elpa1.F90 132 KB
Newer Older
1
2
!    This file is part of ELPA.
!
3
!    The ELPA library was originally created by the ELPA consortium,
4
5
!    consisting of the following organizations:
!
6
!    - Rechenzentrum Garching der Max-Planck-Gesellschaft (RZG),
7
8
9
!    - Bergische Universität Wuppertal, Lehrstuhl für angewandte
!      Informatik,
!    - Technische Universität München, Lehrstuhl für Informatik mit
10
11
12
13
14
!      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
15
16
!    - IBM Deutschland GmbH
!
17
18
19
!    This particular source code file contains additions, changes and
!    enhancements authored by Intel Corporation which is not part of 
!    the ELPA consortium.
20
21
22
23
24
!
!    More information can be found here:
!    http://elpa.rzg.mpg.de/
!
!    ELPA is free software: you can redistribute it and/or modify
25
26
!    it under the terms of the version 3 of the license of the
!    GNU Lesser General Public License as published by the Free
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
!    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
46
!
47
48
49
50
51
52
53
54
55
! 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 ELPA1

56
57
  use elpa_utilities

58
59
60
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
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
  implicit none

  PRIVATE ! By default, all routines contained are private

  ! The following routines are public:

  public :: get_elpa_row_col_comms     ! Sets MPI row/col communicators

  public :: solve_evp_real             ! Driver routine for real eigenvalue problem
  public :: solve_evp_complex          ! Driver routine for complex eigenvalue problem

  public :: tridiag_real               ! Transform real symmetric matrix to tridiagonal form
  public :: trans_ev_real              ! Transform eigenvectors of a tridiagonal matrix back
  public :: mult_at_b_real             ! Multiply real matrices A**T * B

  public :: tridiag_complex            ! Transform complex hermitian matrix to tridiagonal form
  public :: trans_ev_complex           ! Transform eigenvectors of a tridiagonal matrix back
  public :: mult_ah_b_complex          ! Multiply complex matrices A**H * B

  public :: solve_tridi                ! Solve tridiagonal eigensystem with divide and conquer method

  public :: cholesky_real              ! Cholesky factorization of a real matrix
  public :: invert_trm_real            ! Invert real triangular matrix

  public :: cholesky_complex           ! Cholesky factorization of a complex matrix
  public :: invert_trm_complex         ! Invert complex triangular matrix

  public :: local_index                ! Get local index of a block cyclic distributed matrix
  public :: least_common_multiple      ! Get least common multiple

  public :: hh_transform_real
  public :: hh_transform_complex

94
95
96
  public :: elpa_reduce_add_vectors_complex, elpa_reduce_add_vectors_real
  public :: elpa_transpose_vectors_complex, elpa_transpose_vectors_real

97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
!-------------------------------------------------------------------------------

  ! Timing results, set by every call to solve_evp_xxx

  real*8, public :: time_evp_fwd    ! forward transformations (to tridiagonal form)
  real*8, public :: time_evp_solve  ! time for solving the tridiagonal system
  real*8, public :: time_evp_back   ! time for back transformations of eigenvectors

  ! Set elpa_print_times to .true. for explicit timing outputs

  logical, public :: elpa_print_times = .false.

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

  include 'mpif.h'

contains

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

117
function get_elpa_row_col_comms(mpi_comm_global, my_prow, my_pcol, mpi_comm_rows, mpi_comm_cols) result(mpierr)
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

!-------------------------------------------------------------------------------
! get_elpa_row_col_comms:
! All ELPA routines need MPI communicators for communicating within
! rows or columns of processes, these are set here.
! mpi_comm_rows/mpi_comm_cols can be free'd with MPI_Comm_free if not used any more.
!
!  Parameters
!
!  mpi_comm_global   Global communicator for the calculations (in)
!
!  my_prow           Row coordinate of the calling process in the process grid (in)
!
!  my_pcol           Column coordinate of the calling process in the process grid (in)
!
!  mpi_comm_rows     Communicator for communicating within rows of processes (out)
!
!  mpi_comm_cols     Communicator for communicating within columns of processes (out)
!
!-------------------------------------------------------------------------------

   implicit none

   integer, intent(in)  :: mpi_comm_global, my_prow, my_pcol
   integer, intent(out) :: mpi_comm_rows, mpi_comm_cols

   integer :: mpierr

   ! mpi_comm_rows is used for communicating WITHIN rows, i.e. all processes
   ! having the same column coordinate share one mpi_comm_rows.
   ! So the "color" for splitting is my_pcol and the "key" is my row coordinate.
   ! Analogous for mpi_comm_cols

   call mpi_comm_split(mpi_comm_global,my_pcol,my_prow,mpi_comm_rows,mpierr)
   call mpi_comm_split(mpi_comm_global,my_prow,my_pcol,mpi_comm_cols,mpierr)

154
end function get_elpa_row_col_comms
155
156
157

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

158
function solve_evp_real(na, nev, a, lda, ev, q, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols) result(success)
159
160
161
162
163
164
165
166
167
168
169

!-------------------------------------------------------------------------------
!  solve_evp_real: Solves the real eigenvalue problem
!
!  Parameters
!
!  na          Order of matrix a
!
!  nev         Number of eigenvalues needed.
!              The smallest nev eigenvalues/eigenvectors are calculated.
!
170
!  a(lda,matrixCols)    Distributed matrix for which eigenvalues are to be computed.
171
172
173
174
175
176
177
178
!              Distribution is like in Scalapack.
!              The full matrix must be set (not only one half like in scalapack).
!              Destroyed on exit (upper and lower half).
!
!  lda         Leading dimension of a
!
!  ev(na)      On output: eigenvalues of a, every processor gets the complete set
!
179
!  q(ldq,matrixCols)    On output: Eigenvectors of a
180
181
182
183
184
185
186
187
188
189
190
191
192
!              Distribution is like in Scalapack.
!              Must be always dimensioned to the full size (corresponding to (na,na))
!              even if only a part of the eigenvalues is needed.
!
!  ldq         Leading dimension of q
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!
!-------------------------------------------------------------------------------
193
194
195
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
196
197
   implicit none

198
199
   integer, intent(in)  :: na, nev, lda, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols
   real*8               :: a(lda,matrixCols), ev(na), q(ldq,matrixCols)
200

201
202
203
204
   integer              :: my_prow, my_pcol, mpierr
   real*8, allocatable  :: e(:), tau(:)
   real*8               :: ttt0, ttt1
   logical              :: success
205
206
   logical, save        :: firstCall = .true.
   logical              :: wantDebug
207

208
209
210
211
#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("solve_evp_real")
#endif

212
213
214
   call mpi_comm_rank(mpi_comm_rows,my_prow,mpierr)
   call mpi_comm_rank(mpi_comm_cols,my_pcol,mpierr)

215
216
   success = .true.

217
218
219
220
221
222
223
   wantDebug = .false.
   if (firstCall) then
     ! are debug messages desired?
     wantDebug = debug_messages_via_environment_variable()
     firstCall = .false.
   endif

224
225
226
   allocate(e(na), tau(na))

   ttt0 = MPI_Wtime()
227
   call tridiag_real(na, a, lda, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols, ev, e, tau)
228
   ttt1 = MPI_Wtime()
229
   if(my_prow==0 .and. my_pcol==0 .and. elpa_print_times) write(error_unit,*) 'Time tridiag_real :',ttt1-ttt0
230
231
232
   time_evp_fwd = ttt1-ttt0

   ttt0 = MPI_Wtime()
233
   call solve_tridi(na, nev, ev, e, q, ldq, nblk, matrixCols, mpi_comm_rows, &
234
                    mpi_comm_cols, wantDebug, success)
235
236
   if (.not.(success)) return

237
   ttt1 = MPI_Wtime()
238
   if(my_prow==0 .and. my_pcol==0 .and. elpa_print_times) write(error_unit,*) 'Time solve_tridi  :',ttt1-ttt0
239
240
241
   time_evp_solve = ttt1-ttt0

   ttt0 = MPI_Wtime()
242
   call trans_ev_real(na, nev, a, lda, tau, q, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols)
243
   ttt1 = MPI_Wtime()
244
   if(my_prow==0 .and. my_pcol==0 .and. elpa_print_times) write(error_unit,*) 'Time trans_ev_real:',ttt1-ttt0
245
246
247
248
   time_evp_back = ttt1-ttt0

   deallocate(e, tau)

249
250
251
252
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("solve_evp_real")
#endif

253
end function solve_evp_real
254
255
256
257

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


258
function solve_evp_complex(na, nev, a, lda, ev, q, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols) result(success)
259
260
261
262
263
264
265
266
267
268
269

!-------------------------------------------------------------------------------
!  solve_evp_complex: Solves the complex eigenvalue problem
!
!  Parameters
!
!  na          Order of matrix a
!
!  nev         Number of eigenvalues needed
!              The smallest nev eigenvalues/eigenvectors are calculated.
!
270
!  a(lda,matrixCols)    Distributed matrix for which eigenvalues are to be computed.
271
272
273
274
275
276
277
278
!              Distribution is like in Scalapack.
!              The full matrix must be set (not only one half like in scalapack).
!              Destroyed on exit (upper and lower half).
!
!  lda         Leading dimension of a
!
!  ev(na)      On output: eigenvalues of a, every processor gets the complete set
!
279
!  q(ldq,matrixCols)    On output: Eigenvectors of a
280
281
282
283
284
285
286
287
288
289
290
291
292
!              Distribution is like in Scalapack.
!              Must be always dimensioned to the full size (corresponding to (na,na))
!              even if only a part of the eigenvalues is needed.
!
!  ldq         Leading dimension of q
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!
!-------------------------------------------------------------------------------
293
294
295
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
296
297
298

   implicit none

299
300
   integer, intent(in)     :: na, nev, lda, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols
   complex*16              :: a(lda,matrixCols), q(ldq,matrixCols)
301
   real*8                  :: ev(na)
302

303
304
305
   integer                 :: my_prow, my_pcol, np_rows, np_cols, mpierr
   integer                 :: l_rows, l_cols, l_cols_nev
   real*8, allocatable     :: q_real(:,:), e(:)
306
307
308
   complex*16, allocatable :: tau(:)
   real*8 ttt0, ttt1

309
   logical                 :: success
310
311
312
   logical, save           :: firstCall = .true.
   logical                 :: wantDebug

313
314
315
#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("solve_evp_complex")
#endif
316

317
318
319
320
321
   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)

322
323
   success = .true.

324
325
326
327
328
329
330
331
   wantDebug = .false.
   if (firstCall) then
     ! are debug messages desired?
     wantDebug = debug_messages_via_environment_variable()
     firstCall = .false.
   endif


332
333
334
335
336
337
338
339
340
   l_rows = local_index(na, my_prow, np_rows, nblk, -1) ! Local rows of a and q
   l_cols = local_index(na, my_pcol, np_cols, nblk, -1) ! Local columns of q

   l_cols_nev = local_index(nev, my_pcol, np_cols, nblk, -1) ! Local columns corresponding to nev

   allocate(e(na), tau(na))
   allocate(q_real(l_rows,l_cols))

   ttt0 = MPI_Wtime()
341
   call tridiag_complex(na, a, lda, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols, ev, e, tau)
342
   ttt1 = MPI_Wtime()
343
   if(my_prow==0 .and. my_pcol==0 .and. elpa_print_times) write(error_unit,*) 'Time tridiag_complex :',ttt1-ttt0
344
345
346
   time_evp_fwd = ttt1-ttt0

   ttt0 = MPI_Wtime()
347
   call solve_tridi(na, nev, ev, e, q_real, l_rows, nblk, matrixCols, mpi_comm_rows, &
348
                    mpi_comm_cols, wantDebug, success)
349
350
   if (.not.(success)) return

351
   ttt1 = MPI_Wtime()
352
   if(my_prow==0 .and. my_pcol==0 .and. elpa_print_times) write(error_unit,*) 'Time solve_tridi     :',ttt1-ttt0
353
354
355
356
357
   time_evp_solve = ttt1-ttt0

   ttt0 = MPI_Wtime()
   q(1:l_rows,1:l_cols_nev) = q_real(1:l_rows,1:l_cols_nev)

358
   call trans_ev_complex(na, nev, a, lda, tau, q, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols)
359
   ttt1 = MPI_Wtime()
360
   if(my_prow==0 .and. my_pcol==0 .and. elpa_print_times) write(error_unit,*) 'Time trans_ev_complex:',ttt1-ttt0
361
362
363
364
   time_evp_back = ttt1-ttt0

   deallocate(q_real)
   deallocate(e, tau)
365
366
367
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("solve_evp_complex")
#endif
368

369
end function solve_evp_complex
370

371
372
373
374
375
376
377
378
379
380

#define DATATYPE REAL
#define BYTESIZE 8
#define REALCASE 1
#include "elpa_transpose_vectors.X90"
#include "elpa_reduce_add_vectors.X90"
#undef DATATYPE
#undef BYTESIZE
#undef REALCASE

381
382
!-------------------------------------------------------------------------------

383
subroutine tridiag_real(na, a, lda, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols, d, e, tau)
384
385
386
387
388
389
390
391
392

!-------------------------------------------------------------------------------
!  tridiag_real: Reduces a distributed symmetric matrix to tridiagonal form
!                (like Scalapack Routine PDSYTRD)
!
!  Parameters
!
!  na          Order of matrix
!
393
!  a(lda,matrixCols)    Distributed matrix which should be reduced.
394
395
396
397
398
!              Distribution is like in Scalapack.
!              Opposed to PDSYTRD, a(:,:) must be set completely (upper and lower half)
!              a(:,:) is overwritten on exit with the Householder vectors
!
!  lda         Leading dimension of a
399
!  matrixCols  local columns of matrix
400
401
402
403
404
405
406
407
408
409
410
411
412
413
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!
!  d(na)       Diagonal elements (returned), identical on all processors
!
!  e(na)       Off-Diagonal elements (returned), identical on all processors
!
!  tau(na)     Factors for the Householder vectors (returned), needed for back transformation
!
!-------------------------------------------------------------------------------
414
415
416
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
417
418
   implicit none

419
420
   integer na, lda, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols
   real*8 a(lda,matrixCols), d(na), e(na), tau(na)
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441

   integer, parameter :: max_stored_rows = 32

   integer my_prow, my_pcol, np_rows, np_cols, mpierr
   integer totalblocks, max_blocks_row, max_blocks_col, max_local_rows, max_local_cols
   integer l_cols, l_rows, nstor
   integer istep, i, j, lcs, lce, lrs, lre
   integer tile_size, l_rows_tile, l_cols_tile

#ifdef WITH_OPENMP
   integer my_thread, n_threads, max_threads, n_iter
   integer omp_get_thread_num, omp_get_num_threads, omp_get_max_threads
#endif

   real*8 vav, vnorm2, x, aux(2*max_stored_rows), aux1(2), aux2(2), vrl, xf

   real*8, allocatable:: tmp(:), vr(:), vc(:), ur(:), uc(:), vur(:,:), uvc(:,:)
#ifdef WITH_OPENMP
   real*8, allocatable:: ur_p(:,:), uc_p(:,:)
#endif

442
443
444
#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("tridiag_real")
#endif
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

   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)

   ! 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


   totalblocks = (na-1)/nblk + 1
   max_blocks_row = (totalblocks-1)/np_rows + 1
   max_blocks_col = (totalblocks-1)/np_cols + 1

   max_local_rows = max_blocks_row*nblk
   max_local_cols = max_blocks_col*nblk

   allocate(tmp(MAX(max_local_rows,max_local_cols)))
   allocate(vr(max_local_rows+1))
   allocate(ur(max_local_rows))
   allocate(vc(max_local_cols))
   allocate(uc(max_local_cols))

#ifdef WITH_OPENMP
   max_threads = omp_get_max_threads()

   allocate(ur_p(max_local_rows,0:max_threads-1))
   allocate(uc_p(max_local_cols,0:max_threads-1))
#endif

   tmp = 0
   vr = 0
   ur = 0
   vc = 0
   uc = 0

   allocate(vur(max_local_rows,2*max_stored_rows))
   allocate(uvc(max_local_cols,2*max_stored_rows))

   d(:) = 0
   e(:) = 0
   tau(:) = 0

   nstor = 0

   l_rows = local_index(na, my_prow, np_rows, nblk, -1) ! Local rows of a
   l_cols = local_index(na, my_pcol, np_cols, nblk, -1) ! Local cols of a
497
   if(my_prow==prow(na, nblk, np_rows) .and. my_pcol==pcol(na, nblk, np_cols)) d(na) = a(l_rows,l_cols)
498
499
500
501
502
503
504
505
506
507
508
509

   do istep=na,3,-1

      ! Calculate number of local rows and columns of the still remaining matrix
      ! on the local processor

      l_rows = local_index(istep-1, my_prow, np_rows, nblk, -1)
      l_cols = local_index(istep-1, my_pcol, np_cols, nblk, -1)

      ! Calculate vector for Householder transformation on all procs
      ! owning column istep

510
      if(my_pcol==pcol(istep, nblk, np_cols)) then
511
512
513
514
515
516

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

         vr(1:l_rows) = a(1:l_rows,l_cols+1)
         if(nstor>0 .and. l_rows>0) then
517
518
            call DGEMV('N',l_rows,2*nstor,1.d0,vur,ubound(vur,dim=1), &
                       uvc(l_cols+1,1),ubound(uvc,dim=1),1.d0,vr,1)
519
520
         endif

521
         if(my_prow==prow(istep-1, nblk, np_rows)) then
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
            aux1(1) = dot_product(vr(1:l_rows-1),vr(1:l_rows-1))
            aux1(2) = vr(l_rows)
         else
            aux1(1) = dot_product(vr(1:l_rows),vr(1:l_rows))
            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(istep))

         ! Scale vr and store Householder vector for back transformation

         vr(1:l_rows) = vr(1:l_rows) * xf
541
         if(my_prow==prow(istep-1, nblk, np_rows)) then
542
543
544
545
546
547
548
549
550
            vr(l_rows) = 1.
            e(istep-1) = vrl
         endif
         a(1:l_rows,l_cols+1) = vr(1:l_rows) ! store Householder vector for back transformation

      endif

      ! Broadcast the Householder vector (and tau) along columns

551
552
      if(my_pcol==pcol(istep, nblk, np_cols)) vr(l_rows+1) = tau(istep)
      call MPI_Bcast(vr,l_rows+1,MPI_REAL8,pcol(istep, nblk, np_cols),mpi_comm_cols,mpierr)
553
554
555
556
      tau(istep) =  vr(l_rows+1)

      ! Transpose Householder vector vr -> vc

557
558
559
      call elpa_transpose_vectors_real  (vr, ubound(vr,dim=1), mpi_comm_rows, &
                                         vc, ubound(vc,dim=1), mpi_comm_cols, &
                                         1, istep-1, 1, nblk)
560
561
562
563
564
565
566
567
568
569
570
571


      ! Calculate u = (A + VU**T + UV**T)*v

      ! For cache efficiency, we use only the upper half of the matrix tiles for this,
      ! thus the result is partly in uc(:) and partly in ur(:)

      uc(1:l_cols) = 0
      ur(1:l_rows) = 0
      if(l_rows>0 .and. l_cols>0) then

#ifdef WITH_OPENMP
572
573
574
575
576

#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("OpenMP parallel")
#endif

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
!$OMP PARALLEL PRIVATE(my_thread,n_threads,n_iter,i,lcs,lce,j,lrs,lre)

         my_thread = omp_get_thread_num()
         n_threads = omp_get_num_threads()

         n_iter = 0

         uc_p(1:l_cols,my_thread) = 0.
         ur_p(1:l_rows,my_thread) = 0.
#endif
         do i=0,(istep-2)/tile_size
            lcs = i*l_cols_tile+1
            lce = min(l_cols,(i+1)*l_cols_tile)
            if(lce<lcs) cycle
            do j=0,i
               lrs = j*l_rows_tile+1
               lre = min(l_rows,(j+1)*l_rows_tile)
               if(lre<lrs) cycle
#ifdef WITH_OPENMP
               if(mod(n_iter,n_threads) == my_thread) then
                 call DGEMV('T',lre-lrs+1,lce-lcs+1,1.d0,a(lrs,lcs),lda,vr(lrs),1,1.d0,uc_p(lcs,my_thread),1)
                 if(i/=j) call DGEMV('N',lre-lrs+1,lce-lcs+1,1.d0,a(lrs,lcs),lda,vc(lcs),1,1.d0,ur_p(lrs,my_thread),1)
               endif
               n_iter = n_iter+1
#else
               call DGEMV('T',lre-lrs+1,lce-lcs+1,1.d0,a(lrs,lcs),lda,vr(lrs),1,1.d0,uc(lcs),1)
               if(i/=j) call DGEMV('N',lre-lrs+1,lce-lcs+1,1.d0,a(lrs,lcs),lda,vc(lcs),1,1.d0,ur(lrs),1)

#endif
            enddo
         enddo
#ifdef WITH_OPENMP
609
!$OMP END PARALLEL
610
611
612
613
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("OpenMP parallel")
#endif

614
615
616
617
618
619
         do i=0,max_threads-1
            uc(1:l_cols) = uc(1:l_cols) + uc_p(1:l_cols,i)
            ur(1:l_rows) = ur(1:l_rows) + ur_p(1:l_rows,i)
         enddo
#endif
         if(nstor>0) then
620
621
            call DGEMV('T',l_rows,2*nstor,1.d0,vur,ubound(vur,dim=1),vr,1,0.d0,aux,1)
            call DGEMV('N',l_cols,2*nstor,1.d0,uvc,ubound(uvc,dim=1),aux,1,1.d0,uc,1)
622
623
624
625
626
627
628
629
630
631
         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-1) then
632
633
         call elpa_reduce_add_vectors_REAL  (ur, ubound(ur,dim=1), mpi_comm_rows, &
                                        uc, ubound(uc,dim=1), mpi_comm_cols, &
634
635
636
637
638
639
640
641
642
643
                                        istep-1, 1, nblk)
      endif

      ! Sum up all the uc(:) parts, transpose uc -> ur

      if(l_cols>0) then
         tmp(1:l_cols) = uc(1:l_cols)
         call mpi_allreduce(tmp,uc,l_cols,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
      endif

644
645
646
      call elpa_transpose_vectors_real  (uc, ubound(uc,dim=1), mpi_comm_cols, &
                                         ur, ubound(ur,dim=1), mpi_comm_rows, &
                                         1, istep-1, 1, nblk)
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

      ! calculate u**T * v (same as v**T * (A + VU**T + UV**T) * v )

      x = 0
      if(l_cols>0) x = dot_product(vc(1:l_cols),uc(1:l_cols))
      call mpi_allreduce(x,vav,1,MPI_REAL8,MPI_SUM,mpi_comm_cols,mpierr)

      ! store u and v in the matrices U and V
      ! these matrices are stored combined in one here

      do j=1,l_rows
         vur(j,2*nstor+1) = tau(istep)*vr(j)
         vur(j,2*nstor+2) = 0.5*tau(istep)*vav*vr(j) - ur(j)
      enddo
      do j=1,l_cols
         uvc(j,2*nstor+1) = 0.5*tau(istep)*vav*vc(j) - uc(j)
         uvc(j,2*nstor+2) = tau(istep)*vc(j)
      enddo

      nstor = nstor+1

      ! If the limit of max_stored_rows is reached, calculate A + VU**T + UV**T

      if(nstor==max_stored_rows .or. istep==3) then

         do i=0,(istep-2)/tile_size
            lcs = i*l_cols_tile+1
            lce = min(l_cols,(i+1)*l_cols_tile)
            lrs = 1
            lre = min(l_rows,(i+1)*l_rows_tile)
            if(lce<lcs .or. lre<lrs) cycle
            call dgemm('N','T',lre-lrs+1,lce-lcs+1,2*nstor,1.d0, &
679
                       vur(lrs,1),ubound(vur,dim=1),uvc(lcs,1),ubound(uvc,dim=1), &
680
681
682
683
684
685
686
                       1.d0,a(lrs,lcs),lda)
         enddo

         nstor = 0

      endif

687
      if(my_prow==prow(istep-1, nblk, np_rows) .and. my_pcol==pcol(istep-1, nblk, np_cols)) then
688
689
690
691
692
693
694
695
696
         if(nstor>0) a(l_rows,l_cols) = a(l_rows,l_cols) &
                        + dot_product(vur(l_rows,1:2*nstor),uvc(l_cols,1:2*nstor))
         d(istep-1) = a(l_rows,l_cols)
      endif

   enddo

   ! Store e(1) and d(1)

697
698
   if(my_prow==prow(1, nblk, np_rows) .and. my_pcol==pcol(2, nblk, np_cols)) e(1) = a(1,l_cols) ! use last l_cols value of loop above
   if(my_prow==prow(1, nblk, np_rows) .and. my_pcol==pcol(1, nblk, np_cols)) d(1) = a(1,1)
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713

   deallocate(tmp, vr, ur, vc, uc, vur, uvc)

   ! distribute the arrays d and e to all processors

   allocate(tmp(na))
   tmp = d
   call mpi_allreduce(tmp,d,na,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
   tmp = d
   call mpi_allreduce(tmp,d,na,MPI_REAL8,MPI_SUM,mpi_comm_cols,mpierr)
   tmp = e
   call mpi_allreduce(tmp,e,na,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
   tmp = e
   call mpi_allreduce(tmp,e,na,MPI_REAL8,MPI_SUM,mpi_comm_cols,mpierr)
   deallocate(tmp)
714
715
716
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("tridiag_real")
#endif
717
718
719
720
721

end subroutine tridiag_real

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

722
subroutine trans_ev_real(na, nqc, a, lda, tau, q, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols)
723
724
725
726
727
728
729
730
731
732
733
734

!-------------------------------------------------------------------------------
!  trans_ev_real: Transforms the eigenvectors of a tridiagonal matrix back
!                 to the eigenvectors of the original matrix
!                 (like Scalapack Routine PDORMTR)
!
!  Parameters
!
!  na          Order of matrix a, number of rows of matrix q
!
!  nqc         Number of columns of matrix q
!
735
!  a(lda,matrixCols)    Matrix containing the Householder vectors (i.e. matrix a after tridiag_real)
736
737
738
!              Distribution is like in Scalapack.
!
!  lda         Leading dimension of a
739
!  matrixCols  local columns of matrix a and q
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
!
!  tau(na)     Factors of the Householder vectors
!
!  q           On input: Eigenvectors of tridiagonal matrix
!              On output: Transformed eigenvectors
!              Distribution is like in Scalapack.
!
!  ldq         Leading dimension of q
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!
!-------------------------------------------------------------------------------
756
757
758
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
759
760
   implicit none

761
762
   integer na, nqc, lda, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols
   real*8 a(lda,matrixCols), q(ldq,matrixCols), tau(na)
763
764
765
766
767
768
769
770
771
772
773

   integer :: max_stored_rows

   integer my_prow, my_pcol, np_rows, np_cols, mpierr
   integer totalblocks, max_blocks_row, max_blocks_col, max_local_rows, max_local_cols
   integer l_cols, l_rows, l_colh, nstor
   integer istep, i, n, nc, ic, ics, ice, nb, cur_pcol

   real*8, allocatable:: tmp1(:), tmp2(:), hvb(:), hvm(:,:)
   real*8, allocatable:: tmat(:,:), h1(:), h2(:)

774
775
776
#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("trans_ev_real")
#endif
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

   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)


   totalblocks = (na-1)/nblk + 1
   max_blocks_row = (totalblocks-1)/np_rows + 1
   max_blocks_col = ((nqc-1)/nblk)/np_cols + 1  ! Columns of q!

   max_local_rows = max_blocks_row*nblk
   max_local_cols = max_blocks_col*nblk


   max_stored_rows = (63/nblk+1)*nblk

   allocate(tmat(max_stored_rows,max_stored_rows))
   allocate(h1(max_stored_rows*max_stored_rows))
   allocate(h2(max_stored_rows*max_stored_rows))
   allocate(tmp1(max_local_cols*max_stored_rows))
   allocate(tmp2(max_local_cols*max_stored_rows))
   allocate(hvb(max_local_rows*nblk))
   allocate(hvm(max_local_rows,max_stored_rows))

   hvm = 0   ! Must be set to 0 !!!
   hvb = 0   ! Safety only

   l_cols = local_index(nqc, my_pcol, np_cols, nblk, -1) ! Local columns of q

   nstor = 0

   do istep=1,na,nblk

      ics = MAX(istep,3)
      ice = MIN(istep+nblk-1,na)
      if(ice<ics) cycle

815
      cur_pcol = pcol(istep, nblk, np_cols)
816
817
818
819
820
821
822
823
824
825

      nb = 0
      do ic=ics,ice

         l_colh = local_index(ic  , my_pcol, np_cols, nblk, -1) ! Column of Householder vector
         l_rows = local_index(ic-1, my_prow, np_rows, nblk, -1) ! # rows of Householder vector


         if(my_pcol==cur_pcol) then
            hvb(nb+1:nb+l_rows) = a(1:l_rows,l_colh)
826
            if(my_prow==prow(ic-1, nblk, np_rows)) then
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
               hvb(nb+l_rows) = 1.
            endif
         endif

         nb = nb+l_rows
      enddo

      if(nb>0) &
         call MPI_Bcast(hvb,nb,MPI_REAL8,cur_pcol,mpi_comm_cols,mpierr)

      nb = 0
      do ic=ics,ice
         l_rows = local_index(ic-1, my_prow, np_rows, nblk, -1) ! # rows of Householder vector
         hvm(1:l_rows,nstor+1) = hvb(nb+1:nb+l_rows)
         nstor = nstor+1
         nb = nb+l_rows
      enddo

      ! Please note: for smaller matix sizes (na/np_rows<=256), a value of 32 for nstor is enough!
      if(nstor+nblk>max_stored_rows .or. istep+nblk>na .or. (na/np_rows<=256 .and. nstor>=32)) then

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

         tmat = 0
         if(l_rows>0) &
853
            call dsyrk('U','T',nstor,l_rows,1.d0,hvm,ubound(hvm,dim=1),0.d0,tmat,max_stored_rows)
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876

         nc = 0
         do n=1,nstor-1
            h1(nc+1:nc+n) = tmat(1:n,n+1)
            nc = nc+n
         enddo

         if(nc>0) call mpi_allreduce(h1,h2,nc,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)

         ! Calculate triangular matrix T

         nc = 0
         tmat(1,1) = tau(ice-nstor+1)
         do n=1,nstor-1
            call dtrmv('L','T','N',n,tmat,max_stored_rows,h2(nc+1),1)
            tmat(n+1,1:n) = -h2(nc+1:nc+n)*tau(ice-nstor+n+1)
            tmat(n+1,n+1) = tau(ice-nstor+n+1)
            nc = nc+n
         enddo

         ! Q = Q - V * T * V**T * Q

         if(l_rows>0) then
877
            call dgemm('T','N',nstor,l_cols,l_rows,1.d0,hvm,ubound(hvm,dim=1), &
878
879
880
881
882
883
884
                       q,ldq,0.d0,tmp1,nstor)
         else
            tmp1(1:l_cols*nstor) = 0
         endif
         call mpi_allreduce(tmp1,tmp2,nstor*l_cols,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
         if(l_rows>0) then
            call dtrmm('L','L','N','N',nstor,l_cols,1.0d0,tmat,max_stored_rows,tmp2,nstor)
885
            call dgemm('N','N',l_rows,l_cols,nstor,-1.d0,hvm,ubound(hvm,dim=1), &
886
887
888
889
890
891
892
893
894
                       tmp2,nstor,1.d0,q,ldq)
         endif
         nstor = 0
      endif

   enddo

   deallocate(tmat, h1, h2, tmp1, tmp2, hvb, hvm)

895
896
897
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("trans_ev_real")
#endif
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

end subroutine trans_ev_real

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

subroutine mult_at_b_real(uplo_a, uplo_c, na, ncb, a, lda, b, ldb, nblk, mpi_comm_rows, mpi_comm_cols, c, ldc)

!-------------------------------------------------------------------------------
!  mult_at_b_real:  Performs C := A**T * B
!
!      where:  A is a square matrix (na,na) which is optionally upper or lower triangular
!              B is a (na,ncb) matrix
!              C is a (na,ncb) matrix where optionally only the upper or lower
!              triangle may be computed
!
!  Parameters
!
!  uplo_a      'U' if A is upper triangular
!              'L' if A is lower triangular
!              anything else if A is a full matrix
!              Please note: This pertains to the original A (as set in the calling program)
!              whereas the transpose of A is used for calculations
!              If uplo_a is 'U' or 'L', the other triangle is not used at all,
!              i.e. it may contain arbitrary numbers
!
!  uplo_c      'U' if only the upper diagonal part of C is needed
!              'L' if only the upper diagonal part of C is needed
!              anything else if the full matrix C is needed
!              Please note: Even when uplo_c is 'U' or 'L', the other triangle may be
!              written to a certain extent, i.e. one shouldn't rely on the content there!
!
!  na          Number of rows/columns of A, number of rows of B and C
!
!  ncb         Number of columns  of B and C
!
!  a           Matrix A
!
!  lda         Leading dimension of a
!
!  b           Matrix B
!
!  ldb         Leading dimension of b
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!
!  c           Matrix C
!
!  ldc         Leading dimension of c
!
!-------------------------------------------------------------------------------
952
953
954
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
   implicit none

   character*1 uplo_a, uplo_c

   integer na, ncb, lda, ldb, nblk, mpi_comm_rows, mpi_comm_cols, ldc
   real*8 a(lda,*), b(ldb,*), c(ldc,*)

   integer my_prow, my_pcol, np_rows, np_cols, mpierr
   integer l_cols, l_rows, l_rows_np
   integer np, n, nb, nblk_mult, lrs, lre, lcs, lce
   integer gcol_min, gcol, goff
   integer nstor, nr_done, noff, np_bc, n_aux_bc, nvals
   integer, allocatable :: lrs_save(:), lre_save(:)

   logical a_lower, a_upper, c_lower, c_upper

   real*8, allocatable:: aux_mat(:,:), aux_bc(:), tmp1(:,:), tmp2(:,:)

973
974
975
#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("mult_at_b_real")
#endif
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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
   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)

   l_rows = local_index(na,  my_prow, np_rows, nblk, -1) ! Local rows of a and b
   l_cols = local_index(ncb, my_pcol, np_cols, nblk, -1) ! Local cols of b

   ! Block factor for matrix multiplications, must be a multiple of nblk

   if(na/np_rows<=256) then
      nblk_mult = (31/nblk+1)*nblk
   else
      nblk_mult = (63/nblk+1)*nblk
   endif

   allocate(aux_mat(l_rows,nblk_mult))
   allocate(aux_bc(l_rows*nblk))
   allocate(lrs_save(nblk))
   allocate(lre_save(nblk))

   a_lower = .false.
   a_upper = .false.
   c_lower = .false.
   c_upper = .false.

   if(uplo_a=='u' .or. uplo_a=='U') a_upper = .true.
   if(uplo_a=='l' .or. uplo_a=='L') a_lower = .true.
   if(uplo_c=='u' .or. uplo_c=='U') c_upper = .true.
   if(uplo_c=='l' .or. uplo_c=='L') c_lower = .true.

   ! Build up the result matrix by processor rows

   do np = 0, np_rows-1

      ! In this turn, procs of row np assemble the result

      l_rows_np = local_index(na, np, np_rows, nblk, -1) ! local rows on receiving processors

      nr_done = 0 ! Number of rows done
      aux_mat = 0
      nstor = 0   ! Number of columns stored in aux_mat

      ! Loop over the blocks on row np

      do nb=0,(l_rows_np-1)/nblk

         goff  = nb*np_rows + np ! Global offset in blocks corresponding to nb

         ! Get the processor column which owns this block (A is transposed, so we need the column)
         ! and the offset in blocks within this column.
         ! The corresponding block column in A is then broadcast to all for multiplication with B

         np_bc = MOD(goff,np_cols)
         noff = goff/np_cols
         n_aux_bc = 0

         ! Gather up the complete block column of A on the owner

         do n = 1, min(l_rows_np-nb*nblk,nblk) ! Loop over columns to be broadcast

            gcol = goff*nblk + n ! global column corresponding to n
            if(nstor==0 .and. n==1) gcol_min = gcol

            lrs = 1       ! 1st local row number for broadcast
            lre = l_rows  ! last local row number for broadcast
            if(a_lower) lrs = local_index(gcol, my_prow, np_rows, nblk, +1)
            if(a_upper) lre = local_index(gcol, my_prow, np_rows, nblk, -1)

            if(lrs<=lre) then
               nvals = lre-lrs+1
               if(my_pcol == np_bc) aux_bc(n_aux_bc+1:n_aux_bc+nvals) = a(lrs:lre,noff*nblk+n)
               n_aux_bc = n_aux_bc + nvals
            endif

            lrs_save(n) = lrs
            lre_save(n) = lre

         enddo

         ! Broadcast block column

         call MPI_Bcast(aux_bc,n_aux_bc,MPI_REAL8,np_bc,mpi_comm_cols,mpierr)

         ! Insert what we got in aux_mat

         n_aux_bc = 0
         do n = 1, min(l_rows_np-nb*nblk,nblk)
            nstor = nstor+1
            lrs = lrs_save(n)
            lre = lre_save(n)
            if(lrs<=lre) then
               nvals = lre-lrs+1
               aux_mat(lrs:lre,nstor) = aux_bc(n_aux_bc+1:n_aux_bc+nvals)
               n_aux_bc = n_aux_bc + nvals
            endif
         enddo

         ! If we got nblk_mult columns in aux_mat or this is the last block
         ! do the matrix multiplication

         if(nstor==nblk_mult .or. nb*nblk+nblk >= l_rows_np) then

            lrs = 1       ! 1st local row number for multiply
            lre = l_rows  ! last local row number for multiply
            if(a_lower) lrs = local_index(gcol_min, my_prow, np_rows, nblk, +1)
            if(a_upper) lre = local_index(gcol, my_prow, np_rows, nblk, -1)

            lcs = 1       ! 1st local col number for multiply
            lce = l_cols  ! last local col number for multiply
            if(c_upper) lcs = local_index(gcol_min, my_pcol, np_cols, nblk, +1)
            if(c_lower) lce = MIN(local_index(gcol, my_pcol, np_cols, nblk, -1),l_cols)

            if(lcs<=lce) then
               allocate(tmp1(nstor,lcs:lce),tmp2(nstor,lcs:lce))
               if(lrs<=lre) then
1092
                  call dgemm('T','N',nstor,lce-lcs+1,lre-lrs+1,1.d0,aux_mat(lrs,1),ubound(aux_mat,dim=1), &
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
                             b(lrs,lcs),ldb,0.d0,tmp1,nstor)
               else
                  tmp1 = 0
               endif

               ! Sum up the results and send to processor row np
               call mpi_reduce(tmp1,tmp2,nstor*(lce-lcs+1),MPI_REAL8,MPI_SUM,np,mpi_comm_rows,mpierr)

               ! Put the result into C
               if(my_prow==np) c(nr_done+1:nr_done+nstor,lcs:lce) = tmp2(1:nstor,lcs:lce)

               deallocate(tmp1,tmp2)
            endif

            nr_done = nr_done+nstor
            nstor=0
            aux_mat(:,:)=0
         endif
      enddo
   enddo

   deallocate(aux_mat, aux_bc, lrs_save, lre_save)
1115
1116
1117
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("mult_at_b_real")
#endif
1118
1119
1120
1121
1122

end subroutine mult_at_b_real

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

1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133

#define DATATYPE COMPLEX
#define BYTESIZE 16
#define COMPLEXCASE 1
#include "elpa_transpose_vectors.X90"
#include "elpa_reduce_add_vectors.X90"  
#undef DATATYPE
#undef BYTESIZE
#undef COMPLEXCASE

subroutine tridiag_complex(na, a, lda, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols, d, e, tau)
1134
1135
1136
1137
1138
1139
1140
1141
1142

!-------------------------------------------------------------------------------
!  tridiag_complex: Reduces a distributed hermitian matrix to tridiagonal form
!                   (like Scalapack Routine PZHETRD)
!
!  Parameters
!
!  na          Order of matrix
!
1143
!  a(lda,matrixCols)    Distributed matrix which should be reduced.
1144
1145
1146
1147
1148
!              Distribution is like in Scalapack.
!              Opposed to PZHETRD, a(:,:) must be set completely (upper and lower half)
!              a(:,:) is overwritten on exit with the Householder vectors
!
!  lda         Leading dimension of a
1149
!  matrixCols  local columns of matrix a
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!
!  d(na)       Diagonal elements (returned), identical on all processors
!
!  e(na)       Off-Diagonal elements (returned), identical on all processors
!
!  tau(na)     Factors for the Householder vectors (returned), needed for back transformation
!
!-------------------------------------------------------------------------------
1164
1165
1166
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
1167
1168
   implicit none

1169
1170
   integer na, lda, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols
   complex*16 a(lda,matrixCols), tau(na)
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
   real*8 d(na), e(na)

   integer, parameter :: max_stored_rows = 32

   complex*16, parameter :: CZERO = (0.d0,0.d0), CONE = (1.d0,0.d0)

   integer my_prow, my_pcol, np_rows, np_cols, mpierr
   integer totalblocks, max_blocks_row, max_blocks_col, max_local_rows, max_local_cols
   integer l_cols, l_rows, nstor
   integer istep, i, j, lcs, lce, lrs, lre
   integer tile_size, l_rows_tile, l_cols_tile

#ifdef WITH_OPENMP
   integer my_thread, n_threads, max_threads, n_iter
   integer omp_get_thread_num, omp_get_num_threads, omp_get_max_threads
#endif

   real*8 vnorm2
   complex*16 vav, xc, aux(2*max_stored_rows),  aux1(2), aux2(2), vrl, xf

   complex*16, allocatable:: tmp(:), vr(:), vc(:), ur(:), uc(:), vur(:,:), uvc(:,:)
#ifdef WITH_OPENMP
   complex*16, allocatable:: ur_p(:,:), uc_p(:,:)
#endif
   real*8, allocatable:: tmpr(:)

1197
1198
1199
#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("tridiag_complex")
#endif
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251

   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)

   ! 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


   totalblocks = (na-1)/nblk + 1
   max_blocks_row = (totalblocks-1)/np_rows + 1
   max_blocks_col = (totalblocks-1)/np_cols + 1

   max_local_rows = max_blocks_row*nblk
   max_local_cols = max_blocks_col*nblk

   allocate(tmp(MAX(max_local_rows,max_local_cols)))
   allocate(vr(max_local_rows+1))
   allocate(ur(max_local_rows))
   allocate(vc(max_local_cols))
   allocate(uc(max_local_cols))

#ifdef WITH_OPENMP
   max_threads = omp_get_max_threads()

   allocate(ur_p(max_local_rows,0:max_threads-1))
   allocate(uc_p(max_local_cols,0:max_threads-1))
#endif

   tmp = 0
   vr = 0
   ur = 0
   vc = 0
   uc = 0

   allocate(vur(max_local_rows,2*max_stored_rows))
   allocate(uvc(max_local_cols,2*max_stored_rows))

   d(:) = 0
   e(:) = 0
   tau(:) = 0

   nstor = 0

   l_rows = local_index(na, my_prow, np_rows, nblk, -1) ! Local rows of a
   l_cols = local_index(na, my_pcol, np_cols, nblk, -1) ! Local cols of a
1252
   if(my_prow==prow(na, nblk, np_rows) .and. my_pcol==pcol(na, nblk, np_cols)) d(na) = a(l_rows,l_cols)
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264

   do istep=na,3,-1

      ! Calculate number of local rows and columns of the still remaining matrix
      ! on the local processor

      l_rows = local_index(istep-1, my_prow, np_rows, nblk, -1)
      l_cols = local_index(istep-1, my_pcol, np_cols, nblk, -1)

      ! Calculate vector for Householder transformation on all procs
      ! owning column istep

1265
      if(my_pcol==pcol(istep, nblk, np_cols)) then
1266
1267
1268
1269
1270
1271
1272

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

         vr(1:l_rows) = a(1:l_rows,l_cols+1)
         if(nstor>0 .and. l_rows>0) then
            aux(1:2*nstor) = conjg(uvc(l_cols+1,1:2*nstor))
1273
            call ZGEMV('N',l_rows,2*nstor,CONE,vur,ubound(vur,dim=1), &
1274
1275
1276
                       aux,1,CONE,vr,1)
         endif

1277
         if(my_prow==prow(istep-1, nblk, np_rows)) then
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
            aux1(1) = dot_product(vr(1:l_rows-1),vr(1:l_rows-1))
            aux1(2) = vr(l_rows)
         else
            aux1(1) = dot_product(vr(1:l_rows),vr(1:l_rows))
            aux1(2) = 0.
         endif

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

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

         ! Householder transformation

         call hh_transform_complex(vrl, vnorm2, xf, tau(istep))

         ! Scale vr and store Householder vector for back transformation

         vr(1:l_rows) = vr(1:l_rows) * xf
1297
         if(my_prow==prow(istep-1, nblk, np_rows)) then
1298
1299
1300
1301
1302
1303
1304
1305
1306
            vr(l_rows) = 1.
            e(istep-1) = vrl
         endif
         a(1:l_rows,l_cols+1) = vr(1:l_rows) ! store Householder vector for back transformation

      endif

      ! Broadcast the Householder vector (and tau) along columns

1307
1308
      if(my_pcol==pcol(istep, nblk, np_cols)) vr(l_rows+1) = tau(istep)
      call MPI_Bcast(vr,l_rows+1,MPI_DOUBLE_COMPLEX,pcol(istep, nblk, np_cols),mpi_comm_cols,mpierr)
1309
1310
1311
1312
      tau(istep) =  vr(l_rows+1)

      ! Transpose Householder vector vr -> vc

1313
1314
1315
!      call elpa_transpose_vectors  (vr, 2*ubound(vr,dim=1), mpi_comm_rows, &
!                                    vc, 2*ubound(vc,dim=1), mpi_comm_cols, &
!                                    1, 2*(istep-1), 1, 2*nblk)
1316

1317
1318
1319
      call elpa_transpose_vectors_complex  (vr, ubound(vr,dim=1), mpi_comm_rows, &
                                            vc, ubound(vc,dim=1), mpi_comm_cols, &
                                            1, (istep-1), 1, nblk)
1320
1321
1322
1323
1324
1325
1326
1327
      ! Calculate u = (A + VU**T + UV**T)*v

      ! For cache efficiency, we use only the upper half of the matrix tiles for this,
      ! thus the result is partly in uc(:) and partly in ur(:)

      uc(1:l_cols) = 0
      ur(1:l_rows) = 0
      if(l_rows>0 .and. l_cols>0) then
1328

1329
#ifdef WITH_OPENMP
1330
1331
1332
1333
1334

#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("OpenMP parallel")
#endif

1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
!$OMP PARALLEL PRIVATE(my_thread,n_threads,n_iter,i,lcs,lce,j,lrs,lre)

         my_thread = omp_get_thread_num()
         n_threads = omp_get_num_threads()

         n_iter = 0

         uc_p(1:l_cols,my_thread) = 0.
         ur_p(1:l_rows,my_thread) = 0.
#endif

         do i=0,(istep-2)/tile_size
            lcs = i*l_cols_tile+1
            lce = min(l_cols,(i+1)*l_cols_tile)
            if(lce<lcs) cycle
            do j=0,i
               lrs = j*l_rows_tile+1
               lre = min(l_rows,(j+1)*l_rows_tile)
               if(lre<lrs) cycle
#ifdef WITH_OPENMP
               if(mod(n_iter,n_threads) == my_thread) then
                  call ZGEMV('C',lre-lrs+1,lce-lcs+1,CONE,a(lrs,lcs),lda,vr(lrs),1,CONE,uc_p(lcs,my_thread),1)
                  if(i/=j) call ZGEMV('N',lre-lrs+1,lce-lcs+1,CONE,a(lrs,lcs),lda,vc(lcs),1,CONE,ur_p(lrs,my_thread),1)
               endif
               n_iter = n_iter+1
#else
              call ZGEMV('C',lre-lrs+1,lce-lcs+1,CONE,a(lrs,lcs),lda,vr(lrs),1,CONE,uc(lcs),1)
               if(i/=j) call ZGEMV('N',lre-lrs+1,lce-lcs+1,CONE,a(lrs,lcs),lda,vc(lcs),1,CONE,ur(lrs),1)
#endif
            enddo
         enddo
1366

1367
1368
#ifdef WITH_OPENMP
!$OMP END PARALLEL
1369
1370
1371
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("OpenMP parallel")
#endif
1372
1373
1374
1375
1376
1377
1378
1379

         do i=0,max_threads-1
            uc(1:l_cols) = uc(1:l_cols) + uc_p(1:l_cols,i)
            ur(1:l_rows) = ur(1:l_rows) + ur_p(1:l_rows,i)
         enddo
#endif

         if(nstor>0) then
1380
1381
            call ZGEMV('C',l_rows,2*nstor,CONE,vur,ubound(vur,dim=1),vr,1,CZERO,aux,1)
            call ZGEMV('N',l_cols,2*nstor,CONE,uvc,ubound(uvc,dim=1),aux,1,CONE,uc,1)
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
         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-1) then
1392
1393
1394
         call elpa_reduce_add_vectors_COMPLEX  (ur, ubound(ur,dim=1), mpi_comm_rows, &
                                        uc, ubound(uc,dim=1), mpi_comm_cols, &
                                        (istep-1), 1, nblk)
1395
1396
1397
1398
1399
1400
1401
1402
1403
      endif

      ! Sum up all the uc(:) parts, transpose uc -> ur

      if(l_cols>0) then
         tmp(1:l_cols) = uc(1:l_cols)
         call mpi_allreduce(tmp,uc,l_cols,MPI_DOUBLE_COMPLEX,MPI_SUM,mpi_comm_rows,mpierr)
      endif

1404
1405
1406
1407
1408
1409
1410
1411
1412
!      call elpa_transpose_vectors  (uc, 2*ubound(uc,dim=1), mpi_comm_cols, &
!                                    ur, 2*ubound(ur,dim=1), mpi_comm_rows, &
!                                    1, 2*(istep-1), 1, 2*nblk)

      call elpa_transpose_vectors_complex  (uc, ubound(uc,dim=1), mpi_comm_cols, &
                                            ur, ubound(ur,dim=1), mpi_comm_rows, &
                                            1, (istep-1), 1, nblk)


1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444

      ! calculate u**T * v (same as v**T * (A + VU**T + UV**T) * v )

      xc = 0
      if(l_cols>0) xc = dot_product(vc(1:l_cols),uc(1:l_cols))
      call mpi_allreduce(xc,vav,1,MPI_DOUBLE_COMPLEX,MPI_SUM,mpi_comm_cols,mpierr)

      ! store u and v in the matrices U and V
      ! these matrices are stored combined in one here

      do j=1,l_rows
         vur(j,2*nstor+1) = conjg(tau(istep))*vr(j)
         vur(j,2*nstor+2) = 0.5*conjg(tau(istep))*vav*vr(j) - ur(j)
      enddo
      do j=1,l_cols
         uvc(j,2*nstor+1) = 0.5*conjg(tau(istep))*vav*vc(j) - uc(j)
         uvc(j,2*nstor+2) = conjg(tau(istep))*vc(j)
      enddo

      nstor = nstor+1

      ! If the limit of max_stored_rows is reached, calculate A + VU**T + UV**T

      if(nstor==max_stored_rows .or. istep==3) then

         do i=0,(istep-2)/tile_size
            lcs = i*l_cols_tile+1
            lce = min(l_cols,(i+1)*l_cols_tile)
            lrs = 1
            lre = min(l_rows,(i+1)*l_rows_tile)
            if(lce<lcs .or. lre<lrs) cycle
            call ZGEMM('N','C',lre-lrs+1,lce-lcs+1,2*nstor,CONE, &
1445
                       vur(lrs,1),ubound(vur,dim=1),uvc(lcs,1),ubound(uvc,dim=1), &
1446
1447
1448
1449
1450
1451
1452
                       CONE,a(lrs,lcs),lda)
         enddo

         nstor = 0

      endif

1453
      if(my_prow==prow(istep-1, nblk, np_rows) .and. my_pcol==pcol(istep-1, nblk, np_cols)) then
1454
1455
1456
1457
1458
1459
1460
1461
1462
         if(nstor>0) a(l_rows,l_cols) = a(l_rows,l_cols) &
                        + dot_product(vur(l_rows,1:2*nstor),uvc(l_cols,1:2*nstor))
         d(istep-1) = a(l_rows,l_cols)
      endif

   enddo

   ! Store e(1) and d(1)

1463
1464
   if(my_pcol==pcol(2, nblk, np_cols)) then
      if(my_prow==prow(1, nblk, np_rows)) then
1465
1466
1467
1468
1469
1470
         ! We use last l_cols value of loop above
         vrl = a(1,l_cols)
         call hh_transform_complex(vrl, 0.d0, xf, tau(2))
         e(1) = vrl
         a(1,l_cols) = 1. ! for consistency only
      endif
1471
      call mpi_bcast(tau(2),1,MPI_DOUBLE_COMPLEX,prow(1, nblk, np_rows),mpi_comm_rows,mpierr)
1472
   endif
1473
   call mpi_bcast(tau(2),1,MPI_DOUBLE_COMPLEX,pcol(2, nblk, np_cols),mpi_comm_cols,mpierr)
1474

1475
   if(my_prow==prow(1, nblk, np_rows) .and. my_pcol==pcol(1, nblk, np_cols)) d(1) = a(1,1)
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490

   deallocate(tmp, vr, ur, vc, uc, vur, uvc)

   ! distribute the arrays d and e to all processors

   allocate(tmpr(na))
   tmpr = d
   call mpi_allreduce(tmpr,d,na,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
   tmpr = d
   call mpi_allreduce(tmpr,d,na,MPI_REAL8,MPI_SUM,mpi_comm_cols,mpierr)
   tmpr = e
   call mpi_allreduce(tmpr,e,na,MPI_REAL8,MPI_SUM,mpi_comm_rows,mpierr)
   tmpr = e
   call mpi_allreduce(tmpr,e,na,MPI_REAL8,MPI_SUM,mpi_comm_cols,mpierr)
   deallocate(tmpr)
1491
1492
1493
#ifdef HAVE_DETAILED_TIMINGS
   call timer%stop("tridiag_complex")
#endif
1494
1495
1496
1497
1498

end subroutine tridiag_complex

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

1499
subroutine trans_ev_complex(na, nqc, a, lda, tau, q, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols)
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511

!-------------------------------------------------------------------------------
!  trans_ev_complex: Transforms the eigenvectors of a tridiagonal matrix back
!                    to the eigenvectors of the original matrix
!                    (like Scalapack Routine PZUNMTR)
!
!  Parameters
!
!  na          Order of matrix a, number of rows of matrix q
!
!  nqc         Number of columns of matrix q
!
1512
!  a(lda,matrixCols)    Matrix containing the Householder vectors (i.e. matrix a after tridiag_complex)
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
!              Distribution is like in Scalapack.
!
!  lda         Leading dimension of a
!
!  tau(na)     Factors of the Householder vectors
!
!  q           On input: Eigenvectors of tridiagonal matrix
!              On output: Transformed eigenvectors
!              Distribution is like in Scalapack.
!
!  ldq         Leading dimension of q
!
!  nblk        blocksize of cyclic distribution, must be the same in both directions!
!
!  mpi_comm_rows
!  mpi_comm_cols
!              MPI-Communicators for rows/columns
!
!-------------------------------------------------------------------------------
1532
1533
1534
#ifdef HAVE_DETAILED_TIMINGS
 use timings
#endif
1535
1536
   implicit none

1537
1538
   integer na, nqc, lda, ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols
   complex*16 a(lda,matrixCols), q(ldq,matrixCols), tau(na)
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551

   integer :: max_stored_rows

   complex*16, parameter :: CZERO = (0.d0,0.d0), CONE = (1.d0,0.d0)

   integer my_prow, my_pcol, np_rows, np_cols, mpierr
   integer totalblocks, max_blocks_row, max_blocks_col, max_local_rows, max_local_cols
   integer l_cols, l_rows, l_colh, nstor
   integer istep, i, n, nc, ic, ics, ice, nb, cur_pcol

   complex*16, allocatable:: tmp1(:), tmp2(:), hvb(:), hvm(:,:)
   complex*16, allocatable:: tmat(:,:), h1(:), h2(:)

1552
1553
1554
#ifdef HAVE_DETAILED_TIMINGS
   call timer%start("trans_ev_complex")
#endif
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
   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)


   totalblocks = (na-1)/nblk + 1
   max_blocks_row = (totalblocks-1)/np_rows + 1
   max_blocks_col = ((nqc-1)/nblk)/np_cols + 1  ! Columns of q!

   max_local_rows = max_blocks_row*nblk
   max_local_cols = max_blocks_col*nblk


   max_stored_rows = (63/nblk+1)*nblk

   allocate(tmat(max_stored_rows,max_stored_rows))
   allocate(h1(max_stored_rows*max_stored_rows))
   allocate(h2(max_stored_rows*max_stored_rows))
   allocate(tmp1(max_local_cols*max_stored_rows))
   allocate(tmp2(max_local_cols*max_stored_rows))
   allocate(hvb(max_local_rows*nblk))
   allocate(hvm(max_local_rows,max_stored_rows))

   hvm = 0   ! Must be set to 0 !!!
   hvb = 0   ! Safety only

   l_cols = local_index(nqc, my_pcol, np_cols, nblk, -1) ! Local columns of q

   nstor = 0

   ! In the complex case tau(2) /= 0
1587
   if(my_prow == prow(1, nblk, np_rows)) then
1588
1589
1590
1591
1592
1593
1594
1595
1596
      q(1,1:l_cols) = q(1,1:l_cols)*((1.d0,