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 Basic linear algebra operations for complex full matrices.
10 : !> \note
11 : !> - not all functionality implemented
12 : !> \par History
13 : !> Nearly literal copy of Fawzi's routines
14 : !> \author Joost VandeVondele
15 : ! **************************************************************************************************
16 : MODULE cp_cfm_basic_linalg
17 : USE cp_blacs_env, ONLY: cp_blacs_env_type
18 : USE cp_cfm_types, ONLY: cp_cfm_create,&
19 : cp_cfm_get_info,&
20 : cp_cfm_release,&
21 : cp_cfm_to_cfm,&
22 : cp_cfm_type
23 : USE cp_fm_struct, ONLY: cp_fm_struct_equivalent
24 : USE cp_fm_types, ONLY: cp_fm_type
25 : USE cp_log_handling, ONLY: cp_to_string
26 : USE kahan_sum, ONLY: accurate_dot_product
27 : USE kinds, ONLY: dp
28 : USE mathconstants, ONLY: z_one,&
29 : z_zero
30 : USE message_passing, ONLY: mp_comm_type
31 : #include "../base/base_uses.f90"
32 :
33 : IMPLICIT NONE
34 : PRIVATE
35 :
36 : LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .TRUE.
37 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'cp_cfm_basic_linalg'
38 :
39 : PUBLIC :: cp_cfm_column_scale, &
40 : cp_cfm_gemm, &
41 : cp_cfm_lu_decompose, &
42 : cp_cfm_lu_invert, &
43 : cp_cfm_norm, &
44 : cp_cfm_scale, &
45 : cp_cfm_scale_and_add, &
46 : cp_cfm_scale_and_add_fm, &
47 : cp_cfm_schur_product, &
48 : cp_cfm_solve, &
49 : cp_cfm_trace, &
50 : cp_cfm_transpose, &
51 : cp_cfm_triangular_invert, &
52 : cp_cfm_triangular_multiply, &
53 : cp_cfm_rot_rows, &
54 : cp_cfm_rot_cols, &
55 : cp_cfm_det, & ! determinant of a complex matrix with correct sign
56 : cp_cfm_uplo_to_full
57 :
58 : REAL(kind=dp), EXTERNAL :: zlange, pzlange
59 :
60 : INTERFACE cp_cfm_scale
61 : MODULE PROCEDURE cp_cfm_dscale, cp_cfm_zscale
62 : END INTERFACE cp_cfm_scale
63 :
64 : ! **************************************************************************************************
65 :
66 : CONTAINS
67 :
68 : ! **************************************************************************************************
69 : !> \brief Computes the determinant (with a correct sign even in parallel environment!) of a complex square matrix
70 : !> \param matrix_a ...
71 : !> \param det_a ...
72 : !> \author A. Sinyavskiy (andrey.sinyavskiy@chem.uzh.ch)
73 : ! **************************************************************************************************
74 1086 : SUBROUTINE cp_cfm_det(matrix_a, det_a)
75 :
76 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
77 : COMPLEX(KIND=dp), INTENT(OUT) :: det_a
78 : COMPLEX(KIND=dp) :: determinant
79 : TYPE(cp_cfm_type) :: matrix_lu
80 1086 : COMPLEX(KIND=dp), DIMENSION(:, :), POINTER :: a
81 : INTEGER :: n, i, info, P
82 1086 : INTEGER, ALLOCATABLE, DIMENSION(:) :: ipivot
83 1086 : COMPLEX(KIND=dp), DIMENSION(:), POINTER :: diag
84 :
85 : #if defined(__parallel)
86 : INTEGER :: myprow, nprow, npcol, nrow_local, irow_local, &
87 : mypcol, ncol_local, icol_local, j
88 : INTEGER, DIMENSION(9) :: desca
89 : #endif
90 :
91 : CALL cp_cfm_create(matrix=matrix_lu, &
92 : matrix_struct=matrix_a%matrix_struct, &
93 1086 : name="A_lu"//TRIM(ADJUSTL(cp_to_string(1)))//"MATRIX")
94 1086 : CALL cp_cfm_to_cfm(matrix_a, matrix_lu)
95 :
96 1086 : a => matrix_lu%local_data
97 1086 : n = matrix_lu%matrix_struct%nrow_global
98 3258 : ALLOCATE (ipivot(n))
99 6252 : ipivot(:) = 0
100 1086 : P = 0
101 3258 : ALLOCATE (diag(n))
102 6252 : diag(:) = 0.0_dp
103 : #if defined(__parallel)
104 : ! Use LU decomposition
105 10860 : desca(:) = matrix_lu%matrix_struct%descriptor(:)
106 1086 : CALL pzgetrf(n, n, a(1, 1), 1, 1, desca, ipivot, info)
107 1086 : myprow = matrix_lu%matrix_struct%context%mepos(1)
108 1086 : mypcol = matrix_lu%matrix_struct%context%mepos(2)
109 1086 : nprow = matrix_lu%matrix_struct%context%num_pe(1)
110 1086 : npcol = matrix_lu%matrix_struct%context%num_pe(2)
111 1086 : nrow_local = matrix_lu%matrix_struct%nrow_locals(myprow)
112 1086 : ncol_local = matrix_lu%matrix_struct%ncol_locals(mypcol)
113 :
114 3789 : DO irow_local = 1, nrow_local
115 2703 : i = matrix_lu%matrix_struct%row_indices(irow_local)
116 36084 : DO icol_local = 1, ncol_local
117 32295 : j = matrix_lu%matrix_struct%col_indices(icol_local)
118 34998 : IF (i == j) diag(i) = matrix_lu%local_data(irow_local, icol_local)
119 : END DO
120 : END DO
121 11418 : CALL matrix_lu%matrix_struct%para_env%sum(diag)
122 6252 : determinant = PRODUCT(diag)
123 3789 : DO irow_local = 1, nrow_local
124 2703 : i = matrix_lu%matrix_struct%row_indices(irow_local)
125 3789 : IF (ipivot(irow_local) /= i) P = P + 1
126 : END DO
127 1086 : CALL matrix_lu%matrix_struct%para_env%sum(P)
128 : ! very important fix
129 1086 : P = P/npcol
130 : #else
131 : CALL zgetrf(n, n, a(1, 1), n, ipivot, info)
132 : DO i = 1, n
133 : diag(i) = matrix_lu%local_data(i, i)
134 : END DO
135 : determinant = PRODUCT(diag)
136 : DO i = 1, n
137 : IF (ipivot(i) /= i) P = P + 1
138 : END DO
139 : #endif
140 1086 : DEALLOCATE (ipivot)
141 1086 : DEALLOCATE (diag)
142 1086 : CALL cp_cfm_release(matrix_lu)
143 1086 : det_a = determinant*(-2*MOD(P, 2) + 1.0_dp)
144 1086 : END SUBROUTINE cp_cfm_det
145 :
146 : ! **************************************************************************************************
147 : !> \brief Computes the element-wise (Schur) product of two matrices: C = A \circ B .
148 : !> \param matrix_a the first input matrix
149 : !> \param matrix_b the second input matrix
150 : !> \param matrix_c matrix to store the result
151 : ! **************************************************************************************************
152 204 : SUBROUTINE cp_cfm_schur_product(matrix_a, matrix_b, matrix_c)
153 :
154 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a, matrix_b, matrix_c
155 :
156 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_schur_product'
157 :
158 204 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a, b, c
159 : INTEGER :: handle, icol_local, irow_local, mypcol, &
160 : myprow, ncol_local, nrow_local
161 :
162 204 : CALL timeset(routineN, handle)
163 :
164 204 : myprow = matrix_a%matrix_struct%context%mepos(1)
165 204 : mypcol = matrix_a%matrix_struct%context%mepos(2)
166 :
167 204 : a => matrix_a%local_data
168 204 : b => matrix_b%local_data
169 204 : c => matrix_c%local_data
170 :
171 204 : nrow_local = matrix_a%matrix_struct%nrow_locals(myprow)
172 204 : ncol_local = matrix_a%matrix_struct%ncol_locals(mypcol)
173 :
174 1020 : DO icol_local = 1, ncol_local
175 2652 : DO irow_local = 1, nrow_local
176 2448 : c(irow_local, icol_local) = a(irow_local, icol_local)*b(irow_local, icol_local)
177 : END DO
178 : END DO
179 :
180 204 : CALL timestop(handle)
181 :
182 204 : END SUBROUTINE cp_cfm_schur_product
183 :
184 : ! **************************************************************************************************
185 : !> \brief Computes the element-wise (Schur) product of two matrices: C = A \circ conjg(B) .
186 : !> \param matrix_a the first input matrix
187 : !> \param matrix_b the second input matrix
188 : !> \param matrix_c matrix to store the result
189 : ! **************************************************************************************************
190 0 : SUBROUTINE cp_cfm_schur_product_cc(matrix_a, matrix_b, matrix_c)
191 :
192 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a, matrix_b, matrix_c
193 :
194 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_schur_product_cc'
195 :
196 0 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a, b, c
197 : INTEGER :: handle, icol_local, irow_local, mypcol, &
198 : myprow, ncol_local, nrow_local
199 :
200 0 : CALL timeset(routineN, handle)
201 :
202 0 : myprow = matrix_a%matrix_struct%context%mepos(1)
203 0 : mypcol = matrix_a%matrix_struct%context%mepos(2)
204 :
205 0 : a => matrix_a%local_data
206 0 : b => matrix_b%local_data
207 0 : c => matrix_c%local_data
208 :
209 0 : nrow_local = matrix_a%matrix_struct%nrow_locals(myprow)
210 0 : ncol_local = matrix_a%matrix_struct%ncol_locals(mypcol)
211 :
212 0 : DO icol_local = 1, ncol_local
213 0 : DO irow_local = 1, nrow_local
214 0 : c(irow_local, icol_local) = a(irow_local, icol_local)*CONJG(b(irow_local, icol_local))
215 : END DO
216 : END DO
217 :
218 0 : CALL timestop(handle)
219 :
220 0 : END SUBROUTINE cp_cfm_schur_product_cc
221 :
222 : ! **************************************************************************************************
223 : !> \brief Scale and add two BLACS matrices (a = alpha*a + beta*b).
224 : !> \param alpha ...
225 : !> \param matrix_a ...
226 : !> \param beta ...
227 : !> \param matrix_b ...
228 : !> \date 11.06.2001
229 : !> \author Matthias Krack
230 : !> \version 1.0
231 : !> \note
232 : !> Use explicit loops to avoid temporary arrays, as a compiler reasonably assumes that arrays
233 : !> matrix_a%local_data and matrix_b%local_data may overlap (they are referenced by pointers).
234 : !> In general case (alpha*a + beta*b) explicit loops appears to be up to two times more efficient
235 : !> than equivalent LAPACK calls (zscale, zaxpy). This is because using LAPACK calls implies
236 : !> two passes through each array, so data need to be retrieved twice if arrays are large
237 : !> enough to not fit into the processor's cache.
238 : ! **************************************************************************************************
239 238100 : SUBROUTINE cp_cfm_scale_and_add(alpha, matrix_a, beta, matrix_b)
240 : COMPLEX(kind=dp), INTENT(in) :: alpha
241 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
242 : COMPLEX(kind=dp), INTENT(in), OPTIONAL :: beta
243 : TYPE(cp_cfm_type), INTENT(IN), OPTIONAL :: matrix_b
244 :
245 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_scale_and_add'
246 :
247 : COMPLEX(kind=dp) :: my_beta
248 238100 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a, b
249 : INTEGER :: handle, icol_local, irow_local, mypcol, &
250 : myprow, ncol_local, nrow_local
251 :
252 238100 : CALL timeset(routineN, handle)
253 :
254 238100 : my_beta = z_zero
255 238100 : IF (PRESENT(beta)) my_beta = beta
256 238100 : NULLIFY (a, b)
257 :
258 : ! to do: use dscal,dcopy,daxp
259 238100 : myprow = matrix_a%matrix_struct%context%mepos(1)
260 238100 : mypcol = matrix_a%matrix_struct%context%mepos(2)
261 :
262 238100 : nrow_local = matrix_a%matrix_struct%nrow_locals(myprow)
263 238100 : ncol_local = matrix_a%matrix_struct%ncol_locals(mypcol)
264 :
265 238100 : a => matrix_a%local_data
266 :
267 238100 : IF (my_beta == z_zero) THEN
268 :
269 10482 : IF (alpha == z_zero) THEN
270 0 : a(:, :) = z_zero
271 10482 : ELSE IF (alpha == z_one) THEN
272 10482 : CALL timestop(handle)
273 10482 : RETURN
274 : ELSE
275 0 : a(:, :) = alpha*a(:, :)
276 : END IF
277 :
278 : ELSE
279 227618 : CPASSERT(PRESENT(matrix_b))
280 227618 : IF (matrix_a%matrix_struct%context /= matrix_b%matrix_struct%context) &
281 0 : CPABORT("matrixes must be in the same blacs context")
282 :
283 227618 : IF (cp_fm_struct_equivalent(matrix_a%matrix_struct, &
284 : matrix_b%matrix_struct)) THEN
285 :
286 227618 : b => matrix_b%local_data
287 :
288 227618 : IF (alpha == z_zero) THEN
289 0 : IF (my_beta == z_one) THEN
290 : !a(:, :) = b(:, :)
291 0 : DO icol_local = 1, ncol_local
292 0 : DO irow_local = 1, nrow_local
293 0 : a(irow_local, icol_local) = b(irow_local, icol_local)
294 : END DO
295 : END DO
296 : ELSE
297 : !a(:, :) = my_beta*b(:, :)
298 0 : DO icol_local = 1, ncol_local
299 0 : DO irow_local = 1, nrow_local
300 0 : a(irow_local, icol_local) = my_beta*b(irow_local, icol_local)
301 : END DO
302 : END DO
303 : END IF
304 227618 : ELSE IF (alpha == z_one) THEN
305 223830 : IF (my_beta == z_one) THEN
306 : !a(:, :) = a(:, :)+b(:, :)
307 1923243 : DO icol_local = 1, ncol_local
308 27785362 : DO irow_local = 1, nrow_local
309 27619335 : a(irow_local, icol_local) = a(irow_local, icol_local) + b(irow_local, icol_local)
310 : END DO
311 : END DO
312 : ELSE
313 : !a(:, :) = a(:, :)+my_beta*b(:, :)
314 762569 : DO icol_local = 1, ncol_local
315 11180262 : DO irow_local = 1, nrow_local
316 11122459 : a(irow_local, icol_local) = a(irow_local, icol_local) + my_beta*b(irow_local, icol_local)
317 : END DO
318 : END DO
319 : END IF
320 : ELSE
321 : !a(:, :) = alpha*a(:, :)+my_beta*b(:, :)
322 40188 : DO icol_local = 1, ncol_local
323 785788 : DO irow_local = 1, nrow_local
324 782000 : a(irow_local, icol_local) = alpha*a(irow_local, icol_local) + my_beta*b(irow_local, icol_local)
325 : END DO
326 : END DO
327 : END IF
328 : ELSE
329 : #if defined(__parallel)
330 0 : CPABORT("to do (pdscal,pdcopy,pdaxpy)")
331 : #else
332 : CPABORT("")
333 : #endif
334 : END IF
335 : END IF
336 227618 : CALL timestop(handle)
337 238100 : END SUBROUTINE cp_cfm_scale_and_add
338 :
339 : ! **************************************************************************************************
340 : !> \brief Scale and add two BLACS matrices (a = alpha*a + beta*b).
341 : !> where b is a real matrix (adapted from cp_cfm_scale_and_add).
342 : !> \param alpha ...
343 : !> \param matrix_a ...
344 : !> \param beta ...
345 : !> \param matrix_b ...
346 : !> \date 01.08.2014
347 : !> \author JGH
348 : !> \version 1.0
349 : ! **************************************************************************************************
350 131070 : SUBROUTINE cp_cfm_scale_and_add_fm(alpha, matrix_a, beta, matrix_b)
351 : COMPLEX(kind=dp), INTENT(in) :: alpha
352 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
353 : COMPLEX(kind=dp), INTENT(in) :: beta
354 : TYPE(cp_fm_type), INTENT(IN) :: matrix_b
355 :
356 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_scale_and_add_fm'
357 :
358 131070 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a
359 : INTEGER :: handle, icol_local, irow_local, mypcol, &
360 : myprow, ncol_local, nrow_local
361 131070 : REAL(kind=dp), DIMENSION(:, :), POINTER :: b
362 :
363 131070 : CALL timeset(routineN, handle)
364 :
365 131070 : NULLIFY (a, b)
366 :
367 131070 : myprow = matrix_a%matrix_struct%context%mepos(1)
368 131070 : mypcol = matrix_a%matrix_struct%context%mepos(2)
369 :
370 131070 : nrow_local = matrix_a%matrix_struct%nrow_locals(myprow)
371 131070 : ncol_local = matrix_a%matrix_struct%ncol_locals(mypcol)
372 :
373 131070 : a => matrix_a%local_data
374 :
375 131070 : IF (beta == z_zero) THEN
376 :
377 0 : IF (alpha == z_zero) THEN
378 0 : a(:, :) = z_zero
379 0 : ELSE IF (alpha == z_one) THEN
380 0 : CALL timestop(handle)
381 0 : RETURN
382 : ELSE
383 0 : a(:, :) = alpha*a(:, :)
384 : END IF
385 :
386 : ELSE
387 131070 : IF (matrix_a%matrix_struct%context /= matrix_b%matrix_struct%context) &
388 0 : CPABORT("matrices must be in the same blacs context")
389 :
390 131070 : IF (cp_fm_struct_equivalent(matrix_a%matrix_struct, &
391 : matrix_b%matrix_struct)) THEN
392 :
393 131070 : b => matrix_b%local_data
394 :
395 131070 : IF (alpha == z_zero) THEN
396 46804 : IF (beta == z_one) THEN
397 : !a(:, :) = b(:, :)
398 1684144 : DO icol_local = 1, ncol_local
399 73774798 : DO irow_local = 1, nrow_local
400 73728042 : a(irow_local, icol_local) = b(irow_local, icol_local)
401 : END DO
402 : END DO
403 : ELSE
404 : !a(:, :) = beta*b(:, :)
405 912 : DO icol_local = 1, ncol_local
406 8688 : DO irow_local = 1, nrow_local
407 8640 : a(irow_local, icol_local) = beta*b(irow_local, icol_local)
408 : END DO
409 : END DO
410 : END IF
411 84266 : ELSE IF (alpha == z_one) THEN
412 53745 : IF (beta == z_one) THEN
413 : !a(:, :) = a(:, :)+b(:, :)
414 91309 : DO icol_local = 1, ncol_local
415 1495613 : DO irow_local = 1, nrow_local
416 1491480 : a(irow_local, icol_local) = a(irow_local, icol_local) + b(irow_local, icol_local)
417 : END DO
418 : END DO
419 : ELSE
420 : !a(:, :) = a(:, :)+beta*b(:, :)
421 1741608 : DO icol_local = 1, ncol_local
422 74368534 : DO irow_local = 1, nrow_local
423 74318922 : a(irow_local, icol_local) = a(irow_local, icol_local) + beta*b(irow_local, icol_local)
424 : END DO
425 : END DO
426 : END IF
427 : ELSE
428 : !a(:, :) = alpha*a(:, :)+beta*b(:, :)
429 346801 : DO icol_local = 1, ncol_local
430 5761521 : DO irow_local = 1, nrow_local
431 5731000 : a(irow_local, icol_local) = alpha*a(irow_local, icol_local) + beta*b(irow_local, icol_local)
432 : END DO
433 : END DO
434 : END IF
435 : ELSE
436 : #if defined(__parallel)
437 0 : CPABORT("to do (pdscal,pdcopy,pdaxpy)")
438 : #else
439 : CPABORT("")
440 : #endif
441 : END IF
442 : END IF
443 131070 : CALL timestop(handle)
444 131070 : END SUBROUTINE cp_cfm_scale_and_add_fm
445 :
446 : ! **************************************************************************************************
447 : !> \brief Computes LU decomposition of a given matrix.
448 : !> \param matrix_a full matrix
449 : !> \param determinant determinant
450 : !> \date 11.06.2001
451 : !> \author Matthias Krack
452 : !> \version 1.0
453 : !> \note
454 : !> The actual purpose right now is to efficiently compute the determinant of a given matrix.
455 : !> The original content of the matrix is destroyed.
456 : ! **************************************************************************************************
457 0 : SUBROUTINE cp_cfm_lu_decompose(matrix_a, determinant)
458 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
459 : COMPLEX(kind=dp), INTENT(out) :: determinant
460 :
461 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_lu_decompose'
462 :
463 0 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a
464 : INTEGER :: counter, handle, info, irow, nrow_global
465 0 : INTEGER, ALLOCATABLE, DIMENSION(:) :: ipivot
466 :
467 : #if defined(__parallel)
468 : INTEGER :: icol, ncol_local, nrow_local
469 : INTEGER, DIMENSION(9) :: desca
470 0 : INTEGER, DIMENSION(:), POINTER :: col_indices, row_indices
471 : #else
472 : INTEGER :: lda
473 : #endif
474 :
475 0 : CALL timeset(routineN, handle)
476 :
477 0 : nrow_global = matrix_a%matrix_struct%nrow_global
478 0 : a => matrix_a%local_data
479 :
480 0 : ALLOCATE (ipivot(nrow_global))
481 : #if defined(__parallel)
482 : CALL cp_cfm_get_info(matrix_a, nrow_local=nrow_local, ncol_local=ncol_local, &
483 0 : row_indices=row_indices, col_indices=col_indices)
484 :
485 0 : desca(:) = matrix_a%matrix_struct%descriptor(:)
486 0 : CALL pzgetrf(nrow_global, nrow_global, a(1, 1), 1, 1, desca, ipivot, info)
487 :
488 0 : counter = 0
489 0 : DO irow = 1, nrow_local
490 0 : IF (ipivot(irow) .NE. row_indices(irow)) counter = counter + 1
491 : END DO
492 :
493 0 : IF (MOD(counter, 2) == 0) THEN
494 0 : determinant = z_one
495 : ELSE
496 0 : determinant = -z_one
497 : END IF
498 :
499 : ! compute product of diagonal elements
500 : irow = 1
501 : icol = 1
502 0 : DO WHILE (irow <= nrow_local .AND. icol <= ncol_local)
503 0 : IF (row_indices(irow) < col_indices(icol)) THEN
504 0 : irow = irow + 1
505 0 : ELSE IF (row_indices(irow) > col_indices(icol)) THEN
506 0 : icol = icol + 1
507 : ELSE ! diagonal element
508 0 : determinant = determinant*a(irow, icol)
509 0 : irow = irow + 1
510 0 : icol = icol + 1
511 : END IF
512 : END DO
513 0 : CALL matrix_a%matrix_struct%para_env%prod(determinant)
514 : #else
515 : lda = SIZE(a, 1)
516 : CALL zgetrf(nrow_global, nrow_global, a(1, 1), lda, ipivot, info)
517 : counter = 0
518 : determinant = z_one
519 : DO irow = 1, nrow_global
520 : IF (ipivot(irow) .NE. irow) counter = counter + 1
521 : determinant = determinant*a(irow, irow)
522 : END DO
523 : IF (MOD(counter, 2) == 1) determinant = -1.0_dp*determinant
524 : #endif
525 :
526 : ! info is allowed to be zero
527 : ! this does just signal a zero diagonal element
528 0 : DEALLOCATE (ipivot)
529 :
530 0 : CALL timestop(handle)
531 0 : END SUBROUTINE cp_cfm_lu_decompose
532 :
533 : ! **************************************************************************************************
534 : !> \brief Performs one of the matrix-matrix operations:
535 : !> matrix_c = alpha * op1( matrix_a ) * op2( matrix_b ) + beta*matrix_c.
536 : !> \param transa form of op1( matrix_a ):
537 : !> op1( matrix_a ) = matrix_a, when transa == 'N' ,
538 : !> op1( matrix_a ) = matrix_a^T, when transa == 'T' ,
539 : !> op1( matrix_a ) = matrix_a^H, when transa == 'C' ,
540 : !> \param transb form of op2( matrix_b )
541 : !> \param m number of rows of the matrix op1( matrix_a )
542 : !> \param n number of columns of the matrix op2( matrix_b )
543 : !> \param k number of columns of the matrix op1( matrix_a ) as well as
544 : !> number of rows of the matrix op2( matrix_b )
545 : !> \param alpha scale factor
546 : !> \param matrix_a matrix A
547 : !> \param matrix_b matrix B
548 : !> \param beta scale factor
549 : !> \param matrix_c matrix C
550 : !> \param a_first_col (optional) the first column of the matrix_a to multiply
551 : !> \param a_first_row (optional) the first row of the matrix_a to multiply
552 : !> \param b_first_col (optional) the first column of the matrix_b to multiply
553 : !> \param b_first_row (optional) the first row of the matrix_b to multiply
554 : !> \param c_first_col (optional) the first column of the matrix_c
555 : !> \param c_first_row (optional) the first row of the matrix_c
556 : !> \date 07.06.2001
557 : !> \author Matthias Krack
558 : !> \version 1.0
559 : ! **************************************************************************************************
560 76314 : SUBROUTINE cp_cfm_gemm(transa, transb, m, n, k, alpha, matrix_a, matrix_b, beta, &
561 : matrix_c, a_first_col, a_first_row, b_first_col, b_first_row, c_first_col, &
562 : c_first_row)
563 : CHARACTER(len=1), INTENT(in) :: transa, transb
564 : INTEGER, INTENT(in) :: m, n, k
565 : COMPLEX(kind=dp), INTENT(in) :: alpha
566 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a, matrix_b
567 : COMPLEX(kind=dp), INTENT(in) :: beta
568 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_c
569 : INTEGER, INTENT(in), OPTIONAL :: a_first_col, a_first_row, b_first_col, &
570 : b_first_row, c_first_col, c_first_row
571 :
572 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_gemm'
573 :
574 76314 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a, b, c
575 : INTEGER :: handle, i_a, i_b, i_c, j_a, j_b, j_c
576 : #if defined(__parallel)
577 : INTEGER, DIMENSION(9) :: desca, descb, descc
578 : #else
579 : INTEGER :: lda, ldb, ldc
580 : #endif
581 :
582 76314 : CALL timeset(routineN, handle)
583 76314 : a => matrix_a%local_data
584 76314 : b => matrix_b%local_data
585 76314 : c => matrix_c%local_data
586 :
587 76314 : i_a = 1
588 76314 : IF (PRESENT(a_first_row)) i_a = a_first_row
589 :
590 76314 : j_a = 1
591 76314 : IF (PRESENT(a_first_col)) j_a = a_first_col
592 :
593 76314 : i_b = 1
594 76314 : IF (PRESENT(b_first_row)) i_b = b_first_row
595 :
596 76314 : j_b = 1
597 76314 : IF (PRESENT(b_first_col)) j_b = b_first_col
598 :
599 76314 : i_c = 1
600 76314 : IF (PRESENT(c_first_row)) i_c = c_first_row
601 :
602 76314 : j_c = 1
603 76314 : IF (PRESENT(c_first_col)) j_c = c_first_col
604 :
605 : #if defined(__parallel)
606 763140 : desca(:) = matrix_a%matrix_struct%descriptor(:)
607 763140 : descb(:) = matrix_b%matrix_struct%descriptor(:)
608 763140 : descc(:) = matrix_c%matrix_struct%descriptor(:)
609 :
610 : CALL pzgemm(transa, transb, m, n, k, alpha, a(1, 1), i_a, j_a, desca, &
611 76314 : b(1, 1), i_b, j_b, descb, beta, c(1, 1), i_c, j_c, descc)
612 : #else
613 : lda = SIZE(a, 1)
614 : ldb = SIZE(b, 1)
615 : ldc = SIZE(c, 1)
616 :
617 : ! consider zgemm3m
618 : CALL zgemm(transa, transb, m, n, k, alpha, a(i_a, j_a), &
619 : lda, b(i_b, j_b), ldb, beta, c(i_c, j_c), ldc)
620 : #endif
621 76314 : CALL timestop(handle)
622 76314 : END SUBROUTINE cp_cfm_gemm
623 :
624 : ! **************************************************************************************************
625 : !> \brief Scales columns of the full matrix by corresponding factors.
626 : !> \param matrix_a matrix to scale
627 : !> \param scaling scale factors for every column. The actual number of scaled columns is
628 : !> limited by the number of scale factors given or by the actual number of columns
629 : !> whichever is smaller.
630 : !> \author Joost VandeVondele
631 : ! **************************************************************************************************
632 6774 : SUBROUTINE cp_cfm_column_scale(matrix_a, scaling)
633 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
634 : COMPLEX(kind=dp), DIMENSION(:), INTENT(in) :: scaling
635 :
636 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_column_scale'
637 :
638 6774 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a
639 : INTEGER :: handle, icol_local, ncol_local, &
640 : nrow_local
641 : #if defined(__parallel)
642 6774 : INTEGER, DIMENSION(:), POINTER :: col_indices
643 : #endif
644 :
645 6774 : CALL timeset(routineN, handle)
646 :
647 6774 : a => matrix_a%local_data
648 :
649 : #if defined(__parallel)
650 6774 : CALL cp_cfm_get_info(matrix_a, nrow_local=nrow_local, ncol_local=ncol_local, col_indices=col_indices)
651 6774 : ncol_local = MIN(ncol_local, SIZE(scaling))
652 :
653 304952 : DO icol_local = 1, ncol_local
654 304952 : CALL zscal(nrow_local, scaling(col_indices(icol_local)), a(1, icol_local), 1)
655 : END DO
656 : #else
657 : nrow_local = SIZE(a, 1)
658 : ncol_local = MIN(SIZE(a, 2), SIZE(scaling))
659 :
660 : DO icol_local = 1, ncol_local
661 : CALL zscal(nrow_local, scaling(icol_local), a(1, icol_local), 1)
662 : END DO
663 : #endif
664 :
665 6774 : CALL timestop(handle)
666 6774 : END SUBROUTINE cp_cfm_column_scale
667 :
668 : ! **************************************************************************************************
669 : !> \brief Scales a complex matrix by a real number.
670 : !> matrix_a = alpha * matrix_b
671 : !> \param alpha scale factor
672 : !> \param matrix_a complex matrix to scale
673 : ! **************************************************************************************************
674 7168 : SUBROUTINE cp_cfm_dscale(alpha, matrix_a)
675 : REAL(kind=dp), INTENT(in) :: alpha
676 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
677 :
678 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_dscale'
679 :
680 7168 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a
681 : INTEGER :: handle
682 :
683 7168 : CALL timeset(routineN, handle)
684 :
685 7168 : NULLIFY (a)
686 :
687 7168 : a => matrix_a%local_data
688 :
689 21504 : CALL zdscal(SIZE(a), alpha, a(1, 1), 1)
690 :
691 7168 : CALL timestop(handle)
692 7168 : END SUBROUTINE cp_cfm_dscale
693 :
694 : ! **************************************************************************************************
695 : !> \brief Scales a complex matrix by a complex number.
696 : !> matrix_a = alpha * matrix_b
697 : !> \param alpha scale factor
698 : !> \param matrix_a complex matrix to scale
699 : !> \note
700 : !> use cp_fm_set_all to zero (avoids problems with nan)
701 : ! **************************************************************************************************
702 26752 : SUBROUTINE cp_cfm_zscale(alpha, matrix_a)
703 : COMPLEX(kind=dp), INTENT(in) :: alpha
704 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
705 :
706 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_zscale'
707 :
708 26752 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a
709 : INTEGER :: handle
710 :
711 26752 : CALL timeset(routineN, handle)
712 :
713 26752 : NULLIFY (a)
714 :
715 26752 : a => matrix_a%local_data
716 :
717 80256 : CALL zscal(SIZE(a), alpha, a(1, 1), 1)
718 :
719 26752 : CALL timestop(handle)
720 26752 : END SUBROUTINE cp_cfm_zscale
721 :
722 : ! **************************************************************************************************
723 : !> \brief Solve the system of linear equations A*b=A_general using LU decomposition.
724 : !> Pay attention that both matrices are overwritten on exit and that
725 : !> the result is stored into the matrix 'general_a'.
726 : !> \param matrix_a matrix A (overwritten on exit)
727 : !> \param general_a (input) matrix A_general, (output) matrix B
728 : !> \param determinant (optional) determinant
729 : !> \author Florian Schiffmann
730 : ! **************************************************************************************************
731 6526 : SUBROUTINE cp_cfm_solve(matrix_a, general_a, determinant)
732 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a, general_a
733 : COMPLEX(kind=dp), OPTIONAL :: determinant
734 :
735 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_solve'
736 :
737 6526 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: a, a_general
738 : INTEGER :: counter, handle, info, irow, nrow_global
739 6526 : INTEGER, ALLOCATABLE, DIMENSION(:) :: ipivot
740 :
741 : #if defined(__parallel)
742 : INTEGER :: icol, ncol_local, nrow_local
743 : INTEGER, DIMENSION(9) :: desca, descb
744 6526 : INTEGER, DIMENSION(:), POINTER :: col_indices, row_indices
745 : #else
746 : INTEGER :: lda, ldb
747 : #endif
748 :
749 6526 : CALL timeset(routineN, handle)
750 :
751 6526 : a => matrix_a%local_data
752 6526 : a_general => general_a%local_data
753 6526 : nrow_global = matrix_a%matrix_struct%nrow_global
754 19578 : ALLOCATE (ipivot(nrow_global))
755 :
756 : #if defined(__parallel)
757 65260 : desca(:) = matrix_a%matrix_struct%descriptor(:)
758 65260 : descb(:) = general_a%matrix_struct%descriptor(:)
759 6526 : CALL pzgetrf(nrow_global, nrow_global, a(1, 1), 1, 1, desca, ipivot, info)
760 6526 : IF (PRESENT(determinant)) THEN
761 : CALL cp_cfm_get_info(matrix_a, nrow_local=nrow_local, ncol_local=ncol_local, &
762 5238 : row_indices=row_indices, col_indices=col_indices)
763 :
764 5238 : counter = 0
765 15714 : DO irow = 1, nrow_local
766 15714 : IF (ipivot(irow) .NE. row_indices(irow)) counter = counter + 1
767 : END DO
768 :
769 5238 : IF (MOD(counter, 2) == 0) THEN
770 5236 : determinant = z_one
771 : ELSE
772 2 : determinant = -z_one
773 : END IF
774 :
775 : ! compute product of diagonal elements
776 : irow = 1
777 : icol = 1
778 23571 : DO WHILE (irow <= nrow_local .AND. icol <= ncol_local)
779 23571 : IF (row_indices(irow) < col_indices(icol)) THEN
780 0 : irow = irow + 1
781 18333 : ELSE IF (row_indices(irow) > col_indices(icol)) THEN
782 7857 : icol = icol + 1
783 : ELSE ! diagonal element
784 10476 : determinant = determinant*a(irow, icol)
785 10476 : irow = irow + 1
786 10476 : icol = icol + 1
787 : END IF
788 : END DO
789 5238 : CALL matrix_a%matrix_struct%para_env%prod(determinant)
790 : END IF
791 :
792 : CALL pzgetrs("N", nrow_global, nrow_global, a(1, 1), 1, 1, desca, &
793 6526 : ipivot, a_general(1, 1), 1, 1, descb, info)
794 : #else
795 : lda = SIZE(a, 1)
796 : ldb = SIZE(a_general, 1)
797 : CALL zgetrf(nrow_global, nrow_global, a(1, 1), lda, ipivot, info)
798 : IF (PRESENT(determinant)) THEN
799 : counter = 0
800 : determinant = z_one
801 : DO irow = 1, nrow_global
802 : IF (ipivot(irow) .NE. irow) counter = counter + 1
803 : determinant = determinant*a(irow, irow)
804 : END DO
805 : IF (MOD(counter, 2) == 1) determinant = -1.0_dp*determinant
806 : END IF
807 : CALL zgetrs("N", nrow_global, nrow_global, a(1, 1), lda, ipivot, a_general(1, 1), ldb, info)
808 : #endif
809 :
810 : ! info is allowed to be zero
811 : ! this does just signal a zero diagonal element
812 6526 : DEALLOCATE (ipivot)
813 6526 : CALL timestop(handle)
814 :
815 6526 : END SUBROUTINE cp_cfm_solve
816 :
817 : ! **************************************************************************************************
818 : !> \brief Inverts a matrix using LU decomposition. The input matrix will be overwritten.
819 : !> \param matrix input a general square non-singular matrix, outputs its inverse
820 : !> \param info_out optional, if present outputs the info from (p)zgetri
821 : !> \author Lianheng Tong
822 : ! **************************************************************************************************
823 49793 : SUBROUTINE cp_cfm_lu_invert(matrix, info_out)
824 : TYPE(cp_cfm_type), INTENT(IN) :: matrix
825 : INTEGER, INTENT(out), OPTIONAL :: info_out
826 :
827 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_lu_invert'
828 :
829 49793 : COMPLEX(kind=dp), ALLOCATABLE, DIMENSION(:) :: work
830 : COMPLEX(kind=dp), DIMENSION(1) :: work1
831 49793 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: mat
832 : INTEGER :: handle, info, lwork, nrows_global
833 49793 : INTEGER, ALLOCATABLE, DIMENSION(:) :: ipivot
834 :
835 : #if defined(__parallel)
836 : INTEGER :: liwork
837 49793 : INTEGER, ALLOCATABLE, DIMENSION(:) :: iwork
838 : INTEGER, DIMENSION(1) :: iwork1
839 : INTEGER, DIMENSION(9) :: desca
840 : #else
841 : INTEGER :: lda
842 : #endif
843 :
844 49793 : CALL timeset(routineN, handle)
845 :
846 49793 : mat => matrix%local_data
847 49793 : nrows_global = matrix%matrix_struct%nrow_global
848 49793 : CPASSERT(nrows_global .EQ. matrix%matrix_struct%ncol_global)
849 149379 : ALLOCATE (ipivot(nrows_global))
850 :
851 : ! do LU decomposition
852 : #if defined(__parallel)
853 497930 : desca = matrix%matrix_struct%descriptor
854 : CALL pzgetrf(nrows_global, nrows_global, &
855 49793 : mat(1, 1), 1, 1, desca, ipivot, info)
856 : #else
857 : lda = SIZE(mat, 1)
858 : CALL zgetrf(nrows_global, nrows_global, &
859 : mat(1, 1), lda, ipivot, info)
860 : #endif
861 49793 : IF (info /= 0) THEN
862 0 : CALL cp_abort(__LOCATION__, "LU decomposition has failed")
863 : END IF
864 :
865 : ! do inversion
866 : #if defined(__parallel)
867 : CALL pzgetri(nrows_global, mat(1, 1), 1, 1, desca, &
868 49793 : ipivot, work1, -1, iwork1, -1, info)
869 49793 : lwork = INT(work1(1))
870 49793 : liwork = INT(iwork1(1))
871 149379 : ALLOCATE (work(lwork))
872 149379 : ALLOCATE (iwork(liwork))
873 : CALL pzgetri(nrows_global, mat(1, 1), 1, 1, desca, &
874 49793 : ipivot, work, lwork, iwork, liwork, info)
875 49793 : DEALLOCATE (iwork)
876 : #else
877 : CALL zgetri(nrows_global, mat(1, 1), lda, ipivot, work1, -1, info)
878 : lwork = INT(work1(1))
879 : ALLOCATE (work(lwork))
880 : CALL zgetri(nrows_global, mat(1, 1), lda, ipivot, work, lwork, info)
881 : #endif
882 49793 : DEALLOCATE (work)
883 49793 : DEALLOCATE (ipivot)
884 :
885 49793 : IF (PRESENT(info_out)) THEN
886 0 : info_out = info
887 : ELSE
888 49793 : IF (info /= 0) &
889 0 : CALL cp_abort(__LOCATION__, "LU inversion has failed")
890 : END IF
891 :
892 49793 : CALL timestop(handle)
893 :
894 49793 : END SUBROUTINE cp_cfm_lu_invert
895 :
896 : ! **************************************************************************************************
897 : !> \brief Returns the trace of matrix_a^T matrix_b, i.e
898 : !> sum_{i,j}(matrix_a(i,j)*matrix_b(i,j)) .
899 : !> \param matrix_a a complex matrix
900 : !> \param matrix_b another complex matrix
901 : !> \param trace value of the trace operator
902 : !> \par History
903 : !> * 09.2017 created [Sergey Chulkov]
904 : !> \author Sergey Chulkov
905 : !> \note
906 : !> Based on the subroutine cp_fm_trace(). Note the transposition of matrix_a!
907 : ! **************************************************************************************************
908 28555 : SUBROUTINE cp_cfm_trace(matrix_a, matrix_b, trace)
909 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a, matrix_b
910 : COMPLEX(kind=dp), INTENT(out) :: trace
911 :
912 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_trace'
913 :
914 : INTEGER :: handle, mypcol, myprow, ncol_local, &
915 : npcol, nprow, nrow_local
916 : TYPE(cp_blacs_env_type), POINTER :: context
917 : TYPE(mp_comm_type) :: group
918 :
919 28555 : CALL timeset(routineN, handle)
920 :
921 28555 : context => matrix_a%matrix_struct%context
922 28555 : myprow = context%mepos(1)
923 28555 : mypcol = context%mepos(2)
924 28555 : nprow = context%num_pe(1)
925 28555 : npcol = context%num_pe(2)
926 :
927 28555 : group = matrix_a%matrix_struct%para_env
928 :
929 28555 : nrow_local = MIN(matrix_a%matrix_struct%nrow_locals(myprow), matrix_b%matrix_struct%nrow_locals(myprow))
930 28555 : ncol_local = MIN(matrix_a%matrix_struct%ncol_locals(mypcol), matrix_b%matrix_struct%ncol_locals(mypcol))
931 :
932 : ! compute an accurate dot-product
933 : trace = accurate_dot_product(matrix_a%local_data(1:nrow_local, 1:ncol_local), &
934 28555 : matrix_b%local_data(1:nrow_local, 1:ncol_local))
935 :
936 28555 : CALL group%sum(trace)
937 :
938 28555 : CALL timestop(handle)
939 :
940 28555 : END SUBROUTINE cp_cfm_trace
941 :
942 : ! **************************************************************************************************
943 : !> \brief Multiplies in place by a triangular matrix:
944 : !> matrix_b = alpha op(triangular_matrix) matrix_b
945 : !> or (if side='R')
946 : !> matrix_b = alpha matrix_b op(triangular_matrix)
947 : !> op(triangular_matrix) is:
948 : !> triangular_matrix (if transa="N" and invert_tr=.false.)
949 : !> triangular_matrix^T (if transa="T" and invert_tr=.false.)
950 : !> triangular_matrix^H (if transa="C" and invert_tr=.false.)
951 : !> triangular_matrix^(-1) (if transa="N" and invert_tr=.true.)
952 : !> triangular_matrix^(-T) (if transa="T" and invert_tr=.true.)
953 : !> triangular_matrix^(-H) (if transa="C" and invert_tr=.true.)
954 : !> \param triangular_matrix the triangular matrix that multiplies the other
955 : !> \param matrix_b the matrix that gets multiplied and stores the result
956 : !> \param side on which side of matrix_b stays op(triangular_matrix)
957 : !> (defaults to 'L')
958 : !> \param transa_tr ...
959 : !> \param invert_tr if the triangular matrix should be inverted
960 : !> (defaults to false)
961 : !> \param uplo_tr if triangular_matrix is stored in the upper ('U') or
962 : !> lower ('L') triangle (defaults to 'U')
963 : !> \param unit_diag_tr if the diagonal elements of triangular_matrix should
964 : !> be assumed to be 1 (defaults to false)
965 : !> \param n_rows the number of rows of the result (defaults to
966 : !> size(matrix_b,1))
967 : !> \param n_cols the number of columns of the result (defaults to
968 : !> size(matrix_b,2))
969 : !> \param alpha ...
970 : !> \par History
971 : !> 08.2002 created [fawzi]
972 : !> \author Fawzi Mohamed
973 : !> \note
974 : !> needs an mpi env
975 : ! **************************************************************************************************
976 94476 : SUBROUTINE cp_cfm_triangular_multiply(triangular_matrix, matrix_b, side, &
977 : transa_tr, invert_tr, uplo_tr, unit_diag_tr, n_rows, n_cols, &
978 : alpha)
979 : TYPE(cp_cfm_type), INTENT(IN) :: triangular_matrix, matrix_b
980 : CHARACTER, INTENT(in), OPTIONAL :: side, transa_tr
981 : LOGICAL, INTENT(in), OPTIONAL :: invert_tr
982 : CHARACTER, INTENT(in), OPTIONAL :: uplo_tr
983 : LOGICAL, INTENT(in), OPTIONAL :: unit_diag_tr
984 : INTEGER, INTENT(in), OPTIONAL :: n_rows, n_cols
985 : COMPLEX(kind=dp), INTENT(in), OPTIONAL :: alpha
986 :
987 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_triangular_multiply'
988 :
989 : CHARACTER :: side_char, transa, unit_diag, uplo
990 : COMPLEX(kind=dp) :: al
991 : INTEGER :: handle, m, n
992 : LOGICAL :: invert
993 :
994 47238 : CALL timeset(routineN, handle)
995 47238 : side_char = 'L'
996 47238 : unit_diag = 'N'
997 47238 : uplo = 'U'
998 47238 : transa = 'N'
999 47238 : invert = .FALSE.
1000 47238 : al = CMPLX(1.0_dp, 0.0_dp, dp)
1001 47238 : CALL cp_cfm_get_info(matrix_b, nrow_global=m, ncol_global=n)
1002 47238 : IF (PRESENT(side)) side_char = side
1003 47238 : IF (PRESENT(invert_tr)) invert = invert_tr
1004 47238 : IF (PRESENT(uplo_tr)) uplo = uplo_tr
1005 47238 : IF (PRESENT(unit_diag_tr)) THEN
1006 0 : IF (unit_diag_tr) THEN
1007 0 : unit_diag = 'U'
1008 : ELSE
1009 : unit_diag = 'N'
1010 : END IF
1011 : END IF
1012 47238 : IF (PRESENT(transa_tr)) transa = transa_tr
1013 47238 : IF (PRESENT(alpha)) al = alpha
1014 47238 : IF (PRESENT(n_rows)) m = n_rows
1015 47238 : IF (PRESENT(n_cols)) n = n_cols
1016 :
1017 47238 : IF (invert) THEN
1018 :
1019 : #if defined(__parallel)
1020 : CALL pztrsm(side_char, uplo, transa, unit_diag, m, n, al, &
1021 : triangular_matrix%local_data(1, 1), 1, 1, &
1022 : triangular_matrix%matrix_struct%descriptor, &
1023 : matrix_b%local_data(1, 1), 1, 1, &
1024 534 : matrix_b%matrix_struct%descriptor(1))
1025 : #else
1026 : CALL ztrsm(side_char, uplo, transa, unit_diag, m, n, al, &
1027 : triangular_matrix%local_data(1, 1), &
1028 : SIZE(triangular_matrix%local_data, 1), &
1029 : matrix_b%local_data(1, 1), SIZE(matrix_b%local_data, 1))
1030 : #endif
1031 :
1032 : ELSE
1033 :
1034 : #if defined(__parallel)
1035 : CALL pztrmm(side_char, uplo, transa, unit_diag, m, n, al, &
1036 : triangular_matrix%local_data(1, 1), 1, 1, &
1037 : triangular_matrix%matrix_struct%descriptor, &
1038 : matrix_b%local_data(1, 1), 1, 1, &
1039 46704 : matrix_b%matrix_struct%descriptor(1))
1040 : #else
1041 : CALL ztrmm(side_char, uplo, transa, unit_diag, m, n, al, &
1042 : triangular_matrix%local_data(1, 1), &
1043 : SIZE(triangular_matrix%local_data, 1), &
1044 : matrix_b%local_data(1, 1), SIZE(matrix_b%local_data, 1))
1045 : #endif
1046 :
1047 : END IF
1048 :
1049 47238 : CALL timestop(handle)
1050 :
1051 47238 : END SUBROUTINE cp_cfm_triangular_multiply
1052 :
1053 : ! **************************************************************************************************
1054 : !> \brief Inverts a triangular matrix.
1055 : !> \param matrix_a ...
1056 : !> \param uplo ...
1057 : !> \param info_out ...
1058 : !> \author MI
1059 : ! **************************************************************************************************
1060 15568 : SUBROUTINE cp_cfm_triangular_invert(matrix_a, uplo, info_out)
1061 : TYPE(cp_cfm_type), INTENT(IN) :: matrix_a
1062 : CHARACTER, INTENT(in), OPTIONAL :: uplo
1063 : INTEGER, INTENT(out), OPTIONAL :: info_out
1064 :
1065 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_triangular_invert'
1066 :
1067 : CHARACTER :: unit_diag, my_uplo
1068 : INTEGER :: handle, info, ncol_global
1069 : COMPLEX(kind=dp), DIMENSION(:, :), &
1070 15568 : POINTER :: a
1071 : #if defined(__parallel)
1072 : INTEGER, DIMENSION(9) :: desca
1073 : #endif
1074 :
1075 15568 : CALL timeset(routineN, handle)
1076 :
1077 15568 : unit_diag = 'N'
1078 15568 : my_uplo = 'U'
1079 15568 : IF (PRESENT(uplo)) my_uplo = uplo
1080 :
1081 15568 : ncol_global = matrix_a%matrix_struct%ncol_global
1082 :
1083 15568 : a => matrix_a%local_data
1084 :
1085 : #if defined(__parallel)
1086 155680 : desca(:) = matrix_a%matrix_struct%descriptor(:)
1087 15568 : CALL pztrtri(my_uplo, unit_diag, ncol_global, a(1, 1), 1, 1, desca, info)
1088 : #else
1089 : CALL ztrtri(my_uplo, unit_diag, ncol_global, a(1, 1), ncol_global, info)
1090 : #endif
1091 :
1092 15568 : IF (PRESENT(info_out)) THEN
1093 0 : info_out = info
1094 : ELSE
1095 15568 : IF (info /= 0) &
1096 : CALL cp_abort(__LOCATION__, &
1097 0 : "triangular invert failed: matrix is not positive definite or ill-conditioned")
1098 : END IF
1099 :
1100 15568 : CALL timestop(handle)
1101 15568 : END SUBROUTINE cp_cfm_triangular_invert
1102 :
1103 : ! **************************************************************************************************
1104 : !> \brief Transposes a BLACS distributed complex matrix.
1105 : !> \param matrix input matrix
1106 : !> \param trans 'T' for transpose, 'C' for Hermitian conjugate
1107 : !> \param matrixt output matrix
1108 : !> \author Lianheng Tong
1109 : ! **************************************************************************************************
1110 15772 : SUBROUTINE cp_cfm_transpose(matrix, trans, matrixt)
1111 : TYPE(cp_cfm_type), INTENT(IN) :: matrix
1112 : CHARACTER, INTENT(in) :: trans
1113 : TYPE(cp_cfm_type), INTENT(IN) :: matrixt
1114 :
1115 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_transpose'
1116 :
1117 15772 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: aa, cc
1118 : INTEGER :: handle, ncol_global, nrow_global
1119 : #if defined(__parallel)
1120 : INTEGER, DIMENSION(9) :: desca, descc
1121 : #elif !defined(__MKL)
1122 : INTEGER :: ii, jj
1123 : #endif
1124 :
1125 15772 : CALL timeset(routineN, handle)
1126 :
1127 15772 : nrow_global = matrix%matrix_struct%nrow_global
1128 15772 : ncol_global = matrix%matrix_struct%ncol_global
1129 :
1130 15772 : CPASSERT(matrixt%matrix_struct%nrow_global == ncol_global)
1131 15772 : CPASSERT(matrixt%matrix_struct%ncol_global == nrow_global)
1132 :
1133 15772 : aa => matrix%local_data
1134 15772 : cc => matrixt%local_data
1135 :
1136 : #if defined(__parallel)
1137 157720 : desca = matrix%matrix_struct%descriptor
1138 157720 : descc = matrixt%matrix_struct%descriptor
1139 6610 : SELECT CASE (trans)
1140 : CASE ('T')
1141 : CALL pztranu(nrow_global, ncol_global, &
1142 : z_one, aa(1, 1), 1, 1, desca, &
1143 6610 : z_zero, cc(1, 1), 1, 1, descc)
1144 : CASE ('C')
1145 : CALL pztranc(nrow_global, ncol_global, &
1146 : z_one, aa(1, 1), 1, 1, desca, &
1147 9162 : z_zero, cc(1, 1), 1, 1, descc)
1148 : CASE DEFAULT
1149 15772 : CPABORT("trans only accepts 'T' or 'C'")
1150 : END SELECT
1151 : #elif defined(__MKL)
1152 : CALL mkl_zomatcopy('C', trans, nrow_global, ncol_global, 1.0_dp, aa(1, 1), nrow_global, cc(1, 1), ncol_global)
1153 : #else
1154 : SELECT CASE (trans)
1155 : CASE ('T')
1156 : DO jj = 1, ncol_global
1157 : DO ii = 1, nrow_global
1158 : cc(ii, jj) = aa(jj, ii)
1159 : END DO
1160 : END DO
1161 : CASE ('C')
1162 : DO jj = 1, ncol_global
1163 : DO ii = 1, nrow_global
1164 : cc(ii, jj) = CONJG(aa(jj, ii))
1165 : END DO
1166 : END DO
1167 : CASE DEFAULT
1168 : CPABORT("trans only accepts 'T' or 'C'")
1169 : END SELECT
1170 : #endif
1171 :
1172 15772 : CALL timestop(handle)
1173 15772 : END SUBROUTINE cp_cfm_transpose
1174 :
1175 : ! **************************************************************************************************
1176 : !> \brief Norm of matrix using (p)zlange.
1177 : !> \param matrix input a general matrix
1178 : !> \param mode 'M' max abs element value,
1179 : !> '1' or 'O' one norm, i.e. maximum column sum,
1180 : !> 'I' infinity norm, i.e. maximum row sum,
1181 : !> 'F' or 'E' Frobenius norm, i.e. sqrt of sum of all squares of elements
1182 : !> \return the norm according to mode
1183 : !> \author Lianheng Tong
1184 : ! **************************************************************************************************
1185 104990 : FUNCTION cp_cfm_norm(matrix, mode) RESULT(res)
1186 : TYPE(cp_cfm_type), INTENT(IN) :: matrix
1187 : CHARACTER, INTENT(IN) :: mode
1188 : REAL(kind=dp) :: res
1189 :
1190 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_norm'
1191 :
1192 104990 : COMPLEX(kind=dp), DIMENSION(:, :), POINTER :: aa
1193 : INTEGER :: handle, lwork, ncols, ncols_local, &
1194 : nrows, nrows_local
1195 104990 : REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: work
1196 :
1197 : #if defined(__parallel)
1198 : INTEGER, DIMENSION(9) :: desca
1199 : #else
1200 : INTEGER :: lda
1201 : #endif
1202 :
1203 104990 : CALL timeset(routineN, handle)
1204 :
1205 : CALL cp_cfm_get_info(matrix=matrix, &
1206 : nrow_global=nrows, &
1207 : ncol_global=ncols, &
1208 : nrow_local=nrows_local, &
1209 104990 : ncol_local=ncols_local)
1210 104990 : aa => matrix%local_data
1211 :
1212 : SELECT CASE (mode)
1213 : CASE ('M', 'm')
1214 0 : lwork = 1
1215 : CASE ('1', 'O', 'o')
1216 : #if defined(__parallel)
1217 0 : lwork = ncols_local
1218 : #else
1219 : lwork = 1
1220 : #endif
1221 : CASE ('I', 'i')
1222 : #if defined(__parallel)
1223 0 : lwork = nrows_local
1224 : #else
1225 : lwork = nrows
1226 : #endif
1227 : CASE ('F', 'f', 'E', 'e')
1228 0 : lwork = 1
1229 : CASE DEFAULT
1230 104990 : CPABORT("mode input is not valid")
1231 : END SELECT
1232 :
1233 314970 : ALLOCATE (work(lwork))
1234 :
1235 : #if defined(__parallel)
1236 1049900 : desca = matrix%matrix_struct%descriptor
1237 104990 : res = pzlange(mode, nrows, ncols, aa(1, 1), 1, 1, desca, work)
1238 : #else
1239 : lda = SIZE(aa, 1)
1240 : res = zlange(mode, nrows, ncols, aa(1, 1), lda, work)
1241 : #endif
1242 :
1243 104990 : DEALLOCATE (work)
1244 104990 : CALL timestop(handle)
1245 104990 : END FUNCTION cp_cfm_norm
1246 :
1247 : ! **************************************************************************************************
1248 : !> \brief Applies a planar rotation defined by cs and sn to the i'th and j'th rows.
1249 : !> \param matrix ...
1250 : !> \param irow ...
1251 : !> \param jrow ...
1252 : !> \param cs cosine of the rotation angle
1253 : !> \param sn sinus of the rotation angle
1254 : !> \author Ole Schuett
1255 : ! **************************************************************************************************
1256 0 : SUBROUTINE cp_cfm_rot_rows(matrix, irow, jrow, cs, sn)
1257 : TYPE(cp_cfm_type), INTENT(IN) :: matrix
1258 : INTEGER, INTENT(IN) :: irow, jrow
1259 : REAL(dp), INTENT(IN) :: cs, sn
1260 :
1261 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_rot_rows'
1262 : INTEGER :: handle, nrow, ncol
1263 : COMPLEX(KIND=dp) :: sn_cmplx
1264 :
1265 : #if defined(__parallel)
1266 : INTEGER :: info, lwork
1267 : INTEGER, DIMENSION(9) :: desc
1268 0 : REAL(dp), DIMENSION(:), ALLOCATABLE :: work
1269 : #endif
1270 :
1271 0 : CALL timeset(routineN, handle)
1272 0 : CALL cp_cfm_get_info(matrix, nrow_global=nrow, ncol_global=ncol)
1273 0 : sn_cmplx = CMPLX(sn, 0.0_dp, dp)
1274 :
1275 : #if defined(__parallel)
1276 0 : lwork = 2*ncol + 1
1277 0 : ALLOCATE (work(lwork))
1278 0 : desc(:) = matrix%matrix_struct%descriptor(:)
1279 : CALL pzrot(ncol, &
1280 : matrix%local_data(1, 1), irow, 1, desc, ncol, &
1281 : matrix%local_data(1, 1), jrow, 1, desc, ncol, &
1282 0 : cs, sn_cmplx, work, lwork, info)
1283 0 : CPASSERT(info == 0)
1284 0 : DEALLOCATE (work)
1285 : #else
1286 : CALL zrot(ncol, matrix%local_data(irow, 1), ncol, matrix%local_data(jrow, 1), ncol, cs, sn_cmplx)
1287 : #endif
1288 :
1289 0 : CALL timestop(handle)
1290 0 : END SUBROUTINE cp_cfm_rot_rows
1291 :
1292 : ! **************************************************************************************************
1293 : !> \brief Applies a planar rotation defined by cs and sn to the i'th and j'th columnns.
1294 : !> \param matrix ...
1295 : !> \param icol ...
1296 : !> \param jcol ...
1297 : !> \param cs cosine of the rotation angle
1298 : !> \param sn sinus of the rotation angle
1299 : !> \author Ole Schuett
1300 : ! **************************************************************************************************
1301 0 : SUBROUTINE cp_cfm_rot_cols(matrix, icol, jcol, cs, sn)
1302 : TYPE(cp_cfm_type), INTENT(IN) :: matrix
1303 : INTEGER, INTENT(IN) :: icol, jcol
1304 : REAL(dp), INTENT(IN) :: cs, sn
1305 :
1306 : CHARACTER(len=*), PARAMETER :: routineN = 'cp_cfm_rot_cols'
1307 : INTEGER :: handle, nrow, ncol
1308 : COMPLEX(KIND=dp) :: sn_cmplx
1309 :
1310 : #if defined(__parallel)
1311 : INTEGER :: info, lwork
1312 : INTEGER, DIMENSION(9) :: desc
1313 0 : REAL(dp), DIMENSION(:), ALLOCATABLE :: work
1314 : #endif
1315 :
1316 0 : CALL timeset(routineN, handle)
1317 0 : CALL cp_cfm_get_info(matrix, nrow_global=nrow, ncol_global=ncol)
1318 0 : sn_cmplx = CMPLX(sn, 0.0_dp, dp)
1319 :
1320 : #if defined(__parallel)
1321 0 : lwork = 2*nrow + 1
1322 0 : ALLOCATE (work(lwork))
1323 0 : desc(:) = matrix%matrix_struct%descriptor(:)
1324 : CALL pzrot(nrow, &
1325 : matrix%local_data(1, 1), 1, icol, desc, 1, &
1326 : matrix%local_data(1, 1), 1, jcol, desc, 1, &
1327 0 : cs, sn_cmplx, work, lwork, info)
1328 0 : CPASSERT(info == 0)
1329 0 : DEALLOCATE (work)
1330 : #else
1331 : CALL zrot(nrow, matrix%local_data(1, icol), 1, matrix%local_data(1, jcol), 1, cs, sn_cmplx)
1332 : #endif
1333 :
1334 0 : CALL timestop(handle)
1335 0 : END SUBROUTINE cp_cfm_rot_cols
1336 :
1337 : ! **************************************************************************************************
1338 : !> \brief ...
1339 : !> \param matrix ...
1340 : !> \param workspace ...
1341 : !> \param uplo triangular format; defaults to 'U'
1342 : !> \par History
1343 : !> 12.2024 Added optional workspace as input [Rocco Meli]
1344 : !> \author Jan Wilhelm
1345 : ! **************************************************************************************************
1346 10888 : SUBROUTINE cp_cfm_uplo_to_full(matrix, workspace, uplo)
1347 :
1348 : TYPE(cp_cfm_type), INTENT(IN) :: matrix
1349 : TYPE(cp_cfm_type), INTENT(IN), OPTIONAL :: workspace
1350 : CHARACTER, INTENT(IN), OPTIONAL :: uplo
1351 :
1352 : CHARACTER(LEN=*), PARAMETER :: routineN = 'cp_cfm_uplo_to_full'
1353 :
1354 : CHARACTER :: myuplo
1355 : INTEGER :: handle, i_global, iiB, j_global, jjB, &
1356 : ncol_local, nrow_local
1357 5444 : INTEGER, DIMENSION(:), POINTER :: col_indices, row_indices
1358 : TYPE(cp_cfm_type) :: work
1359 :
1360 5444 : CALL timeset(routineN, handle)
1361 :
1362 5444 : IF (.NOT. PRESENT(workspace)) THEN
1363 5054 : CALL cp_cfm_create(work, matrix%matrix_struct)
1364 : ELSE
1365 390 : work = workspace
1366 : END IF
1367 :
1368 5444 : myuplo = 'U'
1369 5444 : IF (PRESENT(uplo)) myuplo = uplo
1370 :
1371 : ! get info of fm_mat_Q
1372 : CALL cp_cfm_get_info(matrix=matrix, &
1373 : nrow_local=nrow_local, &
1374 : ncol_local=ncol_local, &
1375 : row_indices=row_indices, &
1376 5444 : col_indices=col_indices)
1377 :
1378 215586 : DO jjB = 1, ncol_local
1379 210142 : j_global = col_indices(jjB)
1380 7473124 : DO iiB = 1, nrow_local
1381 7257538 : i_global = row_indices(iiB)
1382 7467680 : IF (MERGE(j_global < i_global, j_global > i_global, (myuplo == "U") .OR. (myuplo == "u"))) THEN
1383 3574867 : matrix%local_data(iiB, jjB) = z_zero
1384 3682671 : ELSE IF (j_global == i_global) THEN
1385 107804 : matrix%local_data(iiB, jjB) = matrix%local_data(iiB, jjB)/(2.0_dp, 0.0_dp)
1386 : END IF
1387 : END DO
1388 : END DO
1389 :
1390 5444 : CALL cp_cfm_transpose(matrix, 'C', work)
1391 :
1392 5444 : CALL cp_cfm_scale_and_add(z_one, matrix, z_one, work)
1393 :
1394 5444 : IF (.NOT. PRESENT(workspace)) THEN
1395 5054 : CALL cp_cfm_release(work)
1396 : END IF
1397 :
1398 5444 : CALL timestop(handle)
1399 :
1400 5444 : END SUBROUTINE cp_cfm_uplo_to_full
1401 :
1402 : END MODULE cp_cfm_basic_linalg
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