1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, Universitat Politecnica de Valencia, Spain
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: */
14: #include <slepc/private/dsimpl.h>
15: #include <slepcblaslapack.h>
17: 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 */
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: /* *************************************************** */
34: /* Purpose */
35: /* ======= */
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. */
44: /* Arguments */
45: /* ========= */
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. */
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. */
57: /* BLKCT (input) INTEGER */
58: /* The number of blocks in the sequence to be cut. */
59: /* BLKCT >= 3. */
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. */
65: /* RANKS (input) INTEGER array, dimension (BLKCT-1) */
66: /* The ranks determining the approximations of the off-diagonal */
67: /* blocks in the sequence considered. */
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. */
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. */
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. */
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. */
94: /* Further Details */
95: /* =============== */
97: /* Based on code written by */
98: /* Wilfried Gansterer and Bob Ward, */
99: /* Department of Computer Science, University of Tennessee */
101: /* ===================================================================== */
103: PetscBLASInt i, ksk, kchk, ksum, nhalf, deviat, mindev, minrnk, tmpsum;
106: *info = 0;
107: *lblks = 1;
108: *lsum = 1;
109: *cut = start;
111: if (start < 1) {
112: *info = -1;
113: } else if (n < 3) {
114: *info = -2;
115: } else if (blkct < 3) {
116: *info = -3;
117: }
118: if (*info == 0) {
119: ksum = 0;
120: kchk = 0;
121: for (i = 0; i < blkct; ++i) {
122: ksk = bsizes[i];
123: ksum += ksk;
124: if (ksk < 1) kchk = 1;
125: }
126: if (ksum != n || kchk == 1) *info = -4;
127: }
128: if (*info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong argument %d in CUTLR",-(*info));
130: /* determine smallest rank in the range considered */
132: minrnk = n;
133: for (i = 0; i < blkct-1; ++i) {
134: if (ranks[i] < minrnk) minrnk = ranks[i];
135: }
137: /* determine best cut among those with smallest rank */
139: nhalf = n / 2;
140: tmpsum = 0;
141: mindev = n;
142: for (i = 0; i < blkct; ++i) {
143: tmpsum += bsizes[i];
144: if (ranks[i] == minrnk) {
146: /* determine deviation from "optimal" cut NHALF */
148: deviat = tmpsum - nhalf;
149: if (deviat<0) deviat = -deviat;
151: /* compare to best deviation so far */
153: if (deviat < mindev) {
154: mindev = deviat;
155: *cut = start + i;
156: *lblks = i + 1;
157: *lsum = tmpsum;
158: }
159: }
160: }
162: if (*cut < start || *cut >= start + blkct - 1) {
163: *info = 6;
164: } else if (*lsum < 1 || *lsum >= n) {
165: *info = 7;
166: } else if (*lblks < 1 || *lblks >= blkct) {
167: *info = 8;
168: }
169: return(0);
170: }
172: PetscErrorCode BDC_dibtdc_(const char *jobz,PetscBLASInt n,PetscBLASInt nblks,173: PetscBLASInt *ksizes,PetscReal *d,PetscBLASInt l1d,PetscBLASInt l2d,174: PetscReal *e,PetscBLASInt *rank,PetscBLASInt l1e,PetscBLASInt l2e,175: PetscReal tol,PetscReal *ev,PetscReal *z,PetscBLASInt ldz,PetscReal *work,176: PetscBLASInt lwork,PetscBLASInt *iwork,PetscBLASInt liwork,177: PetscBLASInt *info,PetscBLASInt jobz_len)178: {
179: /* -- Routine written in LAPACK Version 3.0 style -- */
180: /* *************************************************** */
181: /* Written by */
182: /* Michael Moldaschl and Wilfried Gansterer */
183: /* University of Vienna */
184: /* last modification: March 16, 2014 */
186: /* Small adaptations of original code written by */
187: /* Wilfried Gansterer and Bob Ward, */
188: /* Department of Computer Science, University of Tennessee */
189: /* see https://doi.org/10.1137/S1064827501399432 */
190: /* *************************************************** */
192: /* Purpose */
193: /* ======= */
195: /* DIBTDC computes all eigenvalues and corresponding eigenvectors of a */
196: /* symmetric irreducible block tridiagonal matrix with rank RANK matrices */
197: /* as the subdiagonal blocks using a block divide and conquer method. */
199: /* Arguments */
200: /* ========= */
202: /* JOBZ (input) CHARACTER*1 */
203: /* = 'N': Compute eigenvalues only (not implemented); */
204: /* = 'D': Compute eigenvalues and eigenvectors. */
205: /* Eigenvectors are accumulated in the */
206: /* divide-and-conquer process. */
208: /* N (input) INTEGER */
209: /* The dimension of the symmetric irreducible block tridiagonal */
210: /* matrix. N >= 2. */
212: /* NBLKS (input) INTEGER, 2 <= NBLKS <= N */
213: /* The number of diagonal blocks in the matrix. */
215: /* KSIZES (input) INTEGER array, dimension (NBLKS) */
216: /* The dimension of the square diagonal blocks from top left */
217: /* to bottom right. KSIZES(I) >= 1 for all I, and the sum of */
218: /* KSIZES(I) for I = 1 to NBLKS has to be equal to N. */
220: /* D (input) DOUBLE PRECISION array, dimension (L1D,L2D,NBLKS) */
221: /* The lower triangular elements of the symmetric diagonal */
222: /* blocks of the block tridiagonal matrix. Elements of the top */
223: /* left diagonal block, which is of dimension KSIZES(1), are */
224: /* contained in D(*,*,1); the elements of the next diagonal */
225: /* block, which is of dimension KSIZES(2), are contained in */
226: /* D(*,*,2); etc. */
228: /* L1D (input) INTEGER */
229: /* The leading dimension of the array D. L1D >= max(3,KMAX), */
230: /* where KMAX is the dimension of the largest diagonal block. */
232: /* L2D (input) INTEGER */
233: /* The second dimension of the array D. L2D >= max(3,KMAX), */
234: /* where KMAX is as stated in L1D above. */
236: /* E (input) DOUBLE PRECISION array, dimension (L1E,L2E,NBLKS-1) */
237: /* Contains the elements of the scalars (singular values) and */
238: /* vectors (singular vectors) defining the rank RANK subdiagonal */
239: /* blocks of the matrix. */
240: /* E(1:RANK(K),RANK(K)+1,K) holds the RANK(K) scalars, */
241: /* E(:,1:RANK(K),K) holds the RANK(K) column vectors, and */
242: /* E(:,RANK(K)+2:2*RANK(K)+1,K) holds the row vectors for the K-th */
243: /* subdiagonal block. */
245: /* RANK (input) INTEGER array, dimension (NBLKS-1). */
246: /* The ranks of all the subdiagonal blocks contained in the array E. */
247: /* RANK( K ) <= MIN( KSIZES( K ), KSIZES( K+1 ) ) */
249: /* L1E (input) INTEGER */
250: /* The leading dimension of the array E. L1E >= max(3,2*KMAX+1), */
251: /* where KMAX is as stated in L1D above. */
253: /* L2E (input) INTEGER */
254: /* The second dimension of the array E. L2E >= max(3,2*KMAX+1), */
255: /* where KMAX is as stated in L1D above. */
257: /* TOL (input) DOUBLE PRECISION, TOL <= 1.0D-1 */
258: /* User specified deflation tolerance for the routine DMERG2. */
259: /* If ( 1.0D-1 >= TOL >= 20*EPS ) then TOL is used as */
260: /* the deflation tolerance in DSRTDF. */
261: /* If ( TOL < 20*EPS ) then the standard deflation tolerance from */
262: /* LAPACK is used as the deflation tolerance in DSRTDF. */
264: /* EV (output) DOUBLE PRECISION array, dimension (N) */
265: /* If INFO = 0, then EV contains the eigenvalues of the */
266: /* symmetric block tridiagonal matrix in ascending order. */
268: /* Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N) */
269: /* On entry, Z will be the identity matrix. */
270: /* On exit, Z contains the eigenvectors of the block tridiagonal */
271: /* matrix. */
273: /* LDZ (input) INTEGER */
274: /* The leading dimension of the array Z. LDZ >= max(1,N). */
276: /* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) */
278: /* LWORK (input) INTEGER */
279: /* The dimension of the array WORK. */
280: /* In order to guarantee correct results in all cases, */
281: /* LWORK must be at least ( 2*N**2 + 3*N ). In many cases, */
282: /* less workspace is required. The absolute minimum required is */
283: /* ( N**2 + 3*N ). */
284: /* If the workspace provided is not sufficient, the routine will */
285: /* return a corresponding error code and report how much workspace */
286: /* was missing (see INFO). */
288: /* IWORK (workspace) INTEGER array, dimension (LIWORK) */
290: /* LIWORK (input) INTEGER */
291: /* The dimension of the array IWORK. */
292: /* LIWORK must be at least ( 5*N + 3 + 4*NBLKS - 4 ): */
293: /* 5*KMAX+3 for DSYEVD, 5*N for ????, */
294: /* 4*NBLKS-4 for the preprocessing (merging order) */
295: /* Summarizing, the minimum integer workspace needed is */
296: /* MAX( 5*N, 5*KMAX + 3 ) + 4*NBLKS - 4 */
298: /* INFO (output) INTEGER */
299: /* = 0: successful exit. */
300: /* < 0, > -99: illegal arguments. */
301: /* if INFO = -i, the i-th argument had an illegal value. */
302: /* = -99: error in the preprocessing (call of CUTLR). */
303: /* < -200: not enough workspace. Space for ABS(INFO + 200) */
304: /* numbers is required in addition to the workspace provided, */
305: /* otherwise some eigenvectors will be incorrect. */
306: /* > 0: The algorithm failed to compute an eigenvalue while */
307: /* working on the submatrix lying in rows and columns */
308: /* INFO/(N+1) through mod(INFO,N+1). */
310: /* Further Details */
311: /* =============== */
313: /* Based on code written by */
314: /* Wilfried Gansterer and Bob Ward, */
315: /* Department of Computer Science, University of Tennessee */
317: /* This routine is comparable to Dlaed0.f from LAPACK. */
319: /* ===================================================================== */
321: #if defined(SLEPC_MISSING_LAPACK_LACPY) || defined(PETSC_MISSING_LAPACK_SYEV)
323: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LACPY/SYEV - Lapack routine is unavailable");
324: #else
325: PetscBLASInt i, j, k, np, rp1, ksk, one=1;
326: PetscBLASInt cut, mat1, kchk, kbrk, blks, kmax, icut, size, ksum, lsum;
327: PetscBLASInt lblks, rblks, isize, lwmin, ilsum;
328: PetscBLASInt start, vstrt, istck1, istck2, istck3, merged;
329: PetscBLASInt liwmin, matsiz, startp, istrtp;
330: PetscReal rho, done=1.0, dmone=-1.0;
334: *info = 0;
336: if (*(unsigned char *)jobz != 'N' && *(unsigned char *)jobz != 'D') {
337: *info = -1;
338: } else if (n < 2) {
339: *info = -2;
340: } else if (nblks < 2 || nblks > n) {
341: *info = -3;
342: }
343: if (*info == 0) {
344: ksum = 0;
345: kmax = 0;
346: kchk = 0;
347: for (k = 0; k < nblks; ++k) {
348: ksk = ksizes[k];
349: ksum += ksk;
350: if (ksk > kmax) kmax = ksk;
351: if (ksk < 1) kchk = 1;
352: }
353: lwmin = n*n + n * 3;
354: liwmin = PetscMax(n * 5,kmax * 5 + 3) + 4*nblks - 4;
355: if (ksum != n || kchk == 1) {
356: *info = -4;
357: } else if (l1d < PetscMax(3,kmax)) {
358: *info = -6;
359: } else if (l2d < PetscMax(3,kmax)) {
360: *info = -7;
361: } else if (l1e < PetscMax(3,2*kmax + 1)) {
362: *info = -10;
363: } else if (l2e < PetscMax(3,2*kmax + 1)) {
364: *info = -11;
365: } else if (tol > .1) {
366: *info = -12;
367: } else if (ldz < PetscMax(1,n)) {
368: *info = -15;
369: } else if (lwork < lwmin) {
370: *info = -17;
371: } else if (liwork < liwmin) {
372: *info = -19;
373: }
374: }
375: if (*info == 0) {
376: for (k = 0; k < nblks-1; ++k) {
377: if (rank[k] > PetscMin(ksizes[k],ksizes[k+1]) || rank[k] < 1) *info = -9;
378: }
379: }
381: if (*info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong argument %d in DIBTDC",-(*info));
383: /* **************************************************************************** */
385: /* ...Preprocessing..................................................... */
386: /* Determine the optimal order for merging the subblocks and how much */
387: /* workspace will be needed for the merging (determined by the last */
388: /* merge). Cutpoints for the merging operations are determined and stored */
389: /* in reverse chronological order (starting with the final merging */
390: /* operation). */
392: /* integer workspace requirements for the preprocessing: */
393: /* 4*(NBLKS-1) for merging history */
394: /* at most 3*(NBLKS-1) for stack */
396: start = 1;
397: size = n;
398: blks = nblks;
399: merged = 0;
400: k = 0;
402: /* integer workspace used for the stack is not needed any more after the */
403: /* preprocessing and therefore can use part of the 5*N */
404: /* integer workspace needed later on in the code */
406: istck1 = 0;
407: istck2 = istck1 + nblks;
408: istck3 = istck2 + nblks;
410: /* integer workspace used for storing the order of merges starts AFTER */
411: /* the integer workspace 5*N+3 which is needed later on in the code */
412: /* (5*KMAX+3 for DSYEVD, 4*N in DMERG2) */
414: istrtp = n * 5 + 4;
415: icut = istrtp + nblks - 1;
416: isize = icut + nblks - 1;
417: ilsum = isize + nblks - 1;
419: L200:421: if (nblks >= 3) {
423: /* Determine the cut point. Note that in the routine CUTLR it is */
424: /* chosen such that it yields the best balanced merging operation */
425: /* among all the rank modifications with minimum rank. */
427: cutlr_(start, size, blks, &ksizes[start-1], &rank[start-1], &cut,
428: &lsum, &lblks, info);
429: if (*info) SETERRQ1(PETSC_COMM_SELF,1,"dibtdc: Error in cutlr, info = %d",*info);
431: } else {
432: cut = 1;
433: lsum = ksizes[0];
434: lblks = 1;
435: }
437: ++merged;
438: startp = 0;
439: for (i = 0; i < start-1; ++i) startp += ksizes[i];
440: iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
441: iwork[icut + (nblks - 1) - merged-1] = cut;
442: iwork[isize + (nblks - 1) - merged-1] = size;
443: iwork[ilsum + (nblks - 1) - merged-1] = lsum;
445: if (lblks == 2) {
447: /* one merge in left branch, left branch done */
448: ++merged;
449: iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
450: iwork[icut + (nblks - 1) - merged-1] = start;
451: iwork[isize + (nblks - 1) - merged-1] = lsum;
452: iwork[ilsum + (nblks - 1) - merged-1] = ksizes[start-1];
453: }
455: if (lblks == 1 || lblks == 2) {
457: /* left branch done, continue on the right side */
458: start += lblks;
459: size -= lsum;
460: blks -= lblks;
462: if (blks <= 0) SETERRQ1(PETSC_COMM_SELF,1,"dibtdc: Error in preprocessing, blks = %d",blks);
464: if (blks == 2) {
466: /* one merge in right branch, right branch done */
467: ++merged;
468: startp += lsum;
469: iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
470: iwork[icut + (nblks - 1) - merged-1] = start;
471: iwork[isize + (nblks - 1) - merged-1] = size;
472: iwork[ilsum + (nblks - 1) - merged-1] = ksizes[start-1];
473: }
475: if (blks == 1 || blks == 2) {
477: /* get the next subproblem from the stack or finished */
479: if (k >= 1) {
481: /* something left on the stack */
482: start = iwork[istck1 + k-1];
483: size = iwork[istck2 + k-1];
484: blks = iwork[istck3 + k-1];
485: --k;
486: goto L200;
487: } else {
489: /* nothing left on the stack */
490: if (merged != nblks-1) SETERRQ(PETSC_COMM_SELF,1,"ERROR in preprocessing - not enough merges performed");
492: /* exit preprocessing */
494: }
495: } else {
497: /* BLKS.GE.3, and therefore analyze the right side */
499: goto L200;
500: }
501: } else {
503: /* LBLKS.GE.3, and therefore check the right side and */
504: /* put it on the stack if required */
506: rblks = blks - lblks;
507: if (rblks >= 3) {
508: ++k;
509: iwork[istck1 + k-1] = cut + 1;
510: iwork[istck2 + k-1] = size - lsum;
511: iwork[istck3 + k-1] = rblks;
512: } else if (rblks == 2) {
514: /* one merge in right branch, right branch done */
515: /* (note that nothing needs to be done if RBLKS.EQ.1 !) */
517: ++merged;
518: startp += lsum;
519: iwork[istrtp + (nblks - 1) - merged-1] = startp + 1;
520: iwork[icut + (nblks - 1) - merged-1] = start + lblks;
521: iwork[isize + (nblks - 1) - merged-1] = size - lsum;
522: iwork[ilsum + (nblks - 1) - merged-1] = ksizes[start + lblks-1];
523: }
524: if (rblks <= 0) SETERRQ1(PETSC_COMM_SELF,1,"dibtdc: ERROR in preprocessing - rblks = %d",rblks);
526: /* continue on the left side */
528: size = lsum;
529: blks = lblks;
530: goto L200;
531: }
533: /* SIZE = IWORK( ISIZE+NBLKS-2 ) */
534: /* MAT1 = IWORK( ILSUM+NBLKS-2 ) */
536: /* Note: after the dimensions SIZE and MAT1 of the last merging */
537: /* operation have been determined, an upper bound for the workspace */
538: /* requirements which is independent of how much deflation occurs in */
539: /* the last merging operation could be determined as follows */
540: /* (based on (3.15) and (3.19) from UT-CS-00-447): */
542: /* IF( MAT1.LE.N/2 ) THEN */
543: /* WSPREQ = 3*N + 3/2*( SIZE-MAT1 )**2 + N*N/2 + MAT1*MAT1 */
544: /* ELSE */
545: /* WSPREQ = 3*N + 3/2*MAT1*MAT1 + N*N/2 + ( SIZE-MAT1 )**2 */
546: /* END IF */
548: /* IF( LWORK-WSPREQ.LT.0 )THEN */
549: /* not enough work space provided */
550: /* INFO = -200 - ( WSPREQ-LWORK ) */
551: /* RETURN */
552: /* END IF */
553: /* However, this is not really useful, since the actual check whether */
554: /* enough workspace is provided happens in DMERG2.f ! */
556: /* ************************************************************************* */
558: /* ...Solve subproblems................................... */
560: /* Divide the matrix into NBLKS submatrices using rank-r */
561: /* modifications (cuts) and solve for their eigenvalues and */
562: /* eigenvectors. Initialize index array to sort eigenvalues. */
564: /* first block: ...................................... */
566: /* correction for block 1: D1 - V1 \Sigma1 V1^T */
568: ksk = ksizes[0];
569: rp1 = rank[0];
571: /* initialize the proper part of Z with the diagonal block D1 */
572: /* (the correction will be made in Z and then the call of DSYEVD will */
573: /* overwrite it with the eigenvectors) */
575: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, d, &l1d, z, &ldz));
577: /* copy D1 into WORK (in order to be able to restore it afterwards) */
579: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, d, &l1d, work, &ksk));
581: /* copy V1 into the first RANK(1) columns of D1 and then */
582: /* multiply with \Sigma1 */
584: for (i = 0; i < rank[0]; ++i) {
585: PetscStackCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(rp1 + i+1)*l1e], &one, &d[i*l1d], &one));
586: PetscStackCallBLAS("BLASscal",BLASscal_(&ksk, &e[i + rp1*l1e], &d[i*l1d], &one));
587: }
589: /* multiply the first RANK( 1 ) columns of D1 with V1^T and */
590: /* subtract the result from the proper part of Z (previously */
591: /* initialized with D1) */
593: PetscStackCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, rank, &dmone,
594: d, &l1d, &e[(rank[0]+1)*l1e], &l1e, &done, z, &ldz));
596: /* restore the original D1 from WORK */
598: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, work, &ksk, d, &l1d));
600: /* eigenanalysis of block 1 (using DSYEVD) */
602: PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V", "L", &ksk, z, &ldz, ev, work, &lwork, info));
603: if (*info) SETERRQ1(PETSC_COMM_SELF,1,"dibtdc: Error in DSYEVD for block 1, info = %d",*info);
605: /* EV( 1: ) contains the eigenvalues in ascending order */
606: /* (they are returned this way by DSYEVD) */
608: for (i = 0; i < ksk; ++i) iwork[i] = i+1;
610: /* intermediate blocks: .............................. */
612: np = ksk;
614: /* remaining number of blocks */
616: if (nblks > 2) {
617: for (k = 1; k < nblks-1; ++k) {
619: /* correction for block K: */
620: /* Dk - U(k-1) \Sigma(k-1) U(k-1)^T - Vk \Sigmak Vk^T */
622: ksk = ksizes[k];
623: rp1 = rank[k];
625: /* initialize the proper part of Z with the diagonal block Dk */
626: /* (the correction will be made in Z and then the call of DSYEVD will */
627: /* overwrite it with the eigenvectors) */
629: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, &d[k*l1d*l2d], &l1d, &z[np+np*ldz], &ldz));
631: /* copy Dk into WORK (in order to be able to restore it afterwards) */
633: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, &d[k*l1d*l2d], &l1d, work, &ksk));
635: /* copy U(K-1) into the first RANK(K-1) columns of Dk and then */
636: /* multiply with \Sigma(K-1) */
638: for (i = 0; i < rank[k-1]; ++i) {
639: PetscStackCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(i+(k-1)*l2e)*l1e], &one, &d[(i+k*l2d)*l1d], &one));
640: PetscStackCallBLAS("BLASscal",BLASscal_(&ksk, &e[i+(rank[k-1]+(k-1)*l2e)*l1e], &d[(i+k*l2d)*l1d], &one));
641: }
643: /* multiply the first RANK(K-1) columns of Dk with U(k-1)^T and */
644: /* subtract the result from the proper part of Z (previously */
645: /* initialized with Dk) */
647: PetscStackCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, &rank[k-1],
648: &dmone, &d[k*l1d*l2d],
649: &l1d, &e[(k-1)*l1e*l2e], &l1e, &done, &z[np+np*ldz], &ldz));
651: /* copy Vk into the first RANK(K) columns of Dk and then */
652: /* multiply with \Sigmak */
654: for (i = 0; i < rank[k]; ++i) {
655: PetscStackCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(rp1+i+1 + k*l2e)*l1e], &one, &d[(i + k*l2d)*l1d], &one));
656: PetscStackCallBLAS("BLASscal",BLASscal_(&ksk, &e[i + (rp1 + k*l2e)*l1e], &d[(i + k*l2d)*l1d], &one));
657: }
659: /* multiply the first RANK(K) columns of Dk with Vk^T and */
660: /* subtract the result from the proper part of Z (previously */
661: /* updated with [- U(k-1) \Sigma(k-1) U(k-1)^T] ) */
663: PetscStackCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, &rank[k],
664: &dmone, &d[k*l1d*l2d], &l1d,
665: &e[(rank[k]+1 + k*l2e)*l1e], &l1e, &done, &z[np+np*ldz], &ldz));
667: /* restore the original Dk from WORK */
669: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, work, &ksk, &d[k*l1d*l2d], &l1d));
671: /* eigenanalysis of block K (using dsyevd) */
673: PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V", "L", &ksk, &z[np+np*ldz],
674: &ldz, &ev[np], work, &lwork, info));
675: if (*info) SETERRQ2(PETSC_COMM_SELF,1,"dibtdc: Error in DSYEVD for block %d, info = %d",k,*info);
677: /* EV( NPP1: ) contains the eigenvalues in ascending order */
678: /* (they are returned this way by DSYEVD) */
680: for (i = 0; i < ksk; ++i) iwork[np + i] = i+1;
682: /* update NP */
683: np += ksk;
684: }
685: }
687: /* last block: ....................................... */
689: /* correction for block NBLKS: */
690: /* D(nblks) - U(nblks-1) \Sigma(nblks-1) U(nblks-1)^T */
692: ksk = ksizes[nblks-1];
694: /* initialize the proper part of Z with the diagonal block D(nblks) */
695: /* (the correction will be made in Z and then the call of DSYEVD will */
696: /* overwrite it with the eigenvectors) */
698: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, &d[(nblks-1)*l1d*l2d], &l1d, &z[np+np*ldz], &ldz));
700: /* copy D(nblks) into WORK (in order to be able to restore it afterwards) */
702: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, &d[(nblks-1)*l1d*l2d], &l1d, work, &ksk));
704: /* copy U(nblks-1) into the first RANK(nblks-1) columns of D(nblks) and then */
705: /* multiply with \Sigma(nblks-1) */
707: for (i = 0; i < rank[nblks-2]; ++i) {
708: PetscStackCallBLAS("BLAScopy",BLAScopy_(&ksk, &e[(i + (nblks-2)*l2e)*l1e],
709: &one, &d[(i + (nblks-1)*l2d)*l1d], &one));
710: PetscStackCallBLAS("BLASscal",BLASscal_(&ksk,
711: &e[i + (rank[nblks-2] + (nblks-2)*l2e)*l1e],
712: &d[(i + (nblks-1)*l2d)*l1d], &one));
713: }
715: /* multiply the first RANK(nblks-1) columns of D(nblks) with U(nblks-1)^T */
716: /* and subtract the result from the proper part of Z (previously */
717: /* initialized with D(nblks) ) */
719: PetscStackCallBLAS("BLASgemm",BLASgemm_("N", "T", &ksk, &ksk, &rank[nblks - 2],
720: &dmone, &d[(nblks-1)*l1d*l2d], &l1d,
721: &e[(nblks-2)*l1e*l2e], &l1e, &done, &z[np+np*ldz], &ldz));
723: /* restore the original D(nblks) from WORK */
725: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L", &ksk, &ksk, work, &ksk, &d[(nblks-1)*l1d*l2d], &l1d));
727: /* eigenanalysis of block NBLKS (using dsyevd) */
729: PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V", "L", &ksk, &z[np+np*ldz], &ldz, &ev[np], work, &lwork, info));
730: if (*info) SETERRQ2(PETSC_COMM_SELF,1,"dibtdc: Error in DSYEVD for block %d, info = %d",nblks,*info);
732: /* EV( NPP1: ) contains the eigenvalues in ascending order */
733: /* (they are returned this way by DSYEVD) */
735: for (i = 0; i < ksk; ++i) iwork[np + i] = i+1;
737: /* note that from here on the entire workspace is available again */
740: /* Perform all the merging operations. */
742: vstrt = 0;
743: for (i = 0; i < nblks-1; ++i) {
745: /* MATSIZ = total size of the current rank RANK modification problem */
747: matsiz = iwork[isize + i - 1];
748: np = iwork[istrtp + i - 1];
749: kbrk = iwork[icut + i - 1];
750: mat1 = iwork[ilsum + i - 1];
751: vstrt += np;
753: for (j = 0; j < rank[kbrk-1]; ++j) {
755: /* NOTE: The parameter RHO in DMERG2 is modified in DSRTDF */
756: /* (multiplied by 2) ! In order not to change the */
757: /* singular value stored in E( :, RANK( KBRK )+1, KBRK ), */
758: /* we do not pass on this variable as an argument to DMERG2, */
759: /* but we assign a separate variable RHO here which is passed */
760: /* on to DMERG2. */
761: /* Alternative solution in F90: */
762: /* pass E( :,RANK( KBRK )+1,KBRK ) to an INTENT( IN ) parameter */
763: /* in DMERG2. */
765: rho = e[j + (rank[kbrk-1] + (kbrk-1)*l2e)*l1e];
767: /* eigenvectors are accumulated ( JOBZ.EQ.'D' ) */
769: BDC_dmerg2_(jobz, j+1, matsiz, &ev[np-1], &z[np-1+(np-1)*ldz],
770: ldz, &iwork[np-1], &rho, &e[(j + (kbrk-1)*l2e)*l1e],
771: ksizes[kbrk], &e[(rank[kbrk-1]+j+1 + (kbrk-1)*l2e)*l1e],
772: ksizes[kbrk-1], mat1, work, lwork, &iwork[n], tol, info, 1);
773: 774: if (*info) SETERRQ1(PETSC_COMM_SELF,1,"dibtdc: Error in dmerg2, info = %d",*info);
775: }
777: /* at this point all RANK( KBRK ) rank-one modifications corresponding */
778: /* to the current off-diagonal block are finished. */
779: /* Move on to the next off-diagonal block. */
781: }
783: /* Re-merge the eigenvalues/vectors which were deflated at the final */
784: /* merging step by sorting all eigenvalues and eigenvectors according */
785: /* to the permutation stored in IWORK. */
787: /* copy eigenvalues and eigenvectors in ordered form into WORK */
788: /* (eigenvalues into WORK( 1:N ), eigenvectors into WORK( N+1:N+1+N^2 ) ) */
790: for (i = 0; i < n; ++i) {
791: j = iwork[i];
792: work[i] = ev[j-1];
793: PetscStackCallBLAS("BLAScopy",BLAScopy_(&n, &z[(j-1)*ldz], &one, &work[n*(i+1)], &one));
794: }
796: /* copy ordered eigenvalues back from WORK( 1:N ) into EV */
798: PetscStackCallBLAS("BLAScopy",BLAScopy_(&n, work, &one, ev, &one));
800: /* copy ordered eigenvectors back from WORK( N+1:N+1+N^2 ) into Z */
802: PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("A", &n, &n, &work[n], &n, z, &ldz));
803: return(0);
804: #endif
805: }