Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
6 : This file is part of SLEPc.
7 : SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 : */
10 : /*
11 : BDC - Block-divide and conquer (see description in README file)
12 : */
13 :
14 : #include <slepc/private/dsimpl.h>
15 : #include <slepcblaslapack.h>
16 :
17 3 : static PetscErrorCode cutlr_(PetscBLASInt start,PetscBLASInt n,PetscBLASInt blkct,
18 : PetscBLASInt *bsizes,PetscBLASInt *ranks,PetscBLASInt *cut,
19 : PetscBLASInt *lsum,PetscBLASInt *lblks,PetscBLASInt *info)
20 : {
21 : /* -- Routine written in LAPACK Version 3.0 style -- */
22 : /* *************************************************** */
23 : /* Written by */
24 : /* Michael Moldaschl and Wilfried Gansterer */
25 : /* University of Vienna */
26 : /* last modification: March 16, 2014 */
27 :
28 : /* Small adaptations of original code written by */
29 : /* Wilfried Gansterer and Bob Ward, */
30 : /* Department of Computer Science, University of Tennessee */
31 : /* see https://doi.org/10.1137/S1064827501399432 */
32 : /* *************************************************** */
33 :
34 : /* Purpose */
35 : /* ======= */
36 :
37 : /* CUTLR computes the optimal cut in a sequence of BLKCT neighboring */
38 : /* blocks whose sizes are given by the array BSIZES. */
39 : /* The sum of all block sizes in the sequence considered is given by N. */
40 : /* The cut is optimal in the sense that the difference of the sizes of */
41 : /* the resulting two halves is minimum over all cuts with minimum ranks */
42 : /* between blocks of the sequence considered. */
43 :
44 : /* Arguments */
45 : /* ========= */
46 :
47 : /* START (input) INTEGER */
48 : /* In the original array KSIZES of the calling routine DIBTDC, */
49 : /* the position where the sequence considered in this routine starts. */
50 : /* START >= 1. */
51 :
52 : /* N (input) INTEGER */
53 : /* The sum of all the block sizes of the sequence to be cut = */
54 : /* = sum_{i=1}^{BLKCT} BSIZES(I). */
55 : /* N >= 3. */
56 :
57 : /* BLKCT (input) INTEGER */
58 : /* The number of blocks in the sequence to be cut. */
59 : /* BLKCT >= 3. */
60 :
61 : /* BSIZES (input) INTEGER array, dimension (BLKCT) */
62 : /* The dimensions of the (quadratic) blocks of the sequence to be */
63 : /* cut. sum_{i=1}^{BLKCT} BSIZES(I) = N. */
64 :
65 : /* RANKS (input) INTEGER array, dimension (BLKCT-1) */
66 : /* The ranks determining the approximations of the off-diagonal */
67 : /* blocks in the sequence considered. */
68 :
69 : /* CUT (output) INTEGER */
70 : /* After the optimum cut has been determined, the position (in the */
71 : /* overall problem as worked on in DIBTDC !) of the last block in */
72 : /* the first half of the sequence to be cut. */
73 : /* START <= CUT <= START+BLKCT-2. */
74 :
75 : /* LSUM (output) INTEGER */
76 : /* After the optimum cut has been determined, the sum of the */
77 : /* block sizes in the first half of the sequence to be cut. */
78 : /* LSUM < N. */
79 :
80 : /* LBLKS (output) INTEGER */
81 : /* After the optimum cut has been determined, the number of the */
82 : /* blocks in the first half of the sequence to be cut. */
83 : /* 1 <= LBLKS < BLKCT. */
84 :
85 : /* INFO (output) INTEGER */
86 : /* = 0: successful exit. */
87 : /* < 0: illegal arguments. */
88 : /* if INFO = -i, the i-th (input) argument had an illegal */
89 : /* value. */
90 : /* > 0: illegal results. */
91 : /* if INFO = i, the i-th (output) argument had an illegal */
92 : /* value. */
93 :
94 : /* Further Details */
95 : /* =============== */
96 :
97 : /* Based on code written by */
98 : /* Wilfried Gansterer and Bob Ward, */
99 : /* Department of Computer Science, University of Tennessee */
100 :
101 : /* ===================================================================== */
102 :
103 3 : PetscBLASInt i, ksk, kchk, ksum, nhalf, deviat, mindev, minrnk, tmpsum;
104 :
105 3 : PetscFunctionBegin;
106 3 : *info = 0;
107 3 : *lblks = 1;
108 3 : *lsum = 1;
109 3 : *cut = start;
110 :
111 3 : if (start < 1) *info = -1;
112 3 : else if (n < 3) *info = -2;
113 3 : else if (blkct < 3) *info = -3;
114 3 : if (*info == 0) {
115 : ksum = 0;
116 : kchk = 0;
117 19 : for (i = 0; i < blkct; ++i) {
118 16 : ksk = bsizes[i];
119 16 : ksum += ksk;
120 16 : if (ksk < 1) kchk = 1;
121 : }
122 3 : if (ksum != n || kchk == 1) *info = -4;
123 : }
124 3 : PetscCheck(!*info,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong argument %" PetscBLASInt_FMT " in CUTLR",-(*info));
125 :
126 : /* determine smallest rank in the range considered */
127 :
128 : minrnk = n;
129 16 : for (i = 0; i < blkct-1; ++i) {
130 13 : if (ranks[i] < minrnk) minrnk = ranks[i];
131 : }
132 :
133 : /* determine best cut among those with smallest rank */
134 :
135 3 : nhalf = n / 2;
136 3 : tmpsum = 0;
137 3 : mindev = n;
138 19 : for (i = 0; i < blkct; ++i) {
139 16 : tmpsum += bsizes[i];
140 16 : if (ranks[i] == minrnk) {
141 :
142 : /* determine deviation from "optimal" cut NHALF */
143 :
144 14 : deviat = tmpsum - nhalf;
145 14 : if (deviat<0) deviat = -deviat;
146 :
147 : /* compare to best deviation so far */
148 :
149 14 : if (deviat < mindev) {
150 8 : mindev = deviat;
151 8 : *cut = start + i;
152 8 : *lblks = i + 1;
153 8 : *lsum = tmpsum;
154 : }
155 : }
156 : }
157 :
158 3 : if (*cut < start || *cut >= start + blkct - 1) *info = 6;
159 3 : else if (*lsum < 1 || *lsum >= n) *info = 7;
160 3 : else if (*lblks < 1 || *lblks >= blkct) *info = 8;
161 3 : PetscFunctionReturn(PETSC_SUCCESS);
162 : }
163 :
164 1 : PetscErrorCode BDC_dibtdc_(const char *jobz,PetscBLASInt n,PetscBLASInt nblks,
165 : PetscBLASInt *ksizes,PetscReal *d,PetscBLASInt l1d,PetscBLASInt l2d,
166 : PetscReal *e,PetscBLASInt *rank,PetscBLASInt l1e,PetscBLASInt l2e,
167 : PetscReal tol,PetscReal *ev,PetscReal *z,PetscBLASInt ldz,PetscReal *work,
168 : PetscBLASInt lwork,PetscBLASInt *iwork,PetscBLASInt liwork,
169 : PetscBLASInt *info,PetscBLASInt jobz_len)
170 : {
171 : /* -- Routine written in LAPACK Version 3.0 style -- */
172 : /* *************************************************** */
173 : /* Written by */
174 : /* Michael Moldaschl and Wilfried Gansterer */
175 : /* University of Vienna */
176 : /* last modification: March 16, 2014 */
177 :
178 : /* Small adaptations of original code written by */
179 : /* Wilfried Gansterer and Bob Ward, */
180 : /* Department of Computer Science, University of Tennessee */
181 : /* see https://doi.org/10.1137/S1064827501399432 */
182 : /* *************************************************** */
183 :
184 : /* Purpose */
185 : /* ======= */
186 :
187 : /* DIBTDC computes all eigenvalues and corresponding eigenvectors of a */
188 : /* symmetric irreducible block tridiagonal matrix with rank RANK matrices */
189 : /* as the subdiagonal blocks using a block divide and conquer method. */
190 :
191 : /* Arguments */
192 : /* ========= */
193 :
194 : /* JOBZ (input) CHARACTER*1 */
195 : /* = 'N': Compute eigenvalues only (not implemented); */
196 : /* = 'D': Compute eigenvalues and eigenvectors. */
197 : /* Eigenvectors are accumulated in the */
198 : /* divide-and-conquer process. */
199 :
200 : /* N (input) INTEGER */
201 : /* The dimension of the symmetric irreducible block tridiagonal */
202 : /* matrix. N >= 2. */
203 :
204 : /* NBLKS (input) INTEGER, 2 <= NBLKS <= N */
205 : /* The number of diagonal blocks in the matrix. */
206 :
207 : /* KSIZES (input) INTEGER array, dimension (NBLKS) */
208 : /* The dimension of the square diagonal blocks from top left */
209 : /* to bottom right. KSIZES(I) >= 1 for all I, and the sum of */
210 : /* KSIZES(I) for I = 1 to NBLKS has to be equal to N. */
211 :
212 : /* D (input) DOUBLE PRECISION array, dimension (L1D,L2D,NBLKS) */
213 : /* The lower triangular elements of the symmetric diagonal */
214 : /* blocks of the block tridiagonal matrix. Elements of the top */
215 : /* left diagonal block, which is of dimension KSIZES(1), are */
216 : /* contained in D(*,*,1); the elements of the next diagonal */
217 : /* block, which is of dimension KSIZES(2), are contained in */
218 : /* D(*,*,2); etc. */
219 :
220 : /* L1D (input) INTEGER */
221 : /* The leading dimension of the array D. L1D >= max(3,KMAX), */
222 : /* where KMAX is the dimension of the largest diagonal block. */
223 :
224 : /* L2D (input) INTEGER */
225 : /* The second dimension of the array D. L2D >= max(3,KMAX), */
226 : /* where KMAX is as stated in L1D above. */
227 :
228 : /* E (input) DOUBLE PRECISION array, dimension (L1E,L2E,NBLKS-1) */
229 : /* Contains the elements of the scalars (singular values) and */
230 : /* vectors (singular vectors) defining the rank RANK subdiagonal */
231 : /* blocks of the matrix. */
232 : /* E(1:RANK(K),RANK(K)+1,K) holds the RANK(K) scalars, */
233 : /* E(:,1:RANK(K),K) holds the RANK(K) column vectors, and */
234 : /* E(:,RANK(K)+2:2*RANK(K)+1,K) holds the row vectors for the K-th */
235 : /* subdiagonal block. */
236 :
237 : /* RANK (input) INTEGER array, dimension (NBLKS-1). */
238 : /* The ranks of all the subdiagonal blocks contained in the array E. */
239 : /* RANK(K) <= MIN(KSIZES(K), KSIZES(K+1)) */
240 :
241 : /* L1E (input) INTEGER */
242 : /* The leading dimension of the array E. L1E >= max(3,2*KMAX+1), */
243 : /* where KMAX is as stated in L1D above. */
244 :
245 : /* L2E (input) INTEGER */
246 : /* The second dimension of the array E. L2E >= max(3,2*KMAX+1), */
247 : /* where KMAX is as stated in L1D above. */
248 :
249 : /* TOL (input) DOUBLE PRECISION, TOL <= 1.0D-1 */
250 : /* User specified deflation tolerance for the routine DMERG2. */
251 : /* If (1.0D-1 >= TOL >= 20*EPS) then TOL is used as */
252 : /* the deflation tolerance in DSRTDF. */
253 : /* If (TOL < 20*EPS) then the standard deflation tolerance from */
254 : /* LAPACK is used as the deflation tolerance in DSRTDF. */
255 :
256 : /* EV (output) DOUBLE PRECISION array, dimension (N) */
257 : /* If INFO = 0, then EV contains the eigenvalues of the */
258 : /* symmetric block tridiagonal matrix in ascending order. */
259 :
260 : /* Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N) */
261 : /* On entry, Z will be the identity matrix. */
262 : /* On exit, Z contains the eigenvectors of the block tridiagonal */
263 : /* matrix. */
264 :
265 : /* LDZ (input) INTEGER */
266 : /* The leading dimension of the array Z. LDZ >= max(1,N). */
267 :
268 : /* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) */
269 :
270 : /* LWORK (input) INTEGER */
271 : /* The dimension of the array WORK. */
272 : /* In order to guarantee correct results in all cases, */
273 : /* LWORK must be at least (2*N**2 + 3*N). In many cases, */
274 : /* less workspace is required. The absolute minimum required is */
275 : /* (N**2 + 3*N). */
276 : /* If the workspace provided is not sufficient, the routine will */
277 : /* return a corresponding error code and report how much workspace */
278 : /* was missing (see INFO). */
279 :
280 : /* IWORK (workspace) INTEGER array, dimension (LIWORK) */
281 :
282 : /* LIWORK (input) INTEGER */
283 : /* The dimension of the array IWORK. */
284 : /* LIWORK must be at least (5*N + 3 + 4*NBLKS - 4): */
285 : /* 5*KMAX+3 for DSYEVD, 5*N for ????, */
286 : /* 4*NBLKS-4 for the preprocessing (merging order) */
287 : /* Summarizing, the minimum integer workspace needed is */
288 : /* MAX(5*N, 5*KMAX + 3) + 4*NBLKS - 4 */
289 :
290 : /* INFO (output) INTEGER */
291 : /* = 0: successful exit. */
292 : /* < 0, > -99: illegal arguments. */
293 : /* if INFO = -i, the i-th argument had an illegal value. */
294 : /* = -99: error in the preprocessing (call of CUTLR). */
295 : /* < -200: not enough workspace. Space for ABS(INFO + 200) */
296 : /* numbers is required in addition to the workspace provided, */
297 : /* otherwise some eigenvectors will be incorrect. */
298 : /* > 0: The algorithm failed to compute an eigenvalue while */
299 : /* working on the submatrix lying in rows and columns */
300 : /* INFO/(N+1) through mod(INFO,N+1). */
301 :
302 : /* Further Details */
303 : /* =============== */
304 :
305 : /* Based on code written by */
306 : /* Wilfried Gansterer and Bob Ward, */
307 : /* Department of Computer Science, University of Tennessee */
308 :
309 : /* This routine is comparable to Dlaed0.f from LAPACK. */
310 :
311 : /* ===================================================================== */
312 :
313 1 : PetscBLASInt i, j, k, np, rp1, ksk, one=1;
314 1 : PetscBLASInt cut, mat1, kchk, kbrk, blks, kmax, icut, size, ksum, lsum;
315 1 : PetscBLASInt lblks, rblks, isize, lwmin, ilsum;
316 1 : PetscBLASInt start, istck1, istck2, istck3, merged;
317 1 : PetscBLASInt liwmin, matsiz, startp, istrtp;
318 1 : PetscReal rho, done=1.0, dmone=-1.0;
319 :
320 1 : PetscFunctionBegin;
321 1 : *info = 0;
322 :
323 1 : if (*(unsigned char *)jobz != 'N' && *(unsigned char *)jobz != 'D') *info = -1;
324 1 : else if (n < 2) *info = -2;
325 1 : else if (nblks < 2 || nblks > n) *info = -3;
326 1 : if (*info == 0) {
327 : ksum = 0;
328 : kmax = 0;
329 : kchk = 0;
330 9 : for (k = 0; k < nblks; ++k) {
331 8 : ksk = ksizes[k];
332 8 : ksum += ksk;
333 8 : if (ksk > kmax) kmax = ksk;
334 8 : if (ksk < 1) kchk = 1;
335 : }
336 1 : lwmin = n*n + n * 3;
337 1 : liwmin = PetscMax(n * 5,kmax * 5 + 3) + 4*nblks - 4;
338 1 : if (ksum != n || kchk == 1) *info = -4;
339 1 : else if (l1d < PetscMax(3,kmax)) *info = -6;
340 1 : else if (l2d < PetscMax(3,kmax)) *info = -7;
341 1 : else if (l1e < PetscMax(3,2*kmax + 1)) *info = -10;
342 1 : else if (l2e < PetscMax(3,2*kmax + 1)) *info = -11;
343 1 : else if (tol > .1) *info = -12;
344 1 : else if (ldz < PetscMax(1,n)) *info = -15;
345 1 : else if (lwork < lwmin) *info = -17;
346 1 : else if (liwork < liwmin) *info = -19;
347 : }
348 1 : if (*info == 0) {
349 8 : for (k = 0; k < nblks-1; ++k) {
350 7 : if (rank[k] > PetscMin(ksizes[k],ksizes[k+1]) || rank[k] < 1) *info = -9;
351 : }
352 : }
353 :
354 1 : PetscCheck(!*info,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong argument %" PetscBLASInt_FMT " in DIBTDC",-(*info));
355 :
356 : /* **************************************************************************** */
357 :
358 : /* ...Preprocessing..................................................... */
359 : /* Determine the optimal order for merging the subblocks and how much */
360 : /* workspace will be needed for the merging (determined by the last */
361 : /* merge). Cutpoints for the merging operations are determined and stored */
362 : /* in reverse chronological order (starting with the final merging */
363 : /* operation). */
364 :
365 : /* integer workspace requirements for the preprocessing: */
366 : /* 4*(NBLKS-1) for merging history */
367 : /* at most 3*(NBLKS-1) for stack */
368 :
369 1 : start = 1;
370 1 : size = n;
371 1 : blks = nblks;
372 1 : merged = 0;
373 1 : k = 0;
374 :
375 : /* integer workspace used for the stack is not needed any more after the */
376 : /* preprocessing and therefore can use part of the 5*N */
377 : /* integer workspace needed later on in the code */
378 :
379 1 : istck1 = 0;
380 1 : istck2 = istck1 + nblks;
381 1 : istck3 = istck2 + nblks;
382 :
383 : /* integer workspace used for storing the order of merges starts AFTER */
384 : /* the integer workspace 5*N+3 which is needed later on in the code */
385 : /* (5*KMAX+3 for DSYEVD, 4*N in DMERG2) */
386 :
387 1 : istrtp = n * 5 + 4;
388 1 : icut = istrtp + nblks - 1;
389 1 : isize = icut + nblks - 1;
390 1 : ilsum = isize + nblks - 1;
391 :
392 2 : L200:
393 :
394 3 : if (nblks >= 3) {
395 :
396 : /* Determine the cut point. Note that in the routine CUTLR it is */
397 : /* chosen such that it yields the best balanced merging operation */
398 : /* among all the rank modifications with minimum rank. */
399 :
400 3 : PetscCall(cutlr_(start, size, blks, &ksizes[start-1], &rank[start-1], &cut, &lsum, &lblks, info));
401 3 : PetscCheck(!*info,PETSC_COMM_SELF,PETSC_ERR_PLIB,"dibtdc: Error in cutlr, info = %" PetscBLASInt_FMT,*info);
402 :
403 : } else {
404 0 : cut = 1;
405 0 : lsum = ksizes[0];
406 0 : lblks = 1;
407 : }
408 :
409 3 : ++merged;
410 3 : startp = 0;
411 7 : for (i = 0; i < start-1; ++i) startp += ksizes[i];
412 3 : iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
413 3 : iwork[icut + (nblks - 1) - merged-1] = cut;
414 3 : iwork[isize + (nblks - 1) - merged-1] = size;
415 3 : iwork[ilsum + (nblks - 1) - merged-1] = lsum;
416 :
417 3 : if (lblks == 2) {
418 :
419 : /* one merge in left branch, left branch done */
420 2 : ++merged;
421 2 : iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
422 2 : iwork[icut + (nblks - 1) - merged-1] = start;
423 2 : iwork[isize + (nblks - 1) - merged-1] = lsum;
424 2 : iwork[ilsum + (nblks - 1) - merged-1] = ksizes[start-1];
425 : }
426 :
427 3 : if (lblks == 1 || lblks == 2) {
428 :
429 : /* left branch done, continue on the right side */
430 2 : start += lblks;
431 2 : size -= lsum;
432 2 : blks -= lblks;
433 :
434 2 : PetscCheck(blks>0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"dibtdc: Error in preprocessing, blks = %" PetscBLASInt_FMT,blks);
435 :
436 2 : if (blks == 2) {
437 :
438 : /* one merge in right branch, right branch done */
439 2 : ++merged;
440 2 : startp += lsum;
441 2 : iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
442 2 : iwork[icut + (nblks - 1) - merged-1] = start;
443 2 : iwork[isize + (nblks - 1) - merged-1] = size;
444 2 : iwork[ilsum + (nblks - 1) - merged-1] = ksizes[start-1];
445 : }
446 :
447 2 : if (blks == 1 || blks == 2) {
448 :
449 : /* get the next subproblem from the stack or finished */
450 :
451 2 : if (k >= 1) {
452 :
453 : /* something left on the stack */
454 1 : start = iwork[istck1 + k-1];
455 1 : size = iwork[istck2 + k-1];
456 1 : blks = iwork[istck3 + k-1];
457 1 : --k;
458 1 : goto L200;
459 : } else {
460 :
461 : /* nothing left on the stack */
462 1 : PetscCheck(merged==nblks-1,PETSC_COMM_SELF,PETSC_ERR_PLIB,"ERROR in preprocessing - not enough merges performed");
463 :
464 : /* exit preprocessing */
465 :
466 : }
467 : } else {
468 :
469 : /* BLKS.GE.3, and therefore analyze the right side */
470 :
471 0 : goto L200;
472 : }
473 : } else {
474 :
475 : /* LBLKS.GE.3, and therefore check the right side and */
476 : /* put it on the stack if required */
477 :
478 1 : rblks = blks - lblks;
479 1 : if (rblks >= 3) {
480 1 : ++k;
481 1 : iwork[istck1 + k-1] = cut + 1;
482 1 : iwork[istck2 + k-1] = size - lsum;
483 1 : iwork[istck3 + k-1] = rblks;
484 0 : } else if (rblks == 2) {
485 :
486 : /* one merge in right branch, right branch done */
487 : /* (note that nothing needs to be done if RBLKS.EQ.1 !) */
488 :
489 0 : ++merged;
490 0 : startp += lsum;
491 0 : iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
492 0 : iwork[icut + (nblks - 1) - merged-1] = start + lblks;
493 0 : iwork[isize + (nblks - 1) - merged-1] = size - lsum;
494 0 : iwork[ilsum + (nblks - 1) - merged-1] = ksizes[start + lblks-1];
495 : }
496 1 : PetscCheck(rblks>0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"dibtdc: ERROR in preprocessing - rblks = %" PetscBLASInt_FMT,rblks);
497 :
498 : /* continue on the left side */
499 :
500 1 : size = lsum;
501 1 : blks = lblks;
502 1 : goto L200;
503 : }
504 :
505 : /* SIZE = IWORK(ISIZE+NBLKS-2) */
506 : /* MAT1 = IWORK(ILSUM+NBLKS-2) */
507 :
508 : /* Note: after the dimensions SIZE and MAT1 of the last merging */
509 : /* operation have been determined, an upper bound for the workspace */
510 : /* requirements which is independent of how much deflation occurs in */
511 : /* the last merging operation could be determined as follows */
512 : /* (based on (3.15) and (3.19) from UT-CS-00-447): */
513 :
514 : /* IF(MAT1.LE.N/2) THEN */
515 : /* WSPREQ = 3*N + 3/2*(SIZE-MAT1)**2 + N*N/2 + MAT1*MAT1 */
516 : /* ELSE */
517 : /* WSPREQ = 3*N + 3/2*MAT1*MAT1 + N*N/2 + (SIZE-MAT1)**2 */
518 : /* END IF */
519 :
520 : /* IF(LWORK-WSPREQ.LT.0)THEN */
521 : /* not enough work space provided */
522 : /* INFO = -200 - (WSPREQ-LWORK) */
523 : /* RETURN */
524 : /* END IF */
525 : /* However, this is not really useful, since the actual check whether */
526 : /* enough workspace is provided happens in DMERG2.f ! */
527 :
528 : /* ************************************************************************* */
529 :
530 : /* ...Solve subproblems................................... */
531 :
532 : /* Divide the matrix into NBLKS submatrices using rank-r */
533 : /* modifications (cuts) and solve for their eigenvalues and */
534 : /* eigenvectors. Initialize index array to sort eigenvalues. */
535 :
536 : /* first block: ...................................... */
537 :
538 : /* correction for block 1: D1 - V1 \Sigma1 V1^T */
539 :
540 1 : ksk = ksizes[0];
541 1 : rp1 = rank[0];
542 :
543 : /* initialize the proper part of Z with the diagonal block D1 */
544 : /* (the correction will be made in Z and then the call of DSYEVD will */
545 : /* overwrite it with the eigenvectors) */
546 :
547 10 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) z[i+j*ldz] = d[i+j*l1d];
548 :
549 : /* copy D1 into WORK (in order to be able to restore it afterwards) */
550 :
551 10 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) work[i+j*ksk] = d[i+j*l1d];
552 :
553 : /* copy V1 into the first RANK(1) columns of D1 and then */
554 : /* multiply with \Sigma1 */
555 :
556 4 : for (i = 0; i < rank[0]; ++i) {
557 3 : PetscCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(rp1 + i+1)*l1e], &one, &d[i*l1d], &one));
558 3 : PetscCallBLAS("BLASscal",BLASscal_(&ksk, &e[i + rp1*l1e], &d[i*l1d], &one));
559 : }
560 :
561 : /* multiply the first RANK(1) columns of D1 with V1^T and */
562 : /* subtract the result from the proper part of Z (previously */
563 : /* initialized with D1) */
564 :
565 1 : PetscCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, rank, &dmone,
566 : d, &l1d, &e[(rank[0]+1)*l1e], &l1e, &done, z, &ldz));
567 :
568 : /* restore the original D1 from WORK */
569 :
570 10 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) d[i+j*l1d] = work[i+j*ksk];
571 :
572 : /* eigenanalysis of block 1 (using DSYEVD) */
573 :
574 1 : PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V", "L", &ksk, z, &ldz, ev, work, &lwork, info));
575 1 : SlepcCheckLapackInfo("syev",*info);
576 :
577 : /* EV(1:) contains the eigenvalues in ascending order */
578 : /* (they are returned this way by DSYEVD) */
579 :
580 4 : for (i = 0; i < ksk; ++i) iwork[i] = i+1;
581 :
582 : /* intermediate blocks: .............................. */
583 :
584 1 : np = ksk;
585 :
586 : /* remaining number of blocks */
587 :
588 1 : if (nblks > 2) {
589 7 : for (k = 1; k < nblks-1; ++k) {
590 :
591 : /* correction for block K: */
592 : /* Dk - U(k-1) \Sigma(k-1) U(k-1)^T - Vk \Sigmak Vk^T */
593 :
594 6 : ksk = ksizes[k];
595 6 : rp1 = rank[k];
596 :
597 : /* initialize the proper part of Z with the diagonal block Dk */
598 : /* (the correction will be made in Z and then the call of DSYEVD will */
599 : /* overwrite it with the eigenvectors) */
600 :
601 60 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) z[np+i+(np+j)*ldz] = d[i+(j+k*l2d)*l1d];
602 :
603 : /* copy Dk into WORK (in order to be able to restore it afterwards) */
604 :
605 60 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) work[i+j*ksk] = d[i+(j+k*l2d)*l1d];
606 :
607 : /* copy U(K-1) into the first RANK(K-1) columns of Dk and then */
608 : /* multiply with \Sigma(K-1) */
609 :
610 24 : for (i = 0; i < rank[k-1]; ++i) {
611 18 : PetscCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(i+(k-1)*l2e)*l1e], &one, &d[(i+k*l2d)*l1d], &one));
612 18 : PetscCallBLAS("BLASscal",BLASscal_(&ksk, &e[i+(rank[k-1]+(k-1)*l2e)*l1e], &d[(i+k*l2d)*l1d], &one));
613 : }
614 :
615 : /* multiply the first RANK(K-1) columns of Dk with U(k-1)^T and */
616 : /* subtract the result from the proper part of Z (previously */
617 : /* initialized with Dk) */
618 :
619 6 : PetscCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, &rank[k-1],
620 : &dmone, &d[k*l1d*l2d],
621 : &l1d, &e[(k-1)*l1e*l2e], &l1e, &done, &z[np+np*ldz], &ldz));
622 :
623 : /* copy Vk into the first RANK(K) columns of Dk and then */
624 : /* multiply with \Sigmak */
625 :
626 24 : for (i = 0; i < rank[k]; ++i) {
627 18 : PetscCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(rp1+i+1 + k*l2e)*l1e], &one, &d[(i + k*l2d)*l1d], &one));
628 18 : PetscCallBLAS("BLASscal",BLASscal_(&ksk, &e[i + (rp1 + k*l2e)*l1e], &d[(i + k*l2d)*l1d], &one));
629 : }
630 :
631 : /* multiply the first RANK(K) columns of Dk with Vk^T and */
632 : /* subtract the result from the proper part of Z (previously */
633 : /* updated with [- U(k-1) \Sigma(k-1) U(k-1)^T]) */
634 :
635 6 : PetscCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, &rank[k],
636 : &dmone, &d[k*l1d*l2d], &l1d,
637 : &e[(rank[k]+1 + k*l2e)*l1e], &l1e, &done, &z[np+np*ldz], &ldz));
638 :
639 : /* restore the original Dk from WORK */
640 :
641 60 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) d[i+(j+k*l2d)*l1d] = work[i+j*ksk];
642 :
643 : /* eigenanalysis of block K (using dsyevd) */
644 :
645 6 : PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V", "L", &ksk, &z[np+np*ldz],
646 : &ldz, &ev[np], work, &lwork, info));
647 6 : SlepcCheckLapackInfo("syev",*info);
648 :
649 : /* EV(NPP1:) contains the eigenvalues in ascending order */
650 : /* (they are returned this way by DSYEVD) */
651 :
652 24 : for (i = 0; i < ksk; ++i) iwork[np + i] = i+1;
653 :
654 : /* update NP */
655 6 : np += ksk;
656 : }
657 : }
658 :
659 : /* last block: ....................................... */
660 :
661 : /* correction for block NBLKS: */
662 : /* D(nblks) - U(nblks-1) \Sigma(nblks-1) U(nblks-1)^T */
663 :
664 1 : ksk = ksizes[nblks-1];
665 :
666 : /* initialize the proper part of Z with the diagonal block D(nblks) */
667 : /* (the correction will be made in Z and then the call of DSYEVD will */
668 : /* overwrite it with the eigenvectors) */
669 :
670 10 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) z[np+i+(np+j)*ldz] = d[i+(j+(nblks-1)*l2d)*l1d];
671 :
672 : /* copy D(nblks) into WORK (in order to be able to restore it afterwards) */
673 :
674 10 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) work[i+j*ksk] = d[i+(j+(nblks-1)*l2d)*l1d];
675 :
676 : /* copy U(nblks-1) into the first RANK(nblks-1) columns of D(nblks) and then */
677 : /* multiply with \Sigma(nblks-1) */
678 :
679 4 : for (i = 0; i < rank[nblks-2]; ++i) {
680 3 : PetscCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(i + (nblks-2)*l2e)*l1e],
681 : &one, &d[(i + (nblks-1)*l2d)*l1d], &one));
682 3 : PetscCallBLAS("BLASscal",BLASscal_(&ksk,
683 : &e[i + (rank[nblks-2] + (nblks-2)*l2e)*l1e],
684 : &d[(i + (nblks-1)*l2d)*l1d], &one));
685 : }
686 :
687 : /* multiply the first RANK(nblks-1) columns of D(nblks) with U(nblks-1)^T */
688 : /* and subtract the result from the proper part of Z (previously */
689 : /* initialized with D(nblks)) */
690 :
691 1 : PetscCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, &rank[nblks - 2],
692 : &dmone, &d[(nblks-1)*l1d*l2d], &l1d,
693 : &e[(nblks-2)*l1e*l2e], &l1e, &done, &z[np+np*ldz], &ldz));
694 :
695 : /* restore the original D(nblks) from WORK */
696 :
697 10 : for (j=0;j<ksk;j++) for (i=j;i<ksk;i++) d[i+(j+(nblks-1)*l2d)*l1d] = work[i+j*ksk];
698 :
699 : /* eigenanalysis of block NBLKS (using dsyevd) */
700 :
701 1 : PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V", "L", &ksk, &z[np+np*ldz], &ldz, &ev[np], work, &lwork, info));
702 1 : SlepcCheckLapackInfo("syev",*info);
703 :
704 : /* EV(NPP1:) contains the eigenvalues in ascending order */
705 : /* (they are returned this way by DSYEVD) */
706 :
707 4 : for (i = 0; i < ksk; ++i) iwork[np + i] = i+1;
708 :
709 : /* note that from here on the entire workspace is available again */
710 :
711 : /* Perform all the merging operations. */
712 :
713 8 : for (i = 0; i < nblks-1; ++i) {
714 :
715 : /* MATSIZ = total size of the current rank RANK modification problem */
716 :
717 7 : matsiz = iwork[isize + i - 1];
718 7 : np = iwork[istrtp + i - 1];
719 7 : kbrk = iwork[icut + i - 1];
720 7 : mat1 = iwork[ilsum + i - 1];
721 :
722 28 : for (j = 0; j < rank[kbrk-1]; ++j) {
723 :
724 : /* NOTE: The parameter RHO in DMERG2 is modified in DSRTDF */
725 : /* (multiplied by 2) ! In order not to change the */
726 : /* singular value stored in E(:, RANK(KBRK)+1, KBRK), */
727 : /* we do not pass on this variable as an argument to DMERG2, */
728 : /* but we assign a separate variable RHO here which is passed */
729 : /* on to DMERG2. */
730 : /* Alternative solution in F90: */
731 : /* pass E(:,RANK(KBRK)+1,KBRK) to an INTENT(IN) parameter */
732 : /* in DMERG2. */
733 :
734 21 : rho = e[j + (rank[kbrk-1] + (kbrk-1)*l2e)*l1e];
735 :
736 : /* eigenvectors are accumulated (JOBZ.EQ.'D') */
737 :
738 21 : PetscCall(BDC_dmerg2_(jobz, j+1, matsiz, &ev[np-1], &z[np-1+(np-1)*ldz],
739 : ldz, &iwork[np-1], &rho, &e[(j + (kbrk-1)*l2e)*l1e],
740 : ksizes[kbrk], &e[(rank[kbrk-1]+j+1 + (kbrk-1)*l2e)*l1e],
741 : ksizes[kbrk-1], mat1, work, lwork, &iwork[n], tol, info, 1));
742 21 : PetscCheck(!*info,PETSC_COMM_SELF,PETSC_ERR_PLIB,"dibtdc: Error in dmerg2, info = %" PetscBLASInt_FMT,*info);
743 : }
744 :
745 : /* at this point all RANK(KBRK) rank-one modifications corresponding */
746 : /* to the current off-diagonal block are finished. */
747 : /* Move on to the next off-diagonal block. */
748 :
749 : }
750 :
751 : /* Re-merge the eigenvalues/vectors which were deflated at the final */
752 : /* merging step by sorting all eigenvalues and eigenvectors according */
753 : /* to the permutation stored in IWORK. */
754 :
755 : /* copy eigenvalues and eigenvectors in ordered form into WORK */
756 : /* (eigenvalues into WORK(1:N), eigenvectors into WORK(N+1:N+1+N^2)) */
757 :
758 25 : for (i = 0; i < n; ++i) {
759 24 : j = iwork[i];
760 24 : work[i] = ev[j-1];
761 24 : PetscCallBLAS("BLAScopy",BLAScopy_(&n, &z[(j-1)*ldz], &one, &work[n*(i+1)], &one));
762 : }
763 :
764 : /* copy ordered eigenvalues back from WORK(1:N) into EV */
765 :
766 1 : PetscCallBLAS("BLAScopy",BLAScopy_(&n, work, &one, ev, &one));
767 :
768 : /* copy ordered eigenvectors back from WORK(N+1:N+1+N^2) into Z */
769 :
770 601 : for (j=0;j<n;j++) for (i=0;i<n;i++) z[i+j*ldz] = work[i+(j+1)*n];
771 1 : PetscFunctionReturn(PETSC_SUCCESS);
772 : }
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