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 Calculation of overlap matrix condition numbers
10 : !> \par History
11 : !> \author JGH (14.11.2016)
12 : ! **************************************************************************************************
13 : MODULE qs_condnum
14 : USE arnoldi_api, ONLY: arnoldi_conjugate_gradient,&
15 : arnoldi_extremal
16 : USE cp_blacs_env, ONLY: cp_blacs_env_type
17 : USE cp_dbcsr_api, ONLY: &
18 : dbcsr_add, dbcsr_copy, dbcsr_create, dbcsr_desymmetrize, dbcsr_get_block_diag, &
19 : dbcsr_get_info, dbcsr_get_matrix_type, dbcsr_iterator_blocks_left, &
20 : dbcsr_iterator_next_block, dbcsr_iterator_start, dbcsr_iterator_stop, dbcsr_iterator_type, &
21 : dbcsr_p_type, dbcsr_release, dbcsr_type, dbcsr_type_no_symmetry, dbcsr_type_symmetric
22 : USE cp_dbcsr_contrib, ONLY: dbcsr_gershgorin_norm
23 : USE cp_dbcsr_operations, ONLY: copy_dbcsr_to_fm
24 : USE cp_fm_basic_linalg, ONLY: cp_fm_norm
25 : USE cp_fm_diag, ONLY: cp_fm_power
26 : USE cp_fm_struct, ONLY: cp_fm_struct_create,&
27 : cp_fm_struct_release,&
28 : cp_fm_struct_type
29 : USE cp_fm_types, ONLY: cp_fm_create,&
30 : cp_fm_release,&
31 : cp_fm_type
32 : USE kinds, ONLY: dp
33 : USE mathlib, ONLY: invmat
34 : #include "./base/base_uses.f90"
35 :
36 : IMPLICIT NONE
37 :
38 : PRIVATE
39 :
40 : ! *** Global parameters ***
41 :
42 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'qs_condnum'
43 :
44 : ! *** Public subroutines ***
45 :
46 : PUBLIC :: overlap_condnum
47 :
48 : CONTAINS
49 :
50 : ! **************************************************************************************************
51 : !> \brief Calculation of the overlap matrix Condition Number
52 : !> \param matrixkp_s The overlap matrices to be calculated (kpoints, optional)
53 : !> \param condnum Condition numbers for 1 and 2 norm
54 : !> \param iunit output unit
55 : !> \param norml1 logical: calculate estimate to 1-norm
56 : !> \param norml2 logical: calculate estimate to 1-norm and 2-norm condition number
57 : !> \param use_arnoldi logical: use Arnoldi iteration to estimate 2-norm condition number
58 : !> \param blacs_env ...
59 : !> \date 07.11.2016
60 : !> \par History
61 : !> \author JHU
62 : !> \version 1.0
63 : ! **************************************************************************************************
64 274 : SUBROUTINE overlap_condnum(matrixkp_s, condnum, iunit, norml1, norml2, use_arnoldi, blacs_env)
65 :
66 : TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER :: matrixkp_s
67 : REAL(KIND=dp), DIMENSION(2), INTENT(INOUT) :: condnum
68 : INTEGER, INTENT(IN) :: iunit
69 : LOGICAL, INTENT(IN) :: norml1, norml2, use_arnoldi
70 : TYPE(cp_blacs_env_type), POINTER :: blacs_env
71 :
72 : CHARACTER(len=*), PARAMETER :: routineN = 'overlap_condnum'
73 :
74 : INTEGER :: handle, ic, maxiter, nbas, ndep
75 : LOGICAL :: converged
76 : REAL(KIND=dp) :: amnorm, anorm, eps_ev, max_ev, min_ev, &
77 : threshold
78 : REAL(KIND=dp), DIMENSION(2) :: eigvals
79 : TYPE(cp_fm_struct_type), POINTER :: matrix_struct
80 : TYPE(cp_fm_type) :: fmsmat, fmwork
81 : TYPE(dbcsr_type) :: tempmat
82 : TYPE(dbcsr_type), POINTER :: smat
83 :
84 274 : CALL timeset(routineN, handle)
85 :
86 274 : condnum(1:2) = 0.0_dp
87 274 : NULLIFY (smat)
88 274 : IF (SIZE(matrixkp_s, 2) == 1) THEN
89 268 : IF (iunit > 0) WRITE (iunit, '(/,T2,A)') "OVERLAP MATRIX CONDITION NUMBER"
90 268 : smat => matrixkp_s(1, 1)%matrix
91 : ELSE
92 6 : IF (iunit > 0) WRITE (iunit, '(/,T2,A)') "OVERLAP MATRIX CONDITION NUMBER AT GAMMA POINT"
93 6 : ALLOCATE (smat)
94 6 : CALL dbcsr_create(smat, template=matrixkp_s(1, 1)%matrix)
95 6 : CALL dbcsr_copy(smat, matrixkp_s(1, 1)%matrix)
96 2050 : DO ic = 2, SIZE(matrixkp_s, 2)
97 2050 : CALL dbcsr_add(smat, matrixkp_s(1, ic)%matrix, 1.0_dp, 1.0_dp)
98 : END DO
99 : END IF
100 : !
101 274 : IF (ASSOCIATED(smat)) THEN
102 274 : CPASSERT(dbcsr_get_matrix_type(smat) .EQ. dbcsr_type_symmetric)
103 274 : IF (norml1) THEN
104 : ! norm of S
105 40 : anorm = dbcsr_gershgorin_norm(smat)
106 40 : CALL estimate_norm_invmat(smat, amnorm)
107 40 : IF (iunit > 0) THEN
108 20 : WRITE (iunit, '(T2,A)') "1-Norm Condition Number (Estimate)"
109 : WRITE (iunit, '(T4,A,ES11.3E3,T32,A,ES11.3E3,A4,ES11.3E3,T63,A,F8.4)') &
110 20 : "CN : |A|*|A^-1|: ", anorm, " * ", amnorm, "=", anorm*amnorm, "Log(1-CN):", LOG10(anorm*amnorm)
111 : END IF
112 40 : condnum(1) = anorm*amnorm
113 : END IF
114 274 : IF (norml2) THEN
115 246 : eps_ev = 1.0E-14_dp
116 : ! diagonalization
117 246 : CALL dbcsr_get_info(smat, nfullrows_total=nbas)
118 : CALL cp_fm_struct_create(fmstruct=matrix_struct, context=blacs_env, &
119 246 : nrow_global=nbas, ncol_global=nbas)
120 246 : CALL cp_fm_create(fmsmat, matrix_struct)
121 246 : CALL cp_fm_create(fmwork, matrix_struct)
122 : ! transfer to FM
123 246 : CALL dbcsr_create(tempmat, template=smat, matrix_type=dbcsr_type_no_symmetry)
124 246 : CALL dbcsr_desymmetrize(smat, tempmat)
125 246 : CALL copy_dbcsr_to_fm(tempmat, fmsmat)
126 :
127 : ! diagonalize
128 246 : anorm = cp_fm_norm(fmsmat, "1")
129 246 : CALL cp_fm_power(fmsmat, fmwork, -1.0_dp, eps_ev, ndep, eigvals=eigvals)
130 246 : min_ev = eigvals(1)
131 246 : max_ev = eigvals(2)
132 246 : amnorm = cp_fm_norm(fmsmat, "1")
133 :
134 246 : CALL dbcsr_release(tempmat)
135 246 : CALL cp_fm_release(fmsmat)
136 246 : CALL cp_fm_release(fmwork)
137 246 : CALL cp_fm_struct_release(matrix_struct)
138 :
139 246 : IF (iunit > 0) THEN
140 6 : WRITE (iunit, '(T2,A)') "1-Norm and 2-Norm Condition Numbers using Diagonalization"
141 6 : IF (min_ev > 0) THEN
142 : WRITE (iunit, '(T4,A,ES11.3E3,T32,A,ES11.3E3,A4,ES11.3E3,T63,A,F8.4)') &
143 6 : "CN : |A|*|A^-1|: ", anorm, " * ", amnorm, "=", anorm*amnorm, "Log(1-CN):", LOG10(anorm*amnorm)
144 : WRITE (iunit, '(T4,A,ES11.3E3,T32,A,ES11.3E3,A4,ES11.3E3,T63,A,F8.4)') &
145 6 : "CN : max/min ev: ", max_ev, " / ", min_ev, "=", max_ev/min_ev, "Log(2-CN):", LOG10(max_ev/min_ev)
146 : ELSE
147 : WRITE (iunit, '(T4,A,ES11.3E3,T32,A,ES11.3E3,T63,A)') &
148 0 : "CN : max/min EV: ", max_ev, " / ", min_ev, "Log(CN): infinity"
149 : END IF
150 : END IF
151 246 : IF (min_ev > 0) THEN
152 246 : condnum(1) = anorm*amnorm
153 246 : condnum(2) = max_ev/min_ev
154 : ELSE
155 0 : condnum(1:2) = 0.0_dp
156 : END IF
157 : END IF
158 274 : IF (use_arnoldi) THEN
159 : ! parameters for matrix condition test
160 12 : threshold = 1.0E-6_dp
161 12 : maxiter = 1000
162 12 : eps_ev = 1.0E8_dp
163 : CALL arnoldi_extremal(smat, max_ev, min_ev, &
164 12 : threshold=threshold, max_iter=maxiter, converged=converged)
165 12 : IF (iunit > 0) THEN
166 6 : WRITE (iunit, '(T2,A)') "2-Norm Condition Number using Arnoldi iterations"
167 6 : IF (min_ev > 0) THEN
168 : WRITE (iunit, '(T4,A,ES11.3E3,T32,A,ES11.3E3,A4,ES11.3E3,T63,A,F8.4)') &
169 6 : "CN : max/min ev: ", max_ev, " / ", min_ev, "=", max_ev/min_ev, "Log(2-CN):", LOG10(max_ev/min_ev)
170 : ELSE
171 : WRITE (iunit, '(T4,A,ES11.3E3,T32,A,ES11.3E3,T63,A)') &
172 0 : "CN : max/min ev: ", max_ev, " / ", min_ev, "Log(CN): infinity"
173 : END IF
174 : END IF
175 12 : IF (min_ev > 0) THEN
176 12 : condnum(2) = max_ev/min_ev
177 : ELSE
178 0 : condnum(2) = 0.0_dp
179 : END IF
180 12 : IF (converged) THEN
181 12 : IF (min_ev == 0) THEN
182 0 : CPWARN("Ill-conditioned S matrix: basis set is overcomplete.")
183 12 : ELSE IF ((max_ev/min_ev) > eps_ev) THEN
184 0 : CPWARN("Ill-conditioned S matrix: basis set is overcomplete.")
185 : END IF
186 : ELSE
187 0 : CPWARN("Condition number estimate of overlap matrix is not reliable (not converged).")
188 : END IF
189 : END IF
190 : END IF
191 274 : IF (SIZE(matrixkp_s, 2) == 1) THEN
192 : NULLIFY (smat)
193 : ELSE
194 6 : CALL dbcsr_release(smat)
195 6 : DEALLOCATE (smat)
196 : END IF
197 :
198 274 : CALL timestop(handle)
199 :
200 274 : END SUBROUTINE overlap_condnum
201 :
202 : ! **************************************************************************************************
203 : !> \brief Calculates an estimate of the 1-norm of the inverse of a matrix
204 : !> Uses LAPACK norm estimator algorithm
205 : !> NJ Higham, Function of Matrices, Algorithm 3.21, page 66
206 : !> \param amat Sparse, symmetric matrix
207 : !> \param anorm Estimate of ||INV(A)||
208 : !> \date 15.11.2016
209 : !> \par History
210 : !> \author JHU
211 : !> \version 1.0
212 : ! **************************************************************************************************
213 40 : SUBROUTINE estimate_norm_invmat(amat, anorm)
214 : TYPE(dbcsr_type), POINTER :: amat
215 : REAL(KIND=dp), INTENT(OUT) :: anorm
216 :
217 : INTEGER :: i, k, nbas
218 : INTEGER, DIMENSION(1) :: r
219 : REAL(KIND=dp) :: g, gg
220 40 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: x, xsi
221 : REAL(KIND=dp), DIMENSION(2) :: work
222 : REAL(KIND=dp), EXTERNAL :: dlange
223 : TYPE(dbcsr_type) :: pmat
224 :
225 : ! generate a block diagonal preconditioner
226 40 : CALL dbcsr_create(pmat, name="SMAT Preconditioner", template=amat)
227 : ! replicate the diagonal blocks of the overlap matrix
228 40 : CALL dbcsr_get_block_diag(amat, pmat)
229 : ! invert preconditioner
230 40 : CALL smat_precon_diag(pmat)
231 :
232 40 : anorm = 1.0_dp
233 40 : CALL dbcsr_get_info(amat, nfullrows_total=nbas)
234 160 : ALLOCATE (x(nbas), xsi(nbas))
235 1796 : x(1:nbas) = 1._dp/REAL(nbas, KIND=dp)
236 40 : CALL dbcsr_solve(amat, x, pmat)
237 40 : g = dlange("1", nbas, 1, x, nbas, work)
238 1796 : xsi(1:nbas) = SIGN(1._dp, x(1:nbas))
239 1796 : x(1:nbas) = xsi(1:nbas)
240 40 : CALL dbcsr_solve(amat, x, pmat)
241 40 : k = 2
242 : DO
243 1836 : r = MAXLOC(ABS(x))
244 1796 : x(1:nbas) = 0._dp
245 80 : x(r) = 1._dp
246 40 : CALL dbcsr_solve(amat, x, pmat)
247 40 : gg = g
248 40 : g = dlange("1", nbas, 1, x, nbas, work)
249 40 : IF (g <= gg) EXIT
250 1796 : x(1:nbas) = SIGN(1._dp, x(1:nbas))
251 3552 : IF (SUM(ABS(x - xsi)) == 0 .OR. SUM(ABS(x + xsi)) == 0) EXIT
252 1768 : xsi(1:nbas) = x(1:nbas)
253 38 : CALL dbcsr_solve(amat, x, pmat)
254 38 : k = k + 1
255 38 : IF (k > 5) EXIT
256 1808 : IF (SUM(r) == SUM(MAXLOC(ABS(x)))) EXIT
257 : END DO
258 : !
259 40 : IF (nbas > 1) THEN
260 1796 : DO i = 1, nbas
261 1796 : x(i) = -1._dp**(i + 1)*(1._dp + REAL(i - 1, dp)/REAL(nbas - 1, dp))
262 : END DO
263 : ELSE
264 0 : x(1) = 1.0_dp
265 : END IF
266 40 : CALL dbcsr_solve(amat, x, pmat)
267 40 : gg = dlange("1", nbas, 1, x, nbas, work)
268 40 : gg = 2._dp*gg/REAL(3*nbas, dp)
269 40 : anorm = MAX(g, gg)
270 40 : DEALLOCATE (x, xsi)
271 40 : CALL dbcsr_release(pmat)
272 :
273 80 : END SUBROUTINE estimate_norm_invmat
274 :
275 : ! **************************************************************************************************
276 : !> \brief ...
277 : !> \param amat ...
278 : !> \param x ...
279 : !> \param pmat ...
280 : ! **************************************************************************************************
281 198 : SUBROUTINE dbcsr_solve(amat, x, pmat)
282 : TYPE(dbcsr_type), POINTER :: amat
283 : REAL(KIND=dp), DIMENSION(:), INTENT(INOUT) :: x
284 : TYPE(dbcsr_type) :: pmat
285 :
286 : INTEGER :: max_iter, nbas
287 : LOGICAL :: converged
288 : REAL(KIND=dp) :: threshold
289 :
290 198 : CALL dbcsr_get_info(amat, nfullrows_total=nbas)
291 198 : max_iter = MIN(1000, nbas)
292 198 : threshold = 1.e-6_dp
293 198 : CALL arnoldi_conjugate_gradient(amat, x, pmat, converged=converged, threshold=threshold, max_iter=max_iter)
294 :
295 198 : END SUBROUTINE dbcsr_solve
296 :
297 : ! **************************************************************************************************
298 : !> \brief ...
299 : !> \param pmat ...
300 : ! **************************************************************************************************
301 40 : SUBROUTINE smat_precon_diag(pmat)
302 : TYPE(dbcsr_type) :: pmat
303 :
304 : INTEGER :: iatom, info, jatom, n
305 40 : REAL(KIND=dp), DIMENSION(:, :), POINTER :: sblock
306 : TYPE(dbcsr_iterator_type) :: dbcsr_iter
307 :
308 40 : CALL dbcsr_iterator_start(dbcsr_iter, pmat)
309 122 : DO WHILE (dbcsr_iterator_blocks_left(dbcsr_iter))
310 82 : CALL dbcsr_iterator_next_block(dbcsr_iter, iatom, jatom, sblock)
311 82 : CPASSERT(iatom == jatom)
312 82 : n = SIZE(sblock, 1)
313 82 : CALL invmat(sblock(1:n, 1:n), info)
314 122 : CPASSERT(info == 0)
315 : END DO
316 40 : CALL dbcsr_iterator_stop(dbcsr_iter)
317 :
318 40 : END SUBROUTINE smat_precon_diag
319 :
320 : END MODULE qs_condnum
321 :
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