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cp_fm_diag.F
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1!--------------------------------------------------------------------------------------------------!
2! CP2K: A general program to perform molecular dynamics simulations !
3! Copyright 2000-2025 CP2K developers group <https://cp2k.org> !
4! !
5! SPDX-License-Identifier: GPL-2.0-or-later !
6!--------------------------------------------------------------------------------------------------!
7
8! **************************************************************************************************
9!> \brief used for collecting some of the diagonalization schemes available for
10!> cp_fm_type. cp_fm_power also moved here as it is very related
11!> \note
12!> first version : most routines imported
13!> \par History
14!> - unused Jacobi routines removed, cosmetics (05.04.06,MK)
15!> \author Joost VandeVondele (2003-08)
16! **************************************************************************************************
17MODULE cp_fm_diag
18
19 USE cp_blacs_types, ONLY: cp_blacs_type
20 USE cp_blacs_env, ONLY: cp_blacs_env_type
21 USE cp_fm_basic_linalg, ONLY: cp_fm_column_scale, &
22 cp_fm_gemm, &
23 cp_fm_scale, &
24 cp_fm_syrk, &
25 cp_fm_triangular_invert, &
26 cp_fm_triangular_multiply, &
27 cp_fm_uplo_to_full
28 USE cp_fm_cholesky, ONLY: cp_fm_cholesky_decompose
29 USE cp_fm_diag_utils, ONLY: cp_fm_redistribute_end, &
30 cp_fm_redistribute_start
31 USE cp_fm_elpa, ONLY: cp_fm_diag_elpa, &
32 finalize_elpa_library, &
33 initialize_elpa_library, &
34 set_elpa_kernel, &
35 set_elpa_print, &
36 set_elpa_qr
37 USE cp_fm_cusolver_api, ONLY: cp_fm_diag_cusolver, &
38 cp_fm_general_cusolver
39#if defined(__DLAF)
40 USE cp_fm_dlaf_api, ONLY: cp_fm_diag_dlaf, cp_fm_diag_gen_dlaf
41 USE cp_dlaf_utils_api, ONLY: cp_dlaf_initialize, cp_dlaf_finalize
42#endif
43 USE cp_fm_types, ONLY: cp_fm_get_info, &
44 cp_fm_set_element, &
45 cp_fm_to_fm, &
46 cp_fm_type, &
47 cp_fm_create, &
48 cp_fm_get_info, &
49 cp_fm_release, &
50 cp_fm_set_all, &
51 cp_fm_to_fm, &
52 cp_fm_to_fm_submat, &
53 cp_fm_type
54 USE cp_fm_struct, ONLY: cp_fm_struct_equivalent, &
55 cp_fm_struct_create, &
56 cp_fm_struct_release, &
57 cp_fm_struct_type
58 USE cp_log_handling, ONLY: cp_logger_get_default_unit_nr, &
59 cp_get_default_logger, &
60 cp_logger_get_default_io_unit, &
61 cp_logger_type, &
62 cp_to_string
63 USE cp_log_handling, ONLY: cp_get_default_logger, &
64 cp_logger_get_default_unit_nr, &
65 cp_logger_get_unit_nr, &
66 cp_logger_type
67 USE kinds, ONLY: default_string_length, &
68 dp
69 USE machine, ONLY: default_output_unit, &
70 m_memory
71#if defined (__parallel)
72 USE message_passing, ONLY: mp_comm_type
73#endif
74#if defined (__HAS_IEEE_EXCEPTIONS)
75 USE ieee_exceptions, ONLY: ieee_get_halting_mode, &
76 ieee_set_halting_mode, &
77 ieee_all
78#endif
79#include "../base/base_uses.f90"
80
81 IMPLICIT NONE
82
83 PRIVATE
84
85 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'cp_fm_diag'
86
87 REAL(kind=dp), PARAMETER, PUBLIC :: eps_check_diag_default = 5.0e-14_dp
88
89 ! The following saved variables are diagonalization global
90 ! Stores the default library for diagonalization
91 INTEGER, SAVE, PUBLIC :: diag_type = 0
92 ! Minimum number of eigenvectors for the use of the ELPA eigensolver.
93 ! The ScaLAPACK eigensolver is used as fallback for all smaller cases.
94 INTEGER, SAVE :: elpa_neigvec_min = 0
95#if defined(__DLAF)
96 ! Minimum number of eigenvectors for the use of the DLAF eigensolver.
97 ! The ScaLAPACK eigensolver is used as fallback for all smaller cases.
98 INTEGER, SAVE, PUBLIC :: dlaf_neigvec_min = 0
99#endif
100 ! Threshold value for the orthonormality check of the eigenvectors obtained
101 ! after a diagonalization. A negative value disables the check.
102 REAL(kind=dp), SAVE :: eps_check_diag = -1.0_dp
103
104 ! Constants for the diag_type above
105 INTEGER, PARAMETER, PUBLIC :: fm_diag_type_scalapack = 101, &
106 fm_diag_type_elpa = 102, &
107 fm_diag_type_cusolver = 103, &
108 fm_diag_type_dlaf = 104
109#if defined(__CUSOLVERMP)
110 INTEGER, PARAMETER, PUBLIC :: fm_diag_type_default = fm_diag_type_cusolver
111#elif defined(__ELPA)
112 INTEGER, PARAMETER, PUBLIC :: fm_diag_type_default = fm_diag_type_elpa
113#else
114 INTEGER, PARAMETER, PUBLIC :: fm_diag_type_default = fm_diag_type_scalapack
115#endif
116
117 ! Public subroutines
118 PUBLIC :: choose_eigv_solver, &
119 cp_fm_block_jacobi, &
120 cp_fm_power, &
121 cp_fm_syevd, &
122 cp_fm_syevx, &
123 cp_fm_svd, &
124 cp_fm_geeig, &
125 cp_fm_geeig_canon, &
126 diag_init, &
127 diag_finalize
128
129CONTAINS
130
131! **************************************************************************************************
132!> \brief Setup the diagonalization library to be used
133!> \param diag_lib diag_library flag from GLOBAL section in input
134!> \param fallback_applied .TRUE. if support for the requested library was not compiled-in and fallback
135!> to ScaLAPACK was applied, .FALSE. otherwise.
136!> \param elpa_kernel integer that determines which ELPA kernel to use for diagonalization
137!> \param elpa_neigvec_min_input ...
138!> \param elpa_qr logical that determines if ELPA should try to use QR to accelerate the
139!> diagonalization procedure of suitably sized matrices
140!> \param elpa_print logical that determines if information about the ELPA diagonalization should
141!> be printed
142!> \param elpa_qr_unsafe logical that enables potentially unsafe ELPA options
143!> \param dlaf_neigvec_min_input ...
144!> \param eps_check_diag_input ...
145!> \par History
146!> - Add support for DLA-Future (05.09.2023, RMeli)
147!> \author MI 11.2013
148! **************************************************************************************************
149 SUBROUTINE diag_init(diag_lib, fallback_applied, elpa_kernel, elpa_neigvec_min_input, elpa_qr, &
150 elpa_print, elpa_qr_unsafe, dlaf_neigvec_min_input, eps_check_diag_input)
151 CHARACTER(LEN=*), INTENT(IN) :: diag_lib
152 LOGICAL, INTENT(OUT) :: fallback_applied
153 INTEGER, INTENT(IN) :: elpa_kernel, elpa_neigvec_min_input
154 LOGICAL, INTENT(IN) :: elpa_qr, elpa_print, elpa_qr_unsafe
155 INTEGER, INTENT(IN) :: dlaf_neigvec_min_input
156 REAL(kind=dp), INTENT(IN) :: eps_check_diag_input
157
158 LOGICAL, SAVE :: initialized = .false.
159
160 fallback_applied = .false.
161
162 IF (diag_lib == "ScaLAPACK") THEN
163 diag_type = fm_diag_type_scalapack
164 ELSE IF (diag_lib == "ELPA") THEN
165#if defined (__ELPA)
166 ! ELPA is requested and available
167 diag_type = fm_diag_type_elpa
168#else
169 ! ELPA library requested but not linked, switch back to SL
170 diag_type = fm_diag_type_scalapack
171 fallback_applied = .true.
172#endif
173 ELSE IF (diag_lib == "cuSOLVER") THEN
174 diag_type = fm_diag_type_cusolver
175 ELSE IF (diag_lib == "DLAF") THEN
176#if defined (__DLAF)
177 diag_type = fm_diag_type_dlaf
178#else
179 cpabort("ERROR in diag_init: CP2K was not compiled with DLA-Future support")
180#endif
181 ELSE
182 cpabort("ERROR in diag_init: Initialization of unknown diagonalization library requested")
183 END IF
184
185 ! Initialization of requested diagonalization library
186 IF (.NOT. initialized .AND. diag_type == fm_diag_type_elpa) THEN
187 CALL initialize_elpa_library()
188 CALL set_elpa_kernel(elpa_kernel)
189 CALL set_elpa_qr(elpa_qr, elpa_qr_unsafe)
190 CALL set_elpa_print(elpa_print)
191 initialized = .true.
192 END IF
193#if defined(__DLAF)
194 IF (.NOT. initialized .AND. diag_type == fm_diag_type_dlaf) THEN
195 CALL cp_dlaf_initialize()
196 initialized = .true.
197 END IF
198 dlaf_neigvec_min = dlaf_neigvec_min_input
199#else
200 mark_used(dlaf_neigvec_min_input)
201#endif
202
203 elpa_neigvec_min = elpa_neigvec_min_input
204 eps_check_diag = eps_check_diag_input
205
206 END SUBROUTINE diag_init
207
208! **************************************************************************************************
209!> \brief Finalize the diagonalization library
210! **************************************************************************************************
211 SUBROUTINE diag_finalize()
212#if defined (__ELPA)
213 IF (diag_type == fm_diag_type_elpa) &
214 CALL finalize_elpa_library()
215#endif
216#if defined (__DLAF)
217 IF (diag_type == fm_diag_type_dlaf) &
218 CALL cp_dlaf_finalize()
219#endif
220 END SUBROUTINE diag_finalize
221
222! **************************************************************************************************
223!> \brief Choose the Eigensolver depending on which library is available
224!> ELPA seems to be unstable for small systems
225!> \param matrix ...
226!> \param eigenvectors ...
227!> \param eigenvalues ...
228!> \param info ...
229!> \par info If present returns error code and prevents program stops.
230!> Works currently only for cp_fm_syevd with ScaLAPACK.
231!> Other solvers will end the program regardless of PRESENT(info).
232!> \par History
233!> - Do not use ELPA for small matrices and use instead ScaLAPACK as fallback (10.05.2021, MK)
234! **************************************************************************************************
235 SUBROUTINE choose_eigv_solver(matrix, eigenvectors, eigenvalues, info)
236
237 TYPE(cp_fm_type), INTENT(IN) :: matrix, eigenvectors
238 REAL(kind=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
239 INTEGER, INTENT(OUT), OPTIONAL :: info
240
241 CHARACTER(LEN=*), PARAMETER :: routinen = 'choose_eigv_solver'
242
243 ! Sample peak memory
244 CALL m_memory()
245
246 IF (PRESENT(info)) info = 0 ! Default for solvers that do not return an info.
247
248 IF (diag_type == fm_diag_type_scalapack) THEN
249 CALL cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
250
251 ELSE IF (diag_type == fm_diag_type_elpa) THEN
252 IF (matrix%matrix_struct%nrow_global < elpa_neigvec_min) THEN
253 ! We don't trust ELPA with very small matrices.
254 CALL cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
255 ELSE
256 CALL cp_fm_diag_elpa(matrix, eigenvectors, eigenvalues)
257 END IF
258
259 ELSE IF (diag_type == fm_diag_type_cusolver) THEN
260 IF (matrix%matrix_struct%nrow_global < 64) THEN
261 ! We don't trust cuSolver with very small matrices.
262 CALL cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
263 ELSE
264 CALL cp_fm_diag_cusolver(matrix, eigenvectors, eigenvalues)
265 END IF
266
267#if defined(__DLAF)
268 ELSE IF (diag_type == fm_diag_type_dlaf) THEN
269 IF (matrix%matrix_struct%nrow_global < dlaf_neigvec_min) THEN
270 ! Use ScaLAPACK for small matrices
271 CALL cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
272 ELSE
273 CALL cp_fm_diag_dlaf(matrix, eigenvectors, eigenvalues)
274 END IF
275#endif
276
277 ELSE
278 cpabort("ERROR in "//routinen//": Invalid diagonalization type requested")
279 END IF
280
281 CALL check_diag(matrix, eigenvectors, nvec=SIZE(eigenvalues))
282
283 END SUBROUTINE choose_eigv_solver
284
285! **************************************************************************************************
286!> \brief Check result of diagonalization, i.e. the orthonormality of the eigenvectors
287!> \param matrix Work matrix
288!> \param eigenvectors Eigenvectors to be checked
289!> \param nvec ...
290! **************************************************************************************************
291 SUBROUTINE check_diag(matrix, eigenvectors, nvec)
292
293 TYPE(cp_fm_type), INTENT(IN) :: matrix, eigenvectors
294 INTEGER, INTENT(IN) :: nvec
295
296 CHARACTER(LEN=*), PARAMETER :: routinen = 'check_diag'
297
298 CHARACTER(LEN=default_string_length) :: diag_type_name
299 REAL(kind=dp) :: eps, eps_abort, eps_warning, gold, test
300 INTEGER :: handle, i, j, ncol, nrow, output_unit
301 LOGICAL :: check_eigenvectors
302#if defined(__parallel)
303 TYPE(cp_blacs_env_type), POINTER :: context
304 INTEGER :: il, jl, ipcol, iprow, &
305 mypcol, myprow, npcol, nprow
306 INTEGER, DIMENSION(9) :: desca
307#endif
308
309 CALL timeset(routinen, handle)
310
311 output_unit = default_output_unit
312 eps_warning = eps_check_diag_default
313#if defined(__CHECK_DIAG)
314 check_eigenvectors = .true.
315 IF (eps_check_diag >= 0.0_dp) THEN
316 eps_warning = eps_check_diag
317 END IF
318#else
319 IF (eps_check_diag >= 0.0_dp) THEN
320 check_eigenvectors = .true.
321 eps_warning = eps_check_diag
322 ELSE
323 check_eigenvectors = .false.
324 END IF
325#endif
326 eps_abort = 10.0_dp*eps_warning
327
328 gold = 0.0_dp
329 test = 0.0_dp
330 eps = 0.0_dp
331
332 IF (check_eigenvectors) THEN
333#if defined(__parallel)
334 nrow = eigenvectors%matrix_struct%nrow_global
335 ncol = min(eigenvectors%matrix_struct%ncol_global, nvec)
336 CALL cp_fm_gemm("T", "N", ncol, ncol, nrow, 1.0_dp, eigenvectors, eigenvectors, 0.0_dp, matrix)
337 context => matrix%matrix_struct%context
338 myprow = context%mepos(1)
339 mypcol = context%mepos(2)
340 nprow = context%num_pe(1)
341 npcol = context%num_pe(2)
342 desca(:) = matrix%matrix_struct%descriptor(:)
343 outer: DO j = 1, ncol
344 DO i = 1, ncol
345 CALL infog2l(i, j, desca, nprow, npcol, myprow, mypcol, il, jl, iprow, ipcol)
346 IF ((iprow == myprow) .AND. (ipcol == mypcol)) THEN
347 gold = merge(0.0_dp, 1.0_dp, i .NE. j)
348 test = matrix%local_data(il, jl)
349 eps = abs(test - gold)
350 IF (eps > eps_warning) EXIT outer
351 END IF
352 END DO
353 END DO outer
354#else
355 nrow = SIZE(eigenvectors%local_data, 1)
356 ncol = min(SIZE(eigenvectors%local_data, 2), nvec)
357 CALL dgemm("T", "N", ncol, ncol, nrow, 1.0_dp, &
358 eigenvectors%local_data(1, 1), nrow, &
359 eigenvectors%local_data(1, 1), nrow, &
360 0.0_dp, matrix%local_data(1, 1), nrow)
361 outer: DO j = 1, ncol
362 DO i = 1, ncol
363 gold = merge(0.0_dp, 1.0_dp, i .NE. j)
364 test = matrix%local_data(i, j)
365 eps = abs(test - gold)
366 IF (eps > eps_warning) EXIT outer
367 END DO
368 END DO outer
369#endif
370 IF (eps > eps_warning) THEN
371 IF (diag_type == fm_diag_type_scalapack) THEN
372 diag_type_name = "SYEVD"
373 ELSE IF (diag_type == fm_diag_type_elpa) THEN
374 diag_type_name = "ELPA"
375 ELSE IF (diag_type == fm_diag_type_cusolver) THEN
376 diag_type_name = "CUSOLVER"
377 ELSE IF (diag_type == fm_diag_type_dlaf) THEN
378 diag_type_name = "DLAF"
379 ELSE
380 cpabort("Unknown diag_type")
381 END IF
382 WRITE (unit=output_unit, fmt="(/,T2,A,/,T2,A,I0,A,I0,A,F0.15,/,T2,A,F0.0,A,ES10.3)") &
383 "The eigenvectors returned by "//trim(diag_type_name)//" are not orthonormal", &
384 "Matrix element (", i, ", ", j, ") = ", test, &
385 "The deviation from the expected value ", gold, " is", eps
386 IF (eps > eps_abort) THEN
387 cpabort("ERROR in "//routinen//": Check of matrix diagonalization failed")
388 ELSE
389 cpwarn("Check of matrix diagonalization failed in routine "//routinen)
390 END IF
391 END IF
392 END IF
393
394 CALL timestop(handle)
395
396 END SUBROUTINE check_diag
397
398! **************************************************************************************************
399!> \brief Computes all eigenvalues and vectors of a real symmetric matrix
400!> significantly faster than syevx, scales also much better.
401!> Needs workspace to allocate all the eigenvectors
402!> \param matrix ...
403!> \param eigenvectors ...
404!> \param eigenvalues ...
405!> \param info ...
406!> \par matrix is supposed to be in upper triangular form, and overwritten by this routine
407!> \par info If present returns error code and prevents program stops.
408!> Works currently only for scalapack.
409!> Other solvers will end the program regardless of PRESENT(info).
410! **************************************************************************************************
411 SUBROUTINE cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
412
413 TYPE(cp_fm_type), INTENT(IN) :: matrix, eigenvectors
414 REAL(kind=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
415 INTEGER, INTENT(OUT), OPTIONAL :: info
416
417 CHARACTER(LEN=*), PARAMETER :: routinen = 'cp_fm_syevd'
418
419 INTEGER :: handle, myinfo, n, nmo
420 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: eig
421#if defined(__parallel)
422 TYPE(cp_fm_type) :: eigenvectors_new, matrix_new
423#else
424 CHARACTER(LEN=2*default_string_length) :: message
425 INTEGER :: liwork, lwork, nl
426 INTEGER, DIMENSION(:), POINTER :: iwork
427 REAL(kind=dp), DIMENSION(:, :), POINTER :: m
428 REAL(kind=dp), DIMENSION(:), POINTER :: work
429#endif
430
431 CALL timeset(routinen, handle)
432
433 myinfo = 0
434
435 n = matrix%matrix_struct%nrow_global
436 ALLOCATE (eig(n))
437
438#if defined(__parallel)
439 ! Determine if the input matrix needs to be redistributed before diagonalization.
440 ! Heuristics are used to determine the optimal number of CPUs for diagonalization.
441 ! The redistributed matrix is stored in matrix_new, which is just a pointer
442 ! to the original matrix if no redistribution is required
443 CALL cp_fm_redistribute_start(matrix, eigenvectors, matrix_new, eigenvectors_new)
444
445 ! Call scalapack on CPUs that hold the new matrix
446 IF (ASSOCIATED(matrix_new%matrix_struct)) THEN
447 IF (PRESENT(info)) THEN
448 CALL cp_fm_syevd_base(matrix_new, eigenvectors_new, eig, myinfo)
449 ELSE
450 CALL cp_fm_syevd_base(matrix_new, eigenvectors_new, eig)
451 END IF
452 END IF
453 ! Redistribute results and clean up
454 CALL cp_fm_redistribute_end(matrix, eigenvectors, eig, matrix_new, eigenvectors_new)
455#else
456 ! Retrieve the optimal work array sizes first
457 lwork = -1
458 liwork = -1
459 m => matrix%local_data
460 eig(:) = 0.0_dp
461
462 ALLOCATE (work(1))
463 work(:) = 0.0_dp
464 ALLOCATE (iwork(1))
465 iwork(:) = 0
466 nl = SIZE(m, 1)
467
468 CALL dsyevd('V', 'U', n, m(1, 1), nl, eig(1), work(1), lwork, iwork(1), liwork, myinfo)
469
470 IF (myinfo /= 0) THEN
471 WRITE (message, "(A,I0,A)") "ERROR in DSYEVD: Work space query failed (INFO = ", myinfo, ")"
472 IF (PRESENT(info)) THEN
473 cpwarn(trim(message))
474 ELSE
475 cpabort(trim(message))
476 END IF
477 END IF
478
479 ! Reallocate work arrays and perform diagonalisation
480 lwork = int(work(1))
481 DEALLOCATE (work)
482 ALLOCATE (work(lwork))
483 work(:) = 0.0_dp
484
485 liwork = iwork(1)
486 DEALLOCATE (iwork)
487 ALLOCATE (iwork(liwork))
488 iwork(:) = 0
489
490 CALL dsyevd('V', 'U', n, m(1, 1), nl, eig(1), work(1), lwork, iwork(1), liwork, myinfo)
491
492 IF (myinfo /= 0) THEN
493 WRITE (message, "(A,I0,A)") "ERROR in DSYEVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
494 IF (PRESENT(info)) THEN
495 cpwarn(trim(message))
496 ELSE
497 cpabort(trim(message))
498 END IF
499 END IF
500
501 CALL cp_fm_to_fm(matrix, eigenvectors)
502
503 DEALLOCATE (iwork)
504 DEALLOCATE (work)
505#endif
506
507 IF (PRESENT(info)) info = myinfo
508
509 nmo = SIZE(eigenvalues, 1)
510 IF (nmo > n) THEN
511 eigenvalues(1:n) = eig(1:n)
512 ELSE
513 eigenvalues(1:nmo) = eig(1:nmo)
514 END IF
515
516 DEALLOCATE (eig)
517
518 CALL check_diag(matrix, eigenvectors, n)
519
520 CALL timestop(handle)
521
522 END SUBROUTINE cp_fm_syevd
523
524! **************************************************************************************************
525!> \brief ...
526!> \param matrix ...
527!> \param eigenvectors ...
528!> \param eigenvalues ...
529!> \param info ...
530! **************************************************************************************************
531 SUBROUTINE cp_fm_syevd_base(matrix, eigenvectors, eigenvalues, info)
532
533 TYPE(cp_fm_type), INTENT(IN) :: matrix, eigenvectors
534 REAL(kind=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
535 INTEGER, INTENT(OUT), OPTIONAL :: info
536
537 CHARACTER(LEN=*), PARAMETER :: routinen = 'cp_fm_syevd_base'
538
539 CHARACTER(LEN=2*default_string_length) :: message
540 INTEGER :: handle, myinfo
541#if defined(__parallel)
542 TYPE(cp_blacs_env_type), POINTER :: context
543 INTEGER :: liwork, lwork, &
544 mypcol, myprow, n
545 INTEGER, DIMENSION(9) :: descm, descv
546 INTEGER, DIMENSION(:), POINTER :: iwork
547 REAL(kind=dp), DIMENSION(:), POINTER :: work
548 REAL(kind=dp), DIMENSION(:, :), POINTER :: m, v
549#if defined (__HAS_IEEE_EXCEPTIONS)
550 LOGICAL, DIMENSION(5) :: halt
551#endif
552#endif
553
554 CALL timeset(routinen, handle)
555
556 myinfo = 0
557
558#if defined(__parallel)
559
560 n = matrix%matrix_struct%nrow_global
561 m => matrix%local_data
562 context => matrix%matrix_struct%context
563 myprow = context%mepos(1)
564 mypcol = context%mepos(2)
565 descm(:) = matrix%matrix_struct%descriptor(:)
566
567 v => eigenvectors%local_data
568 descv(:) = eigenvectors%matrix_struct%descriptor(:)
569
570 liwork = 7*n + 8*context%num_pe(2) + 2
571 ALLOCATE (iwork(liwork))
572
573 ! Work space query
574 lwork = -1
575 ALLOCATE (work(1))
576
577 CALL pdsyevd('V', 'U', n, m(1, 1), 1, 1, descm, eigenvalues(1), v(1, 1), 1, 1, descv, &
578 work(1), lwork, iwork(1), liwork, myinfo)
579
580 IF (matrix%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
581 WRITE (message, "(A,I0,A)") "ERROR in PDSYEVD: Work space query failed (INFO = ", myinfo, ")"
582 IF (PRESENT(info)) THEN
583 cpwarn(trim(message))
584 ELSE
585 cpabort(trim(message))
586 END IF
587 END IF
588
589 ! look here for a PDORMTR warning :-)
590 ! this routine seems to need more workspace than reported
591 ! (? lapack bug ...)
592 ! arbitrary additional memory ... we give 100000 more words
593 ! (it seems to depend on the block size used)
594
595 lwork = nint(work(1) + 100000)
596 ! lwork = NINT(work(1))
597 DEALLOCATE (work)
598 ALLOCATE (work(lwork))
599
600 ! Scalapack takes advantage of IEEE754 exceptions for speedup.
601 ! Therefore, we disable floating point traps temporarily.
602#if defined (__HAS_IEEE_EXCEPTIONS)
603 CALL ieee_get_halting_mode(ieee_all, halt)
604 CALL ieee_set_halting_mode(ieee_all, .false.)
605#endif
606
607 CALL pdsyevd('V', 'U', n, m(1, 1), 1, 1, descm, eigenvalues(1), v(1, 1), 1, 1, descv, &
608 work(1), lwork, iwork(1), liwork, myinfo)
609
610#if defined (__HAS_IEEE_EXCEPTIONS)
611 CALL ieee_set_halting_mode(ieee_all, halt)
612#endif
613 IF (matrix%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
614 WRITE (message, "(A,I0,A)") "ERROR in PDSYEVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
615 IF (PRESENT(info)) THEN
616 cpwarn(trim(message))
617 ELSE
618 cpabort(trim(message))
619 END IF
620 END IF
621
622 IF (PRESENT(info)) info = myinfo
623
624 DEALLOCATE (work)
625 DEALLOCATE (iwork)
626#else
627 mark_used(matrix)
628 mark_used(eigenvectors)
629 mark_used(eigenvalues)
630 myinfo = -1
631 IF (PRESENT(info)) info = myinfo
632 message = "ERROR in "//trim(routinen)// &
633 ": Matrix diagonalization using PDSYEVD requested without ScaLAPACK support"
634 cpabort(trim(message))
635#endif
636
637 CALL timestop(handle)
638
639 END SUBROUTINE cp_fm_syevd_base
640
641! **************************************************************************************************
642!> \brief compute eigenvalues and optionally eigenvectors of a real symmetric matrix using scalapack.
643!> If eigenvectors are required this routine will replicate a full matrix on each CPU...
644!> if more than a handful of vectors are needed, use cp_fm_syevd instead
645!> \param matrix ...
646!> \param eigenvectors ...
647!> \param eigenvalues ...
648!> \param neig ...
649!> \param work_syevx ...
650!> \par matrix is supposed to be in upper triangular form, and overwritten by this routine
651!> neig is the number of vectors needed (default all)
652!> work_syevx evec calculation only, is the fraction of the working buffer allowed (1.0 use full buffer)
653!> reducing this saves time, but might cause the routine to fail
654! **************************************************************************************************
655 SUBROUTINE cp_fm_syevx(matrix, eigenvectors, eigenvalues, neig, work_syevx)
656
657 ! Diagonalise the symmetric n by n matrix using the LAPACK library.
658
659 TYPE(cp_fm_type), INTENT(IN) :: matrix
660 TYPE(cp_fm_type), OPTIONAL, INTENT(IN) :: eigenvectors
661 REAL(kind=dp), OPTIONAL, INTENT(IN) :: work_syevx
662 INTEGER, INTENT(IN), OPTIONAL :: neig
663 REAL(kind=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
664
665 CHARACTER(LEN=*), PARAMETER :: routinen = "cp_fm_syevx"
666
667#if defined(__parallel)
668 REAL(kind=dp), PARAMETER :: orfac = -1.0_dp
669#endif
670 REAL(kind=dp), PARAMETER :: vl = 0.0_dp, &
671 vu = 0.0_dp
672
673 TYPE(cp_blacs_env_type), POINTER :: context
674 TYPE(cp_logger_type), POINTER :: logger
675 CHARACTER(LEN=1) :: job_type
676 REAL(kind=dp) :: abstol, work_syevx_local
677 INTEGER :: handle, info, &
678 liwork, lwork, m, mypcol, &
679 myprow, n, nb, npcol, &
680 nprow, output_unit, &
681 neig_local
682 LOGICAL :: ionode, needs_evecs
683 INTEGER, DIMENSION(:), ALLOCATABLE :: ifail, iwork
684 REAL(kind=dp), DIMENSION(:), ALLOCATABLE :: w, work
685 REAL(kind=dp), DIMENSION(:, :), POINTER :: a, z
686
687 REAL(kind=dp), EXTERNAL :: dlamch
688
689#if defined(__parallel)
690 INTEGER :: nn, np0, npe, nq0, nz
691 INTEGER, DIMENSION(9) :: desca, descz
692 INTEGER, DIMENSION(:), ALLOCATABLE :: iclustr
693 REAL(kind=dp), DIMENSION(:), ALLOCATABLE :: gap
694 INTEGER, EXTERNAL :: iceil, numroc
695#if defined (__HAS_IEEE_EXCEPTIONS)
696 LOGICAL, DIMENSION(5) :: halt
697#endif
698#else
699 INTEGER :: nla, nlz
700 INTEGER, EXTERNAL :: ilaenv
701#endif
702
703 ! by default all
704 n = matrix%matrix_struct%nrow_global
705 neig_local = n
706 IF (PRESENT(neig)) neig_local = neig
707 IF (neig_local == 0) RETURN
708
709 CALL timeset(routinen, handle)
710
711 needs_evecs = PRESENT(eigenvectors)
712
713 logger => cp_get_default_logger()
714 ionode = logger%para_env%is_source()
715 n = matrix%matrix_struct%nrow_global
716
717 ! by default allocate all needed space
718 work_syevx_local = 1.0_dp
719 IF (PRESENT(work_syevx)) work_syevx_local = work_syevx
720
721 ! set scalapack job type
722 IF (needs_evecs) THEN
723 job_type = "V"
724 ELSE
725 job_type = "N"
726 END IF
727
728 ! target the most accurate calculation of the eigenvalues
729 abstol = 2.0_dp*dlamch("S")
730
731 context => matrix%matrix_struct%context
732 myprow = context%mepos(1)
733 mypcol = context%mepos(2)
734 nprow = context%num_pe(1)
735 npcol = context%num_pe(2)
736
737 ALLOCATE (w(n))
738 eigenvalues(:) = 0.0_dp
739#if defined(__parallel)
740
741 IF (matrix%matrix_struct%nrow_block /= matrix%matrix_struct%ncol_block) THEN
742 cpabort("ERROR in "//routinen//": Invalid blocksize (no square blocks) found")
743 END IF
744
745 a => matrix%local_data
746 desca(:) = matrix%matrix_struct%descriptor(:)
747
748 IF (needs_evecs) THEN
749 z => eigenvectors%local_data
750 descz(:) = eigenvectors%matrix_struct%descriptor(:)
751 ELSE
752 ! z will not be referenced
753 z => matrix%local_data
754 descz = desca
755 END IF
756
757 ! Get the optimal work storage size
758
759 npe = nprow*npcol
760 nb = matrix%matrix_struct%nrow_block
761 nn = max(n, nb, 2)
762 np0 = numroc(nn, nb, 0, 0, nprow)
763 nq0 = max(numroc(nn, nb, 0, 0, npcol), nb)
764
765 IF (needs_evecs) THEN
766 lwork = 5*n + max(5*nn, np0*nq0) + iceil(neig_local, npe)*nn + 2*nb*nb + &
767 int(work_syevx_local*real((neig_local - 1)*n, dp)) !!!! allocates a full matrix on every CPU !!!!!
768 ELSE
769 lwork = 5*n + max(5*nn, nb*(np0 + 1))
770 END IF
771 liwork = 6*max(n, npe + 1, 4)
772
773 ALLOCATE (gap(npe))
774 gap = 0.0_dp
775 ALLOCATE (iclustr(2*npe))
776 iclustr = 0
777 ALLOCATE (ifail(n))
778 ifail = 0
779 ALLOCATE (iwork(liwork))
780 ALLOCATE (work(lwork))
781
782 ! Scalapack takes advantage of IEEE754 exceptions for speedup.
783 ! Therefore, we disable floating point traps temporarily.
784#if defined (__HAS_IEEE_EXCEPTIONS)
785 CALL ieee_get_halting_mode(ieee_all, halt)
786 CALL ieee_set_halting_mode(ieee_all, .false.)
787#endif
788
789 CALL pdsyevx(job_type, "I", "U", n, a(1, 1), 1, 1, desca, vl, vu, 1, neig_local, abstol, m, nz, w(1), orfac, &
790 z(1, 1), 1, 1, descz, work(1), lwork, iwork(1), liwork, ifail(1), iclustr(1), gap, info)
791
792#if defined (__HAS_IEEE_EXCEPTIONS)
793 CALL ieee_set_halting_mode(ieee_all, halt)
794#endif
795
796 ! Error handling
797
798 IF (info /= 0) THEN
799 IF (ionode) THEN
800 output_unit = cp_logger_get_unit_nr(logger, local=.false.)
801 WRITE (unit=output_unit, fmt="(/,(T3,A,T12,1X,I10))") &
802 "info = ", info, &
803 "lwork = ", lwork, &
804 "liwork = ", liwork, &
805 "nz = ", nz
806 IF (info > 0) THEN
807 WRITE (unit=output_unit, fmt="(/,T3,A,(T12,6(1X,I10)))") &
808 "ifail = ", ifail
809 WRITE (unit=output_unit, fmt="(/,T3,A,(T12,6(1X,I10)))") &
810 "iclustr = ", iclustr
811 WRITE (unit=output_unit, fmt="(/,T3,A,(T12,6(1X,E10.3)))") &
812 "gap = ", gap
813 END IF
814 END IF
815 cpabort("ERROR in PDSYEVX (ScaLAPACK)")
816 END IF
817
818 ! Release work storage
819
820 DEALLOCATE (gap)
821 DEALLOCATE (iclustr)
822 DEALLOCATE (ifail)
823 DEALLOCATE (iwork)
824 DEALLOCATE (work)
825
826#else
827
828 a => matrix%local_data
829 IF (needs_evecs) THEN
830 z => eigenvectors%local_data
831 ELSE
832 ! z will not be referenced
833 z => matrix%local_data
834 END IF
835
836 ! Get the optimal work storage size
837
838 nb = max(ilaenv(1, "DSYTRD", "U", n, -1, -1, -1), &
839 ilaenv(1, "DORMTR", "U", n, -1, -1, -1))
840
841 lwork = max((nb + 3)*n, 8*n) + n ! sun bug fix
842 liwork = 5*n
843
844 ALLOCATE (ifail(n))
845 ifail = 0
846 ALLOCATE (iwork(liwork))
847 ALLOCATE (work(lwork))
848 info = 0
849 nla = SIZE(a, 1)
850 nlz = SIZE(z, 1)
851
852 CALL dsyevx(job_type, "I", "U", n, a(1, 1), nla, vl, vu, 1, neig_local, &
853 abstol, m, w, z(1, 1), nlz, work(1), lwork, iwork(1), ifail(1), info)
854
855 ! Error handling
856
857 IF (info /= 0) THEN
858 output_unit = cp_logger_get_unit_nr(logger, local=.false.)
859 WRITE (unit=output_unit, fmt="(/,(T3,A,T12,1X,I10))") &
860 "info = ", info
861 IF (info > 0) THEN
862 WRITE (unit=output_unit, fmt="(/,T3,A,(T12,6(1X,I10)))") &
863 "ifail = ", ifail
864 END IF
865 cpabort("Error in DSYEVX (ScaLAPACK)")
866 END IF
867
868 ! Release work storage
869
870 DEALLOCATE (ifail)
871 DEALLOCATE (iwork)
872 DEALLOCATE (work)
873
874#endif
875 eigenvalues(1:neig_local) = w(1:neig_local)
876 DEALLOCATE (w)
877
878 IF (needs_evecs) CALL check_diag(matrix, eigenvectors, neig_local)
879
880 CALL timestop(handle)
881
882 END SUBROUTINE cp_fm_syevx
883
884! **************************************************************************************************
885!> \brief decomposes a quadratic matrix into its singular value decomposition
886!> \param matrix_a ...
887!> \param matrix_eigvl ...
888!> \param matrix_eigvr_t ...
889!> \param eigval ...
890!> \param info ...
891!> \author Maximilian Graml
892! **************************************************************************************************
893 SUBROUTINE cp_fm_svd(matrix_a, matrix_eigvl, matrix_eigvr_t, eigval, info)
894
895 TYPE(cp_fm_type), INTENT(IN) :: matrix_a
896 TYPE(cp_fm_type), INTENT(INOUT) :: matrix_eigvl, matrix_eigvr_t
897 REAL(kind=dp), DIMENSION(:), POINTER, &
898 INTENT(INOUT) :: eigval
899 INTEGER, INTENT(OUT), OPTIONAL :: info
900
901 CHARACTER(LEN=*), PARAMETER :: routinen = 'cp_fm_svd'
902
903 CHARACTER(LEN=2*default_string_length) :: message
904 INTEGER :: handle, n, m, myinfo, lwork
905 REAL(kind=dp), DIMENSION(:, :), POINTER :: a
906 TYPE(cp_fm_type) :: matrix_lu
907 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: work
908
909#if defined(__parallel)
910 INTEGER, DIMENSION(9) :: desca, descu, descvt
911#endif
912 CALL timeset(routinen, handle)
913
914 CALL cp_fm_create(matrix=matrix_lu, &
915 matrix_struct=matrix_a%matrix_struct, &
916 name="A_lu"//trim(adjustl(cp_to_string(1)))//"MATRIX")
917 CALL cp_fm_to_fm(matrix_a, matrix_lu)
918 a => matrix_lu%local_data
919 m = matrix_lu%matrix_struct%nrow_global
920 n = matrix_lu%matrix_struct%ncol_global
921 ! Assert that incoming matrix is quadratic
922 cpassert(m == n)
923
924 ! Prepare for workspace queries
925 myinfo = 0
926 lwork = -1
927 ALLOCATE (work(1))
928 work(:) = 0.0_dp
929#if defined(__parallel)
930 ! To do: That might need a redistribution check as in cp_fm_syevd
931 desca(:) = matrix_lu%matrix_struct%descriptor(:)
932 descu(:) = matrix_eigvl%matrix_struct%descriptor(:)
933 descvt(:) = matrix_eigvr_t%matrix_struct%descriptor(:)
934
935 ! Workspace query
936 CALL pdgesvd('V', 'V', m, m, matrix_lu%local_data, 1, 1, desca, eigval, matrix_eigvl%local_data, &
937 1, 1, descu, matrix_eigvr_t%local_data, 1, 1, descvt, work, lwork, myinfo)
938
939 IF (matrix_lu%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
940 WRITE (message, "(A,I0,A)") "ERROR in PDGESVD: Work space query failed (INFO = ", myinfo, ")"
941 IF (PRESENT(info)) THEN
942 cpwarn(trim(message))
943 ELSE
944 cpabort(trim(message))
945 END IF
946 END IF
947
948 lwork = int(work(1))
949 DEALLOCATE (work)
950 ALLOCATE (work(lwork))
951 ! SVD
952 CALL pdgesvd('V', 'V', m, m, matrix_lu%local_data, 1, 1, desca, eigval, matrix_eigvl%local_data, &
953 1, 1, descu, matrix_eigvr_t%local_data, 1, 1, descvt, work, lwork, myinfo)
954
955 IF (matrix_lu%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
956 WRITE (message, "(A,I0,A)") "ERROR in PDGESVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
957 IF (PRESENT(info)) THEN
958 cpwarn(trim(message))
959 ELSE
960 cpabort(trim(message))
961 END IF
962 END IF
963#else
964 ! Workspace query
965 CALL dgesvd('S', 'S', m, m, matrix_lu%local_data, m, eigval, matrix_eigvl%local_data, &
966 m, matrix_eigvr_t%local_data, m, work, lwork, myinfo)
967
968 IF (myinfo /= 0) THEN
969 WRITE (message, "(A,I0,A)") "ERROR in DGESVD: Work space query failed (INFO = ", myinfo, ")"
970 IF (PRESENT(info)) THEN
971 cpwarn(trim(message))
972 ELSE
973 cpabort(trim(message))
974 END IF
975 END IF
976
977 ! SVD
978 lwork = int(work(1))
979 DEALLOCATE (work)
980 ALLOCATE (work(lwork))
981 work(:) = 0.0_dp
982
983 CALL dgesvd('S', 'S', m, m, matrix_lu%local_data, m, eigval, matrix_eigvl%local_data, &
984 m, matrix_eigvr_t%local_data, m, work, lwork, myinfo)
985
986 IF (myinfo /= 0) THEN
987 WRITE (message, "(A,I0,A)") "ERROR in DGESVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
988 IF (PRESENT(info)) THEN
989 cpwarn(trim(message))
990 ELSE
991 cpabort(trim(message))
992 END IF
993 END IF
994
995#endif
996 ! Release intermediary matrices
997 DEALLOCATE (work)
998 CALL cp_fm_release(matrix_lu)
999
1000 IF (PRESENT(info)) info = myinfo
1001
1002 CALL timestop(handle)
1003 END SUBROUTINE cp_fm_svd
1004
1005! **************************************************************************************************
1006!> \brief ...
1007!> \param matrix ...
1008!> \param work ...
1009!> \param exponent ...
1010!> \param threshold ...
1011!> \param n_dependent ...
1012!> \param verbose ...
1013!> \param eigvals ...
1014! **************************************************************************************************
1015 SUBROUTINE cp_fm_power(matrix, work, exponent, threshold, n_dependent, verbose, eigvals)
1016
1017 ! Raise the real symmetric n by n matrix to the power given by
1018 ! the exponent. All eigenvectors with a corresponding eigenvalue lower
1019 ! than threshold are quenched. result in matrix
1020
1021 ! - Creation (29.03.1999, Matthias Krack)
1022 ! - Parallelised using BLACS and ScaLAPACK (06.06.2001,MK)
1023
1024 TYPE(cp_fm_type), INTENT(IN) :: matrix, work
1025 REAL(kind=dp), INTENT(IN) :: exponent, threshold
1026 INTEGER, INTENT(OUT) :: n_dependent
1027 LOGICAL, INTENT(IN), OPTIONAL :: verbose
1028 REAL(kind=dp), DIMENSION(2), INTENT(OUT), &
1029 OPTIONAL :: eigvals
1030
1031 CHARACTER(LEN=*), PARAMETER :: routinen = 'cp_fm_power'
1032
1033 INTEGER :: handle, icol_global, &
1034 mypcol, myprow, &
1035 ncol_global, npcol, nprow, &
1036 nrow_global
1037 LOGICAL :: my_verbose
1038 REAL(kind=dp) :: condition_number, f, p
1039 REAL(kind=dp), DIMENSION(:), ALLOCATABLE :: eigenvalues
1040 REAL(kind=dp), DIMENSION(:, :), POINTER :: eigenvectors
1041 TYPE(cp_blacs_env_type), POINTER :: context
1042
1043#if defined(__parallel)
1044 INTEGER :: icol_local, ipcol, iprow, irow_global, &
1045 irow_local
1046#endif
1047
1048 CALL timeset(routinen, handle)
1049
1050 my_verbose = .false.
1051 IF (PRESENT(verbose)) my_verbose = verbose
1052
1053 context => matrix%matrix_struct%context
1054 myprow = context%mepos(1)
1055 mypcol = context%mepos(2)
1056 nprow = context%num_pe(1)
1057 npcol = context%num_pe(2)
1058 n_dependent = 0
1059 p = 0.5_dp*exponent
1060
1061 nrow_global = matrix%matrix_struct%nrow_global
1062 ncol_global = matrix%matrix_struct%ncol_global
1063
1064 ALLOCATE (eigenvalues(ncol_global))
1065
1066 eigenvalues(:) = 0.0_dp
1067
1068 ! Compute the eigenvectors and eigenvalues
1069
1070 CALL choose_eigv_solver(matrix, work, eigenvalues)
1071
1072 IF (PRESENT(eigvals)) THEN
1073 eigvals(1) = eigenvalues(1)
1074 eigvals(2) = eigenvalues(ncol_global)
1075 END IF
1076
1077#if defined(__parallel)
1078 eigenvectors => work%local_data
1079
1080 ! Build matrix**exponent with eigenvector quenching
1081
1082 DO icol_global = 1, ncol_global
1083
1084 IF (eigenvalues(icol_global) < threshold) THEN
1085
1086 n_dependent = n_dependent + 1
1087
1088 ipcol = work%matrix_struct%g2p_col(icol_global)
1089
1090 IF (mypcol == ipcol) THEN
1091 icol_local = work%matrix_struct%g2l_col(icol_global)
1092 DO irow_global = 1, nrow_global
1093 iprow = work%matrix_struct%g2p_row(irow_global)
1094 IF (myprow == iprow) THEN
1095 irow_local = work%matrix_struct%g2l_row(irow_global)
1096 eigenvectors(irow_local, icol_local) = 0.0_dp
1097 END IF
1098 END DO
1099 END IF
1100
1101 ELSE
1102
1103 f = eigenvalues(icol_global)**p
1104
1105 ipcol = work%matrix_struct%g2p_col(icol_global)
1106
1107 IF (mypcol == ipcol) THEN
1108 icol_local = work%matrix_struct%g2l_col(icol_global)
1109 DO irow_global = 1, nrow_global
1110 iprow = work%matrix_struct%g2p_row(irow_global)
1111 IF (myprow == iprow) THEN
1112 irow_local = work%matrix_struct%g2l_row(irow_global)
1113 eigenvectors(irow_local, icol_local) = &
1114 f*eigenvectors(irow_local, icol_local)
1115 END IF
1116 END DO
1117 END IF
1118
1119 END IF
1120
1121 END DO
1122
1123#else
1124
1125 eigenvectors => work%local_data
1126
1127 ! Build matrix**exponent with eigenvector quenching
1128
1129 DO icol_global = 1, ncol_global
1130
1131 IF (eigenvalues(icol_global) < threshold) THEN
1132
1133 n_dependent = n_dependent + 1
1134 eigenvectors(1:nrow_global, icol_global) = 0.0_dp
1135
1136 ELSE
1137
1138 f = eigenvalues(icol_global)**p
1139 eigenvectors(1:nrow_global, icol_global) = &
1140 f*eigenvectors(1:nrow_global, icol_global)
1141
1142 END IF
1143
1144 END DO
1145
1146#endif
1147 CALL cp_fm_syrk("U", "N", ncol_global, 1.0_dp, work, 1, 1, 0.0_dp, matrix)
1148 CALL cp_fm_uplo_to_full(matrix, work)
1149
1150 ! Print some warnings/notes
1151 IF (matrix%matrix_struct%para_env%is_source() .AND. my_verbose) THEN
1152 condition_number = abs(eigenvalues(ncol_global)/eigenvalues(1))
1153 WRITE (unit=cp_logger_get_default_unit_nr(), fmt="(/,(T2,A,ES15.6))") &
1154 "CP_FM_POWER: smallest eigenvalue:", eigenvalues(1), &
1155 "CP_FM_POWER: largest eigenvalue: ", eigenvalues(ncol_global), &
1156 "CP_FM_POWER: condition number: ", condition_number
1157 IF (eigenvalues(1) <= 0.0_dp) THEN
1158 WRITE (unit=cp_logger_get_default_unit_nr(), fmt="(/,T2,A)") &
1159 "WARNING: matrix has a negative eigenvalue, tighten EPS_DEFAULT"
1160 END IF
1161 IF (condition_number > 1.0e12_dp) THEN
1162 WRITE (unit=cp_logger_get_default_unit_nr(), fmt="(/,T2,A)") &
1163 "WARNING: high condition number => possibly ill-conditioned matrix"
1164 END IF
1165 END IF
1166
1167 DEALLOCATE (eigenvalues)
1168
1169 CALL timestop(handle)
1170
1171 END SUBROUTINE cp_fm_power
1172
1173! **************************************************************************************************
1174!> \brief ...
1175!> \param matrix ...
1176!> \param eigenvectors ...
1177!> \param eigval ...
1178!> \param thresh ...
1179!> \param start_sec_block ...
1180! **************************************************************************************************
1181 SUBROUTINE cp_fm_block_jacobi(matrix, eigenvectors, eigval, thresh, &
1182 start_sec_block)
1183
1184 ! Calculates block diagonalization of a full symmetric matrix
1185 ! It has its origin in cp_fm_syevx. This routine rotates only elements
1186 ! which are larger than a threshold values "thresh".
1187 ! start_sec_block is the start of the second block.
1188 ! IT DOES ONLY ONE SWEEP!
1189
1190 ! - Creation (07.10.2002, Martin Fengler)
1191 ! - Cosmetics (05.04.06, MK)
1192
1193 TYPE(cp_fm_type), INTENT(IN) :: eigenvectors, matrix
1194 REAL(kind=dp), DIMENSION(:), INTENT(IN) :: eigval
1195 INTEGER, INTENT(IN) :: start_sec_block
1196 REAL(kind=dp), INTENT(IN) :: thresh
1197
1198 CHARACTER(len=*), PARAMETER :: routinen = 'cp_fm_block_jacobi'
1199
1200 INTEGER :: handle
1201 REAL(kind=dp), DIMENSION(:, :), POINTER :: a, ev
1202
1203 REAL(kind=dp) :: tan_theta, tau, c, s
1204 INTEGER :: q, p, n
1205 REAL(kind=dp), DIMENSION(:), ALLOCATABLE :: c_ip
1206
1207#if defined(__parallel)
1208 TYPE(cp_blacs_env_type), POINTER :: context
1209
1210 INTEGER :: myprow, mypcol, nprow, npcol, block_dim_row, block_dim_col, &
1211 info, ev_row_block_size, iam, mynumrows, mype, npe, &
1212 q_loc
1213 REAL(kind=dp), DIMENSION(:, :), ALLOCATABLE :: a_loc, ev_loc
1214 INTEGER, DIMENSION(9) :: desca, descz, desc_a_block, &
1215 desc_ev_loc
1216 TYPE(mp_comm_type):: allgrp
1217 TYPE(cp_blacs_type) :: ictxt_loc
1218 INTEGER, EXTERNAL :: numroc
1219#endif
1220
1221 ! -------------------------------------------------------------------------
1222
1223 CALL timeset(routinen, handle)
1224
1225#if defined(__parallel)
1226 context => matrix%matrix_struct%context
1227 allgrp = matrix%matrix_struct%para_env
1228
1229 myprow = context%mepos(1)
1230 mypcol = context%mepos(2)
1231 nprow = context%num_pe(1)
1232 npcol = context%num_pe(2)
1233
1234 n = matrix%matrix_struct%nrow_global
1235
1236 a => matrix%local_data
1237 desca(:) = matrix%matrix_struct%descriptor(:)
1238 ev => eigenvectors%local_data
1239 descz(:) = eigenvectors%matrix_struct%descriptor(:)
1240
1241 ! Copy the block to be rotated to the master process firstly and broadcast to all processes
1242 ! start_sec_block defines where the second block starts!
1243 ! Block will be processed together with the OO block
1244
1245 block_dim_row = start_sec_block - 1
1246 block_dim_col = n - block_dim_row
1247 ALLOCATE (a_loc(block_dim_row, block_dim_col))
1248
1249 mype = matrix%matrix_struct%para_env%mepos
1250 npe = matrix%matrix_struct%para_env%num_pe
1251 ! Get a new context
1252 CALL ictxt_loc%gridinit(matrix%matrix_struct%para_env, 'Row-major', nprow*npcol, 1)
1253
1254 CALL descinit(desc_a_block, block_dim_row, block_dim_col, block_dim_row, &
1255 block_dim_col, 0, 0, ictxt_loc%get_handle(), block_dim_row, info)
1256
1257 CALL pdgemr2d(block_dim_row, block_dim_col, a, 1, start_sec_block, desca, &
1258 a_loc, 1, 1, desc_a_block, context%get_handle())
1259 ! Only the master (root) process received data yet
1260 CALL allgrp%bcast(a_loc, 0)
1261
1262 ! Since each process owns now the upper block, the eigenvectors can be re-sorted in such a way that
1263 ! each process has a NN*1 grid, i.e. the process owns a bunch of rows which can be modified locally
1264
1265 ! Initialize distribution of the eigenvectors
1266 iam = mype
1267 ev_row_block_size = n/(nprow*npcol)
1268 mynumrows = numroc(n, ev_row_block_size, iam, 0, nprow*npcol)
1269
1270 ALLOCATE (ev_loc(mynumrows, n), c_ip(mynumrows))
1271
1272 CALL descinit(desc_ev_loc, n, n, ev_row_block_size, n, 0, 0, ictxt_loc%get_handle(), &
1273 mynumrows, info)
1274
1275 CALL pdgemr2d(n, n, ev, 1, 1, descz, ev_loc, 1, 1, desc_ev_loc, context%get_handle())
1276
1277 ! Start block diagonalization of matrix
1278
1279 q_loc = 0
1280
1281 DO q = start_sec_block, n
1282 q_loc = q_loc + 1
1283 DO p = 1, (start_sec_block - 1)
1284
1285 IF (abs(a_loc(p, q_loc)) > thresh) THEN
1286
1287 tau = (eigval(q) - eigval(p))/(2.0_dp*a_loc(p, q_loc))
1288
1289 tan_theta = sign(1.0_dp, tau)/(abs(tau) + sqrt(1.0_dp + tau*tau))
1290
1291 ! Cos(theta)
1292 c = 1.0_dp/sqrt(1.0_dp + tan_theta*tan_theta)
1293 s = tan_theta*c
1294
1295 ! Calculate eigenvectors: Q*J
1296 ! c_ip = c*EV_loc(:,p) - s*EV_loc(:,q)
1297 ! c_iq = s*EV_loc(:,p) + c*EV_loc(:,q)
1298 ! EV(:,p) = c_ip
1299 ! EV(:,q) = c_iq
1300 CALL dcopy(mynumrows, ev_loc(1, p), 1, c_ip(1), 1)
1301 CALL dscal(mynumrows, c, ev_loc(1, p), 1)
1302 CALL daxpy(mynumrows, -s, ev_loc(1, q), 1, ev_loc(1, p), 1)
1303 CALL dscal(mynumrows, c, ev_loc(1, q), 1)
1304 CALL daxpy(mynumrows, s, c_ip(1), 1, ev_loc(1, q), 1)
1305
1306 END IF
1307
1308 END DO
1309 END DO
1310
1311 ! Copy eigenvectors back to the original distribution
1312 CALL pdgemr2d(n, n, ev_loc, 1, 1, desc_ev_loc, ev, 1, 1, descz, context%get_handle())
1313
1314 ! Release work storage
1315 DEALLOCATE (a_loc, ev_loc, c_ip)
1316
1317 CALL ictxt_loc%gridexit()
1318
1319#else
1320
1321 n = matrix%matrix_struct%nrow_global
1322
1323 ALLOCATE (c_ip(n)) ! Local eigenvalue vector
1324
1325 a => matrix%local_data ! Contains the Matrix to be worked on
1326 ev => eigenvectors%local_data ! Contains the eigenvectors up to blocksize, rest is garbage
1327
1328 ! Start matrix diagonalization
1329
1330 tan_theta = 0.0_dp
1331 tau = 0.0_dp
1332
1333 DO q = start_sec_block, n
1334 DO p = 1, (start_sec_block - 1)
1335
1336 IF (abs(a(p, q)) > thresh) THEN
1337
1338 tau = (eigval(q) - eigval(p))/(2.0_dp*a(p, q))
1339
1340 tan_theta = sign(1.0_dp, tau)/(abs(tau) + sqrt(1.0_dp + tau*tau))
1341
1342 ! Cos(theta)
1343 c = 1.0_dp/sqrt(1.0_dp + tan_theta*tan_theta)
1344 s = tan_theta*c
1345
1346 ! Calculate eigenvectors: Q*J
1347 ! c_ip = c*EV(:,p) - s*EV(:,q)
1348 ! c_iq = s*EV(:,p) + c*EV(:,q)
1349 ! EV(:,p) = c_ip
1350 ! EV(:,q) = c_iq
1351 CALL dcopy(n, ev(1, p), 1, c_ip(1), 1)
1352 CALL dscal(n, c, ev(1, p), 1)
1353 CALL daxpy(n, -s, ev(1, q), 1, ev(1, p), 1)
1354 CALL dscal(n, c, ev(1, q), 1)
1355 CALL daxpy(n, s, c_ip(1), 1, ev(1, q), 1)
1356
1357 END IF
1358
1359 END DO
1360 END DO
1361
1362 ! Release work storage
1363
1364 DEALLOCATE (c_ip)
1365
1366#endif
1367
1368 CALL timestop(handle)
1369
1370 END SUBROUTINE cp_fm_block_jacobi
1371
1372! **************************************************************************************************
1373!> \brief General Eigenvalue Problem AX = BXE
1374!> Single option version: Cholesky decomposition of B
1375!> \param amatrix ...
1376!> \param bmatrix ...
1377!> \param eigenvectors ...
1378!> \param eigenvalues ...
1379!> \param work ...
1380! **************************************************************************************************
1381 SUBROUTINE cp_fm_geeig(amatrix, bmatrix, eigenvectors, eigenvalues, work)
1382
1383 TYPE(cp_fm_type), INTENT(IN) :: amatrix, bmatrix, eigenvectors
1384 REAL(kind=dp), DIMENSION(:) :: eigenvalues
1385 TYPE(cp_fm_type), INTENT(IN) :: work
1386
1387 CHARACTER(len=*), PARAMETER :: routinen = 'cp_fm_geeig'
1388
1389 INTEGER :: handle, nao, nmo
1390
1391 CALL timeset(routinen, handle)
1392
1393 CALL cp_fm_get_info(amatrix, nrow_global=nao)
1394 nmo = SIZE(eigenvalues)
1395
1396 IF (diag_type == fm_diag_type_cusolver .AND. nao >= 64) THEN
1397 ! Use cuSolverMP generalized eigenvalue solver for large matrices
1398 CALL cp_fm_general_cusolver(amatrix, bmatrix, eigenvectors, eigenvalues)
1399#if defined(__DLAF)
1400 ELSE IF (diag_type == fm_diag_type_dlaf .AND. amatrix%matrix_struct%nrow_global >= dlaf_neigvec_min) THEN
1401 ! Use DLA-Future generalized eigenvalue solver for large matrices
1402 CALL cp_fm_diag_gen_dlaf(amatrix, bmatrix, eigenvectors, eigenvalues)
1403#endif
1404 ELSE
1405 ! Cholesky decompose S=U(T)U
1406 CALL cp_fm_cholesky_decompose(bmatrix)
1407 ! Invert to get U^(-1)
1408 CALL cp_fm_triangular_invert(bmatrix)
1409 ! Reduce to get U^(-T) * H * U^(-1)
1410 CALL cp_fm_triangular_multiply(bmatrix, amatrix, side="R")
1411 CALL cp_fm_triangular_multiply(bmatrix, amatrix, transpose_tr=.true.)
1412 ! Diagonalize
1413 CALL choose_eigv_solver(matrix=amatrix, eigenvectors=work, &
1414 eigenvalues=eigenvalues)
1415 ! Restore vectors C = U^(-1) * C*
1416 CALL cp_fm_triangular_multiply(bmatrix, work)
1417 CALL cp_fm_to_fm(work, eigenvectors, nmo)
1418 END IF
1419
1420 CALL timestop(handle)
1421
1422 END SUBROUTINE cp_fm_geeig
1423
1424! **************************************************************************************************
1425!> \brief General Eigenvalue Problem AX = BXE
1426!> Use canonical diagonalization : U*s**(-1/2)
1427!> \param amatrix ...
1428!> \param bmatrix ...
1429!> \param eigenvectors ...
1430!> \param eigenvalues ...
1431!> \param work ...
1432!> \param epseig ...
1433! **************************************************************************************************
1434 SUBROUTINE cp_fm_geeig_canon(amatrix, bmatrix, eigenvectors, eigenvalues, work, epseig)
1435
1436 TYPE(cp_fm_type), INTENT(IN) :: amatrix, bmatrix, eigenvectors
1437 REAL(kind=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
1438 TYPE(cp_fm_type), INTENT(IN) :: work
1439 REAL(kind=dp), INTENT(IN) :: epseig
1440
1441 CHARACTER(len=*), PARAMETER :: routinen = 'cp_fm_geeig_canon'
1442
1443 INTEGER :: handle, i, icol, irow, nao, nc, ncol, &
1444 nmo, nx
1445 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: evals
1446
1447 CALL timeset(routinen, handle)
1448
1449 ! Test sizees
1450 CALL cp_fm_get_info(amatrix, nrow_global=nao)
1451 nmo = SIZE(eigenvalues)
1452 ALLOCATE (evals(nao))
1453
1454 ! Diagonalize -S matrix, this way the NULL space is at the end of the spectrum
1455 CALL cp_fm_scale(-1.0_dp, bmatrix)
1456 CALL choose_eigv_solver(matrix=bmatrix, eigenvectors=work, eigenvalues=evals)
1457 evals(:) = -evals(:)
1458 nc = nao
1459 DO i = 1, nao
1460 IF (evals(i) < epseig) THEN
1461 nc = i - 1
1462 EXIT
1463 END IF
1464 END DO
1465 cpassert(nc /= 0)
1466
1467 IF (nc /= nao) THEN
1468 IF (nc < nmo) THEN
1469 ! Copy NULL space definition to last vectors of eigenvectors (if needed)
1470 ncol = nmo - nc
1471 CALL cp_fm_to_fm(work, eigenvectors, ncol, nc + 1, nc + 1)
1472 END IF
1473 ! Set NULL space in eigenvector matrix of S to zero
1474 DO icol = nc + 1, nao
1475 DO irow = 1, nao
1476 CALL cp_fm_set_element(work, irow, icol, 0.0_dp)
1477 END DO
1478 END DO
1479 ! Set small eigenvalues to a dummy save value
1480 evals(nc + 1:nao) = 1.0_dp
1481 END IF
1482 ! Calculate U*s**(-1/2)
1483 evals(:) = 1.0_dp/sqrt(evals(:))
1484 CALL cp_fm_column_scale(work, evals)
1485 ! Reduce to get U^(-T) * H * U^(-1)
1486 CALL cp_fm_gemm("T", "N", nao, nao, nao, 1.0_dp, work, amatrix, 0.0_dp, bmatrix)
1487 CALL cp_fm_gemm("N", "N", nao, nao, nao, 1.0_dp, bmatrix, work, 0.0_dp, amatrix)
1488 IF (nc /= nao) THEN
1489 ! set diagonal values to save large value
1490 DO icol = nc + 1, nao
1491 CALL cp_fm_set_element(amatrix, icol, icol, 10000.0_dp)
1492 END DO
1493 END IF
1494 ! Diagonalize
1495 CALL choose_eigv_solver(matrix=amatrix, eigenvectors=bmatrix, eigenvalues=eigenvalues)
1496 nx = min(nc, nmo)
1497 ! Restore vectors C = U^(-1) * C*
1498 CALL cp_fm_gemm("N", "N", nao, nx, nc, 1.0_dp, work, bmatrix, 0.0_dp, eigenvectors)
1499
1500 DEALLOCATE (evals)
1501
1502 CALL timestop(handle)
1503
1504 END SUBROUTINE cp_fm_geeig_canon
1505
1506END MODULE cp_fm_diag
dgemm
static void dgemm(const char transa, const char transb, const int m, const int n, const int k, const double alpha, const double *a, const int lda, const double *b, const int ldb, const double beta, double *c, const int ldc)
Convenient wrapper to hide Fortran nature of dgemm_, swapping a and b.
Definition grid_cpu_task_list.c:214
cp_fm_types::cp_fm_release
Definition cp_fm_types.F:87
cp_fm_types::cp_fm_to_fm
Definition cp_fm_types.F:82
cp_log_handling::cp_to_string
Definition cp_log_handling.F:90
cp_blacs_env
methods related to the blacs parallel environment
Definition cp_blacs_env.F:15
cp_blacs_types
wrappers for the actual blacs calls. all functionality needed in the code should actually be provide ...
Definition cp_blacs_types.F:18
cp_dlaf_utils_api
Definition cp_dlaf_utils_api.F:8
cp_dlaf_utils_api::cp_dlaf_finalize
subroutine, public cp_dlaf_finalize()
Finalize DLA-Future and pika runtime.
Definition cp_dlaf_utils_api.F:56
cp_dlaf_utils_api::cp_dlaf_initialize
subroutine, public cp_dlaf_initialize()
Initialize DLA-Future and pika runtime.
Definition cp_dlaf_utils_api.F:38
cp_fm_basic_linalg
Basic linear algebra operations for full matrices.
Definition cp_fm_basic_linalg.F:14
cp_fm_basic_linalg::cp_fm_gemm
subroutine, public cp_fm_gemm(transa, transb, m, n, k, alpha, matrix_a, matrix_b, beta, matrix_c, a_first_col, a_first_row, b_first_col, b_first_row, c_first_col, c_first_row)
computes matrix_c = beta * matrix_c + alpha * ( matrix_a ** transa ) * ( matrix_b ** transb )
Definition cp_fm_basic_linalg.F:439
cp_fm_basic_linalg::cp_fm_column_scale
subroutine, public cp_fm_column_scale(matrixa, scaling)
scales column i of matrix a with scaling(i)
Definition cp_fm_basic_linalg.F:1879
cp_fm_basic_linalg::cp_fm_syrk
subroutine, public cp_fm_syrk(uplo, trans, k, alpha, matrix_a, ia, ja, beta, matrix_c)
performs a rank-k update of a symmetric matrix_c matrix_c = beta * matrix_c + alpha * matrix_a * tran...
Definition cp_fm_basic_linalg.F:659
cp_fm_basic_linalg::cp_fm_uplo_to_full
subroutine, public cp_fm_uplo_to_full(matrix, work, uplo)
given a triangular matrix according to uplo, computes the corresponding full matrix
Definition cp_fm_basic_linalg.F:1743
cp_fm_basic_linalg::cp_fm_scale
subroutine, public cp_fm_scale(alpha, matrix_a)
scales a matrix matrix_a = alpha * matrix_b
Definition cp_fm_basic_linalg.F:1661
cp_fm_basic_linalg::cp_fm_triangular_invert
subroutine, public cp_fm_triangular_invert(matrix_a, uplo_tr)
inverts a triangular matrix
Definition cp_fm_basic_linalg.F:2191
cp_fm_basic_linalg::cp_fm_triangular_multiply
subroutine, public cp_fm_triangular_multiply(triangular_matrix, matrix_b, side, transpose_tr, invert_tr, uplo_tr, unit_diag_tr, n_rows, n_cols, alpha)
multiplies in place by a triangular matrix: matrix_b = alpha op(triangular_matrix) matrix_b or (if si...
Definition cp_fm_basic_linalg.F:1572
cp_fm_cholesky
various cholesky decomposition related routines
Definition cp_fm_cholesky.F:14
cp_fm_cholesky::cp_fm_cholesky_decompose
subroutine, public cp_fm_cholesky_decompose(matrix, n, info_out)
used to replace a symmetric positive def. matrix M with its cholesky decomposition U: M = U^T * U,...
Definition cp_fm_cholesky.F:63
cp_fm_cusolver_api
Wrapper for cuSOLVERMp.
Definition cp_fm_cusolver_api.F:12
cp_fm_cusolver_api::cp_fm_general_cusolver
subroutine, public cp_fm_general_cusolver(amatrix, bmatrix, eigenvectors, eigenvalues)
Driver routine to solve generalized eigenvalue problem A*x = lambda*B*x with cuSOLVERMp.
Definition cp_fm_cusolver_api.F:110
cp_fm_cusolver_api::cp_fm_diag_cusolver
subroutine, public cp_fm_diag_cusolver(matrix, eigenvectors, eigenvalues)
Driver routine to diagonalize a FM matrix with the cuSOLVERMp library.
Definition cp_fm_cusolver_api.F:37
cp_fm_diag_utils
Auxiliary tools to redistribute cp_fm_type matrices before and after diagonalization....
Definition cp_fm_diag_utils.F:16
cp_fm_diag_utils::cp_fm_redistribute_end
subroutine, public cp_fm_redistribute_end(matrix, eigenvectors, eig, matrix_new, eigenvectors_new)
Redistributes eigenvectors and eigenvalues back to the original communicator group.
Definition cp_fm_diag_utils.F:456
cp_fm_diag_utils::cp_fm_redistribute_start
subroutine, public cp_fm_redistribute_start(matrix, eigenvectors, matrix_new, eigenvectors_new, caller_is_elpa, redist_info)
Determines the optimal number of CPUs for matrix diagonalization and redistributes the input matrices...
Definition cp_fm_diag_utils.F:264
cp_fm_diag
used for collecting some of the diagonalization schemes available for cp_fm_type. cp_fm_power also mo...
Definition cp_fm_diag.F:17
cp_fm_diag::cp_fm_block_jacobi
subroutine, public cp_fm_block_jacobi(matrix, eigenvectors, eigval, thresh, start_sec_block)
...
Definition cp_fm_diag.F:1183
cp_fm_diag::eps_check_diag_default
real(kind=dp), parameter, public eps_check_diag_default
Definition cp_fm_diag.F:87
cp_fm_diag::cp_fm_power
subroutine, public cp_fm_power(matrix, work, exponent, threshold, n_dependent, verbose, eigvals)
...
Definition cp_fm_diag.F:1016
cp_fm_diag::fm_diag_type_cusolver
integer, parameter, public fm_diag_type_cusolver
Definition cp_fm_diag.F:105
cp_fm_diag::cp_fm_svd
subroutine, public cp_fm_svd(matrix_a, matrix_eigvl, matrix_eigvr_t, eigval, info)
decomposes a quadratic matrix into its singular value decomposition
Definition cp_fm_diag.F:894
cp_fm_diag::fm_diag_type_dlaf
integer, parameter, public fm_diag_type_dlaf
Definition cp_fm_diag.F:105
cp_fm_diag::fm_diag_type_scalapack
integer, parameter, public fm_diag_type_scalapack
Definition cp_fm_diag.F:105
cp_fm_diag::cp_fm_syevd
subroutine, public cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
Computes all eigenvalues and vectors of a real symmetric matrix significantly faster than syevx,...
Definition cp_fm_diag.F:412
cp_fm_diag::diag_finalize
subroutine, public diag_finalize()
Finalize the diagonalization library.
Definition cp_fm_diag.F:212
cp_fm_diag::diag_init
subroutine, public diag_init(diag_lib, fallback_applied, elpa_kernel, elpa_neigvec_min_input, elpa_qr, elpa_print, elpa_qr_unsafe, dlaf_neigvec_min_input, eps_check_diag_input)
Setup the diagonalization library to be used.
Definition cp_fm_diag.F:151
cp_fm_diag::fm_diag_type_default
integer, parameter, public fm_diag_type_default
Definition cp_fm_diag.F:114
cp_fm_diag::cp_fm_geeig
subroutine, public cp_fm_geeig(amatrix, bmatrix, eigenvectors, eigenvalues, work)
General Eigenvalue Problem AX = BXE Single option version: Cholesky decomposition of B.
Definition cp_fm_diag.F:1382
cp_fm_diag::choose_eigv_solver
subroutine, public choose_eigv_solver(matrix, eigenvectors, eigenvalues, info)
Choose the Eigensolver depending on which library is available ELPA seems to be unstable for small sy...
Definition cp_fm_diag.F:236
cp_fm_diag::diag_type
integer, save, public diag_type
Definition cp_fm_diag.F:91
cp_fm_diag::fm_diag_type_elpa
integer, parameter, public fm_diag_type_elpa
Definition cp_fm_diag.F:105
cp_fm_diag::cp_fm_geeig_canon
subroutine, public cp_fm_geeig_canon(amatrix, bmatrix, eigenvectors, eigenvalues, work, epseig)
General Eigenvalue Problem AX = BXE Use canonical diagonalization : U*s**(-1/2)
Definition cp_fm_diag.F:1435
cp_fm_diag::cp_fm_syevx
subroutine, public cp_fm_syevx(matrix, eigenvectors, eigenvalues, neig, work_syevx)
compute eigenvalues and optionally eigenvectors of a real symmetric matrix using scalapack....
Definition cp_fm_diag.F:656
cp_fm_dlaf_api
Definition cp_fm_dlaf_api.F:8
cp_fm_dlaf_api::cp_fm_diag_dlaf
subroutine, public cp_fm_diag_dlaf(matrix, eigenvectors, eigenvalues)
...
Definition cp_fm_dlaf_api.F:206
cp_fm_dlaf_api::cp_fm_diag_gen_dlaf
subroutine, public cp_fm_diag_gen_dlaf(a_matrix, b_matrix, eigenvectors, eigenvalues)
...
Definition cp_fm_dlaf_api.F:314
cp_fm_elpa
Wrapper for ELPA.
Definition cp_fm_elpa.F:12
cp_fm_elpa::set_elpa_print
subroutine, public set_elpa_print(flag)
Sets a flag that determines if additional information about the ELPA diagonalization should be printe...
Definition cp_fm_elpa.F:266
cp_fm_elpa::set_elpa_kernel
subroutine, public set_elpa_kernel(requested_kernel)
Sets the active ELPA kernel.
Definition cp_fm_elpa.F:201
cp_fm_elpa::cp_fm_diag_elpa
subroutine, public cp_fm_diag_elpa(matrix, eigenvectors, eigenvalues)
Driver routine to diagonalize a FM matrix with the ELPA library.
Definition cp_fm_elpa.F:278
cp_fm_elpa::set_elpa_qr
subroutine, public set_elpa_qr(use_qr, use_qr_unsafe)
Sets flags that determines if ELPA should try to use QR during diagonalization If use_qr = ....
Definition cp_fm_elpa.F:254
cp_fm_elpa::initialize_elpa_library
subroutine, public initialize_elpa_library()
Initialize the ELPA library.
Definition cp_fm_elpa.F:177
cp_fm_elpa::finalize_elpa_library
subroutine, public finalize_elpa_library()
Finalize the ELPA library.
Definition cp_fm_elpa.F:189
cp_fm_struct
represent the structure of a full matrix
Definition cp_fm_struct.F:14
cp_fm_struct::cp_fm_struct_create
subroutine, public cp_fm_struct_create(fmstruct, para_env, context, nrow_global, ncol_global, nrow_block, ncol_block, descriptor, first_p_pos, local_leading_dimension, template_fmstruct, square_blocks, force_block)
allocates and initializes a full matrix structure
Definition cp_fm_struct.F:132
cp_fm_struct::cp_fm_struct_equivalent
logical function, public cp_fm_struct_equivalent(fmstruct1, fmstruct2)
returns true if the two matrix structures are equivalent, false otherwise.
Definition cp_fm_struct.F:388
cp_fm_struct::cp_fm_struct_release
subroutine, public cp_fm_struct_release(fmstruct)
releases a full matrix structure
Definition cp_fm_struct.F:351
cp_fm_types
represent a full matrix distributed on many processors
Definition cp_fm_types.F:15
cp_fm_types::cp_fm_get_info
subroutine, public cp_fm_get_info(matrix, name, nrow_global, ncol_global, nrow_block, ncol_block, nrow_local, ncol_local, row_indices, col_indices, local_data, context, nrow_locals, ncol_locals, matrix_struct, para_env)
returns all kind of information about the full matrix
Definition cp_fm_types.F:1009
cp_fm_types::cp_fm_to_fm_submat
subroutine, public cp_fm_to_fm_submat(msource, mtarget, nrow, ncol, s_firstrow, s_firstcol, t_firstrow, t_firstcol)
copy just a part ot the matrix
Definition cp_fm_types.F:1472
cp_fm_types::cp_fm_set_all
subroutine, public cp_fm_set_all(matrix, alpha, beta)
set all elements of a matrix to the same value, and optionally the diagonal to a different one
Definition cp_fm_types.F:528
cp_fm_types::cp_fm_set_element
subroutine, public cp_fm_set_element(matrix, irow_global, icol_global, alpha)
sets an element of a matrix
Definition cp_fm_types.F:693
cp_fm_types::cp_fm_create
subroutine, public cp_fm_create(matrix, matrix_struct, name, use_sp)
creates a new full matrix with the given structure
Definition cp_fm_types.F:164
cp_log_handling
various routines to log and control the output. The idea is that decisions about where to log should ...
Definition cp_log_handling.F:41
cp_log_handling::cp_logger_get_default_unit_nr
recursive integer function, public cp_logger_get_default_unit_nr(logger, local, skip_not_ionode)
asks the default unit number of the given logger. try to use cp_logger_get_unit_nr
Definition cp_log_handling.F:567
cp_log_handling::cp_logger_get_unit_nr
integer function, public cp_logger_get_unit_nr(logger, local)
returns the unit nr for the requested kind of log.
Definition cp_log_handling.F:498
cp_log_handling::cp_logger_get_default_io_unit
integer function, public cp_logger_get_default_io_unit(logger)
returns the unit nr for the ionode (-1 on all other processors) skips as well checks if the procs cal...
Definition cp_log_handling.F:515
cp_log_handling::cp_get_default_logger
type(cp_logger_type) function, pointer, public cp_get_default_logger()
returns the default logger
Definition cp_log_handling.F:234
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
kinds::default_string_length
integer, parameter, public default_string_length
Definition kinds.F:57
machine
Machine interface based on Fortran 2003 and POSIX.
Definition machine.F:17
machine::default_output_unit
integer, parameter, public default_output_unit
Definition machine.F:53
machine::m_memory
subroutine, public m_memory(mem)
Returns the total amount of memory [bytes] in use, if known, zero otherwise.
Definition machine.F:443
message_passing
Interface to the message passing library MPI.
Definition message_passing.F:23
cp_blacs_env::cp_blacs_env_type
represent a blacs multidimensional parallel environment (for the mpi corrispective see cp_paratypes/m...
Definition cp_blacs_env.F:53
cp_blacs_types::cp_blacs_type
Definition cp_blacs_types.F:30
cp_fm_struct::cp_fm_struct_type
keeps the information about the structure of a full matrix
Definition cp_fm_struct.F:82
cp_fm_types::cp_fm_type
represent a full matrix
Definition cp_fm_types.F:113
cp_log_handling::cp_logger_type
type of a logger, at the moment it contains just a print level starting at which level it should be l...
Definition cp_log_handling.F:140
message_passing::mp_comm_type
Definition message_passing.F:189