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