Line data Source code
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 : ! **************************************************************************************************
17 : MODULE 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 :
129 : CONTAINS
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 9835 : 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 9835 : fallback_applied = .FALSE.
161 :
162 9835 : IF (diag_lib == "ScaLAPACK") THEN
163 190 : diag_type = FM_DIAG_TYPE_SCALAPACK
164 9645 : ELSE IF (diag_lib == "ELPA") THEN
165 : #if defined (__ELPA)
166 : ! ELPA is requested and available
167 9645 : 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 0 : ELSE IF (diag_lib == "cuSOLVER") THEN
174 0 : diag_type = FM_DIAG_TYPE_CUSOLVER
175 0 : ELSE IF (diag_lib == "DLAF") THEN
176 : #if defined (__DLAF)
177 : diag_type = FM_DIAG_TYPE_DLAF
178 : #else
179 0 : CPABORT("ERROR in diag_init: CP2K was not compiled with DLA-Future support")
180 : #endif
181 : ELSE
182 0 : CPABORT("ERROR in diag_init: Initialization of unknown diagonalization library requested")
183 : END IF
184 :
185 : ! Initialization of requested diagonalization library
186 9835 : IF (.NOT. initialized .AND. diag_type == FM_DIAG_TYPE_ELPA) THEN
187 9048 : CALL initialize_elpa_library()
188 9048 : CALL set_elpa_kernel(elpa_kernel)
189 9048 : CALL set_elpa_qr(elpa_qr, elpa_qr_unsafe)
190 9048 : CALL set_elpa_print(elpa_print)
191 9048 : 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 9835 : elpa_neigvec_min = elpa_neigvec_min_input
204 9835 : eps_check_diag = eps_check_diag_input
205 :
206 9835 : END SUBROUTINE diag_init
207 :
208 : ! **************************************************************************************************
209 : !> \brief Finalize the diagonalization library
210 : ! **************************************************************************************************
211 9625 : SUBROUTINE diag_finalize()
212 : #if defined (__ELPA)
213 9625 : IF (diag_type == FM_DIAG_TYPE_ELPA) &
214 9435 : 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 9625 : 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 177818 : 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 177818 : CALL m_memory()
245 :
246 177818 : IF (PRESENT(info)) info = 0 ! Default for solvers that do not return an info.
247 :
248 177818 : IF (diag_type == FM_DIAG_TYPE_SCALAPACK) THEN
249 4162 : CALL cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
250 :
251 173656 : ELSE IF (diag_type == FM_DIAG_TYPE_ELPA) THEN
252 173656 : IF (matrix%matrix_struct%nrow_global < elpa_neigvec_min) THEN
253 : ! We don't trust ELPA with very small matrices.
254 109565 : CALL cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
255 : ELSE
256 64091 : CALL cp_fm_diag_elpa(matrix, eigenvectors, eigenvalues)
257 : END IF
258 :
259 0 : ELSE IF (diag_type == FM_DIAG_TYPE_CUSOLVER) THEN
260 0 : IF (matrix%matrix_struct%nrow_global < 64) THEN
261 : ! We don't trust cuSolver with very small matrices.
262 0 : CALL cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
263 : ELSE
264 0 : 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 0 : CPABORT("ERROR in "//routineN//": Invalid diagonalization type requested")
279 : END IF
280 :
281 177818 : CALL check_diag(matrix, eigenvectors, nvec=SIZE(eigenvalues))
282 :
283 177818 : 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 294911 : 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_abort, eps_warning
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 294911 : CALL timeset(routineN, handle)
310 :
311 294911 : IF (diag_type == FM_DIAG_TYPE_SCALAPACK) THEN
312 8324 : diag_type_name = "SYEVD"
313 286587 : ELSE IF (diag_type == FM_DIAG_TYPE_ELPA) THEN
314 286587 : diag_type_name = "ELPA"
315 0 : ELSE IF (diag_type == FM_DIAG_TYPE_CUSOLVER) THEN
316 0 : diag_type_name = "CUSOLVER"
317 0 : ELSE IF (diag_type == FM_DIAG_TYPE_DLAF) THEN
318 0 : diag_type_name = "DLAF"
319 : ELSE
320 0 : CPABORT("Unknown diag_type")
321 : END IF
322 :
323 294911 : output_unit = default_output_unit
324 :
325 294911 : eps_warning = eps_check_diag_default
326 : #if defined(__CHECK_DIAG)
327 : check_eigenvectors = .TRUE.
328 : IF (eps_check_diag >= 0.0_dp) THEN
329 : eps_warning = eps_check_diag
330 : END IF
331 : #else
332 294911 : IF (eps_check_diag >= 0.0_dp) THEN
333 242 : check_eigenvectors = .TRUE.
334 242 : eps_warning = eps_check_diag
335 : ELSE
336 : check_eigenvectors = .FALSE.
337 : END IF
338 : #endif
339 294911 : eps_abort = 10.0_dp*eps_warning
340 :
341 294911 : IF (check_eigenvectors) THEN
342 : #if defined(__parallel)
343 242 : nrow = eigenvectors%matrix_struct%nrow_global
344 242 : ncol = MIN(eigenvectors%matrix_struct%ncol_global, nvec)
345 242 : CALL cp_fm_gemm("T", "N", ncol, ncol, nrow, 1.0_dp, eigenvectors, eigenvectors, 0.0_dp, matrix)
346 242 : context => matrix%matrix_struct%context
347 242 : myprow = context%mepos(1)
348 242 : mypcol = context%mepos(2)
349 242 : nprow = context%num_pe(1)
350 242 : npcol = context%num_pe(2)
351 2420 : desca(:) = matrix%matrix_struct%descriptor(:)
352 2792 : DO i = 1, ncol
353 41810 : DO j = 1, ncol
354 39018 : CALL infog2l(i, j, desca, nprow, npcol, myprow, mypcol, il, jl, iprow, ipcol)
355 41568 : IF ((iprow == myprow) .AND. (ipcol == mypcol)) THEN
356 19509 : IF (i == j) THEN
357 1275 : IF (ABS(matrix%local_data(il, jl) - 1.0_dp) > eps_warning) THEN
358 : WRITE (UNIT=output_unit, FMT="(/,T2,A,/,T2,A,I0,A,I0,A,F0.15,/,T2,A,ES10.3)") &
359 0 : "The eigenvectors returned by "//TRIM(diag_type_name)//" are not orthonormal", &
360 0 : "Matrix element (", i, ", ", j, ") = ", matrix%local_data(il, jl), &
361 0 : "The deviation from the expected value 1 is", ABS(matrix%local_data(il, jl) - 1.0_dp)
362 0 : IF (ABS(matrix%local_data(il, jl) - 1.0_dp) > eps_abort) THEN
363 0 : CPABORT("ERROR in "//routineN//": Check of matrix diagonalization failed")
364 : ELSE
365 0 : CPWARN("Check of matrix diagonalization failed in routine "//routineN)
366 : END IF
367 : END IF
368 : ELSE
369 18234 : IF (ABS(matrix%local_data(il, jl)) > eps_warning) THEN
370 : WRITE (UNIT=output_unit, FMT="(/,T2,A,/,T2,A,I0,A,I0,A,F0.15,/,T2,A,ES10.3)") &
371 0 : "The eigenvectors returned by "//TRIM(diag_type_name)//" are not orthonormal", &
372 0 : "Matrix element (", i, ", ", j, ") = ", matrix%local_data(il, jl), &
373 0 : "The deviation from the expected value 0 is", ABS(matrix%local_data(il, jl))
374 0 : IF (ABS(matrix%local_data(il, jl)) > eps_abort) THEN
375 0 : CPABORT("ERROR in "//routineN//": Check of matrix diagonalization failed")
376 : ELSE
377 0 : CPWARN("Check of matrix diagonalization failed in routine "//routineN)
378 : END IF
379 : END IF
380 : END IF
381 : END IF
382 : END DO
383 : END DO
384 : #else
385 : nrow = SIZE(eigenvectors%local_data, 1)
386 : ncol = MIN(SIZE(eigenvectors%local_data, 2), nvec)
387 : CALL dgemm("T", "N", ncol, ncol, nrow, 1.0_dp, &
388 : eigenvectors%local_data(1, 1), nrow, &
389 : eigenvectors%local_data(1, 1), nrow, &
390 : 0.0_dp, matrix%local_data(1, 1), nrow)
391 : DO i = 1, ncol
392 : DO j = 1, ncol
393 : IF (i == j) THEN
394 : IF (ABS(matrix%local_data(i, j) - 1.0_dp) > eps_warning) THEN
395 : WRITE (UNIT=output_unit, FMT="(/,T2,A,/,T2,A,I0,A,I0,A,F0.15,/,T2,A,ES10.3)") &
396 : "The eigenvectors returned by "//TRIM(diag_type_name)//" are not orthonormal", &
397 : "Matrix element (", i, ", ", j, ") = ", matrix%local_data(i, j), &
398 : "The deviation from the expected value 1 is", ABS(matrix%local_data(i, j) - 1.0_dp)
399 : IF (ABS(matrix%local_data(i, j) - 1.0_dp) > eps_abort) THEN
400 : CPABORT("ERROR in "//routineN//": Check of matrix diagonalization failed")
401 : ELSE
402 : CPWARN("Check of matrix diagonalization failed in routine "//routineN)
403 : END IF
404 : END IF
405 : ELSE
406 : IF (ABS(matrix%local_data(i, j)) > eps_warning) THEN
407 : WRITE (UNIT=output_unit, FMT="(/,T2,A,/,T2,A,I0,A,I0,A,F0.15,/,T2,A,ES10.3)") &
408 : "The eigenvectors returned by "//TRIM(diag_type_name)//" are not orthonormal", &
409 : "Matrix element (", i, ", ", j, ") = ", matrix%local_data(i, j), &
410 : "The deviation from the expected value 0 is", ABS(matrix%local_data(i, j))
411 : IF (ABS(matrix%local_data(i, j)) > eps_abort) THEN
412 : CPABORT("ERROR in "//routineN//": Check of matrix diagonalization failed")
413 : ELSE
414 : CPWARN("Check of matrix diagonalization failed in routine "//routineN)
415 : END IF
416 : END IF
417 : END IF
418 : END DO
419 : END DO
420 : #endif
421 : END IF
422 :
423 294911 : CALL timestop(handle)
424 :
425 294911 : END SUBROUTINE check_diag
426 :
427 : ! **************************************************************************************************
428 : !> \brief Computes all eigenvalues and vectors of a real symmetric matrix
429 : !> significantly faster than syevx, scales also much better.
430 : !> Needs workspace to allocate all the eigenvectors
431 : !> \param matrix ...
432 : !> \param eigenvectors ...
433 : !> \param eigenvalues ...
434 : !> \param info ...
435 : !> \par matrix is supposed to be in upper triangular form, and overwritten by this routine
436 : !> \par info If present returns error code and prevents program stops.
437 : !> Works currently only for scalapack.
438 : !> Other solvers will end the program regardless of PRESENT(info).
439 : ! **************************************************************************************************
440 117053 : SUBROUTINE cp_fm_syevd(matrix, eigenvectors, eigenvalues, info)
441 :
442 : TYPE(cp_fm_type), INTENT(IN) :: matrix, eigenvectors
443 : REAL(KIND=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
444 : INTEGER, INTENT(OUT), OPTIONAL :: info
445 :
446 : CHARACTER(LEN=*), PARAMETER :: routineN = 'cp_fm_syevd'
447 :
448 : INTEGER :: handle, myinfo, n, nmo
449 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: eig
450 : #if defined(__parallel)
451 : TYPE(cp_fm_type) :: eigenvectors_new, matrix_new
452 : #else
453 : CHARACTER(LEN=2*default_string_length) :: message
454 : INTEGER :: liwork, lwork, nl
455 : INTEGER, DIMENSION(:), POINTER :: iwork
456 : REAL(KIND=dp), DIMENSION(:, :), POINTER :: m
457 : REAL(KIND=dp), DIMENSION(:), POINTER :: work
458 : #endif
459 :
460 117053 : CALL timeset(routineN, handle)
461 :
462 117053 : myinfo = 0
463 :
464 117053 : n = matrix%matrix_struct%nrow_global
465 351159 : ALLOCATE (eig(n))
466 :
467 : #if defined(__parallel)
468 : ! Determine if the input matrix needs to be redistributed before diagonalization.
469 : ! Heuristics are used to determine the optimal number of CPUs for diagonalization.
470 : ! The redistributed matrix is stored in matrix_new, which is just a pointer
471 : ! to the original matrix if no redistribution is required
472 117053 : CALL cp_fm_redistribute_start(matrix, eigenvectors, matrix_new, eigenvectors_new)
473 :
474 : ! Call scalapack on CPUs that hold the new matrix
475 117053 : IF (ASSOCIATED(matrix_new%matrix_struct)) THEN
476 59220 : IF (PRESENT(info)) THEN
477 1114 : CALL cp_fm_syevd_base(matrix_new, eigenvectors_new, eig, myinfo)
478 : ELSE
479 58106 : CALL cp_fm_syevd_base(matrix_new, eigenvectors_new, eig)
480 : END IF
481 : END IF
482 : ! Redistribute results and clean up
483 117053 : CALL cp_fm_redistribute_end(matrix, eigenvectors, eig, matrix_new, eigenvectors_new)
484 : #else
485 : ! Retrieve the optimal work array sizes first
486 : lwork = -1
487 : liwork = -1
488 : m => matrix%local_data
489 : eig(:) = 0.0_dp
490 :
491 : ALLOCATE (work(1))
492 : work(:) = 0.0_dp
493 : ALLOCATE (iwork(1))
494 : iwork(:) = 0
495 : nl = SIZE(m, 1)
496 :
497 : CALL dsyevd('V', 'U', n, m(1, 1), nl, eig(1), work(1), lwork, iwork(1), liwork, myinfo)
498 :
499 : IF (myinfo /= 0) THEN
500 : WRITE (message, "(A,I0,A)") "ERROR in DSYEVD: Work space query failed (INFO = ", myinfo, ")"
501 : IF (PRESENT(info)) THEN
502 : CPWARN(TRIM(message))
503 : ELSE
504 : CPABORT(TRIM(message))
505 : END IF
506 : END IF
507 :
508 : ! Reallocate work arrays and perform diagonalisation
509 : lwork = INT(work(1))
510 : DEALLOCATE (work)
511 : ALLOCATE (work(lwork))
512 : work(:) = 0.0_dp
513 :
514 : liwork = iwork(1)
515 : DEALLOCATE (iwork)
516 : ALLOCATE (iwork(liwork))
517 : iwork(:) = 0
518 :
519 : CALL dsyevd('V', 'U', n, m(1, 1), nl, eig(1), work(1), lwork, iwork(1), liwork, myinfo)
520 :
521 : IF (myinfo /= 0) THEN
522 : WRITE (message, "(A,I0,A)") "ERROR in DSYEVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
523 : IF (PRESENT(info)) THEN
524 : CPWARN(TRIM(message))
525 : ELSE
526 : CPABORT(TRIM(message))
527 : END IF
528 : END IF
529 :
530 : CALL cp_fm_to_fm(matrix, eigenvectors)
531 :
532 : DEALLOCATE (iwork)
533 : DEALLOCATE (work)
534 : #endif
535 :
536 117053 : IF (PRESENT(info)) info = myinfo
537 :
538 117053 : nmo = SIZE(eigenvalues, 1)
539 117053 : IF (nmo > n) THEN
540 0 : eigenvalues(1:n) = eig(1:n)
541 : ELSE
542 813209 : eigenvalues(1:nmo) = eig(1:nmo)
543 : END IF
544 :
545 117053 : DEALLOCATE (eig)
546 :
547 117053 : CALL check_diag(matrix, eigenvectors, n)
548 :
549 117053 : CALL timestop(handle)
550 :
551 234106 : END SUBROUTINE cp_fm_syevd
552 :
553 : ! **************************************************************************************************
554 : !> \brief ...
555 : !> \param matrix ...
556 : !> \param eigenvectors ...
557 : !> \param eigenvalues ...
558 : !> \param info ...
559 : ! **************************************************************************************************
560 59220 : SUBROUTINE cp_fm_syevd_base(matrix, eigenvectors, eigenvalues, info)
561 :
562 : TYPE(cp_fm_type), INTENT(IN) :: matrix, eigenvectors
563 : REAL(KIND=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
564 : INTEGER, INTENT(OUT), OPTIONAL :: info
565 :
566 : CHARACTER(LEN=*), PARAMETER :: routineN = 'cp_fm_syevd_base'
567 :
568 : CHARACTER(LEN=2*default_string_length) :: message
569 : INTEGER :: handle, myinfo
570 : #if defined(__parallel)
571 : TYPE(cp_blacs_env_type), POINTER :: context
572 : INTEGER :: liwork, lwork, &
573 : mypcol, myprow, n
574 : INTEGER, DIMENSION(9) :: descm, descv
575 59220 : INTEGER, DIMENSION(:), POINTER :: iwork
576 59220 : REAL(KIND=dp), DIMENSION(:), POINTER :: work
577 59220 : REAL(KIND=dp), DIMENSION(:, :), POINTER :: m, v
578 : #if defined (__HAS_IEEE_EXCEPTIONS)
579 : LOGICAL, DIMENSION(5) :: halt
580 : #endif
581 : #endif
582 :
583 59220 : CALL timeset(routineN, handle)
584 :
585 59220 : myinfo = 0
586 :
587 : #if defined(__parallel)
588 :
589 59220 : n = matrix%matrix_struct%nrow_global
590 59220 : m => matrix%local_data
591 59220 : context => matrix%matrix_struct%context
592 59220 : myprow = context%mepos(1)
593 59220 : mypcol = context%mepos(2)
594 592200 : descm(:) = matrix%matrix_struct%descriptor(:)
595 :
596 59220 : v => eigenvectors%local_data
597 592200 : descv(:) = eigenvectors%matrix_struct%descriptor(:)
598 :
599 59220 : liwork = 7*n + 8*context%num_pe(2) + 2
600 177660 : ALLOCATE (iwork(liwork))
601 :
602 : ! Work space query
603 59220 : lwork = -1
604 59220 : ALLOCATE (work(1))
605 :
606 : CALL pdsyevd('V', 'U', n, m(1, 1), 1, 1, descm, eigenvalues(1), v(1, 1), 1, 1, descv, &
607 59220 : work(1), lwork, iwork(1), liwork, myinfo)
608 :
609 59220 : IF (matrix%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
610 0 : WRITE (message, "(A,I0,A)") "ERROR in PDSYEVD: Work space query failed (INFO = ", myinfo, ")"
611 0 : IF (PRESENT(info)) THEN
612 0 : CPWARN(TRIM(message))
613 : ELSE
614 0 : CPABORT(TRIM(message))
615 : END IF
616 : END IF
617 :
618 : ! look here for a PDORMTR warning :-)
619 : ! this routine seems to need more workspace than reported
620 : ! (? lapack bug ...)
621 : ! arbitrary additional memory ... we give 100000 more words
622 : ! (it seems to depend on the block size used)
623 :
624 59220 : lwork = NINT(work(1) + 100000)
625 : ! lwork = NINT(work(1))
626 59220 : DEALLOCATE (work)
627 177660 : ALLOCATE (work(lwork))
628 :
629 : ! Scalapack takes advantage of IEEE754 exceptions for speedup.
630 : ! Therefore, we disable floating point traps temporarily.
631 : #if defined (__HAS_IEEE_EXCEPTIONS)
632 : CALL ieee_get_halting_mode(IEEE_ALL, halt)
633 : CALL ieee_set_halting_mode(IEEE_ALL, .FALSE.)
634 : #endif
635 :
636 : CALL pdsyevd('V', 'U', n, m(1, 1), 1, 1, descm, eigenvalues(1), v(1, 1), 1, 1, descv, &
637 59220 : work(1), lwork, iwork(1), liwork, myinfo)
638 :
639 : #if defined (__HAS_IEEE_EXCEPTIONS)
640 : CALL ieee_set_halting_mode(IEEE_ALL, halt)
641 : #endif
642 59220 : IF (matrix%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
643 0 : WRITE (message, "(A,I0,A)") "ERROR in PDSYEVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
644 0 : IF (PRESENT(info)) THEN
645 0 : CPWARN(TRIM(message))
646 : ELSE
647 0 : CPABORT(TRIM(message))
648 : END IF
649 : END IF
650 :
651 59220 : IF (PRESENT(info)) info = myinfo
652 :
653 59220 : DEALLOCATE (work)
654 59220 : DEALLOCATE (iwork)
655 : #else
656 : MARK_USED(matrix)
657 : MARK_USED(eigenvectors)
658 : MARK_USED(eigenvalues)
659 : myinfo = -1
660 : IF (PRESENT(info)) info = myinfo
661 : message = "ERROR in "//TRIM(routineN)// &
662 : ": Matrix diagonalization using PDSYEVD requested without ScaLAPACK support"
663 : CPABORT(TRIM(message))
664 : #endif
665 :
666 59220 : CALL timestop(handle)
667 :
668 59220 : END SUBROUTINE cp_fm_syevd_base
669 :
670 : ! **************************************************************************************************
671 : !> \brief compute eigenvalues and optionally eigenvectors of a real symmetric matrix using scalapack.
672 : !> If eigenvectors are required this routine will replicate a full matrix on each CPU...
673 : !> if more than a handful of vectors are needed, use cp_fm_syevd instead
674 : !> \param matrix ...
675 : !> \param eigenvectors ...
676 : !> \param eigenvalues ...
677 : !> \param neig ...
678 : !> \param work_syevx ...
679 : !> \par matrix is supposed to be in upper triangular form, and overwritten by this routine
680 : !> neig is the number of vectors needed (default all)
681 : !> work_syevx evec calculation only, is the fraction of the working buffer allowed (1.0 use full buffer)
682 : !> reducing this saves time, but might cause the routine to fail
683 : ! **************************************************************************************************
684 40 : SUBROUTINE cp_fm_syevx(matrix, eigenvectors, eigenvalues, neig, work_syevx)
685 :
686 : ! Diagonalise the symmetric n by n matrix using the LAPACK library.
687 :
688 : TYPE(cp_fm_type), INTENT(IN) :: matrix
689 : TYPE(cp_fm_type), OPTIONAL, INTENT(IN) :: eigenvectors
690 : REAL(KIND=dp), OPTIONAL, INTENT(IN) :: work_syevx
691 : INTEGER, INTENT(IN), OPTIONAL :: neig
692 : REAL(KIND=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
693 :
694 : CHARACTER(LEN=*), PARAMETER :: routineN = "cp_fm_syevx"
695 :
696 : #if defined(__parallel)
697 : REAL(KIND=dp), PARAMETER :: orfac = -1.0_dp
698 : #endif
699 : REAL(KIND=dp), PARAMETER :: vl = 0.0_dp, &
700 : vu = 0.0_dp
701 :
702 : TYPE(cp_blacs_env_type), POINTER :: context
703 : TYPE(cp_logger_type), POINTER :: logger
704 : CHARACTER(LEN=1) :: job_type
705 : REAL(KIND=dp) :: abstol, work_syevx_local
706 : INTEGER :: handle, info, &
707 : liwork, lwork, m, mypcol, &
708 : myprow, n, nb, npcol, &
709 : nprow, output_unit, &
710 : neig_local
711 : LOGICAL :: ionode, needs_evecs
712 40 : INTEGER, DIMENSION(:), ALLOCATABLE :: ifail, iwork
713 40 : REAL(KIND=dp), DIMENSION(:), ALLOCATABLE :: w, work
714 40 : REAL(KIND=dp), DIMENSION(:, :), POINTER :: a, z
715 :
716 : REAL(KIND=dp), EXTERNAL :: dlamch
717 :
718 : #if defined(__parallel)
719 : INTEGER :: nn, np0, npe, nq0, nz
720 : INTEGER, DIMENSION(9) :: desca, descz
721 40 : INTEGER, DIMENSION(:), ALLOCATABLE :: iclustr
722 40 : REAL(KIND=dp), DIMENSION(:), ALLOCATABLE :: gap
723 : INTEGER, EXTERNAL :: iceil, numroc
724 : #if defined (__HAS_IEEE_EXCEPTIONS)
725 : LOGICAL, DIMENSION(5) :: halt
726 : #endif
727 : #else
728 : INTEGER :: nla, nlz
729 : INTEGER, EXTERNAL :: ilaenv
730 : #endif
731 :
732 : ! by default all
733 40 : n = matrix%matrix_struct%nrow_global
734 40 : neig_local = n
735 40 : IF (PRESENT(neig)) neig_local = neig
736 40 : IF (neig_local == 0) RETURN
737 :
738 40 : CALL timeset(routineN, handle)
739 :
740 40 : needs_evecs = PRESENT(eigenvectors)
741 :
742 40 : logger => cp_get_default_logger()
743 40 : ionode = logger%para_env%is_source()
744 40 : n = matrix%matrix_struct%nrow_global
745 :
746 : ! by default allocate all needed space
747 40 : work_syevx_local = 1.0_dp
748 40 : IF (PRESENT(work_syevx)) work_syevx_local = work_syevx
749 :
750 : ! set scalapack job type
751 40 : IF (needs_evecs) THEN
752 40 : job_type = "V"
753 : ELSE
754 0 : job_type = "N"
755 : END IF
756 :
757 : ! target the most accurate calculation of the eigenvalues
758 40 : abstol = 2.0_dp*dlamch("S")
759 :
760 40 : context => matrix%matrix_struct%context
761 40 : myprow = context%mepos(1)
762 40 : mypcol = context%mepos(2)
763 40 : nprow = context%num_pe(1)
764 40 : npcol = context%num_pe(2)
765 :
766 120 : ALLOCATE (w(n))
767 560 : eigenvalues(:) = 0.0_dp
768 : #if defined(__parallel)
769 :
770 40 : IF (matrix%matrix_struct%nrow_block /= matrix%matrix_struct%ncol_block) THEN
771 0 : CPABORT("ERROR in "//routineN//": Invalid blocksize (no square blocks) found")
772 : END IF
773 :
774 40 : a => matrix%local_data
775 400 : desca(:) = matrix%matrix_struct%descriptor(:)
776 :
777 40 : IF (needs_evecs) THEN
778 40 : z => eigenvectors%local_data
779 400 : descz(:) = eigenvectors%matrix_struct%descriptor(:)
780 : ELSE
781 : ! z will not be referenced
782 0 : z => matrix%local_data
783 0 : descz = desca
784 : END IF
785 :
786 : ! Get the optimal work storage size
787 :
788 40 : npe = nprow*npcol
789 40 : nb = matrix%matrix_struct%nrow_block
790 40 : nn = MAX(n, nb, 2)
791 40 : np0 = numroc(nn, nb, 0, 0, nprow)
792 40 : nq0 = MAX(numroc(nn, nb, 0, 0, npcol), nb)
793 :
794 40 : IF (needs_evecs) THEN
795 : lwork = 5*n + MAX(5*nn, np0*nq0) + iceil(neig_local, npe)*nn + 2*nb*nb + &
796 40 : INT(work_syevx_local*REAL((neig_local - 1)*n, dp)) !!!! allocates a full matrix on every CPU !!!!!
797 : ELSE
798 0 : lwork = 5*n + MAX(5*nn, nb*(np0 + 1))
799 : END IF
800 40 : liwork = 6*MAX(N, npe + 1, 4)
801 :
802 120 : ALLOCATE (gap(npe))
803 120 : gap = 0.0_dp
804 120 : ALLOCATE (iclustr(2*npe))
805 200 : iclustr = 0
806 120 : ALLOCATE (ifail(n))
807 560 : ifail = 0
808 120 : ALLOCATE (iwork(liwork))
809 120 : ALLOCATE (work(lwork))
810 :
811 : ! Scalapack takes advantage of IEEE754 exceptions for speedup.
812 : ! Therefore, we disable floating point traps temporarily.
813 : #if defined (__HAS_IEEE_EXCEPTIONS)
814 : CALL ieee_get_halting_mode(IEEE_ALL, halt)
815 : CALL ieee_set_halting_mode(IEEE_ALL, .FALSE.)
816 : #endif
817 :
818 : CALL pdsyevx(job_type, "I", "U", n, a(1, 1), 1, 1, desca, vl, vu, 1, neig_local, abstol, m, nz, w(1), orfac, &
819 40 : z(1, 1), 1, 1, descz, work(1), lwork, iwork(1), liwork, ifail(1), iclustr(1), gap, info)
820 :
821 : #if defined (__HAS_IEEE_EXCEPTIONS)
822 : CALL ieee_set_halting_mode(IEEE_ALL, halt)
823 : #endif
824 :
825 : ! Error handling
826 :
827 40 : IF (info /= 0) THEN
828 0 : IF (ionode) THEN
829 0 : output_unit = cp_logger_get_unit_nr(logger, local=.FALSE.)
830 : WRITE (unit=output_unit, FMT="(/,(T3,A,T12,1X,I10))") &
831 0 : "info = ", info, &
832 0 : "lwork = ", lwork, &
833 0 : "liwork = ", liwork, &
834 0 : "nz = ", nz
835 0 : IF (info > 0) THEN
836 : WRITE (unit=output_unit, FMT="(/,T3,A,(T12,6(1X,I10)))") &
837 0 : "ifail = ", ifail
838 : WRITE (unit=output_unit, FMT="(/,T3,A,(T12,6(1X,I10)))") &
839 0 : "iclustr = ", iclustr
840 : WRITE (unit=output_unit, FMT="(/,T3,A,(T12,6(1X,E10.3)))") &
841 0 : "gap = ", gap
842 : END IF
843 : END IF
844 0 : CPABORT("ERROR in PDSYEVX (ScaLAPACK)")
845 : END IF
846 :
847 : ! Release work storage
848 :
849 40 : DEALLOCATE (gap)
850 40 : DEALLOCATE (iclustr)
851 40 : DEALLOCATE (ifail)
852 40 : DEALLOCATE (iwork)
853 40 : DEALLOCATE (work)
854 :
855 : #else
856 :
857 : a => matrix%local_data
858 : IF (needs_evecs) THEN
859 : z => eigenvectors%local_data
860 : ELSE
861 : ! z will not be referenced
862 : z => matrix%local_data
863 : END IF
864 :
865 : ! Get the optimal work storage size
866 :
867 : nb = MAX(ilaenv(1, "DSYTRD", "U", n, -1, -1, -1), &
868 : ilaenv(1, "DORMTR", "U", n, -1, -1, -1))
869 :
870 : lwork = MAX((nb + 3)*n, 8*n) + n ! sun bug fix
871 : liwork = 5*n
872 :
873 : ALLOCATE (ifail(n))
874 : ifail = 0
875 : ALLOCATE (iwork(liwork))
876 : ALLOCATE (work(lwork))
877 : info = 0
878 : nla = SIZE(a, 1)
879 : nlz = SIZE(z, 1)
880 :
881 : CALL dsyevx(job_type, "I", "U", n, a(1, 1), nla, vl, vu, 1, neig_local, &
882 : abstol, m, w, z(1, 1), nlz, work(1), lwork, iwork(1), ifail(1), info)
883 :
884 : ! Error handling
885 :
886 : IF (info /= 0) THEN
887 : output_unit = cp_logger_get_unit_nr(logger, local=.FALSE.)
888 : WRITE (unit=output_unit, FMT="(/,(T3,A,T12,1X,I10))") &
889 : "info = ", info
890 : IF (info > 0) THEN
891 : WRITE (unit=output_unit, FMT="(/,T3,A,(T12,6(1X,I10)))") &
892 : "ifail = ", ifail
893 : END IF
894 : CPABORT("Error in DSYEVX (ScaLAPACK)")
895 : END IF
896 :
897 : ! Release work storage
898 :
899 : DEALLOCATE (ifail)
900 : DEALLOCATE (iwork)
901 : DEALLOCATE (work)
902 :
903 : #endif
904 400 : eigenvalues(1:neig_local) = w(1:neig_local)
905 40 : DEALLOCATE (w)
906 :
907 40 : IF (needs_evecs) CALL check_diag(matrix, eigenvectors, neig_local)
908 :
909 40 : CALL timestop(handle)
910 :
911 120 : END SUBROUTINE cp_fm_syevx
912 :
913 : ! **************************************************************************************************
914 : !> \brief decomposes a quadratic matrix into its singular value decomposition
915 : !> \param matrix_a ...
916 : !> \param matrix_eigvl ...
917 : !> \param matrix_eigvr_t ...
918 : !> \param eigval ...
919 : !> \param info ...
920 : !> \author Maximilian Graml
921 : ! **************************************************************************************************
922 100 : SUBROUTINE cp_fm_svd(matrix_a, matrix_eigvl, matrix_eigvr_t, eigval, info)
923 :
924 : TYPE(cp_fm_type), INTENT(IN) :: matrix_a
925 : TYPE(cp_fm_type), INTENT(INOUT) :: matrix_eigvl, matrix_eigvr_t
926 : REAL(KIND=dp), DIMENSION(:), POINTER, &
927 : INTENT(INOUT) :: eigval
928 : INTEGER, INTENT(OUT), OPTIONAL :: info
929 :
930 : CHARACTER(LEN=*), PARAMETER :: routineN = 'cp_fm_svd'
931 :
932 : CHARACTER(LEN=2*default_string_length) :: message
933 : INTEGER :: handle, n, m, myinfo, lwork
934 100 : REAL(KIND=dp), DIMENSION(:, :), POINTER :: a
935 : TYPE(cp_fm_type) :: matrix_lu
936 100 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: work
937 :
938 : #if defined(__parallel)
939 : INTEGER, DIMENSION(9) :: desca, descu, descvt
940 : #endif
941 100 : CALL timeset(routineN, handle)
942 :
943 : CALL cp_fm_create(matrix=matrix_lu, &
944 : matrix_struct=matrix_a%matrix_struct, &
945 100 : name="A_lu"//TRIM(ADJUSTL(cp_to_string(1)))//"MATRIX")
946 100 : CALL cp_fm_to_fm(matrix_a, matrix_lu)
947 100 : a => matrix_lu%local_data
948 100 : m = matrix_lu%matrix_struct%nrow_global
949 100 : n = matrix_lu%matrix_struct%ncol_global
950 : ! Assert that incoming matrix is quadratic
951 100 : CPASSERT(m == n)
952 :
953 : ! Prepare for workspace queries
954 100 : myinfo = 0
955 100 : lwork = -1
956 100 : ALLOCATE (work(1))
957 200 : work(:) = 0.0_dp
958 : #if defined(__parallel)
959 : ! To do: That might need a redistribution check as in cp_fm_syevd
960 1000 : desca(:) = matrix_lu%matrix_struct%descriptor(:)
961 1000 : descu(:) = matrix_eigvl%matrix_struct%descriptor(:)
962 1000 : descvt(:) = matrix_eigvr_t%matrix_struct%descriptor(:)
963 :
964 : ! Workspace query
965 : CALL pdgesvd('V', 'V', m, m, matrix_lu%local_data, 1, 1, desca, eigval, matrix_eigvl%local_data, &
966 100 : 1, 1, descu, matrix_eigvr_t%local_data, 1, 1, descvt, work, lwork, myinfo)
967 :
968 100 : IF (matrix_lu%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
969 0 : WRITE (message, "(A,I0,A)") "ERROR in PDGESVD: Work space query failed (INFO = ", myinfo, ")"
970 0 : IF (PRESENT(info)) THEN
971 0 : CPWARN(TRIM(message))
972 : ELSE
973 0 : CPABORT(TRIM(message))
974 : END IF
975 : END IF
976 :
977 100 : lwork = INT(work(1))
978 100 : DEALLOCATE (work)
979 300 : ALLOCATE (work(lwork))
980 : ! SVD
981 : CALL pdgesvd('V', 'V', m, m, matrix_lu%local_data, 1, 1, desca, eigval, matrix_eigvl%local_data, &
982 100 : 1, 1, descu, matrix_eigvr_t%local_data, 1, 1, descvt, work, lwork, myinfo)
983 :
984 100 : IF (matrix_lu%matrix_struct%para_env%is_source() .AND. (myinfo /= 0)) THEN
985 0 : WRITE (message, "(A,I0,A)") "ERROR in PDGESVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
986 0 : IF (PRESENT(info)) THEN
987 0 : CPWARN(TRIM(message))
988 : ELSE
989 0 : CPABORT(TRIM(message))
990 : END IF
991 : END IF
992 : #else
993 : ! Workspace query
994 : CALL dgesvd('S', 'S', m, m, matrix_lu%local_data, m, eigval, matrix_eigvl%local_data, &
995 : m, matrix_eigvr_t%local_data, m, work, lwork, myinfo)
996 :
997 : IF (myinfo /= 0) THEN
998 : WRITE (message, "(A,I0,A)") "ERROR in DGESVD: Work space query failed (INFO = ", myinfo, ")"
999 : IF (PRESENT(info)) THEN
1000 : CPWARN(TRIM(message))
1001 : ELSE
1002 : CPABORT(TRIM(message))
1003 : END IF
1004 : END IF
1005 :
1006 : ! SVD
1007 : lwork = INT(work(1))
1008 : DEALLOCATE (work)
1009 : ALLOCATE (work(lwork))
1010 : work(:) = 0.0_dp
1011 :
1012 : CALL dgesvd('S', 'S', m, m, matrix_lu%local_data, m, eigval, matrix_eigvl%local_data, &
1013 : m, matrix_eigvr_t%local_data, m, work, lwork, myinfo)
1014 :
1015 : IF (myinfo /= 0) THEN
1016 : WRITE (message, "(A,I0,A)") "ERROR in DGESVD: Matrix diagonalization failed (INFO = ", myinfo, ")"
1017 : IF (PRESENT(info)) THEN
1018 : CPWARN(TRIM(message))
1019 : ELSE
1020 : CPABORT(TRIM(message))
1021 : END IF
1022 : END IF
1023 :
1024 : #endif
1025 : ! Release intermediary matrices
1026 100 : DEALLOCATE (work)
1027 100 : CALL cp_fm_release(matrix_lu)
1028 :
1029 100 : IF (PRESENT(info)) info = myinfo
1030 :
1031 100 : CALL timestop(handle)
1032 100 : END SUBROUTINE cp_fm_svd
1033 :
1034 : ! **************************************************************************************************
1035 : !> \brief ...
1036 : !> \param matrix ...
1037 : !> \param work ...
1038 : !> \param exponent ...
1039 : !> \param threshold ...
1040 : !> \param n_dependent ...
1041 : !> \param verbose ...
1042 : !> \param eigvals ...
1043 : ! **************************************************************************************************
1044 1522 : SUBROUTINE cp_fm_power(matrix, work, exponent, threshold, n_dependent, verbose, eigvals)
1045 :
1046 : ! Raise the real symmetric n by n matrix to the power given by
1047 : ! the exponent. All eigenvectors with a corresponding eigenvalue lower
1048 : ! than threshold are quenched. result in matrix
1049 :
1050 : ! - Creation (29.03.1999, Matthias Krack)
1051 : ! - Parallelised using BLACS and ScaLAPACK (06.06.2001,MK)
1052 :
1053 : TYPE(cp_fm_type), INTENT(IN) :: matrix, work
1054 : REAL(KIND=dp), INTENT(IN) :: exponent, threshold
1055 : INTEGER, INTENT(OUT) :: n_dependent
1056 : LOGICAL, INTENT(IN), OPTIONAL :: verbose
1057 : REAL(KIND=dp), DIMENSION(2), INTENT(OUT), &
1058 : OPTIONAL :: eigvals
1059 :
1060 : CHARACTER(LEN=*), PARAMETER :: routineN = 'cp_fm_power'
1061 :
1062 : INTEGER :: handle, icol_global, &
1063 : mypcol, myprow, &
1064 : ncol_global, npcol, nprow, &
1065 : nrow_global
1066 : LOGICAL :: my_verbose
1067 : REAL(KIND=dp) :: condition_number, f, p
1068 : REAL(KIND=dp), DIMENSION(:), ALLOCATABLE :: eigenvalues
1069 1522 : REAL(KIND=dp), DIMENSION(:, :), POINTER :: eigenvectors
1070 : TYPE(cp_blacs_env_type), POINTER :: context
1071 :
1072 : #if defined(__parallel)
1073 : INTEGER :: icol_local, ipcol, iprow, irow_global, &
1074 : irow_local
1075 : #endif
1076 :
1077 1522 : CALL timeset(routineN, handle)
1078 :
1079 1522 : my_verbose = .FALSE.
1080 1522 : IF (PRESENT(verbose)) my_verbose = verbose
1081 :
1082 1522 : context => matrix%matrix_struct%context
1083 1522 : myprow = context%mepos(1)
1084 1522 : mypcol = context%mepos(2)
1085 1522 : nprow = context%num_pe(1)
1086 1522 : npcol = context%num_pe(2)
1087 1522 : n_dependent = 0
1088 1522 : p = 0.5_dp*exponent
1089 :
1090 1522 : nrow_global = matrix%matrix_struct%nrow_global
1091 1522 : ncol_global = matrix%matrix_struct%ncol_global
1092 :
1093 4566 : ALLOCATE (eigenvalues(ncol_global))
1094 :
1095 38709 : eigenvalues(:) = 0.0_dp
1096 :
1097 : ! Compute the eigenvectors and eigenvalues
1098 :
1099 1522 : CALL choose_eigv_solver(matrix, work, eigenvalues)
1100 :
1101 1522 : IF (PRESENT(eigvals)) THEN
1102 348 : eigvals(1) = eigenvalues(1)
1103 348 : eigvals(2) = eigenvalues(ncol_global)
1104 : END IF
1105 :
1106 : #if defined(__parallel)
1107 1522 : eigenvectors => work%local_data
1108 :
1109 : ! Build matrix**exponent with eigenvector quenching
1110 :
1111 38709 : DO icol_global = 1, ncol_global
1112 :
1113 38709 : IF (eigenvalues(icol_global) < threshold) THEN
1114 :
1115 50 : n_dependent = n_dependent + 1
1116 :
1117 50 : ipcol = work%matrix_struct%g2p_col(icol_global)
1118 :
1119 50 : IF (mypcol == ipcol) THEN
1120 50 : icol_local = work%matrix_struct%g2l_col(icol_global)
1121 5850 : DO irow_global = 1, nrow_global
1122 5800 : iprow = work%matrix_struct%g2p_row(irow_global)
1123 5850 : IF (myprow == iprow) THEN
1124 2900 : irow_local = work%matrix_struct%g2l_row(irow_global)
1125 2900 : eigenvectors(irow_local, icol_local) = 0.0_dp
1126 : END IF
1127 : END DO
1128 : END IF
1129 :
1130 : ELSE
1131 :
1132 37137 : f = eigenvalues(icol_global)**p
1133 :
1134 37137 : ipcol = work%matrix_struct%g2p_col(icol_global)
1135 :
1136 37137 : IF (mypcol == ipcol) THEN
1137 37137 : icol_local = work%matrix_struct%g2l_col(icol_global)
1138 2363936 : DO irow_global = 1, nrow_global
1139 2326799 : iprow = work%matrix_struct%g2p_row(irow_global)
1140 2363936 : IF (myprow == iprow) THEN
1141 1207474 : irow_local = work%matrix_struct%g2l_row(irow_global)
1142 : eigenvectors(irow_local, icol_local) = &
1143 1207474 : f*eigenvectors(irow_local, icol_local)
1144 : END IF
1145 : END DO
1146 : END IF
1147 :
1148 : END IF
1149 :
1150 : END DO
1151 :
1152 : #else
1153 :
1154 : eigenvectors => work%local_data
1155 :
1156 : ! Build matrix**exponent with eigenvector quenching
1157 :
1158 : DO icol_global = 1, ncol_global
1159 :
1160 : IF (eigenvalues(icol_global) < threshold) THEN
1161 :
1162 : n_dependent = n_dependent + 1
1163 : eigenvectors(1:nrow_global, icol_global) = 0.0_dp
1164 :
1165 : ELSE
1166 :
1167 : f = eigenvalues(icol_global)**p
1168 : eigenvectors(1:nrow_global, icol_global) = &
1169 : f*eigenvectors(1:nrow_global, icol_global)
1170 :
1171 : END IF
1172 :
1173 : END DO
1174 :
1175 : #endif
1176 1522 : CALL cp_fm_syrk("U", "N", ncol_global, 1.0_dp, work, 1, 1, 0.0_dp, matrix)
1177 1522 : CALL cp_fm_uplo_to_full(matrix, work)
1178 :
1179 : ! Print some warnings/notes
1180 1522 : IF (matrix%matrix_struct%para_env%is_source() .AND. my_verbose) THEN
1181 0 : condition_number = ABS(eigenvalues(ncol_global)/eigenvalues(1))
1182 : WRITE (UNIT=cp_logger_get_default_unit_nr(), FMT="(/,(T2,A,ES15.6))") &
1183 0 : "CP_FM_POWER: smallest eigenvalue:", eigenvalues(1), &
1184 0 : "CP_FM_POWER: largest eigenvalue: ", eigenvalues(ncol_global), &
1185 0 : "CP_FM_POWER: condition number: ", condition_number
1186 0 : IF (eigenvalues(1) <= 0.0_dp) THEN
1187 : WRITE (UNIT=cp_logger_get_default_unit_nr(), FMT="(/,T2,A)") &
1188 0 : "WARNING: matrix has a negative eigenvalue, tighten EPS_DEFAULT"
1189 : END IF
1190 0 : IF (condition_number > 1.0E12_dp) THEN
1191 : WRITE (UNIT=cp_logger_get_default_unit_nr(), FMT="(/,T2,A)") &
1192 0 : "WARNING: high condition number => possibly ill-conditioned matrix"
1193 : END IF
1194 : END IF
1195 :
1196 1522 : DEALLOCATE (eigenvalues)
1197 :
1198 1522 : CALL timestop(handle)
1199 :
1200 1522 : END SUBROUTINE cp_fm_power
1201 :
1202 : ! **************************************************************************************************
1203 : !> \brief ...
1204 : !> \param matrix ...
1205 : !> \param eigenvectors ...
1206 : !> \param eigval ...
1207 : !> \param thresh ...
1208 : !> \param start_sec_block ...
1209 : ! **************************************************************************************************
1210 18 : SUBROUTINE cp_fm_block_jacobi(matrix, eigenvectors, eigval, thresh, &
1211 : start_sec_block)
1212 :
1213 : ! Calculates block diagonalization of a full symmetric matrix
1214 : ! It has its origin in cp_fm_syevx. This routine rotates only elements
1215 : ! which are larger than a threshold values "thresh".
1216 : ! start_sec_block is the start of the second block.
1217 : ! IT DOES ONLY ONE SWEEP!
1218 :
1219 : ! - Creation (07.10.2002, Martin Fengler)
1220 : ! - Cosmetics (05.04.06, MK)
1221 :
1222 : TYPE(cp_fm_type), INTENT(IN) :: eigenvectors, matrix
1223 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: eigval
1224 : INTEGER, INTENT(IN) :: start_sec_block
1225 : REAL(KIND=dp), INTENT(IN) :: thresh
1226 :
1227 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_fm_block_jacobi'
1228 :
1229 : INTEGER :: handle
1230 : REAL(KIND=dp), DIMENSION(:, :), POINTER :: a, ev
1231 :
1232 : REAL(KIND=dp) :: tan_theta, tau, c, s
1233 : INTEGER :: q, p, N
1234 18 : REAL(KIND=dp), DIMENSION(:), ALLOCATABLE :: c_ip
1235 :
1236 : #if defined(__parallel)
1237 : TYPE(cp_blacs_env_type), POINTER :: context
1238 :
1239 : INTEGER :: myprow, mypcol, nprow, npcol, block_dim_row, block_dim_col, &
1240 : info, ev_row_block_size, iam, mynumrows, mype, npe, &
1241 : q_loc
1242 18 : REAL(KIND=dp), DIMENSION(:, :), ALLOCATABLE :: a_loc, ev_loc
1243 : INTEGER, DIMENSION(9) :: desca, descz, desc_a_block, &
1244 : desc_ev_loc
1245 : TYPE(mp_comm_type):: allgrp
1246 : TYPE(cp_blacs_type) :: ictxt_loc
1247 : INTEGER, EXTERNAL :: numroc
1248 : #endif
1249 :
1250 : ! -------------------------------------------------------------------------
1251 :
1252 18 : CALL timeset(routineN, handle)
1253 :
1254 : #if defined(__parallel)
1255 18 : context => matrix%matrix_struct%context
1256 18 : allgrp = matrix%matrix_struct%para_env
1257 :
1258 18 : myprow = context%mepos(1)
1259 18 : mypcol = context%mepos(2)
1260 18 : nprow = context%num_pe(1)
1261 18 : npcol = context%num_pe(2)
1262 :
1263 18 : N = matrix%matrix_struct%nrow_global
1264 :
1265 18 : A => matrix%local_data
1266 180 : desca(:) = matrix%matrix_struct%descriptor(:)
1267 18 : EV => eigenvectors%local_data
1268 180 : descz(:) = eigenvectors%matrix_struct%descriptor(:)
1269 :
1270 : ! Copy the block to be rotated to the master process firstly and broadcast to all processes
1271 : ! start_sec_block defines where the second block starts!
1272 : ! Block will be processed together with the OO block
1273 :
1274 18 : block_dim_row = start_sec_block - 1
1275 18 : block_dim_col = N - block_dim_row
1276 72 : ALLOCATE (A_loc(block_dim_row, block_dim_col))
1277 :
1278 18 : mype = matrix%matrix_struct%para_env%mepos
1279 18 : npe = matrix%matrix_struct%para_env%num_pe
1280 : ! Get a new context
1281 18 : CALL ictxt_loc%gridinit(matrix%matrix_struct%para_env, 'Row-major', NPROW*NPCOL, 1)
1282 :
1283 : CALL descinit(desc_a_block, block_dim_row, block_dim_col, block_dim_row, &
1284 18 : block_dim_col, 0, 0, ictxt_loc%get_handle(), block_dim_row, info)
1285 :
1286 : CALL pdgemr2d(block_dim_row, block_dim_col, A, 1, start_sec_block, desca, &
1287 18 : A_loc, 1, 1, desc_a_block, context%get_handle())
1288 : ! Only the master (root) process received data yet
1289 18 : CALL allgrp%bcast(A_loc, 0)
1290 :
1291 : ! Since each process owns now the upper block, the eigenvectors can be re-sorted in such a way that
1292 : ! each process has a NN*1 grid, i.e. the process owns a bunch of rows which can be modified locally
1293 :
1294 : ! Initialize distribution of the eigenvectors
1295 18 : iam = mype
1296 18 : ev_row_block_size = n/(nprow*npcol)
1297 18 : mynumrows = NUMROC(N, ev_row_block_size, iam, 0, NPROW*NPCOL)
1298 :
1299 108 : ALLOCATE (EV_loc(mynumrows, N), c_ip(mynumrows))
1300 :
1301 : CALL descinit(desc_ev_loc, N, N, ev_row_block_size, N, 0, 0, ictxt_loc%get_handle(), &
1302 18 : mynumrows, info)
1303 :
1304 18 : CALL pdgemr2d(N, N, EV, 1, 1, descz, EV_loc, 1, 1, desc_ev_loc, context%get_handle())
1305 :
1306 : ! Start block diagonalization of matrix
1307 :
1308 18 : q_loc = 0
1309 :
1310 1170 : DO q = start_sec_block, N
1311 1152 : q_loc = q_loc + 1
1312 148626 : DO p = 1, (start_sec_block - 1)
1313 :
1314 148608 : IF (ABS(A_loc(p, q_loc)) > thresh) THEN
1315 :
1316 117566 : tau = (eigval(q) - eigval(p))/(2.0_dp*A_loc(p, q_loc))
1317 :
1318 117566 : tan_theta = SIGN(1.0_dp, tau)/(ABS(tau) + SQRT(1.0_dp + tau*tau))
1319 :
1320 : ! Cos(theta)
1321 117566 : c = 1.0_dp/SQRT(1.0_dp + tan_theta*tan_theta)
1322 117566 : s = tan_theta*c
1323 :
1324 : ! Calculate eigenvectors: Q*J
1325 : ! c_ip = c*EV_loc(:,p) - s*EV_loc(:,q)
1326 : ! c_iq = s*EV_loc(:,p) + c*EV_loc(:,q)
1327 : ! EV(:,p) = c_ip
1328 : ! EV(:,q) = c_iq
1329 117566 : CALL dcopy(mynumrows, EV_loc(1, p), 1, c_ip(1), 1)
1330 117566 : CALL dscal(mynumrows, c, EV_loc(1, p), 1)
1331 117566 : CALL daxpy(mynumrows, -s, EV_loc(1, q), 1, EV_loc(1, p), 1)
1332 117566 : CALL dscal(mynumrows, c, EV_loc(1, q), 1)
1333 117566 : CALL daxpy(mynumrows, s, c_ip(1), 1, EV_loc(1, q), 1)
1334 :
1335 : END IF
1336 :
1337 : END DO
1338 : END DO
1339 :
1340 : ! Copy eigenvectors back to the original distribution
1341 18 : CALL pdgemr2d(N, N, EV_loc, 1, 1, desc_ev_loc, EV, 1, 1, descz, context%get_handle())
1342 :
1343 : ! Release work storage
1344 18 : DEALLOCATE (A_loc, EV_loc, c_ip)
1345 :
1346 18 : CALL ictxt_loc%gridexit()
1347 :
1348 : #else
1349 :
1350 : N = matrix%matrix_struct%nrow_global
1351 :
1352 : ALLOCATE (c_ip(N)) ! Local eigenvalue vector
1353 :
1354 : A => matrix%local_data ! Contains the Matrix to be worked on
1355 : EV => eigenvectors%local_data ! Contains the eigenvectors up to blocksize, rest is garbage
1356 :
1357 : ! Start matrix diagonalization
1358 :
1359 : tan_theta = 0.0_dp
1360 : tau = 0.0_dp
1361 :
1362 : DO q = start_sec_block, N
1363 : DO p = 1, (start_sec_block - 1)
1364 :
1365 : IF (ABS(A(p, q)) > thresh) THEN
1366 :
1367 : tau = (eigval(q) - eigval(p))/(2.0_dp*A(p, q))
1368 :
1369 : tan_theta = SIGN(1.0_dp, tau)/(ABS(tau) + SQRT(1.0_dp + tau*tau))
1370 :
1371 : ! Cos(theta)
1372 : c = 1.0_dp/SQRT(1.0_dp + tan_theta*tan_theta)
1373 : s = tan_theta*c
1374 :
1375 : ! Calculate eigenvectors: Q*J
1376 : ! c_ip = c*EV(:,p) - s*EV(:,q)
1377 : ! c_iq = s*EV(:,p) + c*EV(:,q)
1378 : ! EV(:,p) = c_ip
1379 : ! EV(:,q) = c_iq
1380 : CALL dcopy(N, EV(1, p), 1, c_ip(1), 1)
1381 : CALL dscal(N, c, EV(1, p), 1)
1382 : CALL daxpy(N, -s, EV(1, q), 1, EV(1, p), 1)
1383 : CALL dscal(N, c, EV(1, q), 1)
1384 : CALL daxpy(N, s, c_ip(1), 1, EV(1, q), 1)
1385 :
1386 : END IF
1387 :
1388 : END DO
1389 : END DO
1390 :
1391 : ! Release work storage
1392 :
1393 : DEALLOCATE (c_ip)
1394 :
1395 : #endif
1396 :
1397 18 : CALL timestop(handle)
1398 :
1399 90 : END SUBROUTINE cp_fm_block_jacobi
1400 :
1401 : ! **************************************************************************************************
1402 : !> \brief General Eigenvalue Problem AX = BXE
1403 : !> Single option version: Cholesky decomposition of B
1404 : !> \param amatrix ...
1405 : !> \param bmatrix ...
1406 : !> \param eigenvectors ...
1407 : !> \param eigenvalues ...
1408 : !> \param work ...
1409 : ! **************************************************************************************************
1410 280 : SUBROUTINE cp_fm_geeig(amatrix, bmatrix, eigenvectors, eigenvalues, work)
1411 :
1412 : TYPE(cp_fm_type), INTENT(IN) :: amatrix, bmatrix, eigenvectors
1413 : REAL(KIND=dp), DIMENSION(:) :: eigenvalues
1414 : TYPE(cp_fm_type), INTENT(IN) :: work
1415 :
1416 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_fm_geeig'
1417 :
1418 : INTEGER :: handle, nao, nmo
1419 :
1420 280 : CALL timeset(routineN, handle)
1421 :
1422 280 : CALL cp_fm_get_info(amatrix, nrow_global=nao)
1423 280 : nmo = SIZE(eigenvalues)
1424 :
1425 280 : IF (diag_type == FM_DIAG_TYPE_CUSOLVER .AND. nao >= 64) THEN
1426 : ! Use cuSolverMP generalized eigenvalue solver for large matrices
1427 0 : CALL cp_fm_general_cusolver(amatrix, bmatrix, eigenvectors, eigenvalues)
1428 : #if defined(__DLAF)
1429 : ELSE IF (diag_type == FM_DIAG_TYPE_DLAF .AND. amatrix%matrix_struct%nrow_global >= dlaf_neigvec_min) THEN
1430 : ! Use DLA-Future generalized eigenvalue solver for large matrices
1431 : CALL cp_fm_diag_gen_dlaf(amatrix, bmatrix, eigenvectors, eigenvalues)
1432 : #endif
1433 : ELSE
1434 : ! Cholesky decompose S=U(T)U
1435 280 : CALL cp_fm_cholesky_decompose(bmatrix)
1436 : ! Invert to get U^(-1)
1437 280 : CALL cp_fm_triangular_invert(bmatrix)
1438 : ! Reduce to get U^(-T) * H * U^(-1)
1439 280 : CALL cp_fm_triangular_multiply(bmatrix, amatrix, side="R")
1440 280 : CALL cp_fm_triangular_multiply(bmatrix, amatrix, transpose_tr=.TRUE.)
1441 : ! Diagonalize
1442 : CALL choose_eigv_solver(matrix=amatrix, eigenvectors=work, &
1443 280 : eigenvalues=eigenvalues)
1444 : ! Restore vectors C = U^(-1) * C*
1445 280 : CALL cp_fm_triangular_multiply(bmatrix, work)
1446 280 : CALL cp_fm_to_fm(work, eigenvectors, nmo)
1447 : END IF
1448 :
1449 280 : CALL timestop(handle)
1450 :
1451 280 : END SUBROUTINE cp_fm_geeig
1452 :
1453 : ! **************************************************************************************************
1454 : !> \brief General Eigenvalue Problem AX = BXE
1455 : !> Use canonical diagonalization : U*s**(-1/2)
1456 : !> \param amatrix ...
1457 : !> \param bmatrix ...
1458 : !> \param eigenvectors ...
1459 : !> \param eigenvalues ...
1460 : !> \param work ...
1461 : !> \param epseig ...
1462 : ! **************************************************************************************************
1463 66 : SUBROUTINE cp_fm_geeig_canon(amatrix, bmatrix, eigenvectors, eigenvalues, work, epseig)
1464 :
1465 : TYPE(cp_fm_type), INTENT(IN) :: amatrix, bmatrix, eigenvectors
1466 : REAL(KIND=dp), DIMENSION(:), INTENT(OUT) :: eigenvalues
1467 : TYPE(cp_fm_type), INTENT(IN) :: work
1468 : REAL(KIND=dp), INTENT(IN) :: epseig
1469 :
1470 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_fm_geeig_canon'
1471 :
1472 : INTEGER :: handle, i, icol, irow, nao, nc, ncol, &
1473 : nmo, nx
1474 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: evals
1475 :
1476 66 : CALL timeset(routineN, handle)
1477 :
1478 : ! Test sizees
1479 66 : CALL cp_fm_get_info(amatrix, nrow_global=nao)
1480 66 : nmo = SIZE(eigenvalues)
1481 198 : ALLOCATE (evals(nao))
1482 :
1483 : ! Diagonalize -S matrix, this way the NULL space is at the end of the spectrum
1484 66 : CALL cp_fm_scale(-1.0_dp, bmatrix)
1485 66 : CALL choose_eigv_solver(matrix=bmatrix, eigenvectors=work, eigenvalues=evals)
1486 4720 : evals(:) = -evals(:)
1487 66 : nc = nao
1488 4428 : DO i = 1, nao
1489 4428 : IF (evals(i) < epseig) THEN
1490 40 : nc = i - 1
1491 40 : EXIT
1492 : END IF
1493 : END DO
1494 66 : CPASSERT(nc /= 0)
1495 :
1496 66 : IF (nc /= nao) THEN
1497 40 : IF (nc < nmo) THEN
1498 : ! Copy NULL space definition to last vectors of eigenvectors (if needed)
1499 0 : ncol = nmo - nc
1500 0 : CALL cp_fm_to_fm(work, eigenvectors, ncol, nc + 1, nc + 1)
1501 : END IF
1502 : ! Set NULL space in eigenvector matrix of S to zero
1503 332 : DO icol = nc + 1, nao
1504 36172 : DO irow = 1, nao
1505 36132 : CALL cp_fm_set_element(work, irow, icol, 0.0_dp)
1506 : END DO
1507 : END DO
1508 : ! Set small eigenvalues to a dummy save value
1509 332 : evals(nc + 1:nao) = 1.0_dp
1510 : END IF
1511 : ! Calculate U*s**(-1/2)
1512 4720 : evals(:) = 1.0_dp/SQRT(evals(:))
1513 66 : CALL cp_fm_column_scale(work, evals)
1514 : ! Reduce to get U^(-T) * H * U^(-1)
1515 66 : CALL cp_fm_gemm("T", "N", nao, nao, nao, 1.0_dp, work, amatrix, 0.0_dp, bmatrix)
1516 66 : CALL cp_fm_gemm("N", "N", nao, nao, nao, 1.0_dp, bmatrix, work, 0.0_dp, amatrix)
1517 66 : IF (nc /= nao) THEN
1518 : ! set diagonal values to save large value
1519 332 : DO icol = nc + 1, nao
1520 332 : CALL cp_fm_set_element(amatrix, icol, icol, 10000.0_dp)
1521 : END DO
1522 : END IF
1523 : ! Diagonalize
1524 66 : CALL choose_eigv_solver(matrix=amatrix, eigenvectors=bmatrix, eigenvalues=eigenvalues)
1525 66 : nx = MIN(nc, nmo)
1526 : ! Restore vectors C = U^(-1) * C*
1527 66 : CALL cp_fm_gemm("N", "N", nao, nx, nc, 1.0_dp, work, bmatrix, 0.0_dp, eigenvectors)
1528 :
1529 66 : DEALLOCATE (evals)
1530 :
1531 66 : CALL timestop(handle)
1532 :
1533 66 : END SUBROUTINE cp_fm_geeig_canon
1534 :
1535 : END MODULE cp_fm_diag
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