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ct_methods.F
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1!--------------------------------------------------------------------------------------------------!
2! CP2K: A general program to perform molecular dynamics simulations !
3! Copyright 2000-2026 CP2K developers group <https://cp2k.org> !
4! !
5! SPDX-License-Identifier: GPL-2.0-or-later !
6!--------------------------------------------------------------------------------------------------!
7
8! **************************************************************************************************
9!> \brief Cayley transformation methods
10!> \par History
11!> 2011.06 created [Rustam Z Khaliullin]
12!> \author Rustam Z Khaliullin
13! **************************************************************************************************
14MODULE ct_methods
15 USE cp_dbcsr_api, ONLY: &
16 dbcsr_add, dbcsr_copy, dbcsr_create, dbcsr_desymmetrize, dbcsr_filter, dbcsr_finalize, &
17 dbcsr_get_info, dbcsr_iterator_blocks_left, dbcsr_iterator_next_block, &
18 dbcsr_iterator_readonly_start, dbcsr_iterator_start, dbcsr_iterator_stop, &
19 dbcsr_iterator_type, dbcsr_multiply, dbcsr_put_block, dbcsr_release, dbcsr_scale, &
20 dbcsr_set, dbcsr_transposed, dbcsr_type, dbcsr_type_no_symmetry, dbcsr_work_create
21 USE cp_dbcsr_cholesky, ONLY: cp_dbcsr_cholesky_decompose,&
22 cp_dbcsr_cholesky_invert
23 USE cp_dbcsr_contrib, ONLY: dbcsr_add_on_diag,&
24 dbcsr_dot,&
25 dbcsr_frobenius_norm,&
26 dbcsr_get_diag,&
27 dbcsr_hadamard_product,&
28 dbcsr_maxabs,&
29 dbcsr_reserve_diag_blocks,&
30 dbcsr_set_diag
31 USE cp_dbcsr_diag, ONLY: cp_dbcsr_syevd
32 USE cp_log_handling, ONLY: cp_get_default_logger,&
33 cp_logger_get_default_unit_nr,&
34 cp_logger_type
35 USE ct_types, ONLY: ct_step_env_type
36 USE input_constants, ONLY: &
37 cg_dai_yuan, cg_fletcher, cg_fletcher_reeves, cg_hager_zhang, cg_hestenes_stiefel, &
38 cg_liu_storey, cg_polak_ribiere, cg_zero, tensor_orthogonal, tensor_up_down
39 USE iterate_matrix, ONLY: matrix_sqrt_newton_schulz
40 USE kinds, ONLY: dp
41 USE machine, ONLY: m_walltime
42 USE mathconstants, ONLY: pi
43#include "./base/base_uses.f90"
44
45 IMPLICIT NONE
46
47 PRIVATE
48
49 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'ct_methods'
50
51 ! Public subroutines
52 PUBLIC :: ct_step_execute, analytic_line_search, diagonalize_diagonal_blocks
53
54CONTAINS
55
56! **************************************************************************************************
57!> \brief Performs Cayley transformation
58!> \param cts_env ...
59!> \par History
60!> 2011.06 created [Rustam Z Khaliullin]
61!> \author Rustam Z Khaliullin
62! **************************************************************************************************
63 SUBROUTINE ct_step_execute(cts_env)
64
65 TYPE(ct_step_env_type) :: cts_env
66
67 CHARACTER(len=*), PARAMETER :: routinen = 'ct_step_execute'
68
69 INTEGER :: handle, n, preconditioner_type, unit_nr
70 REAL(kind=dp) :: gap_estimate, safety_margin
71 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: evals
72 TYPE(cp_logger_type), POINTER :: logger
73 TYPE(dbcsr_type) :: matrix_pp, matrix_pq, matrix_qp, &
74 matrix_qp_save, matrix_qq, oo1, &
75 oo1_sqrt, oo1_sqrt_inv, t_corr, tmp1, &
76 u_pp, u_qq
77
78!TYPE(dbcsr_type) :: rst_x1, rst_x2
79!REAL(KIND=dp) :: ener_tmp
80!TYPE(dbcsr_iterator_type) :: iter
81!INTEGER :: iblock_row,iblock_col,&
82! iblock_row_size,iblock_col_size
83!REAL(KIND=dp), DIMENSION(:,:), POINTER :: data_p
84
85 CALL timeset(routinen, handle)
86
87 logger => cp_get_default_logger()
88 IF (logger%para_env%is_source()) THEN
89 unit_nr = cp_logger_get_default_unit_nr(logger, local=.true.)
90 ELSE
91 unit_nr = -1
92 END IF
93
94 ! check if all input is in place and flags are consistent
95 IF (cts_env%update_q .AND. (.NOT. cts_env%update_p)) THEN
96 cpabort("q-update is possible only with p-update")
97 END IF
98
99 IF (cts_env%tensor_type == tensor_up_down) THEN
100 cpabort("riccati is not implemented for biorthogonal basis")
101 END IF
102
103 IF (.NOT. ASSOCIATED(cts_env%matrix_ks)) THEN
104 cpabort("KS matrix is not associated")
105 END IF
106
107 IF (cts_env%use_virt_orbs .AND. (.NOT. cts_env%use_occ_orbs)) THEN
108 cpabort("virtual orbs can be used only with occupied orbs")
109 END IF
110
111 IF (cts_env%use_occ_orbs) THEN
112 IF (.NOT. ASSOCIATED(cts_env%matrix_t)) THEN
113 cpabort("T matrix is not associated")
114 END IF
115 IF (.NOT. ASSOCIATED(cts_env%matrix_qp_template)) THEN
116 cpabort("QP template is not associated")
117 END IF
118 IF (.NOT. ASSOCIATED(cts_env%matrix_pq_template)) THEN
119 cpabort("PQ template is not associated")
120 END IF
121 END IF
122
123 IF (cts_env%use_virt_orbs) THEN
124 IF (.NOT. ASSOCIATED(cts_env%matrix_v)) THEN
125 cpabort("V matrix is not associated")
126 END IF
127 ELSE
128 IF (.NOT. ASSOCIATED(cts_env%matrix_p)) THEN
129 cpabort("P matrix is not associated")
130 END IF
131 END IF
132
133 IF (cts_env%tensor_type /= tensor_up_down .AND. &
134 cts_env%tensor_type /= tensor_orthogonal) THEN
135 cpabort("illegal tensor flag")
136 END IF
137
138 ! start real calculations
139 IF (cts_env%use_occ_orbs) THEN
140
141 ! create matrices for various ks blocks
142 CALL dbcsr_create(matrix_pp, &
143 template=cts_env%p_index_up, &
144 matrix_type=dbcsr_type_no_symmetry)
145 CALL dbcsr_create(matrix_qp, &
146 template=cts_env%matrix_qp_template, &
147 matrix_type=dbcsr_type_no_symmetry)
148 CALL dbcsr_create(matrix_qq, &
149 template=cts_env%q_index_up, &
150 matrix_type=dbcsr_type_no_symmetry)
151 CALL dbcsr_create(matrix_pq, &
152 template=cts_env%matrix_pq_template, &
153 matrix_type=dbcsr_type_no_symmetry)
154
155 ! create the residue matrix
156 CALL dbcsr_create(cts_env%matrix_res, &
157 template=cts_env%matrix_qp_template)
158
159 CALL assemble_ks_qp_blocks(cts_env%matrix_ks, &
160 cts_env%matrix_p, &
161 cts_env%matrix_t, &
162 cts_env%matrix_v, &
163 cts_env%q_index_down, &
164 cts_env%p_index_up, &
165 cts_env%q_index_up, &
166 matrix_pp, &
167 matrix_qq, &
168 matrix_qp, &
169 matrix_pq, &
170 cts_env%tensor_type, &
171 cts_env%use_virt_orbs, &
172 cts_env%eps_filter)
173
174 ! create a matrix of single-excitation amplitudes
175 CALL dbcsr_create(cts_env%matrix_x, &
176 template=cts_env%matrix_qp_template)
177 IF (ASSOCIATED(cts_env%matrix_x_guess)) THEN
178 CALL dbcsr_copy(cts_env%matrix_x, &
179 cts_env%matrix_x_guess)
180 IF (cts_env%tensor_type == tensor_orthogonal) THEN
181 ! bring x from contravariant-covariant representation
182 ! to the orthogonal/cholesky representation
183 ! use res as temporary storage
184 CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%q_index_down, &
185 cts_env%matrix_x, 0.0_dp, cts_env%matrix_res, &
186 filter_eps=cts_env%eps_filter)
187 CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%matrix_res, &
188 cts_env%p_index_up, 0.0_dp, &
189 cts_env%matrix_x, &
190 filter_eps=cts_env%eps_filter)
191 END IF
192 ELSE
193 ! set amplitudes to zero
194 CALL dbcsr_set(cts_env%matrix_x, 0.0_dp)
195 END IF
196
197 !SELECT CASE (cts_env%preconditioner_type)
198 !CASE (prec_eigenvector_blocks,prec_eigenvector_full)
199 preconditioner_type = 1
200 safety_margin = 2.0_dp
201 gap_estimate = 0.0001_dp
202 SELECT CASE (preconditioner_type)
203 CASE (1, 2)
204!RZK-warning diagonalization works only with orthogonal tensor!!!
205 ! find a better basis by diagonalizing diagonal blocks
206 ! first pp
207 CALL dbcsr_create(u_pp, template=matrix_pp, &
208 matrix_type=dbcsr_type_no_symmetry)
209 !IF (cts_env%preconditioner_type.eq.prec_eigenvector_full) THEN
210 IF (.true.) THEN
211 CALL dbcsr_get_info(matrix_pp, nfullrows_total=n)
212 ALLOCATE (evals(n))
213 CALL cp_dbcsr_syevd(matrix_pp, u_pp, evals, &
214 cts_env%para_env, cts_env%blacs_env)
215 DEALLOCATE (evals)
216 ELSE
217 CALL diagonalize_diagonal_blocks(matrix_pp, u_pp)
218 END IF
219 ! and now qq
220 CALL dbcsr_create(u_qq, template=matrix_qq, &
221 matrix_type=dbcsr_type_no_symmetry)
222 !IF (cts_env%preconditioner_type.eq.prec_eigenvector_full) THEN
223 IF (.true.) THEN
224 CALL dbcsr_get_info(matrix_qq, nfullrows_total=n)
225 ALLOCATE (evals(n))
226 CALL cp_dbcsr_syevd(matrix_qq, u_qq, evals, &
227 cts_env%para_env, cts_env%blacs_env)
228 DEALLOCATE (evals)
229 ELSE
230 CALL diagonalize_diagonal_blocks(matrix_qq, u_qq)
231 END IF
232
233 ! apply the transformation to all matrices
234 CALL matrix_forward_transform(matrix_pp, u_pp, u_pp, &
235 cts_env%eps_filter)
236 CALL matrix_forward_transform(matrix_qq, u_qq, u_qq, &
237 cts_env%eps_filter)
238 CALL matrix_forward_transform(matrix_qp, u_qq, u_pp, &
239 cts_env%eps_filter)
240 CALL matrix_forward_transform(matrix_pq, u_pp, u_qq, &
241 cts_env%eps_filter)
242 CALL matrix_forward_transform(cts_env%matrix_x, u_qq, u_pp, &
243 cts_env%eps_filter)
244
245 IF (cts_env%max_iter >= 0) THEN
246
247 CALL solve_riccati_equation( &
248 pp=matrix_pp, &
249 qq=matrix_qq, &
250 qp=matrix_qp, &
251 pq=matrix_pq, &
252 x=cts_env%matrix_x, &
253 res=cts_env%matrix_res, &
254 neglect_quadratic_term=cts_env%neglect_quadratic_term, &
255 conjugator=cts_env%conjugator, &
256 max_iter=cts_env%max_iter, &
257 eps_convergence=cts_env%eps_convergence, &
258 eps_filter=cts_env%eps_filter, &
259 converged=cts_env%converged)
260
261 IF (cts_env%converged) THEN
262 !IF (unit_nr>0) THEN
263 ! WRITE(unit_nr,*)
264 ! WRITE(unit_nr,'(T6,A)') &
265 ! "RICCATI equations solved"
266 ! CALL m_flush(unit_nr)
267 !ENDIF
268 ELSE
269 cpabort("RICCATI: CG algorithm has NOT converged")
270 END IF
271
272 END IF
273
274 IF (cts_env%calculate_energy_corr) THEN
275
276 CALL dbcsr_dot(matrix_qp, cts_env%matrix_x, cts_env%energy_correction)
277
278 END IF
279
280 CALL dbcsr_release(matrix_pp)
281 CALL dbcsr_release(matrix_qp)
282 CALL dbcsr_release(matrix_qq)
283 CALL dbcsr_release(matrix_pq)
284
285 ! back-transform to the original basis
286 CALL matrix_backward_transform(cts_env%matrix_x, u_qq, &
287 u_pp, cts_env%eps_filter)
288
289 CALL dbcsr_release(u_qq)
290 CALL dbcsr_release(u_pp)
291
292 !CASE (prec_cholesky_inverse)
293 CASE (3)
294
295! RZK-warning implemented only for orthogonal tensors!!!
296! generalization to up_down should be easy
297 CALL dbcsr_create(u_pp, template=matrix_pp, &
298 matrix_type=dbcsr_type_no_symmetry)
299 CALL dbcsr_copy(u_pp, matrix_pp)
300 CALL dbcsr_scale(u_pp, -1.0_dp)
301 CALL dbcsr_add_on_diag(u_pp, &
302 abs(safety_margin*gap_estimate))
303 CALL cp_dbcsr_cholesky_decompose(u_pp, &
304 para_env=cts_env%para_env, &
305 blacs_env=cts_env%blacs_env)
306 CALL cp_dbcsr_cholesky_invert(u_pp, &
307 para_env=cts_env%para_env, &
308 blacs_env=cts_env%blacs_env, &
309 uplo_to_full=.true.)
310 !CALL dbcsr_scale(u_pp,-1.0_dp)
311
312 CALL dbcsr_create(u_qq, template=matrix_qq, &
313 matrix_type=dbcsr_type_no_symmetry)
314 CALL dbcsr_copy(u_qq, matrix_qq)
315 CALL dbcsr_add_on_diag(u_qq, &
316 abs(safety_margin*gap_estimate))
317 CALL cp_dbcsr_cholesky_decompose(u_qq, &
318 para_env=cts_env%para_env, &
319 blacs_env=cts_env%blacs_env)
320 CALL cp_dbcsr_cholesky_invert(u_qq, &
321 para_env=cts_env%para_env, &
322 blacs_env=cts_env%blacs_env, &
323 uplo_to_full=.true.)
324
325 ! transform all riccati matrices (left-right preconditioner)
326 CALL dbcsr_create(tmp1, template=matrix_qq, &
327 matrix_type=dbcsr_type_no_symmetry)
328 CALL dbcsr_multiply("N", "N", 1.0_dp, u_qq, &
329 matrix_qq, 0.0_dp, tmp1, &
330 filter_eps=cts_env%eps_filter)
331 CALL dbcsr_copy(matrix_qq, tmp1)
332 CALL dbcsr_release(tmp1)
333
334 CALL dbcsr_create(tmp1, template=matrix_pp, &
335 matrix_type=dbcsr_type_no_symmetry)
336 CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_pp, &
337 u_pp, 0.0_dp, tmp1, &
338 filter_eps=cts_env%eps_filter)
339 CALL dbcsr_copy(matrix_pp, tmp1)
340 CALL dbcsr_release(tmp1)
341
342 CALL dbcsr_create(matrix_qp_save, template=matrix_qp, &
343 matrix_type=dbcsr_type_no_symmetry)
344 CALL dbcsr_copy(matrix_qp_save, matrix_qp)
345
346 CALL dbcsr_create(tmp1, template=matrix_qp, &
347 matrix_type=dbcsr_type_no_symmetry)
348 CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_qp, &
349 u_pp, 0.0_dp, tmp1, &
350 filter_eps=cts_env%eps_filter)
351 CALL dbcsr_multiply("N", "N", 1.0_dp, u_qq, tmp1, &
352 0.0_dp, matrix_qp, &
353 filter_eps=cts_env%eps_filter)
354 CALL dbcsr_release(tmp1)
355!CALL dbcsr_print(matrix_qq)
356!CALL dbcsr_print(matrix_qp)
357!CALL dbcsr_print(matrix_pp)
358
359 IF (cts_env%max_iter >= 0) THEN
360
361 CALL solve_riccati_equation( &
362 pp=matrix_pp, &
363 qq=matrix_qq, &
364 qp=matrix_qp, &
365 pq=matrix_pq, &
366 oo=u_pp, &
367 vv=u_qq, &
368 x=cts_env%matrix_x, &
369 res=cts_env%matrix_res, &
370 neglect_quadratic_term=cts_env%neglect_quadratic_term, &
371 conjugator=cts_env%conjugator, &
372 max_iter=cts_env%max_iter, &
373 eps_convergence=cts_env%eps_convergence, &
374 eps_filter=cts_env%eps_filter, &
375 converged=cts_env%converged)
376
377 IF (cts_env%converged) THEN
378 !IF (unit_nr>0) THEN
379 ! WRITE(unit_nr,*)
380 ! WRITE(unit_nr,'(T6,A)') &
381 ! "RICCATI equations solved"
382 ! CALL m_flush(unit_nr)
383 !ENDIF
384 ELSE
385 cpabort("RICCATI: CG algorithm has NOT converged")
386 END IF
387
388 END IF
389
390 IF (cts_env%calculate_energy_corr) THEN
391
392 CALL dbcsr_dot(matrix_qp_save, cts_env%matrix_x, cts_env%energy_correction)
393
394 END IF
395 CALL dbcsr_release(matrix_qp_save)
396
397 CALL dbcsr_release(matrix_pp)
398 CALL dbcsr_release(matrix_qp)
399 CALL dbcsr_release(matrix_qq)
400 CALL dbcsr_release(matrix_pq)
401
402 CALL dbcsr_release(u_qq)
403 CALL dbcsr_release(u_pp)
404
405 CASE DEFAULT
406 cpabort("illegal preconditioner type")
407 END SELECT ! preconditioner type
408
409 IF (cts_env%update_p) THEN
410
411 IF (cts_env%tensor_type == tensor_up_down) THEN
412 cpabort("orbital update is NYI for this tensor type")
413 END IF
414
415 ! transform occupied orbitals
416 ! in a way that preserves the overlap metric
417 CALL dbcsr_create(oo1, &
418 template=cts_env%p_index_up, &
419 matrix_type=dbcsr_type_no_symmetry)
420 CALL dbcsr_create(oo1_sqrt_inv, &
421 template=oo1)
422 CALL dbcsr_create(oo1_sqrt, &
423 template=oo1)
424
425 ! Compute (1+tr(X).X)^(-1/2)_up_down
426 CALL dbcsr_multiply("T", "N", 1.0_dp, cts_env%matrix_x, &
427 cts_env%matrix_x, 0.0_dp, oo1, &
428 filter_eps=cts_env%eps_filter)
429 CALL dbcsr_add_on_diag(oo1, 1.0_dp)
430 CALL matrix_sqrt_newton_schulz(oo1_sqrt, &
431 oo1_sqrt_inv, &
432 oo1, &
433 !if cholesky is used then sqrt
434 !guess cannot be provided
435 !matrix_sqrt_inv_guess=cts_env%p_index_up,&
436 !matrix_sqrt_guess=cts_env%p_index_down,&
437 threshold=cts_env%eps_filter, &
438 order=cts_env%order_lanczos, &
439 eps_lanczos=cts_env%eps_lancsoz, &
440 max_iter_lanczos=cts_env%max_iter_lanczos)
441 CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%p_index_up, &
442 oo1_sqrt_inv, 0.0_dp, oo1, &
443 filter_eps=cts_env%eps_filter)
444 CALL dbcsr_multiply("N", "N", 1.0_dp, oo1, &
445 cts_env%p_index_down, 0.0_dp, oo1_sqrt, &
446 filter_eps=cts_env%eps_filter)
447 CALL dbcsr_release(oo1)
448 CALL dbcsr_release(oo1_sqrt_inv)
449
450 ! bring x to contravariant-covariant representation now
451 CALL dbcsr_create(matrix_qp, &
452 template=cts_env%matrix_qp_template, &
453 matrix_type=dbcsr_type_no_symmetry)
454 CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%q_index_up, &
455 cts_env%matrix_x, 0.0_dp, matrix_qp, &
456 filter_eps=cts_env%eps_filter)
457 CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_qp, &
458 cts_env%p_index_down, 0.0_dp, &
459 cts_env%matrix_x, &
460 filter_eps=cts_env%eps_filter)
461 CALL dbcsr_release(matrix_qp)
462
463 ! update T=T+X or T=T+V.X (whichever is appropriate)
464 CALL dbcsr_create(t_corr, template=cts_env%matrix_t)
465 IF (cts_env%use_virt_orbs) THEN
466 CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%matrix_v, &
467 cts_env%matrix_x, 0.0_dp, t_corr, &
468 filter_eps=cts_env%eps_filter)
469 CALL dbcsr_add(cts_env%matrix_t, t_corr, &
470 1.0_dp, 1.0_dp)
471 ELSE
472 CALL dbcsr_add(cts_env%matrix_t, cts_env%matrix_x, &
473 1.0_dp, 1.0_dp)
474 END IF
475 ! adjust T so the metric is preserved: T=(T+X).(1+tr(X).X)^(-1/2)
476 CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%matrix_t, oo1_sqrt, &
477 0.0_dp, t_corr, filter_eps=cts_env%eps_filter)
478 CALL dbcsr_copy(cts_env%matrix_t, t_corr)
479
480 CALL dbcsr_release(t_corr)
481 CALL dbcsr_release(oo1_sqrt)
482
483 ELSE ! do not update p
484
485 IF (cts_env%tensor_type == tensor_orthogonal) THEN
486 ! bring x to contravariant-covariant representation
487 CALL dbcsr_create(matrix_qp, &
488 template=cts_env%matrix_qp_template, &
489 matrix_type=dbcsr_type_no_symmetry)
490 CALL dbcsr_multiply("N", "N", 1.0_dp, cts_env%q_index_up, &
491 cts_env%matrix_x, 0.0_dp, matrix_qp, &
492 filter_eps=cts_env%eps_filter)
493 CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_qp, &
494 cts_env%p_index_down, 0.0_dp, &
495 cts_env%matrix_x, &
496 filter_eps=cts_env%eps_filter)
497 CALL dbcsr_release(matrix_qp)
498 END IF
499
500 END IF
501
502 ELSE
503 cpabort("illegal occ option")
504 END IF
505
506 CALL timestop(handle)
507
508 END SUBROUTINE ct_step_execute
509
510! **************************************************************************************************
511!> \brief computes oo, ov, vo, and vv blocks of the ks matrix
512!> \param ks ...
513!> \param p ...
514!> \param t ...
515!> \param v ...
516!> \param q_index_down ...
517!> \param p_index_up ...
518!> \param q_index_up ...
519!> \param pp ...
520!> \param qq ...
521!> \param qp ...
522!> \param pq ...
523!> \param tensor_type ...
524!> \param use_virt_orbs ...
525!> \param eps_filter ...
526!> \par History
527!> 2011.06 created [Rustam Z Khaliullin]
528!> \author Rustam Z Khaliullin
529! **************************************************************************************************
530 SUBROUTINE assemble_ks_qp_blocks(ks, p, t, v, q_index_down, &
531 p_index_up, q_index_up, pp, qq, qp, pq, tensor_type, use_virt_orbs, eps_filter)
532
533 TYPE(dbcsr_type), INTENT(IN) :: ks, p, t, v, q_index_down, p_index_up, &
534 q_index_up
535 TYPE(dbcsr_type), INTENT(OUT) :: pp, qq, qp, pq
536 INTEGER, INTENT(IN) :: tensor_type
537 LOGICAL, INTENT(IN) :: use_virt_orbs
538 REAL(kind=dp), INTENT(IN) :: eps_filter
539
540 CHARACTER(len=*), PARAMETER :: routinen = 'assemble_ks_qp_blocks'
541
542 INTEGER :: handle
543 LOGICAL :: library_fixed
544 TYPE(dbcsr_type) :: kst, ksv, no, on, oo, q_index_up_nosym, &
545 sp, spf, t_or, v_or
546
547 CALL timeset(routinen, handle)
548
549 IF (use_virt_orbs) THEN
550
551 ! orthogonalize the orbitals
552 CALL dbcsr_create(t_or, template=t)
553 CALL dbcsr_create(v_or, template=v)
554 CALL dbcsr_multiply("N", "N", 1.0_dp, t, p_index_up, &
555 0.0_dp, t_or, filter_eps=eps_filter)
556 CALL dbcsr_multiply("N", "N", 1.0_dp, v, q_index_up, &
557 0.0_dp, v_or, filter_eps=eps_filter)
558
559 ! KS.T
560 CALL dbcsr_create(kst, template=t)
561 CALL dbcsr_multiply("N", "N", 1.0_dp, ks, t_or, &
562 0.0_dp, kst, filter_eps=eps_filter)
563 ! pp=tr(T)*KS.T
564 CALL dbcsr_multiply("T", "N", 1.0_dp, t_or, kst, &
565 0.0_dp, pp, filter_eps=eps_filter)
566 ! qp=tr(V)*KS.T
567 CALL dbcsr_multiply("T", "N", 1.0_dp, v_or, kst, &
568 0.0_dp, qp, filter_eps=eps_filter)
569 CALL dbcsr_release(kst)
570
571 ! KS.V
572 CALL dbcsr_create(ksv, template=v)
573 CALL dbcsr_multiply("N", "N", 1.0_dp, ks, v_or, &
574 0.0_dp, ksv, filter_eps=eps_filter)
575 ! tr(T)*KS.V
576 CALL dbcsr_multiply("T", "N", 1.0_dp, t_or, ksv, &
577 0.0_dp, pq, filter_eps=eps_filter)
578 ! tr(V)*KS.V
579 CALL dbcsr_multiply("T", "N", 1.0_dp, v_or, ksv, &
580 0.0_dp, qq, filter_eps=eps_filter)
581 CALL dbcsr_release(ksv)
582
583 CALL dbcsr_release(t_or)
584 CALL dbcsr_release(v_or)
585
586 ELSE ! no virtuals, use projected AOs
587
588! THIS PROCEDURE HAS NOT BEEN UPDATED FOR CHOLESKY p/q_index_up/down
589 CALL dbcsr_create(sp, template=q_index_down, &
590 matrix_type=dbcsr_type_no_symmetry)
591 CALL dbcsr_create(spf, template=q_index_down, &
592 matrix_type=dbcsr_type_no_symmetry)
593
594 ! qp=KS*T
595 CALL dbcsr_multiply("N", "N", 1.0_dp, ks, t, 0.0_dp, qp, &
596 filter_eps=eps_filter)
597 ! pp=tr(T)*KS.T
598 CALL dbcsr_multiply("T", "N", 1.0_dp, t, qp, 0.0_dp, pp, &
599 filter_eps=eps_filter)
600 ! sp=-S_*P
601 CALL dbcsr_multiply("N", "N", -1.0_dp, q_index_down, p, 0.0_dp, sp, &
602 filter_eps=eps_filter)
603
604 ! sp=1/S^-S_.P
605 SELECT CASE (tensor_type)
606 CASE (tensor_up_down)
607 CALL dbcsr_add_on_diag(sp, 1.0_dp)
608 CASE (tensor_orthogonal)
609 CALL dbcsr_create(q_index_up_nosym, template=q_index_up, &
610 matrix_type=dbcsr_type_no_symmetry)
611 CALL dbcsr_desymmetrize(q_index_up, q_index_up_nosym)
612 CALL dbcsr_add(sp, q_index_up_nosym, 1.0_dp, 1.0_dp)
613 CALL dbcsr_release(q_index_up_nosym)
614 END SELECT
615
616 ! spf=(1/S^-S_.P)*KS
617 CALL dbcsr_multiply("N", "N", 1.0_dp, sp, ks, 0.0_dp, spf, &
618 filter_eps=eps_filter)
619
620 ! qp=spf*T
621 CALL dbcsr_multiply("N", "N", 1.0_dp, spf, t, 0.0_dp, qp, &
622 filter_eps=eps_filter)
623
624 SELECT CASE (tensor_type)
625 CASE (tensor_up_down)
626 ! pq=tr(qp)
627 CALL dbcsr_transposed(pq, qp, transpose_distribution=.false.)
628 CASE (tensor_orthogonal)
629 ! pq=sig^.tr(qp)
630 CALL dbcsr_multiply("N", "T", 1.0_dp, p_index_up, qp, 0.0_dp, pq, &
631 filter_eps=eps_filter)
632 library_fixed = .false.
633 IF (library_fixed) THEN
634 CALL dbcsr_transposed(qp, pq, transpose_distribution=.false.)
635 ELSE
636 CALL dbcsr_create(no, template=qp, &
637 matrix_type=dbcsr_type_no_symmetry)
638 CALL dbcsr_multiply("N", "N", 1.0_dp, qp, p_index_up, 0.0_dp, no, &
639 filter_eps=eps_filter)
640 CALL dbcsr_copy(qp, no)
641 CALL dbcsr_release(no)
642 END IF
643 END SELECT
644
645 ! qq=spf*tr(sp)
646 CALL dbcsr_multiply("N", "T", 1.0_dp, spf, sp, 0.0_dp, qq, &
647 filter_eps=eps_filter)
648
649 SELECT CASE (tensor_type)
650 CASE (tensor_up_down)
651
652 CALL dbcsr_create(oo, template=pp, &
653 matrix_type=dbcsr_type_no_symmetry)
654 CALL dbcsr_create(no, template=qp, &
655 matrix_type=dbcsr_type_no_symmetry)
656
657 ! first index up
658 CALL dbcsr_multiply("N", "N", 1.0_dp, q_index_up, qq, 0.0_dp, spf, &
659 filter_eps=eps_filter)
660 CALL dbcsr_copy(qq, spf)
661 CALL dbcsr_multiply("N", "N", 1.0_dp, q_index_up, qp, 0.0_dp, no, &
662 filter_eps=eps_filter)
663 CALL dbcsr_copy(qp, no)
664 CALL dbcsr_multiply("N", "N", 1.0_dp, p_index_up, pp, 0.0_dp, oo, &
665 filter_eps=eps_filter)
666 CALL dbcsr_copy(pp, oo)
667 CALL dbcsr_multiply("N", "N", 1.0_dp, p_index_up, pq, 0.0_dp, on, &
668 filter_eps=eps_filter)
669 CALL dbcsr_copy(pq, on)
670
671 CALL dbcsr_release(no)
672 CALL dbcsr_release(oo)
673
674 CASE (tensor_orthogonal)
675
676 CALL dbcsr_create(oo, template=pp, &
677 matrix_type=dbcsr_type_no_symmetry)
678
679 ! both indeces up in the pp block
680 CALL dbcsr_multiply("N", "N", 1.0_dp, p_index_up, pp, 0.0_dp, oo, &
681 filter_eps=eps_filter)
682 CALL dbcsr_multiply("N", "N", 1.0_dp, oo, p_index_up, 0.0_dp, pp, &
683 filter_eps=eps_filter)
684
685 CALL dbcsr_release(oo)
686
687 END SELECT
688
689 CALL dbcsr_release(sp)
690 CALL dbcsr_release(spf)
691
692 END IF
693
694 CALL timestop(handle)
695
696 END SUBROUTINE assemble_ks_qp_blocks
697
698! **************************************************************************************************
699!> \brief Solves the generalized Riccati or Sylvester eqation
700!> using the preconditioned conjugate gradient algorithm
701!> qp + qq.x.oo - vv.x.pp - vv.x.pq.x.oo = 0 [oo and vv are optional]
702!> qp + qq.x - x.pp - x.pq.x = 0
703!> \param pp ...
704!> \param qq ...
705!> \param qp ...
706!> \param pq ...
707!> \param oo ...
708!> \param vv ...
709!> \param x ...
710!> \param res ...
711!> \param neglect_quadratic_term ...
712!> \param conjugator ...
713!> \param max_iter ...
714!> \param eps_convergence ...
715!> \param eps_filter ...
716!> \param converged ...
717!> \par History
718!> 2011.06 created [Rustam Z Khaliullin]
719!> 2011.11 generalized [Rustam Z Khaliullin]
720!> \author Rustam Z Khaliullin
721! **************************************************************************************************
722 RECURSIVE SUBROUTINE solve_riccati_equation(pp, qq, qp, pq, oo, vv, x, res, &
723 neglect_quadratic_term, &
724 conjugator, max_iter, eps_convergence, eps_filter, &
725 converged)
726
727 TYPE(dbcsr_type), INTENT(IN) :: pp, qq
728 TYPE(dbcsr_type), INTENT(INOUT) :: qp
729 TYPE(dbcsr_type), INTENT(IN) :: pq
730 TYPE(dbcsr_type), INTENT(IN), OPTIONAL :: oo, vv
731 TYPE(dbcsr_type), INTENT(INOUT) :: x
732 TYPE(dbcsr_type), INTENT(OUT) :: res
733 LOGICAL, INTENT(IN) :: neglect_quadratic_term
734 INTEGER, INTENT(IN) :: conjugator, max_iter
735 REAL(kind=dp), INTENT(IN) :: eps_convergence, eps_filter
736 LOGICAL, INTENT(OUT) :: converged
737
738 CHARACTER(len=*), PARAMETER :: routinen = 'solve_riccati_equation'
739
740 INTEGER :: handle, istep, iteration, nsteps, &
741 unit_nr, update_prec_freq
742 LOGICAL :: prepare_to_exit, present_oo, present_vv, &
743 quadratic_term, restart_conjugator
744 REAL(kind=dp) :: best_norm, best_step_size, beta, c0, c1, &
745 c2, c3, denom, kappa, numer, &
746 obj_function, t1, t2, tau
747 REAL(kind=dp), DIMENSION(3) :: step_size
748 TYPE(cp_logger_type), POINTER :: logger
749 TYPE(dbcsr_type) :: aux1, aux2, grad, m, n, oo1, oo2, prec, &
750 res_trial, step, step_oo, vv_step
751
752!TYPE(dbcsr_type) :: qqqq, pppp, zero_pq, zero_qp
753
754 CALL timeset(routinen, handle)
755
756 logger => cp_get_default_logger()
757 IF (logger%para_env%is_source()) THEN
758 unit_nr = cp_logger_get_default_unit_nr(logger, local=.true.)
759 ELSE
760 unit_nr = -1
761 END IF
762
763 t1 = m_walltime()
764
765!IF (level.gt.5) THEN
766! CPErrorMessage(cp_failure_level,routineP,"recursion level is too high")
767! CPPrecondition(.FALSE.,cp_failure_level,routineP,failure)
768!ENDIF
769!IF (unit_nr>0) THEN
770! WRITE(unit_nr,*) &
771! "========== LEVEL ",level,"=========="
772!ENDIF
773!CALL dbcsr_print(qq)
774!CALL dbcsr_print(pp)
775!CALL dbcsr_print(qp)
776!!CALL dbcsr_print(pq)
777!IF (unit_nr>0) THEN
778! WRITE(unit_nr,*) &
779! "====== END LEVEL ",level,"=========="
780!ENDIF
781
782 quadratic_term = .NOT. neglect_quadratic_term
783 present_oo = PRESENT(oo)
784 present_vv = PRESENT(vv)
785
786 ! create aux1 matrix and init
787 CALL dbcsr_create(aux1, template=pp)
788 CALL dbcsr_copy(aux1, pp)
789 CALL dbcsr_scale(aux1, -1.0_dp)
790
791 ! create aux2 matrix and init
792 CALL dbcsr_create(aux2, template=qq)
793 CALL dbcsr_copy(aux2, qq)
794
795 ! create the gradient matrix and init
796 CALL dbcsr_create(grad, template=x)
797 CALL dbcsr_set(grad, 0.0_dp)
798
799 ! create a preconditioner
800 ! RZK-warning how to apply it to up_down tensor?
801 CALL dbcsr_create(prec, template=x)
802 !CALL create_preconditioner(prec,aux1,aux2,qp,res,tensor_type,eps_filter)
803 !CALL dbcsr_set(prec,1.0_dp)
804
805 ! create the step matrix and init
806 CALL dbcsr_create(step, template=x)
807 !CALL dbcsr_hadamard_product(prec,grad,step)
808 !CALL dbcsr_scale(step,-1.0_dp)
809
810 CALL dbcsr_create(n, template=x)
811 CALL dbcsr_create(m, template=x)
812 CALL dbcsr_create(oo1, template=pp)
813 CALL dbcsr_create(oo2, template=pp)
814 CALL dbcsr_create(res_trial, template=res)
815 CALL dbcsr_create(vv_step, template=res)
816 CALL dbcsr_create(step_oo, template=res)
817
818 ! start conjugate gradient iterations
819 iteration = 0
820 converged = .false.
821 prepare_to_exit = .false.
822 beta = 0.0_dp
823 best_step_size = 0.0_dp
824 best_norm = 1.0e+100_dp
825 !ecorr=0.0_dp
826 !change_ecorr=0.0_dp
827 restart_conjugator = .false.
828 update_prec_freq = 20
829 DO
830
831 ! (re)-compute the residuals
832 IF (iteration == 0) THEN
833 CALL dbcsr_copy(res, qp)
834 IF (present_oo) THEN
835 CALL dbcsr_multiply("N", "N", +1.0_dp, qq, x, 0.0_dp, res_trial, &
836 filter_eps=eps_filter)
837 CALL dbcsr_multiply("N", "N", +1.0_dp, res_trial, oo, 1.0_dp, res, &
838 filter_eps=eps_filter)
839 ELSE
840 CALL dbcsr_multiply("N", "N", +1.0_dp, qq, x, 1.0_dp, res, &
841 filter_eps=eps_filter)
842 END IF
843 IF (present_vv) THEN
844 CALL dbcsr_multiply("N", "N", -1.0_dp, x, pp, 0.0_dp, res_trial, &
845 filter_eps=eps_filter)
846 CALL dbcsr_multiply("N", "N", +1.0_dp, vv, res_trial, 1.0_dp, res, &
847 filter_eps=eps_filter)
848 ELSE
849 CALL dbcsr_multiply("N", "N", -1.0_dp, x, pp, 1.0_dp, res, &
850 filter_eps=eps_filter)
851 END IF
852 IF (quadratic_term) THEN
853 IF (present_oo) THEN
854 CALL dbcsr_multiply("N", "N", +1.0_dp, pq, x, 0.0_dp, oo1, &
855 filter_eps=eps_filter)
856 CALL dbcsr_multiply("N", "N", +1.0_dp, oo1, oo, 0.0_dp, oo2, &
857 filter_eps=eps_filter)
858 ELSE
859 CALL dbcsr_multiply("N", "N", +1.0_dp, pq, x, 0.0_dp, oo2, &
860 filter_eps=eps_filter)
861 END IF
862 IF (present_vv) THEN
863 CALL dbcsr_multiply("N", "N", -1.0_dp, x, oo2, 0.0_dp, res_trial, &
864 filter_eps=eps_filter)
865 CALL dbcsr_multiply("N", "N", +1.0_dp, vv, res_trial, 1.0_dp, res, &
866 filter_eps=eps_filter)
867 ELSE
868 CALL dbcsr_multiply("N", "N", -1.0_dp, x, oo2, 1.0_dp, res, &
869 filter_eps=eps_filter)
870 END IF
871 END IF
872 best_norm = dbcsr_maxabs(res)
873 ELSE
874 CALL dbcsr_add(res, m, 1.0_dp, best_step_size)
875 CALL dbcsr_add(res, n, 1.0_dp, -best_step_size*best_step_size)
876 CALL dbcsr_filter(res, eps_filter)
877 END IF
878
879 ! check convergence and other exit criteria
880 converged = (best_norm < eps_convergence)
881 IF (converged .OR. (iteration >= max_iter)) THEN
882 prepare_to_exit = .true.
883 END IF
884
885 IF (.NOT. prepare_to_exit) THEN
886
887 ! update aux1=-pp-pq.x.oo and aux2=qq-vv.x.pq
888 IF (quadratic_term) THEN
889 IF (iteration == 0) THEN
890 IF (present_oo) THEN
891 CALL dbcsr_multiply("N", "N", -1.0_dp, pq, x, 0.0_dp, oo1, &
892 filter_eps=eps_filter)
893 CALL dbcsr_multiply("N", "N", +1.0_dp, oo1, oo, 1.0_dp, aux1, &
894 filter_eps=eps_filter)
895 ELSE
896 CALL dbcsr_multiply("N", "N", -1.0_dp, pq, x, 1.0_dp, aux1, &
897 filter_eps=eps_filter)
898 END IF
899 IF (present_vv) THEN
900 CALL dbcsr_multiply("N", "N", -1.0_dp, vv, x, 0.0_dp, res_trial, &
901 filter_eps=eps_filter)
902 CALL dbcsr_multiply("N", "N", +1.0_dp, res_trial, pq, 1.0_dp, aux2, &
903 filter_eps=eps_filter)
904 ELSE
905 CALL dbcsr_multiply("N", "N", -1.0_dp, x, pq, 1.0_dp, aux2, &
906 filter_eps=eps_filter)
907 END IF
908 ELSE
909 IF (present_oo) THEN
910 CALL dbcsr_multiply("N", "N", -best_step_size, pq, step_oo, 1.0_dp, aux1, &
911 filter_eps=eps_filter)
912 ELSE
913 CALL dbcsr_multiply("N", "N", -best_step_size, pq, step, 1.0_dp, aux1, &
914 filter_eps=eps_filter)
915 END IF
916 IF (present_vv) THEN
917 CALL dbcsr_multiply("N", "N", -best_step_size, vv_step, pq, 1.0_dp, aux2, &
918 filter_eps=eps_filter)
919 ELSE
920 CALL dbcsr_multiply("N", "N", -best_step_size, step, pq, 1.0_dp, aux2, &
921 filter_eps=eps_filter)
922 END IF
923 END IF
924 END IF
925
926 ! recompute the gradient, do not update it yet
927 ! use m matrix as a temporary storage
928 ! grad=t(vv).res.t(aux1)+t(aux2).res.t(oo)
929 IF (present_vv) THEN
930 CALL dbcsr_multiply("N", "T", 1.0_dp, res, aux1, 0.0_dp, res_trial, &
931 filter_eps=eps_filter)
932 CALL dbcsr_multiply("T", "N", 1.0_dp, vv, res_trial, 0.0_dp, m, &
933 filter_eps=eps_filter)
934 ELSE
935 CALL dbcsr_multiply("N", "T", 1.0_dp, res, aux1, 0.0_dp, m, &
936 filter_eps=eps_filter)
937 END IF
938 IF (present_oo) THEN
939 CALL dbcsr_multiply("T", "N", 1.0_dp, aux1, res, 0.0_dp, res_trial, &
940 filter_eps=eps_filter)
941 CALL dbcsr_multiply("N", "T", 1.0_dp, res_trial, oo, 1.0_dp, m, &
942 filter_eps=eps_filter)
943 ELSE
944 CALL dbcsr_multiply("T", "N", 1.0_dp, aux2, res, 1.0_dp, m, &
945 filter_eps=eps_filter)
946 END IF
947
948 ! compute preconditioner
949 !IF (iteration.eq.0.OR.(mod(iteration,update_prec_freq).eq.0)) THEN
950 IF (iteration == 0) THEN
951 CALL create_preconditioner(prec, aux1, aux2, eps_filter)
952 !restart_conjugator=.TRUE.
953!CALL dbcsr_set(prec,1.0_dp)
954!CALL dbcsr_print(prec)
955 END IF
956
957 ! compute the conjugation coefficient - beta
958 IF ((iteration == 0) .OR. restart_conjugator) THEN
959 beta = 0.0_dp
960 ELSE
961 restart_conjugator = .false.
962 SELECT CASE (conjugator)
963 CASE (cg_hestenes_stiefel)
964 CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
965 CALL dbcsr_hadamard_product(prec, grad, n)
966 CALL dbcsr_dot(n, m, numer)
967 CALL dbcsr_dot(grad, step, denom)
968 beta = numer/denom
969 CASE (cg_fletcher_reeves)
970 CALL dbcsr_hadamard_product(prec, grad, n)
971 CALL dbcsr_dot(grad, n, denom)
972 CALL dbcsr_hadamard_product(prec, m, n)
973 CALL dbcsr_dot(m, n, numer)
974 beta = numer/denom
975 CASE (cg_polak_ribiere)
976 CALL dbcsr_hadamard_product(prec, grad, n)
977 CALL dbcsr_dot(grad, n, denom)
978 CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
979 CALL dbcsr_hadamard_product(prec, grad, n)
980 CALL dbcsr_dot(n, m, numer)
981 beta = numer/denom
982 CASE (cg_fletcher)
983 CALL dbcsr_hadamard_product(prec, m, n)
984 CALL dbcsr_dot(m, n, numer)
985 CALL dbcsr_dot(grad, step, denom)
986 beta = -1.0_dp*numer/denom
987 CASE (cg_liu_storey)
988 CALL dbcsr_dot(grad, step, denom)
989 CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
990 CALL dbcsr_hadamard_product(prec, grad, n)
991 CALL dbcsr_dot(n, m, numer)
992 beta = -1.0_dp*numer/denom
993 CASE (cg_dai_yuan)
994 CALL dbcsr_hadamard_product(prec, m, n)
995 CALL dbcsr_dot(m, n, numer)
996 CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
997 CALL dbcsr_dot(grad, step, denom)
998 beta = numer/denom
999 CASE (cg_hager_zhang)
1000 CALL dbcsr_add(grad, m, -1.0_dp, 1.0_dp)
1001 CALL dbcsr_dot(grad, step, denom)
1002 CALL dbcsr_hadamard_product(prec, grad, n)
1003 CALL dbcsr_dot(n, grad, numer)
1004 kappa = 2.0_dp*numer/denom
1005 CALL dbcsr_dot(n, m, numer)
1006 tau = numer/denom
1007 CALL dbcsr_dot(step, m, numer)
1008 beta = tau - kappa*numer/denom
1009 CASE (cg_zero)
1010 beta = 0.0_dp
1011 CASE DEFAULT
1012 cpabort("illegal conjugator")
1013 END SELECT
1014 END IF ! iteration.eq.0
1015
1016 ! move the current gradient to its storage
1017 CALL dbcsr_copy(grad, m)
1018
1019 ! precondition new gradient (use m as tmp storage)
1020 CALL dbcsr_hadamard_product(prec, grad, m)
1021 CALL dbcsr_filter(m, eps_filter)
1022
1023 ! recompute the step direction
1024 CALL dbcsr_add(step, m, beta, -1.0_dp)
1025 CALL dbcsr_filter(step, eps_filter)
1026
1027!! ALTERNATIVE METHOD TO OBTAIN THE STEP FROM THE GRADIENT
1028!CALL dbcsr_init(qqqq)
1029!CALL dbcsr_create(qqqq,template=qq)
1030!CALL dbcsr_init(pppp)
1031!CALL dbcsr_create(pppp,template=pp)
1032!CALL dbcsr_init(zero_pq)
1033!CALL dbcsr_create(zero_pq,template=pq)
1034!CALL dbcsr_init(zero_qp)
1035!CALL dbcsr_create(zero_qp,template=qp)
1036!CALL dbcsr_multiply("T","N",1.0_dp,aux2,aux2,0.0_dp,qqqq,&
1037! filter_eps=eps_filter)
1038!CALL dbcsr_multiply("N","T",-1.0_dp,aux1,aux1,0.0_dp,pppp,&
1039! filter_eps=eps_filter)
1040!CALL dbcsr_set(zero_qp,0.0_dp)
1041!CALL dbcsr_set(zero_pq,0.0_dp)
1042!CALL solve_riccati_equation(pppp,qqqq,grad,zero_pq,zero_qp,zero_qp,&
1043! .TRUE.,tensor_type,&
1044! conjugator,max_iter,eps_convergence,eps_filter,&
1045! converged,level+1)
1046!CALL dbcsr_release(qqqq)
1047!CALL dbcsr_release(pppp)
1048!CALL dbcsr_release(zero_qp)
1049!CALL dbcsr_release(zero_pq)
1050
1051 ! calculate the optimal step size
1052 ! m=step.aux1+aux2.step
1053 IF (present_vv) THEN
1054 CALL dbcsr_multiply("N", "N", 1.0_dp, vv, step, 0.0_dp, vv_step, &
1055 filter_eps=eps_filter)
1056 CALL dbcsr_multiply("N", "N", 1.0_dp, vv_step, aux1, 0.0_dp, m, &
1057 filter_eps=eps_filter)
1058 ELSE
1059 CALL dbcsr_multiply("N", "N", 1.0_dp, step, aux1, 0.0_dp, m, &
1060 filter_eps=eps_filter)
1061 END IF
1062 IF (present_oo) THEN
1063 CALL dbcsr_multiply("N", "N", 1.0_dp, step, oo, 0.0_dp, step_oo, &
1064 filter_eps=eps_filter)
1065 CALL dbcsr_multiply("N", "N", 1.0_dp, aux2, step_oo, 1.0_dp, m, &
1066 filter_eps=eps_filter)
1067 ELSE
1068 CALL dbcsr_multiply("N", "N", 1.0_dp, aux2, step, 1.0_dp, m, &
1069 filter_eps=eps_filter)
1070 END IF
1071
1072 IF (quadratic_term) THEN
1073 ! n=step.pq.step
1074 IF (present_oo) THEN
1075 CALL dbcsr_multiply("N", "N", 1.0_dp, pq, step, 0.0_dp, oo1, &
1076 filter_eps=eps_filter)
1077 CALL dbcsr_multiply("N", "N", 1.0_dp, oo1, oo, 0.0_dp, oo2, &
1078 filter_eps=eps_filter)
1079 ELSE
1080 CALL dbcsr_multiply("N", "N", 1.0_dp, pq, step, 0.0_dp, oo2, &
1081 filter_eps=eps_filter)
1082 END IF
1083 IF (present_vv) THEN
1084 CALL dbcsr_multiply("N", "N", 1.0_dp, step, oo2, 0.0_dp, res_trial, &
1085 filter_eps=eps_filter)
1086 CALL dbcsr_multiply("N", "N", 1.0_dp, vv, res_trial, 0.0_dp, n, &
1087 filter_eps=eps_filter)
1088 ELSE
1089 CALL dbcsr_multiply("N", "N", 1.0_dp, step, oo2, 0.0_dp, n, &
1090 filter_eps=eps_filter)
1091 END IF
1092
1093 ELSE
1094 CALL dbcsr_set(n, 0.0_dp)
1095 END IF
1096
1097 ! calculate coefficients of the cubic eq for alpha - step size
1098 c0 = 2.0_dp*(dbcsr_frobenius_norm(n))**2
1099
1100 CALL dbcsr_dot(m, n, c1)
1101 c1 = -3.0_dp*c1
1102
1103 CALL dbcsr_dot(res, n, c2)
1104 c2 = -2.0_dp*c2 + (dbcsr_frobenius_norm(m))**2
1105
1106 CALL dbcsr_dot(res, m, c3)
1107
1108 ! find step size
1109 CALL analytic_line_search(c0, c1, c2, c3, step_size, nsteps)
1110
1111 IF (nsteps == 0) THEN
1112 cpabort("no step sizes!")
1113 END IF
1114 ! if we have several possible step sizes
1115 ! choose one with the lowest objective function
1116 best_norm = 1.0e+100_dp
1117 best_step_size = 0.0_dp
1118 DO istep = 1, nsteps
1119 ! recompute the residues
1120 CALL dbcsr_copy(res_trial, res)
1121 CALL dbcsr_add(res_trial, m, 1.0_dp, step_size(istep))
1122 CALL dbcsr_add(res_trial, n, 1.0_dp, -step_size(istep)*step_size(istep))
1123 CALL dbcsr_filter(res_trial, eps_filter)
1124 ! RZK-warning objective function might be different in the case of
1125 ! tensor_up_down
1126 !obj_function=0.5_dp*(dbcsr_frobenius_norm(res_trial))**2
1127 obj_function = dbcsr_maxabs(res_trial)
1128 IF (obj_function < best_norm) THEN
1129 best_norm = obj_function
1130 best_step_size = step_size(istep)
1131 END IF
1132 END DO
1133
1134 END IF
1135
1136 ! update X along the line
1137 CALL dbcsr_add(x, step, 1.0_dp, best_step_size)
1138 CALL dbcsr_filter(x, eps_filter)
1139
1140 ! evaluate current energy correction
1141 !change_ecorr=ecorr
1142 !CALL dbcsr_dot(qp,x,ecorr,"T","N")
1143 !change_ecorr=ecorr-change_ecorr
1144
1145 ! check convergence and other exit criteria
1146 converged = (best_norm < eps_convergence)
1147 IF (converged .OR. (iteration >= max_iter)) THEN
1148 prepare_to_exit = .true.
1149 END IF
1150
1151 t2 = m_walltime()
1152
1153 IF (unit_nr > 0) THEN
1154 WRITE (unit_nr, '(T6,A,1X,I4,1X,E12.3,F8.3)') &
1155 "RICCATI iter ", iteration, best_norm, t2 - t1
1156 !WRITE(unit_nr,'(T6,A,1X,I4,1X,F15.9,F15.9,E12.3,F8.3)') &
1157 ! "RICCATI iter ",iteration,ecorr,change_ecorr,best_norm,t2-t1
1158 END IF
1159
1160 t1 = m_walltime()
1161
1162 iteration = iteration + 1
1163
1164 IF (prepare_to_exit) EXIT
1165
1166 END DO
1167
1168 CALL dbcsr_release(aux1)
1169 CALL dbcsr_release(aux2)
1170 CALL dbcsr_release(grad)
1171 CALL dbcsr_release(step)
1172 CALL dbcsr_release(n)
1173 CALL dbcsr_release(m)
1174 CALL dbcsr_release(oo1)
1175 CALL dbcsr_release(oo2)
1176 CALL dbcsr_release(res_trial)
1177 CALL dbcsr_release(vv_step)
1178 CALL dbcsr_release(step_oo)
1179
1180 CALL timestop(handle)
1181
1182 END SUBROUTINE solve_riccati_equation
1183
1184! **************************************************************************************************
1185!> \brief Computes a preconditioner from diagonal elements of ~f_oo, ~f_vv
1186!> The preconditioner is approximately equal to
1187!> prec_ai ~ (e_a - e_i)^(-2)
1188!> However, the real expression is more complex
1189!> \param prec ...
1190!> \param pp ...
1191!> \param qq ...
1192!> \param eps_filter ...
1193!> \par History
1194!> 2011.07 created [Rustam Z Khaliullin]
1195!> \author Rustam Z Khaliullin
1196! **************************************************************************************************
1197 SUBROUTINE create_preconditioner(prec, pp, qq, eps_filter)
1198
1199 TYPE(dbcsr_type), INTENT(OUT) :: prec
1200 TYPE(dbcsr_type), INTENT(IN) :: pp, qq
1201 REAL(kind=dp), INTENT(IN) :: eps_filter
1202
1203 CHARACTER(len=*), PARAMETER :: routinen = 'create_preconditioner'
1204
1205 INTEGER :: handle, p_nrows, q_nrows
1206 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: p_diagonal, q_diagonal
1207 REAL(kind=dp), DIMENSION(:, :), POINTER :: block
1208 TYPE(dbcsr_iterator_type) :: iter
1209 TYPE(dbcsr_type) :: pp_diag, qq_diag, t1, t2, tmp
1210
1211!LOGICAL, INTENT(IN) :: use_virt_orbs
1212
1213 CALL timeset(routinen, handle)
1214
1215! ! copy diagonal elements
1216! CALL dbcsr_get_info(pp,nfullrows_total=nrows)
1217! CALL dbcsr_init(pp_diag)
1218! CALL dbcsr_create(pp_diag,template=pp)
1219! ALLOCATE(diagonal(nrows))
1220! CALL dbcsr_get_diag(pp,diagonal)
1221! CALL dbcsr_add_on_diag(pp_diag,1.0_dp)
1222! CALL dbcsr_set_diag(pp_diag,diagonal)
1223! DEALLOCATE(diagonal)
1224!
1225 ! initialize a matrix to 1.0
1226 CALL dbcsr_create(tmp, template=prec)
1227 CALL dbcsr_reserve_diag_blocks(tmp)
1228 CALL dbcsr_iterator_start(iter, tmp)
1229 DO WHILE (dbcsr_iterator_blocks_left(iter))
1230 CALL dbcsr_iterator_next_block(iter, block=block)
1231 block(:, :) = 1.0_dp
1232 END DO
1233 CALL dbcsr_iterator_stop(iter)
1234
1235 ! copy diagonal elements of pp into cols of a matrix
1236 CALL dbcsr_get_info(pp, nfullrows_total=p_nrows)
1237 CALL dbcsr_create(pp_diag, template=pp)
1238 ALLOCATE (p_diagonal(p_nrows))
1239 CALL dbcsr_get_diag(pp, p_diagonal)
1240 CALL dbcsr_add_on_diag(pp_diag, 1.0_dp)
1241 CALL dbcsr_set_diag(pp_diag, p_diagonal)
1242 ! RZK-warning is it possible to use dbcsr_scale_by_vector?
1243 ! or even insert elements directly in the prev cycles
1244 CALL dbcsr_create(t2, template=prec)
1245 CALL dbcsr_multiply("N", "N", 1.0_dp, tmp, pp_diag, &
1246 0.0_dp, t2, filter_eps=eps_filter)
1247
1248 ! copy diagonal elements qq into rows of a matrix
1249 CALL dbcsr_get_info(qq, nfullrows_total=q_nrows)
1250 CALL dbcsr_create(qq_diag, template=qq)
1251 ALLOCATE (q_diagonal(q_nrows))
1252 CALL dbcsr_get_diag(qq, q_diagonal)
1253 CALL dbcsr_add_on_diag(qq_diag, 1.0_dp)
1254 CALL dbcsr_set_diag(qq_diag, q_diagonal)
1255 CALL dbcsr_set(tmp, 1.0_dp)
1256 CALL dbcsr_create(t1, template=prec)
1257 CALL dbcsr_multiply("N", "N", 1.0_dp, qq_diag, tmp, &
1258 0.0_dp, t1, filter_eps=eps_filter)
1259
1260 CALL dbcsr_hadamard_product(t1, t2, prec)
1261 CALL dbcsr_release(t1)
1262 CALL dbcsr_scale(prec, 2.0_dp)
1263
1264 ! Get the diagonal of tr(qq).qq
1265 CALL dbcsr_multiply("T", "N", 1.0_dp, qq, qq, &
1266 0.0_dp, qq_diag, retain_sparsity=.true., &
1267 filter_eps=eps_filter)
1268 CALL dbcsr_get_diag(qq_diag, q_diagonal)
1269 CALL dbcsr_set(qq_diag, 0.0_dp)
1270 CALL dbcsr_add_on_diag(qq_diag, 1.0_dp)
1271 CALL dbcsr_set_diag(qq_diag, q_diagonal)
1272 DEALLOCATE (q_diagonal)
1273 CALL dbcsr_set(tmp, 1.0_dp)
1274 CALL dbcsr_multiply("N", "N", 1.0_dp, qq_diag, tmp, &
1275 0.0_dp, t2, filter_eps=eps_filter)
1276 CALL dbcsr_release(qq_diag)
1277 CALL dbcsr_add(prec, t2, 1.0_dp, 1.0_dp)
1278
1279 ! Get the diagonal of pp.tr(pp)
1280 CALL dbcsr_multiply("N", "T", 1.0_dp, pp, pp, &
1281 0.0_dp, pp_diag, retain_sparsity=.true., &
1282 filter_eps=eps_filter)
1283 CALL dbcsr_get_diag(pp_diag, p_diagonal)
1284 CALL dbcsr_set(pp_diag, 0.0_dp)
1285 CALL dbcsr_add_on_diag(pp_diag, 1.0_dp)
1286 CALL dbcsr_set_diag(pp_diag, p_diagonal)
1287 DEALLOCATE (p_diagonal)
1288 CALL dbcsr_set(tmp, 1.0_dp)
1289 CALL dbcsr_multiply("N", "N", 1.0_dp, tmp, pp_diag, &
1290 0.0_dp, t2, filter_eps=eps_filter)
1291 CALL dbcsr_release(tmp)
1292 CALL dbcsr_release(pp_diag)
1293 CALL dbcsr_add(prec, t2, 1.0_dp, 1.0_dp)
1294
1295 ! now add the residual component
1296 !CALL dbcsr_hadamard_product(res,qp,t2)
1297 !CALL dbcsr_add(prec,t2,1.0_dp,-2.0_dp)
1298 CALL dbcsr_release(t2)
1299 CALL inverse_of_elements(prec)
1300 CALL dbcsr_filter(prec, eps_filter)
1301
1302 CALL timestop(handle)
1303
1304 END SUBROUTINE create_preconditioner
1305
1306! **************************************************************************************************
1307!> \brief Computes 1/x of the matrix elements.
1308!> \param matrix ...
1309!> \author Ole Schuett
1310! **************************************************************************************************
1311 SUBROUTINE inverse_of_elements(matrix)
1312 TYPE(dbcsr_type), INTENT(INOUT) :: matrix
1313
1314 CHARACTER(len=*), PARAMETER :: routinen = 'inverse_of_elements'
1315
1316 INTEGER :: handle
1317 REAL(kind=dp), DIMENSION(:, :), POINTER :: block
1318 TYPE(dbcsr_iterator_type) :: iter
1319
1320 CALL timeset(routinen, handle)
1321 CALL dbcsr_iterator_start(iter, matrix)
1322 DO WHILE (dbcsr_iterator_blocks_left(iter))
1323 CALL dbcsr_iterator_next_block(iter, block=block)
1324 block = 1.0_dp/block
1325 END DO
1326 CALL dbcsr_iterator_stop(iter)
1327 CALL timestop(handle)
1328
1329 END SUBROUTINE inverse_of_elements
1330
1331! **************************************************************************************************
1332!> \brief Finds real roots of a cubic equation
1333!> > a*x**3 + b*x**2 + c*x + d = 0
1334!> and returns only those roots for which the derivative is positive
1335!>
1336!> Step 0: Check the true order of the equation. Cubic, quadratic, linear?
1337!> Step 1: Calculate p and q
1338!> p = ( 3*c/a - (b/a)**2 ) / 3
1339!> q = ( 2*(b/a)**3 - 9*b*c/a/a + 27*d/a ) / 27
1340!> Step 2: Calculate discriminant D
1341!> D = (p/3)**3 + (q/2)**2
1342!> Step 3: Depending on the sign of D, we follow different strategy.
1343!> If D<0, three distinct real roots.
1344!> If D=0, three real roots of which at least two are equal.
1345!> If D>0, one real and two complex roots.
1346!> Step 3a: For D>0 and D=0,
1347!> Calculate u and v
1348!> u = cubic_root(-q/2 + sqrt(D))
1349!> v = cubic_root(-q/2 - sqrt(D))
1350!> Find the three transformed roots
1351!> y1 = u + v
1352!> y2 = -(u+v)/2 + i (u-v)*sqrt(3)/2
1353!> y3 = -(u+v)/2 - i (u-v)*sqrt(3)/2
1354!> Step 3b Alternately, for D<0, a trigonometric formulation is more convenient
1355!> y1 = 2 * sqrt(|p|/3) * cos(phi/3)
1356!> y2 = -2 * sqrt(|p|/3) * cos((phi+pi)/3)
1357!> y3 = -2 * sqrt(|p|/3) * cos((phi-pi)/3)
1358!> where phi = acos(-q/2/sqrt(|p|**3/27))
1359!> pi = 3.141592654...
1360!> Step 4 Find the real roots
1361!> x = y - b/a/3
1362!> Step 5 Check the derivative and return only those real roots
1363!> for which the derivative is positive
1364!>
1365!> \param a ...
1366!> \param b ...
1367!> \param c ...
1368!> \param d ...
1369!> \param minima ...
1370!> \param nmins ...
1371!> \par History
1372!> 2011.06 created [Rustam Z Khaliullin]
1373!> \author Rustam Z Khaliullin
1374! **************************************************************************************************
1375 SUBROUTINE analytic_line_search(a, b, c, d, minima, nmins)
1376
1377 REAL(kind=dp), INTENT(IN) :: a, b, c, d
1378 REAL(kind=dp), DIMENSION(3), INTENT(OUT) :: minima
1379 INTEGER, INTENT(OUT) :: nmins
1380
1381 INTEGER :: i, nroots
1382 REAL(kind=dp) :: dd, der, p, phi, q, temp1, temp2, u, v, &
1383 y1, y2, y2i, y2r, y3
1384 REAL(kind=dp), DIMENSION(3) :: x
1385
1386! CALL timeset(routineN,handle)
1387
1388 ! Step 0: Check coefficients and find the true order of the eq
1389 IF (a == 0.0_dp) THEN
1390 IF (b == 0.0_dp) THEN
1391 IF (c == 0.0_dp) THEN
1392 ! Non-equation, no valid solutions
1393 nroots = 0
1394 ELSE
1395 ! Linear equation with one root.
1396 nroots = 1
1397 x(1) = -d/c
1398 END IF
1399 ELSE
1400 ! Quadratic equation with max two roots.
1401 dd = c*c - 4.0_dp*b*d
1402 IF (dd > 0.0_dp) THEN
1403 nroots = 2
1404 x(1) = (-c + sqrt(dd))/2.0_dp/b
1405 x(2) = (-c - sqrt(dd))/2.0_dp/b
1406 ELSE IF (dd < 0.0_dp) THEN
1407 nroots = 0
1408 ELSE
1409 nroots = 1
1410 x(1) = -c/2.0_dp/b
1411 END IF
1412 END IF
1413 ELSE
1414 ! Cubic equation with max three roots
1415 ! Calculate p and q
1416 p = c/a - b*b/a/a/3.0_dp
1417 q = (2.0_dp*b*b*b/a/a/a - 9.0_dp*b*c/a/a + 27.0_dp*d/a)/27.0_dp
1418
1419 ! Calculate DD
1420 dd = p*p*p/27.0_dp + q*q/4.0_dp
1421
1422 IF (dd < 0.0_dp) THEN
1423 ! three real unequal roots -- use the trigonometric formulation
1424 phi = acos(-q/2.0_dp/sqrt(abs(p*p*p)/27.0_dp))
1425 temp1 = 2.0_dp*sqrt(abs(p)/3.0_dp)
1426 y1 = temp1*cos(phi/3.0_dp)
1427 y2 = -temp1*cos((phi + pi)/3.0_dp)
1428 y3 = -temp1*cos((phi - pi)/3.0_dp)
1429 ELSE
1430 ! 1 real & 2 conjugate complex roots OR 3 real roots (some are equal)
1431 temp1 = -q/2.0_dp + sqrt(dd)
1432 temp2 = -q/2.0_dp - sqrt(dd)
1433 u = abs(temp1)**(1.0_dp/3.0_dp)
1434 v = abs(temp2)**(1.0_dp/3.0_dp)
1435 IF (temp1 < 0.0_dp) u = -u
1436 IF (temp2 < 0.0_dp) v = -v
1437 y1 = u + v
1438 y2r = -(u + v)/2.0_dp
1439 y2i = (u - v)*sqrt(3.0_dp)/2.0_dp
1440 END IF
1441
1442 ! Final transformation
1443 temp1 = b/a/3.0_dp
1444 y1 = y1 - temp1
1445 y2 = y2 - temp1
1446 y3 = y3 - temp1
1447 y2r = y2r - temp1
1448
1449 ! Assign answers
1450 IF (dd < 0.0_dp) THEN
1451 nroots = 3
1452 x(1) = y1
1453 x(2) = y2
1454 x(3) = y3
1455 ELSE IF (dd == 0.0_dp) THEN
1456 nroots = 2
1457 x(1) = y1
1458 x(2) = y2r
1459 !x(3) = cmplx(y2r, 0.)
1460 ELSE
1461 nroots = 1
1462 x(1) = y1
1463 !x(2) = cmplx(y2r, y2i)
1464 !x(3) = cmplx(y2r,-y2i)
1465 END IF
1466
1467 END IF
1468
1469!write(*,'(i2,a)') nroots, ' real root(s)'
1470 nmins = 0
1471 DO i = 1, nroots
1472 ! maximum or minimum? use the derivative
1473 ! 3*a*x**2+2*b*x+c
1474 der = 3.0_dp*a*x(i)*x(i) + 2.0_dp*b*x(i) + c
1475 IF (der > 0.0_dp) THEN
1476 nmins = nmins + 1
1477 minima(nmins) = x(i)
1478!write(*,'(a,i2,a,f10.5)') 'Minimum ', i, ', value: ', x(i)
1479 END IF
1480 END DO
1481
1482! CALL timestop(handle)
1483
1484 END SUBROUTINE analytic_line_search
1485
1486! **************************************************************************************************
1487!> \brief Diagonalizes diagonal blocks of a symmetric dbcsr matrix
1488!> and returs its eigenvectors
1489!> \param matrix ...
1490!> \param c ...
1491!> \param e ...
1492!> \par History
1493!> 2011.07 created [Rustam Z Khaliullin]
1494!> \author Rustam Z Khaliullin
1495! **************************************************************************************************
1496 SUBROUTINE diagonalize_diagonal_blocks(matrix, c, e)
1497
1498 TYPE(dbcsr_type), INTENT(IN) :: matrix
1499 TYPE(dbcsr_type), INTENT(OUT) :: c
1500 TYPE(dbcsr_type), INTENT(OUT), OPTIONAL :: e
1501
1502 CHARACTER(len=*), PARAMETER :: routinen = 'diagonalize_diagonal_blocks'
1503
1504 INTEGER :: handle, iblock_col, iblock_row, &
1505 iblock_size, info, lwork, orbital
1506 LOGICAL :: block_needed, do_eigenvalues
1507 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: eigenvalues, work
1508 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :) :: data_copy, new_block
1509 REAL(kind=dp), DIMENSION(:, :), POINTER :: data_p
1510 TYPE(dbcsr_iterator_type) :: iter
1511
1512 CALL timeset(routinen, handle)
1513
1514 IF (PRESENT(e)) THEN
1515 do_eigenvalues = .true.
1516 ELSE
1517 do_eigenvalues = .false.
1518 END IF
1519
1520 ! create a matrix for eigenvectors
1521 CALL dbcsr_work_create(c, work_mutable=.true.)
1522 IF (do_eigenvalues) THEN
1523 CALL dbcsr_work_create(e, work_mutable=.true.)
1524 END IF
1525
1526 CALL dbcsr_iterator_readonly_start(iter, matrix)
1527
1528 DO WHILE (dbcsr_iterator_blocks_left(iter))
1529
1530 CALL dbcsr_iterator_next_block(iter, iblock_row, iblock_col, data_p, row_size=iblock_size)
1531
1532 block_needed = .false.
1533 IF (iblock_row == iblock_col) block_needed = .true.
1534
1535 IF (block_needed) THEN
1536
1537 ! Prepare data
1538 ALLOCATE (eigenvalues(iblock_size))
1539 ALLOCATE (data_copy(iblock_size, iblock_size))
1540 data_copy(:, :) = data_p(:, :)
1541
1542 ! Query the optimal workspace for dsyev
1543 lwork = -1
1544 ALLOCATE (work(max(1, lwork)))
1545 CALL dsyev('V', 'L', iblock_size, data_copy, iblock_size, eigenvalues, work, lwork, info)
1546 lwork = int(work(1))
1547 DEALLOCATE (work)
1548
1549 ! Allocate the workspace and solve the eigenproblem
1550 ALLOCATE (work(max(1, lwork)))
1551 CALL dsyev('V', 'L', iblock_size, data_copy, iblock_size, eigenvalues, work, lwork, info)
1552 IF (info /= 0) cpabort("DSYEV failed")
1553
1554 ! copy eigenvectors into a cp_dbcsr matrix
1555 CALL dbcsr_put_block(c, iblock_row, iblock_col, block=data_copy)
1556
1557 ! if requested copy eigenvalues into a cp_dbcsr matrix
1558 IF (do_eigenvalues) THEN
1559 ALLOCATE (new_block(iblock_size, iblock_size))
1560 new_block(:, :) = 0.0_dp
1561 DO orbital = 1, iblock_size
1562 new_block(orbital, orbital) = eigenvalues(orbital)
1563 END DO
1564 CALL dbcsr_put_block(e, iblock_row, iblock_col, new_block)
1565 DEALLOCATE (new_block)
1566 END IF
1567
1568 DEALLOCATE (work)
1569 DEALLOCATE (data_copy)
1570 DEALLOCATE (eigenvalues)
1571
1572 END IF
1573
1574 END DO
1575
1576 CALL dbcsr_iterator_stop(iter)
1577
1578 CALL dbcsr_finalize(c)
1579 IF (do_eigenvalues) CALL dbcsr_finalize(e)
1580
1581 CALL timestop(handle)
1582
1583 END SUBROUTINE diagonalize_diagonal_blocks
1584
1585! **************************************************************************************************
1586!> \brief Transforms a matrix M_out = tr(U1) * M_in * U2
1587!> \param matrix ...
1588!> \param u1 ...
1589!> \param u2 ...
1590!> \param eps_filter ...
1591!> \par History
1592!> 2011.10 created [Rustam Z Khaliullin]
1593!> \author Rustam Z Khaliullin
1594! **************************************************************************************************
1595 SUBROUTINE matrix_forward_transform(matrix, u1, u2, eps_filter)
1596
1597 TYPE(dbcsr_type), INTENT(INOUT) :: matrix
1598 TYPE(dbcsr_type), INTENT(IN) :: u1, u2
1599 REAL(kind=dp), INTENT(IN) :: eps_filter
1600
1601 CHARACTER(len=*), PARAMETER :: routinen = 'matrix_forward_transform'
1602
1603 INTEGER :: handle
1604 TYPE(dbcsr_type) :: tmp
1605
1606 CALL timeset(routinen, handle)
1607
1608 CALL dbcsr_create(tmp, template=matrix, &
1609 matrix_type=dbcsr_type_no_symmetry)
1610 CALL dbcsr_multiply("N", "N", 1.0_dp, matrix, u2, 0.0_dp, tmp, &
1611 filter_eps=eps_filter)
1612 CALL dbcsr_multiply("T", "N", 1.0_dp, u1, tmp, 0.0_dp, matrix, &
1613 filter_eps=eps_filter)
1614 CALL dbcsr_release(tmp)
1615
1616 CALL timestop(handle)
1617
1618 END SUBROUTINE matrix_forward_transform
1619
1620! **************************************************************************************************
1621!> \brief Transforms a matrix M_out = U1 * M_in * tr(U2)
1622!> \param matrix ...
1623!> \param u1 ...
1624!> \param u2 ...
1625!> \param eps_filter ...
1626!> \par History
1627!> 2011.10 created [Rustam Z Khaliullin]
1628!> \author Rustam Z Khaliullin
1629! **************************************************************************************************
1630 SUBROUTINE matrix_backward_transform(matrix, u1, u2, eps_filter)
1631
1632 TYPE(dbcsr_type), INTENT(INOUT) :: matrix
1633 TYPE(dbcsr_type), INTENT(IN) :: u1, u2
1634 REAL(kind=dp), INTENT(IN) :: eps_filter
1635
1636 CHARACTER(len=*), PARAMETER :: routinen = 'matrix_backward_transform'
1637
1638 INTEGER :: handle
1639 TYPE(dbcsr_type) :: tmp
1640
1641 CALL timeset(routinen, handle)
1642
1643 CALL dbcsr_create(tmp, template=matrix, &
1644 matrix_type=dbcsr_type_no_symmetry)
1645 CALL dbcsr_multiply("N", "T", 1.0_dp, matrix, u2, 0.0_dp, tmp, &
1646 filter_eps=eps_filter)
1647 CALL dbcsr_multiply("N", "N", 1.0_dp, u1, tmp, 0.0_dp, matrix, &
1648 filter_eps=eps_filter)
1649 CALL dbcsr_release(tmp)
1650
1651 CALL timestop(handle)
1652
1653 END SUBROUTINE matrix_backward_transform
1654
1655!! **************************************************************************************************
1656!!> \brief Transforms to a representation in which diagonal blocks
1657!!> of qq and pp matrices are diagonal. This can improve convergence
1658!!> of PCG
1659!!> \par History
1660!!> 2011.07 created [Rustam Z Khaliullin]
1661!!> \author Rustam Z Khaliullin
1662!! **************************************************************************************************
1663! SUBROUTINE transform_matrices_to_blk_diag(matrix_pp,matrix_qq,matrix_qp,&
1664! matrix_pq,eps_filter)
1665!
1666! TYPE(dbcsr_type), INTENT(INOUT) :: matrix_pp, matrix_qq,&
1667! matrix_qp, matrix_pq
1668! REAL(KIND=dp), INTENT(IN) :: eps_filter
1669!
1670! CHARACTER(len=*), PARAMETER :: routineN = 'transform_matrices_to_blk_diag',&
1671! routineP = moduleN//':'//routineN
1672!
1673! TYPE(dbcsr_type) :: tmp_pp, tmp_qq,&
1674! tmp_qp, tmp_pq,&
1675! blk, blk2
1676! INTEGER :: handle
1677!
1678! CALL timeset(routineN,handle)
1679!
1680! ! find a better basis by diagonalizing diagonal blocks
1681! ! first pp
1682! CALL dbcsr_init(blk)
1683! CALL dbcsr_create(blk,template=matrix_pp)
1684! CALL diagonalize_diagonal_blocks(matrix_pp,blk)
1685!
1686! ! convert matrices to the new basis
1687! CALL dbcsr_init(tmp_pp)
1688! CALL dbcsr_create(tmp_pp,template=matrix_pp)
1689! CALL dbcsr_multiply("N","N",1.0_dp,matrix_pp,blk,0.0_dp,tmp_pp,&
1690! filter_eps=eps_filter)
1691! CALL dbcsr_multiply("T","N",1.0_dp,blk,tmp_pp,0.0_dp,matrix_pp,&
1692! filter_eps=eps_filter)
1693! CALL dbcsr_release(tmp_pp)
1694!
1695! ! now qq
1696! CALL dbcsr_init(blk2)
1697! CALL dbcsr_create(blk2,template=matrix_qq)
1698! CALL diagonalize_diagonal_blocks(matrix_qq,blk2)
1699!
1700! CALL dbcsr_init(tmp_qq)
1701! CALL dbcsr_create(tmp_qq,template=matrix_qq)
1702! CALL dbcsr_multiply("N","N",1.0_dp,matrix_qq,blk2,0.0_dp,tmp_qq,&
1703! filter_eps=eps_filter)
1704! CALL dbcsr_multiply("T","N",1.0_dp,blk2,tmp_qq,0.0_dp,matrix_qq,&
1705! filter_eps=eps_filter)
1706! CALL dbcsr_release(tmp_qq)
1707!
1708! ! transform pq
1709! CALL dbcsr_init(tmp_pq)
1710! CALL dbcsr_create(tmp_pq,template=matrix_pq)
1711! CALL dbcsr_multiply("T","N",1.0_dp,blk,matrix_pq,0.0_dp,tmp_pq,&
1712! filter_eps=eps_filter)
1713! CALL dbcsr_multiply("N","N",1.0_dp,tmp_pq,blk2,0.0_dp,matrix_pq,&
1714! filter_eps=eps_filter)
1715! CALL dbcsr_release(tmp_pq)
1716!
1717! ! transform qp
1718! CALL dbcsr_init(tmp_qp)
1719! CALL dbcsr_create(tmp_qp,template=matrix_qp)
1720! CALL dbcsr_multiply("N","N",1.0_dp,matrix_qp,blk,0.0_dp,tmp_qp,&
1721! filter_eps=eps_filter)
1722! CALL dbcsr_multiply("T","N",1.0_dp,blk2,tmp_qp,0.0_dp,matrix_qp,&
1723! filter_eps=eps_filter)
1724! CALL dbcsr_release(tmp_qp)
1725!
1726! CALL dbcsr_release(blk2)
1727! CALL dbcsr_release(blk)
1728!
1729! CALL timestop(handle)
1730!
1731! END SUBROUTINE transform_matrices_to_blk_diag
1732
1733! **************************************************************************************************
1734!> \brief computes oo, ov, vo, and vv blocks of the ks matrix
1735!> \par History
1736!> 2011.06 created [Rustam Z Khaliullin]
1737!> \author Rustam Z Khaliullin
1738! **************************************************************************************************
1739! SUBROUTINE ct_step_env_execute(env)
1740!
1741! TYPE(ct_step_env_type) :: env
1742!
1743! CHARACTER(len=*), PARAMETER :: routineN = 'ct_step_env_execute', &
1744! routineP = moduleN//':'//routineN
1745!
1746! INTEGER :: handle
1747!
1748! CALL timeset(routineN,handle)
1749!
1750!
1751! CALL timestop(handle)
1752!
1753! END SUBROUTINE ct_step_env_execute
1754
1755END MODULE ct_methods
1756
cp_dbcsr_api::dbcsr_create
Definition cp_dbcsr_api.F:194
cp_dbcsr_api
Definition cp_dbcsr_api.F:8
cp_dbcsr_api::dbcsr_transposed
subroutine, public dbcsr_transposed(transposed, normal, shallow_data_copy, transpose_distribution, use_distribution)
...
Definition cp_dbcsr_api.F:1242
cp_dbcsr_api::dbcsr_scale
subroutine, public dbcsr_scale(matrix, alpha_scalar)
...
Definition cp_dbcsr_api.F:1188
cp_dbcsr_api::dbcsr_iterator_blocks_left
logical function, public dbcsr_iterator_blocks_left(iterator)
...
Definition cp_dbcsr_api.F:944
cp_dbcsr_api::dbcsr_iterator_stop
subroutine, public dbcsr_iterator_stop(iterator)
...
Definition cp_dbcsr_api.F:1050
cp_dbcsr_api::dbcsr_desymmetrize
subroutine, public dbcsr_desymmetrize(matrix_a, matrix_b)
...
Definition cp_dbcsr_api.F:525
cp_dbcsr_api::dbcsr_copy
subroutine, public dbcsr_copy(matrix_b, matrix_a, name, keep_sparsity, keep_imaginary)
...
Definition cp_dbcsr_api.F:371
cp_dbcsr_api::dbcsr_multiply
subroutine, public dbcsr_multiply(transa, transb, alpha, matrix_a, matrix_b, beta, matrix_c, first_row, last_row, first_column, last_column, first_k, last_k, retain_sparsity, filter_eps, flop)
...
Definition cp_dbcsr_api.F:1096
cp_dbcsr_api::dbcsr_get_info
subroutine, public dbcsr_get_info(matrix, nblkrows_total, nblkcols_total, nfullrows_total, nfullcols_total, nblkrows_local, nblkcols_local, nfullrows_local, nfullcols_local, my_prow, my_pcol, local_rows, local_cols, proc_row_dist, proc_col_dist, row_blk_size, col_blk_size, row_blk_offset, col_blk_offset, distribution, name, matrix_type, group)
...
Definition cp_dbcsr_api.F:808
cp_dbcsr_api::dbcsr_work_create
subroutine, public dbcsr_work_create(matrix, nblks_guess, sizedata_guess, n, work_mutable)
...
Definition cp_dbcsr_api.F:1307
cp_dbcsr_api::dbcsr_iterator_next_block
subroutine, public dbcsr_iterator_next_block(iterator, row, column, block, block_number_argument_has_been_removed, row_size, col_size, row_offset, col_offset, transposed)
...
Definition cp_dbcsr_api.F:971
cp_dbcsr_api::dbcsr_filter
subroutine, public dbcsr_filter(matrix, eps)
...
Definition cp_dbcsr_api.F:658
cp_dbcsr_api::dbcsr_finalize
subroutine, public dbcsr_finalize(matrix)
...
Definition cp_dbcsr_api.F:673
cp_dbcsr_api::dbcsr_iterator_start
subroutine, public dbcsr_iterator_start(iterator, matrix, shared, dynamic, dynamic_byrows)
...
Definition cp_dbcsr_api.F:1012
cp_dbcsr_api::dbcsr_set
subroutine, public dbcsr_set(matrix, alpha)
...
Definition cp_dbcsr_api.F:1204
cp_dbcsr_api::dbcsr_release
subroutine, public dbcsr_release(matrix)
...
Definition cp_dbcsr_api.F:1142
cp_dbcsr_api::dbcsr_iterator_readonly_start
subroutine, public dbcsr_iterator_readonly_start(iterator, matrix, shared, dynamic, dynamic_byrows)
Like dbcsr_iterator_start() but with matrix being INTENT(IN). When invoking this routine,...
Definition cp_dbcsr_api.F:1033
cp_dbcsr_api::dbcsr_put_block
subroutine, public dbcsr_put_block(matrix, row, col, block, summation)
...
Definition cp_dbcsr_api.F:1125
cp_dbcsr_api::dbcsr_add
subroutine, public dbcsr_add(matrix_a, matrix_b, alpha_scalar, beta_scalar)
...
Definition cp_dbcsr_api.F:254
cp_dbcsr_cholesky
Interface to (sca)lapack for the Cholesky based procedures.
Definition cp_dbcsr_cholesky.F:17
cp_dbcsr_cholesky::cp_dbcsr_cholesky_decompose
subroutine, public cp_dbcsr_cholesky_decompose(matrix, n, para_env, blacs_env)
used to replace a symmetric positive def. matrix M with its cholesky decomposition U: M = U^T * U,...
Definition cp_dbcsr_cholesky.F:61
cp_dbcsr_cholesky::cp_dbcsr_cholesky_invert
subroutine, public cp_dbcsr_cholesky_invert(matrix, n, para_env, blacs_env, uplo_to_full)
used to replace the cholesky decomposition by the inverse
Definition cp_dbcsr_cholesky.F:114
cp_dbcsr_contrib
Definition cp_dbcsr_contrib.F:8
cp_dbcsr_contrib::dbcsr_set_diag
subroutine, public dbcsr_set_diag(matrix, diag)
Copies the diagonal elements from the given array into the given matrix.
Definition cp_dbcsr_contrib.F:585
cp_dbcsr_contrib::dbcsr_get_diag
subroutine, public dbcsr_get_diag(matrix, diag)
Copies the diagonal elements from the given matrix into the given array.
Definition cp_dbcsr_contrib.F:544
cp_dbcsr_contrib::dbcsr_add_on_diag
subroutine, public dbcsr_add_on_diag(matrix, alpha)
Adds the given scalar to the diagonal of the matrix. Reserves any missing diagonal blocks.
Definition cp_dbcsr_contrib.F:331
cp_dbcsr_contrib::dbcsr_maxabs
real(dp) function, public dbcsr_maxabs(matrix)
Compute the maxabs norm of a dbcsr matrix.
Definition cp_dbcsr_contrib.F:94
cp_dbcsr_contrib::dbcsr_frobenius_norm
real(dp) function, public dbcsr_frobenius_norm(matrix)
Compute the frobenius norm of a dbcsr matrix.
Definition cp_dbcsr_contrib.F:127
cp_dbcsr_contrib::dbcsr_dot
subroutine, public dbcsr_dot(matrix_a, matrix_b, trace)
Computes the dot product of two matrices, also known as the trace of their matrix product.
Definition cp_dbcsr_contrib.F:367
cp_dbcsr_contrib::dbcsr_hadamard_product
subroutine, public dbcsr_hadamard_product(matrix_a, matrix_b, matrix_c)
Hadamard product: C = A . B (C needs to be different from A and B)
Definition cp_dbcsr_contrib.F:53
cp_dbcsr_contrib::dbcsr_reserve_diag_blocks
subroutine, public dbcsr_reserve_diag_blocks(matrix)
Reserves all diagonal blocks.
Definition cp_dbcsr_contrib.F:255
cp_dbcsr_diag
Interface to (sca)lapack for the Cholesky based procedures.
Definition cp_dbcsr_diag.F:17
cp_dbcsr_diag::cp_dbcsr_syevd
subroutine, public cp_dbcsr_syevd(matrix, eigenvectors, eigenvalues, para_env, blacs_env)
...
Definition cp_dbcsr_diag.F:67
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:576
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
ct_methods
Cayley transformation methods.
Definition ct_methods.F:14
ct_methods::analytic_line_search
subroutine, public analytic_line_search(a, b, c, d, minima, nmins)
Finds real roots of a cubic equation ‍ a*x**3 + b*x**2 + c*x + d = 0 and returns only those roots for...
Definition ct_methods.F:1376
ct_methods::diagonalize_diagonal_blocks
subroutine, public diagonalize_diagonal_blocks(matrix, c, e)
Diagonalizes diagonal blocks of a symmetric dbcsr matrix and returs its eigenvectors.
Definition ct_methods.F:1497
ct_methods::ct_step_execute
subroutine, public ct_step_execute(cts_env)
Performs Cayley transformation.
Definition ct_methods.F:64
ct_types
Types for all cayley transformation methods.
Definition ct_types.F:14
input_constants
collects all constants needed in input so that they can be used without circular dependencies
Definition input_constants.F:18
input_constants::cg_hestenes_stiefel
integer, parameter, public cg_hestenes_stiefel
Definition input_constants.F:1065
input_constants::cg_fletcher
integer, parameter, public cg_fletcher
Definition input_constants.F:1065
input_constants::cg_fletcher_reeves
integer, parameter, public cg_fletcher_reeves
Definition input_constants.F:1065
input_constants::tensor_up_down
integer, parameter, public tensor_up_down
Definition input_constants.F:1090
input_constants::tensor_orthogonal
integer, parameter, public tensor_orthogonal
Definition input_constants.F:1090
input_constants::cg_dai_yuan
integer, parameter, public cg_dai_yuan
Definition input_constants.F:1065
input_constants::cg_liu_storey
integer, parameter, public cg_liu_storey
Definition input_constants.F:1065
input_constants::cg_hager_zhang
integer, parameter, public cg_hager_zhang
Definition input_constants.F:1065
input_constants::cg_zero
integer, parameter, public cg_zero
Definition input_constants.F:1065
input_constants::cg_polak_ribiere
integer, parameter, public cg_polak_ribiere
Definition input_constants.F:1065
iterate_matrix
Routines useful for iterative matrix calculations.
Definition iterate_matrix.F:13
iterate_matrix::matrix_sqrt_newton_schulz
subroutine, public matrix_sqrt_newton_schulz(matrix_sqrt, matrix_sqrt_inv, matrix, threshold, order, eps_lanczos, max_iter_lanczos, symmetrize, converged, iounit)
compute the sqrt of a matrix via the sign function and the corresponding Newton-Schulz iterations the...
Definition iterate_matrix.F:1627
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
kinds::sp
integer, parameter, public sp
Definition kinds.F:33
machine
Machine interface based on Fortran 2003 and POSIX.
Definition machine.F:17
machine::m_walltime
real(kind=dp) function, public m_walltime()
returns time from a real-time clock, protected against rolling early/easily
Definition machine.F:141
mathconstants
Definition of mathematical constants and functions.
Definition mathconstants.F:16
mathconstants::pi
real(kind=dp), parameter, public pi
Definition mathconstants.F:110
cp_dbcsr_api::dbcsr_iterator_type
Definition cp_dbcsr_api.F:188
cp_dbcsr_api::dbcsr_type
Definition cp_dbcsr_api.F:176
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
ct_types::ct_step_env_type
Definition ct_types.F:37
orbital
Orbital angular momentum.
Definition grid_common.h:133