cuda_memcpy2d(loc(a(1, lc_start)), lda*size_of_real_datatype,         &
                                    (a_dev + ((lc_start-1) * lda*size_of_real_datatype)),    &
                                    lda*size_of_real_datatype, lr_end*size_of_real_datatype, &
                                    (lc_end - lc_start+1), cudaMemcpyDeviceToHost)
         if (.not.(successCUDA)) then
           print *,"bandred_real: error in cudaMemcpy2d"
           stop
         endif

       endif
     endif ! useGPU

     ! Reduce current block to lower triangular form

     if (useQR) then
       if (which_qr_decomposition == 1) then
         call qr_pdgeqrf_2dcomm(a, lda, vmrCPU, max(l_rows,1), tauvector(1), &
                                  tmat(1,1,istep), nbw, work_blocked,       &
                                  work_size, na, n_cols, nblk, nblk,        &
                                  istep*nbw+n_cols-nbw, istep*nbw+n_cols, 1,&
                                  0, PQRPARAM, mpi_comm_rows, mpi_comm_cols,&
                                  blockheuristic)
       endif
     else

       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))
             aux1(2) = 0.
           endif

           call mpi_allreduce(aux1,aux2,2,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)

           vnorm2 = aux2(1)
           vrl    = aux2(2)

           ! Householder transformation

           call hh_transform_real(vrl, vnorm2, xf, tau)

           ! 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
             vr(lr) = 1.
           else
             a(1:lr,lch) = vr(1:lr)
           endif

         endif

         ! Broadcast Householder vector and tau along columns

         vr(lr+1) = tau
         call MPI_Bcast(vr,lr+1,MPI_REAL8,cur_pcol,mpi_comm_cols,mpierr)

         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

         tau = vr(lr+1)
         tmat(lc,lc,istep) = tau ! Store tau in diagonal of tmat

         ! Transform remaining columns in current block with Householder vector
         ! Local dot product

         aux1 = 0

         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
         if (nlc>0) call mpi_allreduce(aux1,aux2,nlc,MPI_REAL8,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) - tau*aux2(nlc)*vr(1:lr)
           endif
         enddo

       enddo

       if (useGPU) then
         ! store column tiles back to GPU
         cur_pcol = pcol(istep*nbw+1, nblk, np_cols)
         if (my_pcol == cur_pcol) then
           successCUDA = cuda_memcpy2d((a_dev+((lc_start-1)*lda*size_of_real_datatype)),          &
                                        lda*size_of_real_datatype, loc(a(1, lc_start)),           &
                                        lda*size_of_real_datatype,  lr_end*size_of_real_datatype, &
                                        (lc_end - lc_start+1),cudaMemcpyHostToDevice)
           if (.not.(successCUDA)) then
             print *,"bandred_real: error in cudaMemcpy2d"
             stop
           endif

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

       vav = 0
       if (useGPU) then
         if (l_rows>0) &
           call dsyrk('U','T',n_cols,l_rows,1.d0,vmrCUDA,cur_l_rows,0.d0,vav,ubound(vav,dim=1))
       else
         if (l_rows>0) &
           call dsyrk('U','T',n_cols,l_rows,1.d0,vmrCPU,ubound(vmrCPU,dim=1),0.d0,vav,ubound(vav,dim=1))

       endif
       call symm_matrix_allreduce(n_cols,vav, nbw, nbw,mpi_comm_rows)

       ! Calculate triangular matrix T for block Householder Transformation

       do lc=n_cols,1,-1
         tau = tmat(lc,lc,istep)
         if (lc<n_cols) then
           call dtrmv('U','T','N',n_cols-lc,tmat(lc+1,lc+1,istep),ubound(tmat,dim=1),vav(lc+1,lc),1)
           tmat(lc,lc+1:n_cols,istep) = -tau * vav(lc+1:n_cols,lc)
         endif
       enddo
     endif

    ! Transpose vmr -> vmc (stored in umc, second half)

    if (useGPU) then
      call elpa_transpose_vectors_real  (vmrCUDA, cur_l_rows, mpi_comm_rows, &
                                         umcCUDA(cur_l_cols * n_cols + 1), cur_l_cols, mpi_comm_cols, &
                                         1, istep*nbw, n_cols, nblk)
    else
      call elpa_transpose_vectors_real  (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

    ! 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

    if (useGPU) then
      umcCUDA(1 : l_cols * n_cols) = 0.d0
      vmrCUDA(cur_l_rows * n_cols + 1 : cur_l_rows * n_cols * 2) = 0
    else
      umcCPU(1:l_cols,1:n_cols) = 0.d0
      vmrCPU(1:l_rows,n_cols+1:2*n_cols) = 0
    endif

    if (l_cols>0 .and. l_rows>0) then

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

        successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_real_datatype,cudaMemcpyHostToDevice)
        if (.not.(successCUDA)) then
          print *,"bandred_real: error in cudaMemcpy"
          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 cublas_dgemm('T','N',lce-lcs+1,n_cols,lre, &
                            1.d0, (a_dev + ((lcs-1)*lda*size_of_real_datatype)), lda, vmr_dev,cur_l_rows, &
                            1.d0, (umc_dev+ (lcs-1)*size_of_real_datatype), cur_l_cols)

          if(i==0) cycle
          lre = min(l_rows,i*l_rows_tile)

          call cublas_dgemm('N','N',lre,n_cols,lce-lcs+1,&
                            1.d0, (a_dev+ ((lcs-1)*lda*size_of_real_datatype)),lda,                  &
                            (umc_dev+(cur_l_cols * n_cols+lcs-1)*size_of_real_datatype), cur_l_cols, &
                            1.d0, (vmr_dev+(cur_l_rows * n_cols)*size_of_real_datatype), cur_l_rows)
        else
          call DGEMM('T','N',lce-lcs+1,n_cols,lre,1.d0,a(1,lcs),ubound(a,dim=1), &
                       vmrCPU,ubound(vmrCPU,dim=1),1.d0,umcCPU(lcs,1),ubound(umcCPU,dim=1))

          if (i==0) cycle
          lre = min(l_rows,i*l_rows_tile)
          call DGEMM('N','N',lre,n_cols,lce-lcs+1,1.d0,a(1,lcs),lda, &
                       umcCPU(lcs,n_cols+1),ubound(umcCPU,dim=1),1.d0,vmrCPU(1,n_cols+1),ubound(vmrCPU,dim=1))
        endif

      enddo

      if (useGPU) then
        successCUDA = cuda_memcpy(loc(vmrCUDA(1)), vmr_dev,vmr_size*size_of_real_datatype,cudaMemcpyDeviceToHost)
        if (.not.(successCUDA)) then
          print *,"bandred_real: error in cudaMemcpy"
          stop
        endif

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

    endif

    ! 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

    if (tile_size < istep*nbw) then
      if (useGPU) then
        call elpa_reduce_add_vectors_real  (vmrCUDA(cur_l_rows * n_cols + 1),cur_l_rows,mpi_comm_rows, &
                                            umcCUDA, cur_l_cols, mpi_comm_cols, &
                                            istep*nbw, n_cols, nblk)
      else
        call elpa_reduce_add_vectors_real  (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
    endif

    if (l_cols>0) then
      if (useGPU) 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

        call mpi_allreduce(umcCUDA,tmpCUDA,l_cols*n_cols,MPI_REAL8,MPI_SUM,mpi_comm_rows,ierr)
        umcCUDA(1 : l_cols * n_cols) = tmpCUDA(1 : l_cols * n_cols)
      else
        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

        call mpi_allreduce(umcCPU,tmpCPU,l_cols*n_cols,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
        umcCPU(1:l_cols,1:n_cols) = tmpCPU(1:l_cols,1:n_cols)
      endif

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

    ! U = U * Tmat**T
    if (useGPU) then
      successCUDA = cuda_memcpy(umc_dev, loc(umcCUDA(1)), umc_size*size_of_real_datatype, cudaMemcpyHostToDevice)
      if (.not.(successCUDA)) then
        print *,"bandred_real: error in cudaMemcpy"
        stop
      endif

      successCUDA = cuda_memcpy(tmat_dev,loc(tmat(1,1,istep)),nbw*nbw*size_of_real_datatype,cudaMemcpyHostToDevice)
      if (.not.(successCUDA)) then
        print *,"bandred_real: error in cudaMemcpy"
        stop
      endif

      call cublas_dtrmm('Right','Upper','Trans','Nonunit',l_cols,n_cols, &
                        1.d0, tmat_dev,nbw,umc_dev,cur_l_cols)

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

      successCUDA = cuda_memcpy(vav_dev,loc(vav(1,1)), nbw*nbw*size_of_real_datatype,cudaMemcpyHostToDevice)
      if (.not.(successCUDA)) then
        print *,"bandred_real: error in cudaMemcpy"
        stop
      endif

      call cublas_dgemm('T','N',n_cols,n_cols,l_cols, &
                        1.d0, umc_dev,cur_l_cols,(umc_dev+(cur_l_cols * n_cols )*size_of_real_datatype),cur_l_cols, &
                        0.d0, vav_dev,nbw)

      call cublas_dtrmm('Right','Upper','Trans','Nonunit',n_cols,n_cols, &
                        1.d0, tmat_dev,nbw, vav_dev, nbw)


      successCUDA = cuda_memcpy(loc(vav(1,1)), vav_dev, nbw*nbw*size_of_real_datatype, cudaMemcpyDeviceToHost)
      if (.not.(successCUDA)) then
        print *,"bandred_real: error in cudaMemcpy"
        stop
      endif

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

      successCUDA = cuda_memcpy(vav_dev, loc(vav(1,1)), nbw*nbw*size_of_real_datatype,cudaMemcpyHostToDevice)
      if (.not.(successCUDA)) then
        print *,"bandred_real: error in cudaMemcpy"
        stop
      endif
    else

      call dtrmm('Right','Upper','Trans','Nonunit',l_cols,n_cols,1.d0,tmat(1,1,istep), &
                 ubound(tmat,dim=1),umcCPU,ubound(umcCPU,dim=1))

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

      call dgemm('T','N',n_cols,n_cols,l_cols,1.d0,umcCPU,ubound(umcCPU,dim=1),umcCPU(1,n_cols+1), &
                 ubound(umcCPU,dim=1),0.d0,vav,ubound(vav,dim=1))
      call dtrmm('Right','Upper','Trans','Nonunit',n_cols,n_cols,1.d0,tmat(1,1,istep), &
                 ubound(tmat,dim=1),vav,ubound(vav,dim=1))

      call symm_matrix_allreduce(n_cols,vav,nbw,nbw,mpi_comm_cols)
    endif

    ! U = U - 0.5 * V * VAV
    if (useGPU) then
      call cublas_dgemm('N','N',l_cols,n_cols,n_cols,&
                        -0.5d0, (umc_dev+(cur_l_cols * n_cols )*size_of_real_datatype),cur_l_cols, vav_dev,nbw,&
                        1.0d0, umc_dev,cur_l_cols)

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

      ! Transpose umc -> umr (stored in vmr, second half)

      call elpa_transpose_vectors_real  (umcCUDA, cur_l_cols, mpi_comm_cols, &
                                         vmrCUDA(cur_l_rows * n_cols + 1), cur_l_rows, mpi_comm_rows, &
                                         1, istep*nbw, n_cols, nblk)
      successCUDA = cuda_memcpy(vmr_dev, loc(vmrCUDA(1)), vmr_size*size_of_real_datatype, cudaMemcpyHostToDevice)
      if (.not.(successCUDA)) then
        print *,"bandred_real: error in cudaMemcpy"
        stop
      endif

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

    else
      call dgemm('N','N',l_cols,n_cols,n_cols,-0.5d0,umcCPU(1,n_cols+1),ubound(umcCPU,dim=1),vav, &
                 ubound(vav,dim=1),1.d0,umcCPU,ubound(umcCPU,dim=1))

      ! Transpose umc -> umr (stored in vmr, second half)

      call elpa_transpose_vectors_real  (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 cublas_dgemm('N', 'T', lre, lce-lcs+1, 2*n_cols, -1.d0, &
                          vmr_dev,cur_l_rows,(umc_dev +(lcs-1)*size_of_real_datatype),cur_l_cols, &
                          1.d0,(a_dev+(lcs-1)*lda*size_of_real_datatype),lda)
      else
        call dgemm('N','T',lre,lce-lcs+1,2*n_cols,-1.d0, &
                   vmrCPU,ubound(vmrCPU,dim=1),umcCPU(lcs,1),ubound(umcCPU,dim=1), &
                   1.d0,a(1,lcs),lda)
      endif
    enddo

    if (.not.(useGPU)) then
      if (allocated(vr)) then
        deallocate(vr, stat=istat, errmsg=errorMessage)
        if (istat .ne. 0) then
          print *,"bandred_real: error when deallocating vr "//errorMessage
          stop
        endif
      endif

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

      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

    endif !useGPU

  enddo ! istep


  if (useGPU) then
    successCUDA = cuda_memcpy ( loc (a), a_dev, lda*na_cols*size_of_real_datatype,cudaMemcpyDeviceToHost)
    if (.not.(successCUDA)) then
      print *,"bandred_real: error in cudaMemcpy"
      stop
    endif

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

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

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


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

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

  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

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

    successCUDA = cuda_free(umc_dev)
    if (.not.(successCUDA)) then
      print *,"bandred_real: error in cudaFree"
      stop
    endif
    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
    endif
    if (allocated(vmrCUDA)) then
      deallocate(vmrCUDA, stat=istat, errmsg=errorMessage)
      if (istat .ne. 0) then
        print *,"bandred_real: error when deallocating vmrCUDA "//errorMessage
        stop
      endif
    endif

  endif ! useGPU

  if (useQR) then
    if (which_qr_decomposition == 1) then
      deallocate(work_blocked, stat=istat, errmsg=errorMessage)
      if (istat .ne. 0) then
        print *,"bandred_real: error when deallocating work_blocked "//errorMessage
        stop
      endif

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

    endif
  endif

#ifdef HAVE_DETAILED_TIMINGS
  call timer%stop("bandred_real")
#endif
end subroutine bandred_real ! slower for gpu on 10000 10000 ???

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

subroutine symm_matrix_allreduce(n,a,lda,ldb,comm)

!-------------------------------------------------------------------------------
!  symm_matrix_allreduce: Does an mpi_allreduce for a symmetric matrix A.
!  On entry, only the upper half of A needs to be set
!  On exit, the complete matrix is set
!-------------------------------------------------------------------------------
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
   implicit none
For faster browsing, not all history is shown. View entire blame