Actual source code: bddcprivate.c

  1: #include <../src/mat/impls/aij/seq/aij.h>
  2: #include <petsc/private/pcbddcimpl.h>
  3: #include <petsc/private/pcbddcprivateimpl.h>
  4: #include <petsc/private/kernels/blockinvert.h>
  5: #include <../src/mat/impls/dense/seq/dense.h>
  6: #include <petscdmplex.h>
  7: #include <petscblaslapack.h>
  8: #include <petsc/private/sfimpl.h>
  9: #include <petsc/private/dmpleximpl.h>
 10: #include <petscdmda.h>

 12: static PetscErrorCode MatMPIAIJRestrict(Mat, MPI_Comm, Mat *);

 14: /* if range is true,  it returns B s.t. span{B} = range(A)
 15:    if range is false, it returns B s.t. range(B) _|_ range(A) */
 16: static PetscErrorCode MatDenseOrthogonalRangeOrComplement(Mat A, PetscBool range, PetscInt lw, PetscScalar *work, PetscReal *rwork, Mat *B)
 17: {
 18:   PetscScalar *uwork, *data, *U, ds = 0.;
 19:   PetscReal   *sing;
 20:   PetscBLASInt bM, bN, lwork, lierr, di = 1;
 21:   PetscInt     ulw, i, nr, nc, n;
 22: #if defined(PETSC_USE_COMPLEX)
 23:   PetscReal *rwork2;
 24: #endif

 26:   PetscFunctionBegin;
 27:   PetscCall(MatGetSize(A, &nr, &nc));
 28:   if (!nr || !nc) PetscFunctionReturn(PETSC_SUCCESS);

 30:   /* workspace */
 31:   if (!work) {
 32:     ulw = PetscMax(PetscMax(1, 5 * PetscMin(nr, nc)), 3 * PetscMin(nr, nc) + PetscMax(nr, nc));
 33:     PetscCall(PetscMalloc1(ulw, &uwork));
 34:   } else {
 35:     ulw   = lw;
 36:     uwork = work;
 37:   }
 38:   n = PetscMin(nr, nc);
 39:   if (!rwork) {
 40:     PetscCall(PetscMalloc1(n, &sing));
 41:   } else {
 42:     sing = rwork;
 43:   }

 45:   /* SVD */
 46:   PetscCall(PetscMalloc1(nr * nr, &U));
 47:   PetscCall(PetscBLASIntCast(nr, &bM));
 48:   PetscCall(PetscBLASIntCast(nc, &bN));
 49:   PetscCall(PetscBLASIntCast(ulw, &lwork));
 50:   PetscCall(MatDenseGetArray(A, &data));
 51:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
 52: #if !defined(PETSC_USE_COMPLEX)
 53:   PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("A", "N", &bM, &bN, data, &bM, sing, U, &bM, &ds, &di, uwork, &lwork, &lierr));
 54: #else
 55:   PetscCall(PetscMalloc1(5 * n, &rwork2));
 56:   PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("A", "N", &bM, &bN, data, &bM, sing, U, &bM, &ds, &di, uwork, &lwork, rwork2, &lierr));
 57:   PetscCall(PetscFree(rwork2));
 58: #endif
 59:   PetscCall(PetscFPTrapPop());
 60:   PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GESVD Lapack routine %" PetscBLASInt_FMT, lierr);
 61:   PetscCall(MatDenseRestoreArray(A, &data));
 62:   for (i = 0; i < n; i++)
 63:     if (sing[i] < PETSC_SMALL) break;
 64:   if (!rwork) PetscCall(PetscFree(sing));
 65:   if (!work) PetscCall(PetscFree(uwork));
 66:   /* create B */
 67:   if (!range) {
 68:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nr, nr - i, NULL, B));
 69:     PetscCall(MatDenseGetArray(*B, &data));
 70:     PetscCall(PetscArraycpy(data, U + nr * i, (nr - i) * nr));
 71:   } else {
 72:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nr, i, NULL, B));
 73:     PetscCall(MatDenseGetArray(*B, &data));
 74:     PetscCall(PetscArraycpy(data, U, i * nr));
 75:   }
 76:   PetscCall(MatDenseRestoreArray(*B, &data));
 77:   PetscCall(PetscFree(U));
 78:   PetscFunctionReturn(PETSC_SUCCESS);
 79: }

 81: /* TODO REMOVE */
 82: #if defined(PRINT_GDET)
 83: static int inc = 0;
 84: static int lev = 0;
 85: #endif

 87: static PetscErrorCode PCBDDCComputeNedelecChangeEdge(Mat lG, IS edge, IS extrow, IS extcol, IS corners, Mat *Gins, Mat *GKins, PetscScalar cvals[2], PetscScalar *work, PetscReal *rwork)
 88: {
 89:   Mat          GE, GEd;
 90:   PetscInt     rsize, csize, esize;
 91:   PetscScalar *ptr;

 93:   PetscFunctionBegin;
 94:   PetscCall(ISGetSize(edge, &esize));
 95:   if (!esize) PetscFunctionReturn(PETSC_SUCCESS);
 96:   PetscCall(ISGetSize(extrow, &rsize));
 97:   PetscCall(ISGetSize(extcol, &csize));

 99:   /* gradients */
100:   ptr = work + 5 * esize;
101:   PetscCall(MatCreateSubMatrix(lG, extrow, extcol, MAT_INITIAL_MATRIX, &GE));
102:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, rsize, csize, ptr, Gins));
103:   PetscCall(MatConvert(GE, MATSEQDENSE, MAT_REUSE_MATRIX, Gins));
104:   PetscCall(MatDestroy(&GE));

106:   /* constants */
107:   ptr += rsize * csize;
108:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, esize, csize, ptr, &GEd));
109:   PetscCall(MatCreateSubMatrix(lG, edge, extcol, MAT_INITIAL_MATRIX, &GE));
110:   PetscCall(MatConvert(GE, MATSEQDENSE, MAT_REUSE_MATRIX, &GEd));
111:   PetscCall(MatDestroy(&GE));
112:   PetscCall(MatDenseOrthogonalRangeOrComplement(GEd, PETSC_FALSE, 5 * esize, work, rwork, GKins));
113:   PetscCall(MatDestroy(&GEd));

115:   if (corners) {
116:     Mat                GEc;
117:     const PetscScalar *vals;
118:     PetscScalar        v;

120:     PetscCall(MatCreateSubMatrix(lG, edge, corners, MAT_INITIAL_MATRIX, &GEc));
121:     PetscCall(MatTransposeMatMult(GEc, *GKins, MAT_INITIAL_MATRIX, 1.0, &GEd));
122:     PetscCall(MatDenseGetArrayRead(GEd, &vals));
123:     /* v       = PetscAbsScalar(vals[0]); */
124:     v        = 1.;
125:     cvals[0] = vals[0] / v;
126:     cvals[1] = vals[1] / v;
127:     PetscCall(MatDenseRestoreArrayRead(GEd, &vals));
128:     PetscCall(MatScale(*GKins, 1. / v));
129: #if defined(PRINT_GDET)
130:     {
131:       PetscViewer viewer;
132:       char        filename[256];
133:       PetscCall(PetscSNPrintf(filename, PETSC_STATIC_ARRAY_LENGTH(filename), "Gdet_l%d_r%d_cc%d.m", lev, PetscGlobalRank, inc++));
134:       PetscCall(PetscViewerASCIIOpen(PETSC_COMM_SELF, filename, &viewer));
135:       PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
136:       PetscCall(PetscObjectSetName((PetscObject)GEc, "GEc"));
137:       PetscCall(MatView(GEc, viewer));
138:       PetscCall(PetscObjectSetName((PetscObject)*GKins, "GK"));
139:       PetscCall(MatView(*GKins, viewer));
140:       PetscCall(PetscObjectSetName((PetscObject)GEd, "Gproj"));
141:       PetscCall(MatView(GEd, viewer));
142:       PetscCall(PetscViewerDestroy(&viewer));
143:     }
144: #endif
145:     PetscCall(MatDestroy(&GEd));
146:     PetscCall(MatDestroy(&GEc));
147:   }
148:   PetscFunctionReturn(PETSC_SUCCESS);
149: }

151: static PetscErrorCode MatAIJExtractRows(Mat, IS, Mat *);

153: PetscErrorCode PCBDDCNedelecSupport(PC pc)
154: {
155:   PC_BDDC               *pcbddc = (PC_BDDC *)pc->data;
156:   Mat_IS                *matis  = (Mat_IS *)pc->pmat->data;
157:   Mat                    G, T, conn, lG, lGt, lGis, lGall, lGe, lGinit;
158:   PetscSF                sfv;
159:   ISLocalToGlobalMapping el2g, vl2g, fl2g, al2g;
160:   MPI_Comm               comm;
161:   IS                     lned, primals, allprimals, nedfieldlocal, elements_corners = NULL;
162:   IS                    *eedges, *extrows, *extcols, *alleedges;
163:   PetscBT                btv, bte, btvc, btb, btbd, btvcand, btvi, btee, bter;
164:   PetscScalar           *vals, *work;
165:   PetscReal             *rwork;
166:   const PetscInt        *idxs, *ii, *jj, *iit, *jjt;
167:   PetscInt               ne, nv, Lv, order, n, field;
168:   PetscInt               i, j, extmem, cum, maxsize, nee;
169:   PetscInt              *extrow, *extrowcum, *marks, *vmarks, *gidxs;
170:   PetscInt              *sfvleaves, *sfvroots;
171:   PetscInt              *corners, *cedges;
172:   PetscInt              *ecount, **eneighs, *vcount, **vneighs;
173:   PetscInt              *emarks;
174:   PetscBool              print, eerr, done, lrc[2], conforming, global, setprimal;

176:   PetscFunctionBegin;
177:   /* If the discrete gradient is defined for a subset of dofs and global is true,
178:      it assumes G is given in global ordering for all the dofs.
179:      Otherwise, the ordering is global for the Nedelec field */
180:   order      = pcbddc->nedorder;
181:   conforming = pcbddc->conforming;
182:   field      = pcbddc->nedfield;
183:   global     = pcbddc->nedglobal;
184:   setprimal  = PETSC_FALSE;
185:   print      = PETSC_FALSE;

187:   /* Command line customization */
188:   PetscOptionsBegin(PetscObjectComm((PetscObject)pc), ((PetscObject)pc)->prefix, "BDDC Nedelec options", "PC");
189:   PetscCall(PetscOptionsBool("-pc_bddc_nedelec_field_primal", "All edge dofs set as primals: Toselli's algorithm C", NULL, setprimal, &setprimal, NULL));
190:   /* print debug info and adaptive order TODO: to be removed */
191:   PetscCall(PetscOptionsInt("-pc_bddc_nedelec_order", "Test variable order code (to be removed)", NULL, order, &order, NULL));
192:   PetscCall(PetscOptionsBool("-pc_bddc_nedelec_print", "Print debug info", NULL, print, &print, NULL));
193:   PetscOptionsEnd();

195:   /* Return if there are no edges in the decomposition */
196:   PetscCall(MatISGetLocalToGlobalMapping(pc->pmat, &al2g, NULL));
197:   PetscCall(ISLocalToGlobalMappingGetSize(al2g, &n));
198:   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
199:   PetscCall(VecGetArrayRead(matis->counter, (const PetscScalar **)&vals));
200:   lrc[0] = PETSC_FALSE;
201:   for (i = 0; i < n; i++) {
202:     if (PetscRealPart(vals[i]) > 2.) {
203:       lrc[0] = PETSC_TRUE;
204:       break;
205:     }
206:   }
207:   PetscCall(VecRestoreArrayRead(matis->counter, (const PetscScalar **)&vals));
208:   PetscCallMPI(MPIU_Allreduce(&lrc[0], &lrc[1], 1, MPIU_BOOL, MPI_LOR, comm));
209:   if (!lrc[1]) PetscFunctionReturn(PETSC_SUCCESS);

211:   /* Get Nedelec field */
212:   PetscCheck(!pcbddc->n_ISForDofsLocal || field < pcbddc->n_ISForDofsLocal, comm, PETSC_ERR_USER, "Invalid field for Nedelec %" PetscInt_FMT ": number of fields is %" PetscInt_FMT, field, pcbddc->n_ISForDofsLocal);
213:   if (pcbddc->n_ISForDofsLocal && field >= 0) {
214:     PetscCall(PetscObjectReference((PetscObject)pcbddc->ISForDofsLocal[field]));
215:     nedfieldlocal = pcbddc->ISForDofsLocal[field];
216:     PetscCall(ISGetLocalSize(nedfieldlocal, &ne));
217:   } else if (!pcbddc->n_ISForDofsLocal && field != PETSC_DECIDE) {
218:     ne            = n;
219:     nedfieldlocal = NULL;
220:     global        = PETSC_TRUE;
221:   } else if (field == PETSC_DECIDE) {
222:     PetscInt rst, ren, *idx;

224:     PetscCall(PetscArrayzero(matis->sf_leafdata, n));
225:     PetscCall(PetscArrayzero(matis->sf_rootdata, pc->pmat->rmap->n));
226:     PetscCall(MatGetOwnershipRange(pcbddc->discretegradient, &rst, &ren));
227:     for (i = rst; i < ren; i++) {
228:       PetscInt nc;

230:       PetscCall(MatGetRow(pcbddc->discretegradient, i, &nc, NULL, NULL));
231:       if (nc > 1) matis->sf_rootdata[i - rst] = 1;
232:       PetscCall(MatRestoreRow(pcbddc->discretegradient, i, &nc, NULL, NULL));
233:     }
234:     PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
235:     PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
236:     PetscCall(PetscMalloc1(n, &idx));
237:     for (i = 0, ne = 0; i < n; i++)
238:       if (matis->sf_leafdata[i]) idx[ne++] = i;
239:     PetscCall(ISCreateGeneral(comm, ne, idx, PETSC_OWN_POINTER, &nedfieldlocal));
240:   } else {
241:     SETERRQ(comm, PETSC_ERR_USER, "When multiple fields are present, the Nedelec field has to be specified");
242:   }

244:   /* Sanity checks */
245:   PetscCheck(order || conforming, comm, PETSC_ERR_SUP, "Variable order and non-conforming spaces are not supported at the same time");
246:   PetscCheck(!pcbddc->user_ChangeOfBasisMatrix, comm, PETSC_ERR_SUP, "Cannot generate Nedelec support with user defined change of basis");
247:   PetscCheck(!order || (ne % order == 0), PETSC_COMM_SELF, PETSC_ERR_USER, "The number of local edge dofs %" PetscInt_FMT " is not a multiple of the order %" PetscInt_FMT, ne, order);

249:   /* Just set primal dofs and return */
250:   if (setprimal) {
251:     IS        enedfieldlocal;
252:     PetscInt *eidxs;

254:     PetscCall(PetscMalloc1(ne, &eidxs));
255:     PetscCall(VecGetArrayRead(matis->counter, (const PetscScalar **)&vals));
256:     if (nedfieldlocal) {
257:       PetscCall(ISGetIndices(nedfieldlocal, &idxs));
258:       for (i = 0, cum = 0; i < ne; i++) {
259:         if (PetscRealPart(vals[idxs[i]]) > 2.) eidxs[cum++] = idxs[i];
260:       }
261:       PetscCall(ISRestoreIndices(nedfieldlocal, &idxs));
262:     } else {
263:       for (i = 0, cum = 0; i < ne; i++) {
264:         if (PetscRealPart(vals[i]) > 2.) eidxs[cum++] = i;
265:       }
266:     }
267:     PetscCall(VecRestoreArrayRead(matis->counter, (const PetscScalar **)&vals));
268:     PetscCall(ISCreateGeneral(comm, cum, eidxs, PETSC_COPY_VALUES, &enedfieldlocal));
269:     PetscCall(PCBDDCSetPrimalVerticesLocalIS(pc, enedfieldlocal));
270:     PetscCall(PetscFree(eidxs));
271:     PetscCall(ISDestroy(&nedfieldlocal));
272:     PetscCall(ISDestroy(&enedfieldlocal));
273:     PetscFunctionReturn(PETSC_SUCCESS);
274:   }

276:   /* Compute some l2g maps */
277:   if (nedfieldlocal) {
278:     IS is;

280:     /* need to map from the local Nedelec field to local numbering */
281:     PetscCall(ISLocalToGlobalMappingCreateIS(nedfieldlocal, &fl2g));
282:     /* need to map from the local Nedelec field to global numbering for the whole dofs*/
283:     PetscCall(ISLocalToGlobalMappingApplyIS(al2g, nedfieldlocal, &is));
284:     PetscCall(ISLocalToGlobalMappingCreateIS(is, &al2g));
285:     /* need to map from the local Nedelec field to global numbering (for Nedelec only) */
286:     if (global) {
287:       PetscCall(PetscObjectReference((PetscObject)al2g));
288:       el2g = al2g;
289:     } else {
290:       IS gis;

292:       PetscCall(ISRenumber(is, NULL, NULL, &gis));
293:       PetscCall(ISLocalToGlobalMappingCreateIS(gis, &el2g));
294:       PetscCall(ISDestroy(&gis));
295:     }
296:     PetscCall(ISDestroy(&is));
297:   } else {
298:     /* one ref for the destruction of al2g, one for el2g */
299:     PetscCall(PetscObjectReference((PetscObject)al2g));
300:     PetscCall(PetscObjectReference((PetscObject)al2g));
301:     el2g = al2g;
302:     fl2g = NULL;
303:   }

305:   /* Start communication to drop connections for interior edges (for cc analysis only) */
306:   PetscCall(PetscArrayzero(matis->sf_leafdata, n));
307:   PetscCall(PetscArrayzero(matis->sf_rootdata, pc->pmat->rmap->n));
308:   if (nedfieldlocal) {
309:     PetscCall(ISGetIndices(nedfieldlocal, &idxs));
310:     for (i = 0; i < ne; i++) matis->sf_leafdata[idxs[i]] = 1;
311:     PetscCall(ISRestoreIndices(nedfieldlocal, &idxs));
312:   } else {
313:     for (i = 0; i < ne; i++) matis->sf_leafdata[i] = 1;
314:   }
315:   PetscCall(PetscSFReduceBegin(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_SUM));
316:   PetscCall(PetscSFReduceEnd(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_SUM));

318:   /* There's no way to detect all possible corner candidates in a element-by-element case in a pure algebraic setting
319:      Firedrake attaches a index set to identify them upfront. If it is present, we assume we are in such a case */
320:   if (matis->allow_repeated) PetscCall(PetscObjectQuery((PetscObject)pcbddc->discretegradient, "_elements_corners", (PetscObject *)&elements_corners));

322:   /* drop connections with interior edges to avoid unneeded communications and memory movements */
323:   PetscCall(MatViewFromOptions(pcbddc->discretegradient, (PetscObject)pc, "-pc_bddc_discrete_gradient_view"));
324:   PetscCall(MatDuplicate(pcbddc->discretegradient, MAT_COPY_VALUES, &G));
325:   PetscCall(MatSetOption(G, MAT_KEEP_NONZERO_PATTERN, PETSC_FALSE));
326:   if (global) {
327:     PetscInt rst;

329:     PetscCall(MatGetOwnershipRange(G, &rst, NULL));
330:     for (i = 0, cum = 0; i < pc->pmat->rmap->n; i++) {
331:       if (matis->sf_rootdata[i] < 2) matis->sf_rootdata[cum++] = i + rst;
332:     }
333:     PetscCall(MatSetOption(G, MAT_NO_OFF_PROC_ZERO_ROWS, PETSC_TRUE));
334:     PetscCall(MatZeroRows(G, cum, matis->sf_rootdata, 0., NULL, NULL));
335:   } else {
336:     PetscInt *tbz;

338:     PetscCall(PetscMalloc1(ne, &tbz));
339:     PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
340:     PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
341:     PetscCall(ISGetIndices(nedfieldlocal, &idxs));
342:     for (i = 0, cum = 0; i < ne; i++)
343:       if (matis->sf_leafdata[idxs[i]] == 1) tbz[cum++] = i;
344:     PetscCall(ISRestoreIndices(nedfieldlocal, &idxs));
345:     PetscCall(ISLocalToGlobalMappingApply(el2g, cum, tbz, tbz));
346:     PetscCall(MatZeroRows(G, cum, tbz, 0., NULL, NULL));
347:     PetscCall(PetscFree(tbz));
348:   }

350:   /* Extract subdomain relevant rows of G  */
351:   PetscCall(ISLocalToGlobalMappingGetIndices(el2g, &idxs));
352:   PetscCall(ISCreateGeneral(comm, ne, idxs, PETSC_USE_POINTER, &lned));
353:   PetscCall(MatAIJExtractRows(G, lned, &lGall));
354:   /* PetscCall(MatCreateSubMatrix(G, lned, NULL, MAT_INITIAL_MATRIX, &lGall)); */
355:   PetscCall(ISLocalToGlobalMappingRestoreIndices(el2g, &idxs));
356:   PetscCall(ISDestroy(&lned));
357:   PetscCall(MatConvert(lGall, MATIS, MAT_INITIAL_MATRIX, &lGis));
358:   PetscCall(MatDestroy(&lGall));
359:   PetscCall(MatISGetLocalMat(lGis, &lG));
360:   if (matis->allow_repeated) { /* multi-element support */
361:     Mat                   *lGn, B;
362:     IS                    *is_rows, *tcols, tmap, nmap;
363:     PetscInt               subnv;
364:     const PetscInt        *subvidxs;
365:     ISLocalToGlobalMapping mapn;

367:     PetscCall(PetscCalloc1(pcbddc->n_local_subs * pcbddc->n_local_subs, &lGn));
368:     PetscCall(PetscMalloc1(pcbddc->n_local_subs, &is_rows));
369:     PetscCall(PetscMalloc1(pcbddc->n_local_subs, &tcols));
370:     for (PetscInt i = 0; i < pcbddc->n_local_subs; i++) {
371:       if (fl2g) {
372:         PetscCall(ISGlobalToLocalMappingApplyIS(fl2g, IS_GTOLM_MASK, pcbddc->local_subs[i], &is_rows[i]));
373:       } else {
374:         PetscCall(PetscObjectReference((PetscObject)pcbddc->local_subs[i]));
375:         is_rows[i] = pcbddc->local_subs[i];
376:       }
377:       PetscCall(MatCreateSubMatrix(lG, is_rows[i], NULL, MAT_INITIAL_MATRIX, &lGn[i * (1 + pcbddc->n_local_subs)]));
378:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(lGn[i * (1 + pcbddc->n_local_subs)], &mapn));
379:       PetscCall(ISLocalToGlobalMappingGetSize(mapn, &subnv));
380:       PetscCall(ISLocalToGlobalMappingGetIndices(mapn, &subvidxs));
381:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, subnv, subvidxs, PETSC_COPY_VALUES, &tcols[i]));
382:       PetscCall(ISLocalToGlobalMappingRestoreIndices(mapn, &subvidxs));
383:       PetscCall(ISLocalToGlobalMappingDestroy(&mapn));
384:     }

386:     /* Create new MATIS with repeated vertices */
387:     PetscCall(MatCreate(comm, &B));
388:     PetscCall(MatSetSizes(B, lGis->rmap->n, lGis->cmap->n, lGis->rmap->N, lGis->cmap->N));
389:     PetscCall(MatSetType(B, MATIS));
390:     PetscCall(MatISSetAllowRepeated(B, PETSC_TRUE));
391:     PetscCall(ISConcatenate(PETSC_COMM_SELF, pcbddc->n_local_subs, tcols, &tmap));
392:     PetscCall(ISLocalToGlobalMappingApplyIS(lGis->cmap->mapping, tmap, &nmap));
393:     PetscCall(ISDestroy(&tmap));
394:     PetscCall(ISGetLocalSize(nmap, &subnv));
395:     PetscCall(ISGetIndices(nmap, &subvidxs));
396:     PetscCall(ISCreateGeneral(comm, subnv, subvidxs, PETSC_USE_POINTER, &tmap));
397:     PetscCall(ISRestoreIndices(nmap, &subvidxs));
398:     PetscCall(ISLocalToGlobalMappingCreateIS(tmap, &mapn));
399:     PetscCall(ISDestroy(&tmap));
400:     PetscCall(ISDestroy(&nmap));
401:     PetscCall(MatSetLocalToGlobalMapping(B, lGis->rmap->mapping, mapn));
402:     PetscCall(ISLocalToGlobalMappingDestroy(&mapn));
403:     PetscCall(MatCreateNest(PETSC_COMM_SELF, pcbddc->n_local_subs, is_rows, pcbddc->n_local_subs, NULL, lGn, &lG));
404:     for (PetscInt i = 0; i < pcbddc->n_local_subs; i++) {
405:       PetscCall(MatDestroy(&lGn[i * (1 + pcbddc->n_local_subs)]));
406:       PetscCall(ISDestroy(&is_rows[i]));
407:       PetscCall(ISDestroy(&tcols[i]));
408:     }
409:     PetscCall(MatConvert(lG, MATSEQAIJ, MAT_INPLACE_MATRIX, &lG));
410:     PetscCall(PetscFree(lGn));
411:     PetscCall(PetscFree(is_rows));
412:     PetscCall(PetscFree(tcols));
413:     PetscCall(MatISSetLocalMat(B, lG));
414:     PetscCall(MatDestroy(&lG));

416:     PetscCall(MatDestroy(&lGis));
417:     lGis = B;

419:     lGis->assembled = PETSC_TRUE;
420:   }
421:   PetscCall(MatViewFromOptions(lGis, (PetscObject)pc, "-pc_bddc_nedelec_init_G_view"));

423:   /* SF for nodal dofs communications */
424:   PetscCall(MatGetLocalSize(G, NULL, &Lv));
425:   PetscCall(MatISGetLocalToGlobalMapping(lGis, NULL, &vl2g));
426:   PetscCall(PetscObjectReference((PetscObject)vl2g));
427:   PetscCall(ISLocalToGlobalMappingGetSize(vl2g, &nv));
428:   PetscCall(PetscSFCreate(comm, &sfv));
429:   PetscCall(ISLocalToGlobalMappingGetIndices(vl2g, &idxs));
430:   PetscCall(PetscSFSetGraphLayout(sfv, lGis->cmap, nv, NULL, PETSC_OWN_POINTER, idxs));
431:   PetscCall(ISLocalToGlobalMappingRestoreIndices(vl2g, &idxs));

433:   if (elements_corners) {
434:     IS      tmp;
435:     Vec     global, local;
436:     Mat_IS *tGis = (Mat_IS *)lGis->data;

438:     PetscCall(MatCreateVecs(lGis, &global, NULL));
439:     PetscCall(MatCreateVecs(tGis->A, &local, NULL));
440:     PetscCall(PCBDDCGlobalToLocal(tGis->cctx, global, local, elements_corners, &tmp));
441:     PetscCall(VecDestroy(&global));
442:     PetscCall(VecDestroy(&local));
443:     elements_corners = tmp;
444:   }

446:   /* Destroy temporary G */
447:   PetscCall(MatISGetLocalMat(lGis, &lG));
448:   PetscCall(PetscObjectReference((PetscObject)lG));
449:   PetscCall(MatDestroy(&G));
450:   PetscCall(MatDestroy(&lGis));

452:   if (print) {
453:     PetscCall(PetscObjectSetName((PetscObject)lG, "initial_lG"));
454:     PetscCall(MatView(lG, NULL));
455:   }

457:   /* Save lG for values insertion in change of basis */
458:   PetscCall(MatDuplicate(lG, MAT_COPY_VALUES, &lGinit));

460:   /* Analyze the edge-nodes connections (duplicate lG) */
461:   PetscCall(MatDuplicate(lG, MAT_COPY_VALUES, &lGe));
462:   PetscCall(MatSetOption(lGe, MAT_KEEP_NONZERO_PATTERN, PETSC_FALSE));
463:   PetscCall(PetscBTCreate(nv, &btv));
464:   PetscCall(PetscBTCreate(ne, &bte));
465:   PetscCall(PetscBTCreate(ne, &btb));
466:   PetscCall(PetscBTCreate(ne, &btbd));
467:   /* need to import the boundary specification to ensure the
468:      proper detection of coarse edges' endpoints */
469:   if (pcbddc->DirichletBoundariesLocal) {
470:     IS is;

472:     if (fl2g) {
473:       PetscCall(ISGlobalToLocalMappingApplyIS(fl2g, IS_GTOLM_MASK, pcbddc->DirichletBoundariesLocal, &is));
474:     } else {
475:       is = pcbddc->DirichletBoundariesLocal;
476:     }
477:     PetscCall(ISGetLocalSize(is, &cum));
478:     PetscCall(ISGetIndices(is, &idxs));
479:     for (i = 0; i < cum; i++) {
480:       if (idxs[i] >= 0 && idxs[i] < ne) {
481:         PetscCall(PetscBTSet(btb, idxs[i]));
482:         PetscCall(PetscBTSet(btbd, idxs[i]));
483:       }
484:     }
485:     PetscCall(ISRestoreIndices(is, &idxs));
486:     if (fl2g) PetscCall(ISDestroy(&is));
487:   }
488:   if (pcbddc->NeumannBoundariesLocal) {
489:     IS is;

491:     if (fl2g) {
492:       PetscCall(ISGlobalToLocalMappingApplyIS(fl2g, IS_GTOLM_MASK, pcbddc->NeumannBoundariesLocal, &is));
493:     } else {
494:       is = pcbddc->NeumannBoundariesLocal;
495:     }
496:     PetscCall(ISGetLocalSize(is, &cum));
497:     PetscCall(ISGetIndices(is, &idxs));
498:     for (i = 0; i < cum; i++) {
499:       if (idxs[i] >= 0 && idxs[i] < ne) PetscCall(PetscBTSet(btb, idxs[i]));
500:     }
501:     PetscCall(ISRestoreIndices(is, &idxs));
502:     if (fl2g) PetscCall(ISDestroy(&is));
503:   }

505:   /* Count neighs per dof */
506:   PetscCall(ISLocalToGlobalMappingGetNodeInfo(el2g, NULL, &ecount, NULL));
507:   PetscCall(ISLocalToGlobalMappingGetNodeInfo(vl2g, NULL, &vcount, NULL));

509:   /* need to remove coarse faces' dofs and coarse edges' dirichlet dofs
510:      for proper detection of coarse edges' endpoints */
511:   PetscCall(PetscBTCreate(ne, &btee));
512:   for (i = 0; i < ne; i++) {
513:     if ((ecount[i] > 2 && !PetscBTLookup(btbd, i)) || (ecount[i] == 2 && PetscBTLookup(btb, i))) PetscCall(PetscBTSet(btee, i));
514:   }
515:   PetscCall(PetscMalloc1(ne, &marks));
516:   if (!conforming) {
517:     PetscCall(MatTranspose(lGe, MAT_INITIAL_MATRIX, &lGt));
518:     PetscCall(MatGetRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
519:   }
520:   PetscCall(MatGetRowIJ(lGe, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
521:   PetscCall(MatSeqAIJGetArray(lGe, &vals));
522:   cum = 0;
523:   for (i = 0; i < ne; i++) {
524:     /* eliminate rows corresponding to edge dofs belonging to coarse faces */
525:     if (!PetscBTLookup(btee, i)) {
526:       marks[cum++] = i;
527:       continue;
528:     }
529:     /* set badly connected edge dofs as primal */
530:     if (!conforming) {
531:       if (ii[i + 1] - ii[i] != order + 1) { /* every row of G on the coarse edge should list order+1 nodal dofs */
532:         marks[cum++] = i;
533:         PetscCall(PetscBTSet(bte, i));
534:         for (j = ii[i]; j < ii[i + 1]; j++) PetscCall(PetscBTSet(btv, jj[j]));
535:       } else {
536:         /* every edge dofs should be connected through a certain number of nodal dofs
537:            to other edge dofs belonging to coarse edges
538:            - at most 2 endpoints
539:            - order-1 interior nodal dofs
540:            - no undefined nodal dofs (nconn < order)
541:         */
542:         PetscInt ends = 0, ints = 0, undef = 0;
543:         for (j = ii[i]; j < ii[i + 1]; j++) {
544:           PetscInt v     = jj[j], k;
545:           PetscInt nconn = iit[v + 1] - iit[v];
546:           for (k = iit[v]; k < iit[v + 1]; k++)
547:             if (!PetscBTLookup(btee, jjt[k])) nconn--;
548:           if (nconn > order) ends++;
549:           else if (nconn == order) ints++;
550:           else undef++;
551:         }
552:         if (undef || ends > 2 || ints != order - 1) {
553:           marks[cum++] = i;
554:           PetscCall(PetscBTSet(bte, i));
555:           for (j = ii[i]; j < ii[i + 1]; j++) PetscCall(PetscBTSet(btv, jj[j]));
556:         }
557:       }
558:     }
559:     /* We assume the order on the element edge is ii[i+1]-ii[i]-1 */
560:     if (!order && ii[i + 1] != ii[i]) {
561:       PetscScalar val = 1. / (ii[i + 1] - ii[i] - 1);
562:       for (j = ii[i]; j < ii[i + 1]; j++) vals[j] = val;
563:     }
564:   }
565:   PetscCall(PetscBTDestroy(&btee));
566:   PetscCall(MatSeqAIJRestoreArray(lGe, &vals));
567:   PetscCall(MatRestoreRowIJ(lGe, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
568:   if (!conforming) {
569:     PetscCall(MatRestoreRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
570:     PetscCall(MatDestroy(&lGt));
571:   }
572:   PetscCall(MatZeroRows(lGe, cum, marks, 0., NULL, NULL));

574:   /* identify splitpoints and corner candidates */
575:   PetscCall(PetscMalloc2(nv, &sfvleaves, Lv, &sfvroots));
576:   PetscCall(PetscBTCreate(nv, &btvcand));
577:   if (elements_corners) {
578:     PetscCall(ISGetLocalSize(elements_corners, &cum));
579:     PetscCall(ISGetIndices(elements_corners, &idxs));
580:     for (i = 0; i < cum; i++) PetscCall(PetscBTSet(btvcand, idxs[i]));
581:     PetscCall(ISRestoreIndices(elements_corners, &idxs));
582:   }

584:   if (matis->allow_repeated) { /* assign a uniq global id to edge local subsets and communicate it with nodal space */
585:     PetscSF   emlsf, vmlsf;
586:     PetscInt *eleaves, *vleaves, *meleaves, *mvleaves;
587:     PetscInt  cum_subs = 0, n_subs = pcbddc->n_local_subs, bs, emnr, emnl, vmnr, vmnl;

589:     PetscCall(ISLocalToGlobalMappingGetBlockSize(el2g, &bs));
590:     PetscCheck(bs == 1, comm, PETSC_ERR_SUP, "Not coded");
591:     PetscCall(ISLocalToGlobalMappingGetBlockSize(vl2g, &bs));
592:     PetscCheck(bs == 1, comm, PETSC_ERR_SUP, "Not coded");

594:     PetscCall(ISLocalToGlobalMappingGetBlockMultiLeavesSF(el2g, &emlsf));
595:     PetscCall(ISLocalToGlobalMappingGetBlockMultiLeavesSF(vl2g, &vmlsf));

597:     PetscCall(PetscSFGetGraph(emlsf, &emnr, &emnl, NULL, NULL));
598:     for (i = 0, j = 0; i < ne; i++) j += ecount[i];
599:     PetscCheck(emnr == ne, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of roots in edge multi-leaves SF %" PetscInt_FMT " != %" PetscInt_FMT, emnr, ne);
600:     PetscCheck(emnl == j, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of leaves in edge multi-leaves SF %" PetscInt_FMT " != %" PetscInt_FMT, emnl, j);

602:     PetscCall(PetscSFGetGraph(vmlsf, &vmnr, &vmnl, NULL, NULL));
603:     for (i = 0, j = 0; i < nv; i++) j += vcount[i];
604:     PetscCheck(vmnr == nv, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of roots in nodal multi-leaves SF %" PetscInt_FMT " != %" PetscInt_FMT, vmnr, nv);
605:     PetscCheck(vmnl == j, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of leaves in nodal multi-leaves SF %" PetscInt_FMT " != %" PetscInt_FMT, vmnl, j);

607:     PetscCall(PetscMalloc1(ne, &eleaves));
608:     PetscCall(PetscMalloc1(nv, &vleaves));
609:     for (i = 0; i < ne; i++) eleaves[i] = PETSC_INT_MAX;
610:     for (i = 0; i < nv; i++) vleaves[i] = PETSC_INT_MAX;
611:     PetscCall(PetscMalloc1(emnl, &meleaves));
612:     PetscCall(PetscMalloc1(vmnl, &mvleaves));

614:     PetscCallMPI(MPI_Exscan(&n_subs, &cum_subs, 1, MPIU_INT, MPI_SUM, comm));
615:     PetscCall(MatGetRowIJ(lGinit, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
616:     for (i = 0; i < n_subs; i++) {
617:       const PetscInt *idxs;
618:       const PetscInt  subid = cum_subs + i;
619:       PetscInt        ns;

621:       PetscCall(ISGetLocalSize(pcbddc->local_subs[i], &ns));
622:       PetscCall(ISGetIndices(pcbddc->local_subs[i], &idxs));
623:       for (j = 0; j < ns; j++) {
624:         const PetscInt e = idxs[j];

626:         eleaves[e] = subid;
627:         for (PetscInt k = ii[e]; k < ii[e + 1]; k++) vleaves[jj[k]] = subid;
628:       }
629:       PetscCall(ISRestoreIndices(pcbddc->local_subs[i], &idxs));
630:     }
631:     PetscCall(MatRestoreRowIJ(lGinit, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
632:     PetscCall(PetscSFBcastBegin(emlsf, MPIU_INT, eleaves, meleaves, MPI_REPLACE));
633:     PetscCall(PetscSFBcastEnd(emlsf, MPIU_INT, eleaves, meleaves, MPI_REPLACE));
634:     PetscCall(PetscSFBcastBegin(vmlsf, MPIU_INT, vleaves, mvleaves, MPI_REPLACE));
635:     PetscCall(PetscSFBcastEnd(vmlsf, MPIU_INT, vleaves, mvleaves, MPI_REPLACE));
636:     PetscCall(PetscFree(eleaves));
637:     PetscCall(PetscFree(vleaves));

639:     PetscCall(PetscMalloc1(ne + 1, &eneighs));
640:     eneighs[0] = meleaves;
641:     for (i = 0; i < ne; i++) {
642:       PetscCall(PetscSortInt(ecount[i], eneighs[i]));
643:       eneighs[i + 1] = eneighs[i] + ecount[i];
644:     }
645:     PetscCall(PetscMalloc1(nv + 1, &vneighs));
646:     vneighs[0] = mvleaves;
647:     for (i = 0; i < nv; i++) {
648:       PetscCall(PetscSortInt(vcount[i], vneighs[i]));
649:       vneighs[i + 1] = vneighs[i] + vcount[i];
650:     }
651:   } else {
652:     PetscCall(ISLocalToGlobalMappingGetNodeInfo(el2g, NULL, NULL, &eneighs));
653:     PetscCall(ISLocalToGlobalMappingGetNodeInfo(vl2g, NULL, NULL, &vneighs));
654:   }

656:   PetscCall(MatTranspose(lGe, MAT_INITIAL_MATRIX, &lGt));
657:   if (print) {
658:     PetscCall(PetscObjectSetName((PetscObject)lGe, "edgerestr_lG"));
659:     PetscCall(MatView(lGe, NULL));
660:     PetscCall(PetscObjectSetName((PetscObject)lGt, "edgerestr_lGt"));
661:     PetscCall(MatView(lGt, NULL));
662:   }
663:   PetscCall(MatGetRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
664:   PetscCall(MatSeqAIJGetArray(lGt, &vals));
665:   for (i = 0; i < nv; i++) {
666:     PetscInt  ord = order, test = ii[i + 1] - ii[i], vc = vcount[i];
667:     PetscBool sneighs = PETSC_TRUE, bdir = PETSC_FALSE;
668:     if (!order) { /* variable order */
669:       PetscReal vorder = 0.;

671:       for (j = ii[i]; j < ii[i + 1]; j++) vorder += PetscRealPart(vals[j]);
672:       test = PetscFloorReal(vorder + 10. * PETSC_SQRT_MACHINE_EPSILON);
673:       PetscCheck(vorder - test <= PETSC_SQRT_MACHINE_EPSILON, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected value for vorder: %g (%" PetscInt_FMT ")", (double)vorder, test);
674:       ord = 1;
675:     }
676:     for (j = ii[i]; j < ii[i + 1] && sneighs; j++) {
677:       const PetscInt e = jj[j];

679:       if (PetscBTLookup(btbd, e)) {
680:         bdir = PETSC_TRUE;
681:         break;
682:       }
683:       if (vc != ecount[e]) {
684:         sneighs = PETSC_FALSE;
685:       } else {
686:         const PetscInt *vn = vneighs[i], *en = eneighs[e];

688:         for (PetscInt k = 0; k < vc; k++) {
689:           if (vn[k] != en[k]) {
690:             sneighs = PETSC_FALSE;
691:             break;
692:           }
693:         }
694:       }
695:     }
696:     if (elements_corners) test = 0;
697:     if (!sneighs || test >= 3 * ord || bdir) { /* splitpoints */
698:       if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "SPLITPOINT %" PetscInt_FMT " (%s %s %s)\n", i, PetscBools[!sneighs], PetscBools[test >= 3 * ord], PetscBools[bdir]));
699:       PetscCall(PetscBTSet(btv, i));
700:     } else if (test == ord) {
701:       if (order == 1 || (!order && ii[i + 1] - ii[i] == 1)) {
702:         if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "ENDPOINT %" PetscInt_FMT "\n", i));
703:         PetscCall(PetscBTSet(btv, i));
704:       } else if (!elements_corners) {
705:         if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "CORNER CANDIDATE %" PetscInt_FMT "\n", i));
706:         PetscCall(PetscBTSet(btvcand, i));
707:       }
708:     }
709:   }
710:   PetscCall(PetscBTDestroy(&btbd));

712:   /* a candidate is valid if it is connected to another candidate via a non-primal edge dof */
713:   if (order != 1) {
714:     if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "INSPECTING CANDIDATES\n"));
715:     PetscCall(MatGetRowIJ(lGe, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
716:     for (i = 0; i < nv; i++) {
717:       if (PetscBTLookup(btvcand, i)) {
718:         PetscBool found = PETSC_FALSE;
719:         for (j = ii[i]; j < ii[i + 1] && !found; j++) {
720:           PetscInt k, e = jj[j];
721:           if (PetscBTLookup(bte, e)) continue;
722:           for (k = iit[e]; k < iit[e + 1]; k++) {
723:             PetscInt v = jjt[k];
724:             if (v != i && PetscBTLookup(btvcand, v)) {
725:               found = PETSC_TRUE;
726:               break;
727:             }
728:           }
729:         }
730:         if (!found) {
731:           if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  CANDIDATE %" PetscInt_FMT " CLEARED\n", i));
732:           PetscCall(PetscBTClear(btvcand, i));
733:         } else {
734:           if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  CANDIDATE %" PetscInt_FMT " ACCEPTED\n", i));
735:         }
736:       }
737:     }
738:     PetscCall(MatRestoreRowIJ(lGe, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
739:   }
740:   PetscCall(MatSeqAIJRestoreArray(lGt, &vals));
741:   PetscCall(MatRestoreRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
742:   PetscCall(MatDestroy(&lGe));

744:   /* Get the local G^T explicitly */
745:   PetscCall(MatDestroy(&lGt));
746:   PetscCall(MatTranspose(lG, MAT_INITIAL_MATRIX, &lGt));
747:   PetscCall(MatSetOption(lGt, MAT_KEEP_NONZERO_PATTERN, PETSC_FALSE));

749:   /* Mark shared nodal dofs */
750:   PetscCall(PetscBTCreate(nv, &btvi));
751:   for (i = 0; i < nv; i++) {
752:     if (vcount[i] > 1) PetscCall(PetscBTSet(btvi, i));
753:   }

755:   if (matis->allow_repeated) {
756:     PetscCall(PetscFree(eneighs[0]));
757:     PetscCall(PetscFree(vneighs[0]));
758:     PetscCall(PetscFree(eneighs));
759:     PetscCall(PetscFree(vneighs));
760:   }
761:   PetscCall(ISLocalToGlobalMappingRestoreNodeInfo(el2g, NULL, &ecount, &eneighs));
762:   PetscCall(ISLocalToGlobalMappingRestoreNodeInfo(vl2g, NULL, &vcount, &vneighs));

764:   /* communicate corners and splitpoints */
765:   PetscCall(PetscMalloc1(nv, &vmarks));
766:   PetscCall(PetscArrayzero(sfvleaves, nv));
767:   PetscCall(PetscArrayzero(sfvroots, Lv));
768:   for (i = 0; i < nv; i++)
769:     if (PetscUnlikely(PetscBTLookup(btv, i))) sfvleaves[i] = 1;

771:   if (print) {
772:     IS tbz;

774:     cum = 0;
775:     for (i = 0; i < nv; i++)
776:       if (sfvleaves[i]) vmarks[cum++] = i;

778:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cum, vmarks, PETSC_COPY_VALUES, &tbz));
779:     PetscCall(PetscObjectSetName((PetscObject)tbz, "corners_to_be_zeroed_local"));
780:     PetscCall(ISView(tbz, NULL));
781:     PetscCall(ISDestroy(&tbz));
782:   }

784:   PetscCall(PetscSFReduceBegin(sfv, MPIU_INT, sfvleaves, sfvroots, MPI_SUM));
785:   PetscCall(PetscSFReduceEnd(sfv, MPIU_INT, sfvleaves, sfvroots, MPI_SUM));
786:   PetscCall(PetscSFBcastBegin(sfv, MPIU_INT, sfvroots, sfvleaves, MPI_REPLACE));
787:   PetscCall(PetscSFBcastEnd(sfv, MPIU_INT, sfvroots, sfvleaves, MPI_REPLACE));

789:   /* Zero rows of lGt corresponding to identified corners
790:      and interior nodal dofs */
791:   cum = 0;
792:   for (i = 0; i < nv; i++) {
793:     if (sfvleaves[i]) {
794:       vmarks[cum++] = i;
795:       PetscCall(PetscBTSet(btv, i));
796:     } else if (!PetscBTLookup(btvi, i)) vmarks[cum++] = i;
797:   }
798:   PetscCall(PetscBTDestroy(&btvi));
799:   if (print) {
800:     IS tbz;

802:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cum, vmarks, PETSC_COPY_VALUES, &tbz));
803:     PetscCall(PetscObjectSetName((PetscObject)tbz, "corners_to_be_zeroed_with_interior"));
804:     PetscCall(ISView(tbz, NULL));
805:     PetscCall(ISDestroy(&tbz));
806:   }
807:   PetscCall(MatZeroRows(lGt, cum, vmarks, 0., NULL, NULL));
808:   PetscCall(PetscFree(vmarks));
809:   PetscCall(PetscSFDestroy(&sfv));
810:   PetscCall(PetscFree2(sfvleaves, sfvroots));

812:   /* Recompute G */
813:   PetscCall(MatDestroy(&lG));
814:   PetscCall(MatTranspose(lGt, MAT_INITIAL_MATRIX, &lG));
815:   if (print) {
816:     PetscCall(PetscObjectSetName((PetscObject)lG, "used_lG"));
817:     PetscCall(MatView(lG, NULL));
818:     PetscCall(PetscObjectSetName((PetscObject)lGt, "used_lGt"));
819:     PetscCall(MatView(lGt, NULL));
820:   }

822:   /* Get primal dofs (if any) */
823:   cum = 0;
824:   for (i = 0; i < ne; i++) {
825:     if (PetscUnlikely(PetscBTLookup(bte, i))) marks[cum++] = i;
826:   }
827:   if (fl2g) PetscCall(ISLocalToGlobalMappingApply(fl2g, cum, marks, marks));
828:   PetscCall(ISCreateGeneral(comm, cum, marks, PETSC_COPY_VALUES, &primals));
829:   if (print) {
830:     PetscCall(PetscObjectSetName((PetscObject)primals, "prescribed_primal_dofs"));
831:     PetscCall(ISView(primals, NULL));
832:   }
833:   PetscCall(PetscBTDestroy(&bte));
834:   /* TODO: what if the user passed in some of them ?  */
835:   PetscCall(PCBDDCSetPrimalVerticesLocalIS(pc, primals));
836:   PetscCall(ISDestroy(&primals));

838:   /* Compute edge connectivity */
839:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)lG, "econn_"));

841:   /* Symbolic conn = lG*lGt */
842:   if (!elements_corners) { /* if present, we assume we are in the element-by-element case and the CSR graph is not needed */
843:     PetscCall(MatProductCreate(lG, lGt, NULL, &conn));
844:     PetscCall(MatProductSetType(conn, MATPRODUCT_AB));
845:     PetscCall(MatProductSetAlgorithm(conn, "default"));
846:     PetscCall(MatProductSetFill(conn, PETSC_DEFAULT));
847:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)conn, "econn_"));
848:     PetscCall(MatProductSetFromOptions(conn));
849:     PetscCall(MatProductSymbolic(conn));
850:     PetscCall(MatGetRowIJ(conn, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
851:     if (fl2g) {
852:       PetscBT   btf;
853:       PetscInt *iia, *jja, *iiu, *jju;
854:       PetscBool rest = PETSC_FALSE, free = PETSC_FALSE;

856:       /* create CSR for all local dofs */
857:       PetscCall(PetscMalloc1(n + 1, &iia));
858:       if (pcbddc->mat_graph->nvtxs_csr) { /* the user has passed in a CSR graph */
859:         PetscCheck(pcbddc->mat_graph->nvtxs_csr == n, PETSC_COMM_SELF, PETSC_ERR_USER, "Invalid size of CSR graph %" PetscInt_FMT ". Should be %" PetscInt_FMT, pcbddc->mat_graph->nvtxs_csr, n);
860:         iiu = pcbddc->mat_graph->xadj;
861:         jju = pcbddc->mat_graph->adjncy;
862:       } else if (pcbddc->use_local_adj) {
863:         rest = PETSC_TRUE;
864:         PetscCall(MatGetRowIJ(matis->A, 0, PETSC_TRUE, PETSC_FALSE, &i, (const PetscInt **)&iiu, (const PetscInt **)&jju, &done));
865:       } else {
866:         free = PETSC_TRUE;
867:         PetscCall(PetscMalloc2(n + 1, &iiu, n, &jju));
868:         iiu[0] = 0;
869:         for (i = 0; i < n; i++) {
870:           iiu[i + 1] = i + 1;
871:           jju[i]     = -1;
872:         }
873:       }

875:       /* import sizes of CSR */
876:       iia[0] = 0;
877:       for (i = 0; i < n; i++) iia[i + 1] = iiu[i + 1] - iiu[i];

879:       /* overwrite entries corresponding to the Nedelec field */
880:       PetscCall(PetscBTCreate(n, &btf));
881:       PetscCall(ISGetIndices(nedfieldlocal, &idxs));
882:       for (i = 0; i < ne; i++) {
883:         PetscCall(PetscBTSet(btf, idxs[i]));
884:         iia[idxs[i] + 1] = ii[i + 1] - ii[i];
885:       }

887:       /* iia in CSR */
888:       for (i = 0; i < n; i++) iia[i + 1] += iia[i];

890:       /* jja in CSR */
891:       PetscCall(PetscMalloc1(iia[n], &jja));
892:       for (i = 0; i < n; i++)
893:         if (!PetscBTLookup(btf, i))
894:           for (j = 0; j < iiu[i + 1] - iiu[i]; j++) jja[iia[i] + j] = jju[iiu[i] + j];

896:       /* map edge dofs connectivity */
897:       if (jj) {
898:         PetscCall(ISLocalToGlobalMappingApply(fl2g, ii[ne], jj, (PetscInt *)jj));
899:         for (i = 0; i < ne; i++) {
900:           PetscInt e = idxs[i];
901:           for (j = 0; j < ii[i + 1] - ii[i]; j++) jja[iia[e] + j] = jj[ii[i] + j];
902:         }
903:       }
904:       PetscCall(ISRestoreIndices(nedfieldlocal, &idxs));
905:       PetscCall(PCBDDCSetLocalAdjacencyGraph(pc, n, iia, jja, PETSC_COPY_VALUES));
906:       if (rest) PetscCall(MatRestoreRowIJ(matis->A, 0, PETSC_TRUE, PETSC_FALSE, &i, (const PetscInt **)&iiu, (const PetscInt **)&jju, &done));
907:       if (free) PetscCall(PetscFree2(iiu, jju));
908:       PetscCall(PetscBTDestroy(&btf));
909:     } else {
910:       PetscCall(PCBDDCSetLocalAdjacencyGraph(pc, n, ii, jj, PETSC_COPY_VALUES));
911:     }
912:     PetscCall(MatRestoreRowIJ(conn, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
913:     PetscCall(MatDestroy(&conn));
914:   }

916:   /* Analyze interface for edge dofs */
917:   PetscCall(PCBDDCAnalyzeInterface(pc));
918:   pcbddc->mat_graph->twodim = PETSC_FALSE;

920:   /* Get coarse edges in the edge space */
921:   PetscCall(PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph, NULL, NULL, &nee, &alleedges, &allprimals));

923:   if (fl2g) {
924:     PetscCall(ISGlobalToLocalMappingApplyIS(fl2g, IS_GTOLM_DROP, allprimals, &primals));
925:     PetscCall(PetscMalloc1(nee, &eedges));
926:     for (i = 0; i < nee; i++) PetscCall(ISGlobalToLocalMappingApplyIS(fl2g, IS_GTOLM_DROP, alleedges[i], &eedges[i]));
927:   } else {
928:     eedges  = alleedges;
929:     primals = allprimals;
930:   }

932:   /* Mark fine edge dofs with their coarse edge id */
933:   PetscCall(PetscArrayzero(marks, ne));
934:   PetscCall(ISGetLocalSize(primals, &cum));
935:   PetscCall(ISGetIndices(primals, &idxs));
936:   for (i = 0; i < cum; i++) marks[idxs[i]] = nee + 1;
937:   PetscCall(ISRestoreIndices(primals, &idxs));
938:   if (print) {
939:     PetscCall(PetscObjectSetName((PetscObject)primals, "obtained_primal_dofs"));
940:     PetscCall(ISView(primals, NULL));
941:   }

943:   maxsize = 0;
944:   for (i = 0; i < nee; i++) {
945:     PetscInt size, mark = i + 1;

947:     PetscCall(ISGetLocalSize(eedges[i], &size));
948:     PetscCall(ISGetIndices(eedges[i], &idxs));
949:     for (j = 0; j < size; j++) marks[idxs[j]] = mark;
950:     PetscCall(ISRestoreIndices(eedges[i], &idxs));
951:     maxsize = PetscMax(maxsize, size);
952:   }

954:   /* Find coarse edge endpoints */
955:   PetscCall(MatGetRowIJ(lG, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
956:   PetscCall(MatGetRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
957:   for (i = 0; i < nee; i++) {
958:     PetscInt mark = i + 1, size;

960:     PetscCall(ISGetLocalSize(eedges[i], &size));
961:     if (!size && nedfieldlocal) continue;
962:     PetscCheck(size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected zero sized edge %" PetscInt_FMT, i);
963:     PetscCall(ISGetIndices(eedges[i], &idxs));
964:     if (print) {
965:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "ENDPOINTS ANALYSIS EDGE %" PetscInt_FMT "\n", i));
966:       PetscCall(ISView(eedges[i], NULL));
967:     }
968:     for (j = 0; j < size; j++) {
969:       PetscInt k, ee = idxs[j];
970:       if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  idx %" PetscInt_FMT "\n", ee));
971:       for (k = ii[ee]; k < ii[ee + 1]; k++) {
972:         if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "    inspect %" PetscInt_FMT "\n", jj[k]));
973:         if (PetscBTLookup(btv, jj[k])) {
974:           if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "      corner found (already set) %" PetscInt_FMT "\n", jj[k]));
975:         } else if (PetscBTLookup(btvcand, jj[k])) { /* is it ok? */
976:           PetscInt  k2;
977:           PetscBool corner = PETSC_FALSE;
978:           for (k2 = iit[jj[k]]; k2 < iit[jj[k] + 1]; k2++) {
979:             if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "        INSPECTING %" PetscInt_FMT ": mark %" PetscInt_FMT " (ref mark %" PetscInt_FMT "), boundary %d\n", jjt[k2], marks[jjt[k2]], mark, (int)!!PetscBTLookup(btb, jjt[k2])));
980:             /* it's a corner if either is connected with an edge dof belonging to a different cc or
981:                if the edge dof lie on the natural part of the boundary */
982:             if ((marks[jjt[k2]] && marks[jjt[k2]] != mark) || (!marks[jjt[k2]] && PetscBTLookup(btb, jjt[k2]))) {
983:               corner = PETSC_TRUE;
984:               break;
985:             }
986:           }
987:           if (corner) { /* found the nodal dof corresponding to the endpoint of the edge */
988:             if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "        corner found %" PetscInt_FMT "\n", jj[k]));
989:             PetscCall(PetscBTSet(btv, jj[k]));
990:           } else {
991:             if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "        no corners found\n"));
992:           }
993:         }
994:       }
995:     }
996:     PetscCall(ISRestoreIndices(eedges[i], &idxs));
997:   }
998:   PetscCall(MatRestoreRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
999:   PetscCall(MatRestoreRowIJ(lG, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1000:   PetscCall(PetscBTDestroy(&btb));

1002:   /* Reset marked primal dofs */
1003:   PetscCall(ISGetLocalSize(primals, &cum));
1004:   PetscCall(ISGetIndices(primals, &idxs));
1005:   for (i = 0; i < cum; i++) marks[idxs[i]] = 0;
1006:   PetscCall(ISRestoreIndices(primals, &idxs));

1008:   /* Now use the initial lG */
1009:   PetscCall(MatDestroy(&lG));
1010:   PetscCall(MatDestroy(&lGt));
1011:   lG = lGinit;
1012:   PetscCall(MatTranspose(lG, MAT_INITIAL_MATRIX, &lGt));

1014:   /* Compute extended cols indices */
1015:   PetscCall(PetscBTCreate(nv, &btvc));
1016:   PetscCall(PetscBTCreate(nee, &bter));
1017:   PetscCall(MatGetRowIJ(lG, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1018:   PetscCall(MatSeqAIJGetMaxRowNonzeros(lG, &i));
1019:   i *= maxsize;
1020:   PetscCall(PetscCalloc1(nee, &extcols));
1021:   PetscCall(PetscMalloc2(i, &extrow, i, &gidxs));
1022:   eerr = PETSC_FALSE;
1023:   for (i = 0; i < nee; i++) {
1024:     PetscInt size, found = 0;

1026:     cum = 0;
1027:     PetscCall(ISGetLocalSize(eedges[i], &size));
1028:     if (!size && nedfieldlocal) continue;
1029:     PetscCheck(size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected zero sized edge %" PetscInt_FMT, i);
1030:     PetscCall(ISGetIndices(eedges[i], &idxs));
1031:     PetscCall(PetscBTMemzero(nv, btvc));
1032:     for (j = 0; j < size; j++) {
1033:       PetscInt k, ee = idxs[j];
1034:       for (k = ii[ee]; k < ii[ee + 1]; k++) {
1035:         PetscInt vv = jj[k];
1036:         if (!PetscBTLookup(btv, vv)) extrow[cum++] = vv;
1037:         else if (!PetscBTLookupSet(btvc, vv)) found++;
1038:       }
1039:     }
1040:     PetscCall(ISRestoreIndices(eedges[i], &idxs));
1041:     PetscCall(PetscSortRemoveDupsInt(&cum, extrow));
1042:     PetscCall(ISLocalToGlobalMappingApply(vl2g, cum, extrow, gidxs));
1043:     PetscCall(PetscSortIntWithArray(cum, gidxs, extrow));
1044:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cum, extrow, PETSC_COPY_VALUES, &extcols[i]));
1045:     /* it may happen that endpoints are not defined at this point
1046:        if it is the case, mark this edge for a second pass */
1047:     if (cum != size - 1 || found != 2) {
1048:       PetscCall(PetscBTSet(bter, i));
1049:       if (print) {
1050:         PetscCall(PetscObjectSetName((PetscObject)eedges[i], "error_edge"));
1051:         PetscCall(ISView(eedges[i], NULL));
1052:         PetscCall(PetscObjectSetName((PetscObject)extcols[i], "error_extcol"));
1053:         PetscCall(ISView(extcols[i], NULL));
1054:       }
1055:       eerr = PETSC_TRUE;
1056:     }
1057:   }
1058:   /* PetscCheck(!eerr,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected SIZE OF EDGE > EXTCOL FIRST PASS"); */
1059:   PetscCallMPI(MPIU_Allreduce(&eerr, &done, 1, MPIU_BOOL, MPI_LOR, comm));
1060:   if (done) {
1061:     PetscInt *newprimals;

1063:     PetscCall(PetscMalloc1(ne, &newprimals));
1064:     PetscCall(ISGetLocalSize(primals, &cum));
1065:     PetscCall(ISGetIndices(primals, &idxs));
1066:     PetscCall(PetscArraycpy(newprimals, idxs, cum));
1067:     PetscCall(ISRestoreIndices(primals, &idxs));
1068:     PetscCall(MatGetRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
1069:     if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "DOING SECOND PASS (eerr %s)\n", PetscBools[eerr]));
1070:     for (i = 0; i < nee; i++) {
1071:       PetscBool has_candidates = PETSC_FALSE;
1072:       if (PetscBTLookup(bter, i)) {
1073:         PetscInt size, mark = i + 1;

1075:         PetscCall(ISGetLocalSize(eedges[i], &size));
1076:         PetscCall(ISGetIndices(eedges[i], &idxs));
1077:         /* for (j=0;j<size;j++) newprimals[cum++] = idxs[j]; */
1078:         for (j = 0; j < size; j++) {
1079:           PetscInt k, ee = idxs[j];
1080:           if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Inspecting edge dof %" PetscInt_FMT " [%" PetscInt_FMT " %" PetscInt_FMT ")\n", ee, ii[ee], ii[ee + 1]));
1081:           for (k = ii[ee]; k < ii[ee + 1]; k++) {
1082:             /* set all candidates located on the edge as corners */
1083:             if (PetscBTLookup(btvcand, jj[k])) {
1084:               PetscInt k2, vv = jj[k];
1085:               has_candidates = PETSC_TRUE;
1086:               if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Candidate set to vertex %" PetscInt_FMT "\n", vv));
1087:               PetscCall(PetscBTSet(btv, vv));
1088:               /* set all edge dofs connected to candidate as primals */
1089:               for (k2 = iit[vv]; k2 < iit[vv + 1]; k2++) {
1090:                 if (marks[jjt[k2]] == mark) {
1091:                   PetscInt k3, ee2 = jjt[k2];
1092:                   if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "    Connected edge dof set to primal %" PetscInt_FMT "\n", ee2));
1093:                   newprimals[cum++] = ee2;
1094:                   /* finally set the new corners */
1095:                   for (k3 = ii[ee2]; k3 < ii[ee2 + 1]; k3++) {
1096:                     if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "      Connected nodal dof set to vertex %" PetscInt_FMT "\n", jj[k3]));
1097:                     PetscCall(PetscBTSet(btv, jj[k3]));
1098:                   }
1099:                 }
1100:               }
1101:             } else {
1102:               if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Not a candidate vertex %" PetscInt_FMT "\n", jj[k]));
1103:             }
1104:           }
1105:         }
1106:         if (!has_candidates) { /* circular edge */
1107:           PetscInt k, ee = idxs[0], *tmarks;

1109:           PetscCall(PetscCalloc1(ne, &tmarks));
1110:           if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Circular edge %" PetscInt_FMT "\n", i));
1111:           for (k = ii[ee]; k < ii[ee + 1]; k++) {
1112:             PetscInt k2;
1113:             if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "    Set to corner %" PetscInt_FMT "\n", jj[k]));
1114:             PetscCall(PetscBTSet(btv, jj[k]));
1115:             for (k2 = iit[jj[k]]; k2 < iit[jj[k] + 1]; k2++) tmarks[jjt[k2]]++;
1116:           }
1117:           for (j = 0; j < size; j++) {
1118:             if (tmarks[idxs[j]] > 1) {
1119:               if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Edge dof set to primal %" PetscInt_FMT "\n", idxs[j]));
1120:               newprimals[cum++] = idxs[j];
1121:             }
1122:           }
1123:           PetscCall(PetscFree(tmarks));
1124:         }
1125:         PetscCall(ISRestoreIndices(eedges[i], &idxs));
1126:       }
1127:       PetscCall(ISDestroy(&extcols[i]));
1128:     }
1129:     PetscCall(PetscFree(extcols));
1130:     PetscCall(MatRestoreRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &iit, &jjt, &done));
1131:     PetscCall(PetscSortRemoveDupsInt(&cum, newprimals));
1132:     if (fl2g) {
1133:       PetscCall(ISLocalToGlobalMappingApply(fl2g, cum, newprimals, newprimals));
1134:       PetscCall(ISDestroy(&primals));
1135:       for (i = 0; i < nee; i++) PetscCall(ISDestroy(&eedges[i]));
1136:       PetscCall(PetscFree(eedges));
1137:     }
1138:     PetscCall(PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph, NULL, NULL, &nee, &alleedges, &allprimals));
1139:     PetscCall(ISCreateGeneral(comm, cum, newprimals, PETSC_COPY_VALUES, &primals));
1140:     PetscCall(PetscFree(newprimals));
1141:     PetscCall(PCBDDCSetPrimalVerticesLocalIS(pc, primals));
1142:     PetscCall(ISDestroy(&primals));
1143:     PetscCall(PCBDDCAnalyzeInterface(pc));
1144:     pcbddc->mat_graph->twodim = PETSC_FALSE;
1145:     PetscCall(PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph, NULL, NULL, &nee, &alleedges, &allprimals));
1146:     if (fl2g) {
1147:       PetscCall(ISGlobalToLocalMappingApplyIS(fl2g, IS_GTOLM_DROP, allprimals, &primals));
1148:       PetscCall(PetscMalloc1(nee, &eedges));
1149:       for (i = 0; i < nee; i++) PetscCall(ISGlobalToLocalMappingApplyIS(fl2g, IS_GTOLM_DROP, alleedges[i], &eedges[i]));
1150:     } else {
1151:       eedges  = alleedges;
1152:       primals = allprimals;
1153:     }
1154:     PetscCall(PetscCalloc1(nee, &extcols));

1156:     /* Mark again */
1157:     PetscCall(PetscArrayzero(marks, ne));
1158:     for (i = 0; i < nee; i++) {
1159:       PetscInt size, mark = i + 1;

1161:       PetscCall(ISGetLocalSize(eedges[i], &size));
1162:       PetscCall(ISGetIndices(eedges[i], &idxs));
1163:       for (j = 0; j < size; j++) marks[idxs[j]] = mark;
1164:       PetscCall(ISRestoreIndices(eedges[i], &idxs));
1165:     }
1166:     if (print) {
1167:       PetscCall(PetscObjectSetName((PetscObject)primals, "obtained_primal_dofs_secondpass"));
1168:       PetscCall(ISView(primals, NULL));
1169:     }

1171:     /* Recompute extended cols */
1172:     eerr = PETSC_FALSE;
1173:     for (i = 0; i < nee; i++) {
1174:       PetscInt size;

1176:       cum = 0;
1177:       PetscCall(ISGetLocalSize(eedges[i], &size));
1178:       if (!size && nedfieldlocal) continue;
1179:       PetscCheck(size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected zero sized edge %" PetscInt_FMT, i);
1180:       PetscCall(ISGetIndices(eedges[i], &idxs));
1181:       for (j = 0; j < size; j++) {
1182:         PetscInt k, ee = idxs[j];
1183:         for (k = ii[ee]; k < ii[ee + 1]; k++)
1184:           if (!PetscBTLookup(btv, jj[k])) extrow[cum++] = jj[k];
1185:       }
1186:       PetscCall(ISRestoreIndices(eedges[i], &idxs));
1187:       PetscCall(PetscSortRemoveDupsInt(&cum, extrow));
1188:       PetscCall(ISLocalToGlobalMappingApply(vl2g, cum, extrow, gidxs));
1189:       PetscCall(PetscSortIntWithArray(cum, gidxs, extrow));
1190:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cum, extrow, PETSC_COPY_VALUES, &extcols[i]));
1191:       if (cum != size - 1) {
1192:         if (print) {
1193:           PetscCall(PetscObjectSetName((PetscObject)eedges[i], "error_edge_secondpass"));
1194:           PetscCall(ISView(eedges[i], NULL));
1195:           PetscCall(PetscObjectSetName((PetscObject)extcols[i], "error_extcol_secondpass"));
1196:           PetscCall(ISView(extcols[i], NULL));
1197:         }
1198:         eerr = PETSC_TRUE;
1199:       }
1200:     }
1201:   }
1202:   PetscCall(MatRestoreRowIJ(lG, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1203:   PetscCall(PetscFree2(extrow, gidxs));
1204:   PetscCall(PetscBTDestroy(&bter));
1205:   if (print) PetscCall(PCBDDCGraphASCIIView(pcbddc->mat_graph, 5, PETSC_VIEWER_STDOUT_SELF));
1206:   /* an error should not occur at this point */
1207:   PetscCheck(!eerr, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected SIZE OF EDGE > EXTCOL SECOND PASS");

1209:   /* Check the number of endpoints */
1210:   PetscCall(MatGetRowIJ(lG, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1211:   PetscCall(PetscMalloc1(2 * nee, &corners));
1212:   PetscCall(PetscMalloc1(nee, &cedges));
1213:   for (i = 0; i < nee; i++) {
1214:     PetscInt size, found = 0, gc[2];

1216:     /* init with defaults */
1217:     cedges[i] = corners[i * 2] = corners[i * 2 + 1] = -1;
1218:     PetscCall(ISGetLocalSize(eedges[i], &size));
1219:     if (!size && nedfieldlocal) continue;
1220:     PetscCheck(size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected zero sized edge %" PetscInt_FMT, i);
1221:     PetscCall(ISGetIndices(eedges[i], &idxs));
1222:     PetscCall(PetscBTMemzero(nv, btvc));
1223:     for (j = 0; j < size; j++) {
1224:       PetscInt k, ee = idxs[j];
1225:       for (k = ii[ee]; k < ii[ee + 1]; k++) {
1226:         PetscInt vv = jj[k];
1227:         if (PetscBTLookup(btv, vv) && !PetscBTLookupSet(btvc, vv)) {
1228:           PetscCheck(found != 2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Found more than two corners for edge %" PetscInt_FMT, i);
1229:           corners[i * 2 + found++] = vv;
1230:         }
1231:       }
1232:     }
1233:     if (found != 2) {
1234:       PetscInt e;
1235:       if (fl2g) {
1236:         PetscCall(ISLocalToGlobalMappingApply(fl2g, 1, idxs, &e));
1237:       } else {
1238:         e = idxs[0];
1239:       }
1240:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Found %" PetscInt_FMT " corners for edge %" PetscInt_FMT " (astart %" PetscInt_FMT ", estart %" PetscInt_FMT ")", found, i, e, idxs[0]);
1241:     }

1243:     /* get primal dof index on this coarse edge */
1244:     PetscCall(ISLocalToGlobalMappingApply(vl2g, 2, corners + 2 * i, gc));
1245:     if (gc[0] > gc[1]) {
1246:       PetscInt swap      = corners[2 * i];
1247:       corners[2 * i]     = corners[2 * i + 1];
1248:       corners[2 * i + 1] = swap;
1249:     }
1250:     cedges[i] = idxs[size - 1];
1251:     PetscCall(ISRestoreIndices(eedges[i], &idxs));
1252:     if (print) PetscCall(PetscPrintf(PETSC_COMM_SELF, "EDGE %" PetscInt_FMT ": ce %" PetscInt_FMT ", corners (%" PetscInt_FMT ",%" PetscInt_FMT ")\n", i, cedges[i], corners[2 * i], corners[2 * i + 1]));
1253:   }
1254:   PetscCall(MatRestoreRowIJ(lG, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1255:   PetscCall(PetscBTDestroy(&btvc));

1257:   if (PetscDefined(USE_DEBUG)) {
1258:     /* Inspects columns of lG (rows of lGt) and make sure the change of basis will
1259:      not interfere with neighbouring coarse edges */
1260:     PetscCall(PetscMalloc1(nee + 1, &emarks));
1261:     PetscCall(MatGetRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1262:     for (i = 0; i < nv; i++) {
1263:       PetscInt emax = 0, eemax = 0;

1265:       if (ii[i + 1] == ii[i] || PetscBTLookup(btv, i)) continue;
1266:       PetscCall(PetscArrayzero(emarks, nee + 1));
1267:       for (j = ii[i]; j < ii[i + 1]; j++) emarks[marks[jj[j]]]++;
1268:       for (j = 1; j < nee + 1; j++) {
1269:         if (emax < emarks[j]) {
1270:           emax  = emarks[j];
1271:           eemax = j;
1272:         }
1273:       }
1274:       /* not relevant for edges */
1275:       if (!eemax) continue;

1277:       for (j = ii[i]; j < ii[i + 1]; j++) {
1278:         PetscCheck(!marks[jj[j]] || marks[jj[j]] == eemax, PETSC_COMM_SELF, PETSC_ERR_SUP, "Found 2 coarse edges (id %" PetscInt_FMT " and %" PetscInt_FMT ") connected through the %" PetscInt_FMT " nodal dof at edge dof %" PetscInt_FMT, marks[jj[j]] - 1, eemax, i, jj[j]);
1279:       }
1280:     }
1281:     PetscCall(PetscFree(emarks));
1282:     PetscCall(MatRestoreRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1283:   }

1285:   /* Compute extended rows indices for edge blocks of the change of basis */
1286:   PetscCall(MatGetRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1287:   PetscCall(MatSeqAIJGetMaxRowNonzeros(lGt, &extmem));
1288:   extmem *= maxsize;
1289:   PetscCall(PetscMalloc1(extmem * nee, &extrow));
1290:   PetscCall(PetscMalloc1(nee, &extrows));
1291:   PetscCall(PetscCalloc1(nee, &extrowcum));
1292:   for (i = 0; i < nv; i++) {
1293:     PetscInt mark = 0, size, start;

1295:     if (ii[i + 1] == ii[i] || PetscBTLookup(btv, i)) continue;
1296:     for (j = ii[i]; j < ii[i + 1]; j++)
1297:       if (marks[jj[j]] && !mark) mark = marks[jj[j]];

1299:     /* not relevant */
1300:     if (!mark) continue;

1302:     /* import extended row */
1303:     mark--;
1304:     start = mark * extmem + extrowcum[mark];
1305:     size  = ii[i + 1] - ii[i];
1306:     PetscCheck(extrowcum[mark] + size <= extmem, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Not enough memory allocated %" PetscInt_FMT " > %" PetscInt_FMT, extrowcum[mark] + size, extmem);
1307:     PetscCall(PetscArraycpy(extrow + start, jj + ii[i], size));
1308:     extrowcum[mark] += size;
1309:   }
1310:   PetscCall(MatRestoreRowIJ(lGt, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &done));
1311:   PetscCall(MatDestroy(&lGt));
1312:   PetscCall(PetscFree(marks));

1314:   /* Compress extrows */
1315:   cum = 0;
1316:   for (i = 0; i < nee; i++) {
1317:     PetscInt size = extrowcum[i], *start = extrow + i * extmem;
1318:     PetscCall(PetscSortRemoveDupsInt(&size, start));
1319:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, size, start, PETSC_USE_POINTER, &extrows[i]));
1320:     cum = PetscMax(cum, size);
1321:   }
1322:   PetscCall(PetscFree(extrowcum));
1323:   PetscCall(PetscBTDestroy(&btv));
1324:   PetscCall(PetscBTDestroy(&btvcand));

1326:   /* Workspace for lapack inner calls and VecSetValues */
1327:   PetscCall(PetscMalloc2((5 + cum + maxsize) * maxsize, &work, maxsize, &rwork));

1329:   /* Create change of basis matrix (preallocation can be improved) */
1330:   PetscCall(MatCreate(comm, &T));
1331:   PetscCall(MatSetLayouts(T, pc->mat->rmap, pc->mat->cmap));
1332:   PetscCall(MatSetType(T, MATAIJ));
1333:   PetscCall(MatSeqAIJSetPreallocation(T, maxsize, NULL));
1334:   PetscCall(MatMPIAIJSetPreallocation(T, maxsize, NULL, maxsize, NULL));
1335:   PetscCall(MatSetLocalToGlobalMapping(T, al2g, al2g));
1336:   PetscCall(MatSetOption(T, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
1337:   PetscCall(MatSetOption(T, MAT_ROW_ORIENTED, PETSC_FALSE));
1338:   PetscCall(ISLocalToGlobalMappingDestroy(&al2g));

1340:   /* Defaults to identity */
1341:   for (i = pc->mat->rmap->rstart; i < pc->mat->rmap->rend; i++) PetscCall(MatSetValue(T, i, i, 1.0, INSERT_VALUES));

1343:   /* Create discrete gradient for the coarser level if needed */
1344:   PetscCall(MatDestroy(&pcbddc->nedcG));
1345:   PetscCall(ISDestroy(&pcbddc->nedclocal));
1346:   if (pcbddc->current_level < pcbddc->max_levels) {
1347:     ISLocalToGlobalMapping cel2g, cvl2g;
1348:     IS                     wis, gwis;
1349:     PetscInt               cnv, cne;

1351:     PetscCall(ISCreateGeneral(comm, nee, cedges, PETSC_COPY_VALUES, &wis));
1352:     if (fl2g) {
1353:       PetscCall(ISLocalToGlobalMappingApplyIS(fl2g, wis, &pcbddc->nedclocal));
1354:     } else {
1355:       PetscCall(PetscObjectReference((PetscObject)wis));
1356:       pcbddc->nedclocal = wis;
1357:     }
1358:     PetscCall(ISLocalToGlobalMappingApplyIS(el2g, wis, &gwis));
1359:     PetscCall(ISDestroy(&wis));
1360:     PetscCall(ISRenumber(gwis, NULL, &cne, &wis));
1361:     PetscCall(ISLocalToGlobalMappingCreateIS(wis, &cel2g));
1362:     PetscCall(ISDestroy(&wis));
1363:     PetscCall(ISDestroy(&gwis));

1365:     PetscCall(ISCreateGeneral(comm, 2 * nee, corners, PETSC_USE_POINTER, &wis));
1366:     PetscCall(ISLocalToGlobalMappingApplyIS(vl2g, wis, &gwis));
1367:     PetscCall(ISDestroy(&wis));
1368:     PetscCall(ISRenumber(gwis, NULL, &cnv, &wis));
1369:     PetscCall(ISLocalToGlobalMappingCreateIS(wis, &cvl2g));
1370:     PetscCall(ISDestroy(&wis));
1371:     PetscCall(ISDestroy(&gwis));

1373:     PetscCall(MatCreate(comm, &pcbddc->nedcG));
1374:     PetscCall(MatSetSizes(pcbddc->nedcG, PETSC_DECIDE, PETSC_DECIDE, cne, cnv));
1375:     PetscCall(MatSetType(pcbddc->nedcG, MATAIJ));
1376:     PetscCall(MatSeqAIJSetPreallocation(pcbddc->nedcG, 2, NULL));
1377:     PetscCall(MatMPIAIJSetPreallocation(pcbddc->nedcG, 2, NULL, 2, NULL));
1378:     PetscCall(MatSetLocalToGlobalMapping(pcbddc->nedcG, cel2g, cvl2g));
1379:     PetscCall(ISLocalToGlobalMappingDestroy(&cel2g));
1380:     PetscCall(ISLocalToGlobalMappingDestroy(&cvl2g));
1381:   }
1382:   PetscCall(ISLocalToGlobalMappingDestroy(&vl2g));

1384: #if defined(PRINT_GDET)
1385:   inc = 0;
1386:   lev = pcbddc->current_level;
1387: #endif

1389:   /* Insert values in the change of basis matrix */
1390:   for (i = 0; i < nee; i++) {
1391:     Mat         Gins = NULL, GKins = NULL;
1392:     IS          cornersis = NULL;
1393:     PetscScalar cvals[2];

1395:     if (pcbddc->nedcG) PetscCall(ISCreateGeneral(PETSC_COMM_SELF, 2, corners + 2 * i, PETSC_USE_POINTER, &cornersis));
1396:     PetscCall(PCBDDCComputeNedelecChangeEdge(lG, eedges[i], extrows[i], extcols[i], cornersis, &Gins, &GKins, cvals, work, rwork));
1397:     if (Gins && GKins) {
1398:       const PetscScalar *data;
1399:       const PetscInt    *rows, *cols;
1400:       PetscInt           nrh, nch, nrc, ncc;

1402:       PetscCall(ISGetIndices(eedges[i], &cols));
1403:       /* H1 */
1404:       PetscCall(ISGetIndices(extrows[i], &rows));
1405:       PetscCall(MatGetSize(Gins, &nrh, &nch));
1406:       PetscCall(MatDenseGetArrayRead(Gins, &data));
1407:       PetscCall(MatSetValuesLocal(T, nrh, rows, nch, cols, data, INSERT_VALUES));
1408:       PetscCall(MatDenseRestoreArrayRead(Gins, &data));
1409:       PetscCall(ISRestoreIndices(extrows[i], &rows));
1410:       /* complement */
1411:       PetscCall(MatGetSize(GKins, &nrc, &ncc));
1412:       PetscCheck(ncc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Constant function has not been generated for coarse edge %" PetscInt_FMT, i);
1413:       PetscCheck(ncc + nch == nrc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "The sum of the number of columns of GKins %" PetscInt_FMT " and Gins %" PetscInt_FMT " does not match %" PetscInt_FMT " for coarse edge %" PetscInt_FMT, ncc, nch, nrc, i);
1414:       PetscCheck(ncc == 1 || !pcbddc->nedcG, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot generate the coarse discrete gradient for coarse edge %" PetscInt_FMT " with ncc %" PetscInt_FMT, i, ncc);
1415:       PetscCall(MatDenseGetArrayRead(GKins, &data));
1416:       PetscCall(MatSetValuesLocal(T, nrc, cols, ncc, cols + nch, data, INSERT_VALUES));
1417:       PetscCall(MatDenseRestoreArrayRead(GKins, &data));

1419:       /* coarse discrete gradient */
1420:       if (pcbddc->nedcG) {
1421:         PetscInt cols[2];

1423:         cols[0] = 2 * i;
1424:         cols[1] = 2 * i + 1;
1425:         PetscCall(MatSetValuesLocal(pcbddc->nedcG, 1, &i, 2, cols, cvals, INSERT_VALUES));
1426:       }
1427:       PetscCall(ISRestoreIndices(eedges[i], &cols));
1428:     }
1429:     PetscCall(ISDestroy(&extrows[i]));
1430:     PetscCall(ISDestroy(&extcols[i]));
1431:     PetscCall(ISDestroy(&cornersis));
1432:     PetscCall(MatDestroy(&Gins));
1433:     PetscCall(MatDestroy(&GKins));
1434:   }

1436:   /* for FDM element-by-element: first dof on the edge only constraint. Why? */
1437:   if (elements_corners && pcbddc->mat_graph->multi_element) {
1438:     ISLocalToGlobalMapping map;
1439:     MatNullSpace           nnsp;
1440:     Vec                    quad_vec;

1442:     PetscCall(MatCreateVecs(pc->pmat, &quad_vec, NULL));
1443:     PetscCall(PCBDDCNullSpaceCreate(PetscObjectComm((PetscObject)pc), PETSC_FALSE, 1, &quad_vec, &nnsp));
1444:     PetscCall(VecLockReadPop(quad_vec));
1445:     PetscCall(MatISGetLocalToGlobalMapping(pc->pmat, &map, NULL));
1446:     PetscCall(VecSetLocalToGlobalMapping(quad_vec, map));
1447:     for (i = 0; i < nee; i++) {
1448:       const PetscInt *idxs;
1449:       PetscScalar     one = 1.0;

1451:       PetscCall(ISGetLocalSize(alleedges[i], &cum));
1452:       if (!cum) continue;
1453:       PetscCall(ISGetIndices(alleedges[i], &idxs));
1454:       PetscCall(VecSetValuesLocal(quad_vec, 1, idxs, &one, INSERT_VALUES));
1455:       PetscCall(ISRestoreIndices(alleedges[i], &idxs));
1456:     }
1457:     PetscCall(VecLockReadPush(quad_vec));
1458:     PetscCall(VecDestroy(&quad_vec));
1459:     PetscCall(MatSetNearNullSpace(pc->pmat, nnsp));
1460:     PetscCall(MatNullSpaceDestroy(&nnsp));
1461:   }
1462:   PetscCall(ISLocalToGlobalMappingDestroy(&el2g));

1464:   /* Start assembling */
1465:   PetscCall(MatAssemblyBegin(T, MAT_FINAL_ASSEMBLY));
1466:   if (pcbddc->nedcG) PetscCall(MatAssemblyBegin(pcbddc->nedcG, MAT_FINAL_ASSEMBLY));

1468:   /* Free */
1469:   if (fl2g) {
1470:     PetscCall(ISDestroy(&primals));
1471:     for (i = 0; i < nee; i++) PetscCall(ISDestroy(&eedges[i]));
1472:     PetscCall(PetscFree(eedges));
1473:   }

1475:   /* hack mat_graph with primal dofs on the coarse edges */
1476:   {
1477:     PCBDDCGraph graph  = pcbddc->mat_graph;
1478:     PetscInt   *oqueue = graph->queue;
1479:     PetscInt   *ocptr  = graph->cptr;
1480:     PetscInt    ncc, *idxs;

1482:     /* find first primal edge */
1483:     if (pcbddc->nedclocal) {
1484:       PetscCall(ISGetIndices(pcbddc->nedclocal, (const PetscInt **)&idxs));
1485:     } else {
1486:       if (fl2g) PetscCall(ISLocalToGlobalMappingApply(fl2g, nee, cedges, cedges));
1487:       idxs = cedges;
1488:     }
1489:     cum = 0;
1490:     while (cum < nee && cedges[cum] < 0) cum++;

1492:     /* adapt connected components */
1493:     PetscCall(PetscMalloc2(graph->nvtxs + 1, &graph->cptr, ocptr[graph->ncc], &graph->queue));
1494:     graph->cptr[0] = 0;
1495:     for (i = 0, ncc = 0; i < graph->ncc; i++) {
1496:       PetscInt lc = ocptr[i + 1] - ocptr[i];
1497:       if (cum != nee && oqueue[ocptr[i + 1] - 1] == cedges[cum]) { /* this cc has a primal dof */
1498:         graph->cptr[ncc + 1]           = graph->cptr[ncc] + 1;
1499:         graph->queue[graph->cptr[ncc]] = cedges[cum];
1500:         ncc++;
1501:         lc--;
1502:         cum++;
1503:         while (cum < nee && cedges[cum] < 0) cum++;
1504:       }
1505:       graph->cptr[ncc + 1] = graph->cptr[ncc] + lc;
1506:       for (j = 0; j < lc; j++) graph->queue[graph->cptr[ncc] + j] = oqueue[ocptr[i] + j];
1507:       ncc++;
1508:     }
1509:     graph->ncc = ncc;
1510:     if (pcbddc->nedclocal) PetscCall(ISRestoreIndices(pcbddc->nedclocal, (const PetscInt **)&idxs));
1511:     PetscCall(PetscFree2(ocptr, oqueue));
1512:   }
1513:   PetscCall(ISLocalToGlobalMappingDestroy(&fl2g));
1514:   PetscCall(PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph, NULL, NULL, &nee, &alleedges, &allprimals));
1515:   PetscCall(PCBDDCGraphResetCSR(pcbddc->mat_graph));

1517:   PetscCall(ISDestroy(&nedfieldlocal));
1518:   PetscCall(PetscFree(extrow));
1519:   PetscCall(PetscFree2(work, rwork));
1520:   PetscCall(PetscFree(corners));
1521:   PetscCall(PetscFree(cedges));
1522:   PetscCall(PetscFree(extrows));
1523:   PetscCall(PetscFree(extcols));
1524:   PetscCall(MatDestroy(&lG));

1526:   /* Complete assembling */
1527:   PetscCall(MatAssemblyEnd(T, MAT_FINAL_ASSEMBLY));
1528:   PetscCall(MatViewFromOptions(T, (PetscObject)pc, "-pc_bddc_nedelec_change_view"));
1529:   if (pcbddc->nedcG) {
1530:     PetscCall(MatAssemblyEnd(pcbddc->nedcG, MAT_FINAL_ASSEMBLY));
1531:     PetscCall(MatViewFromOptions(pcbddc->nedcG, (PetscObject)pc, "-pc_bddc_nedelec_coarse_change_view"));
1532:   }

1534:   PetscCall(ISDestroy(&elements_corners));

1536:   /* set change of basis */
1537:   PetscCall(PCBDDCSetChangeOfBasisMat(pc, T, PETSC_FALSE));
1538:   PetscCall(MatDestroy(&T));
1539:   PetscFunctionReturn(PETSC_SUCCESS);
1540: }

1542: /* the near-null space of BDDC carries information on quadrature weights,
1543:    and these can be collinear -> so cheat with MatNullSpaceCreate
1544:    and create a suitable set of basis vectors first */
1545: PetscErrorCode PCBDDCNullSpaceCreate(MPI_Comm comm, PetscBool has_const, PetscInt nvecs, Vec quad_vecs[], MatNullSpace *nnsp)
1546: {
1547:   PetscInt i;

1549:   PetscFunctionBegin;
1550:   for (i = 0; i < nvecs; i++) {
1551:     PetscInt first, last;

1553:     PetscCall(VecGetOwnershipRange(quad_vecs[i], &first, &last));
1554:     PetscCheck(last - first >= 2 * nvecs || !has_const, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
1555:     if (i >= first && i < last) {
1556:       PetscScalar *data;
1557:       PetscCall(VecGetArray(quad_vecs[i], &data));
1558:       if (!has_const) {
1559:         data[i - first] = 1.;
1560:       } else {
1561:         data[2 * i - first]     = 1. / PetscSqrtReal(2.);
1562:         data[2 * i - first + 1] = -1. / PetscSqrtReal(2.);
1563:       }
1564:       PetscCall(VecRestoreArray(quad_vecs[i], &data));
1565:     }
1566:     PetscCall(PetscObjectStateIncrease((PetscObject)quad_vecs[i]));
1567:   }
1568:   PetscCall(MatNullSpaceCreate(comm, has_const, nvecs, quad_vecs, nnsp));
1569:   for (i = 0; i < nvecs; i++) { /* reset vectors */
1570:     PetscInt first, last;
1571:     PetscCall(VecLockReadPop(quad_vecs[i]));
1572:     PetscCall(VecGetOwnershipRange(quad_vecs[i], &first, &last));
1573:     if (i >= first && i < last) {
1574:       PetscScalar *data;
1575:       PetscCall(VecGetArray(quad_vecs[i], &data));
1576:       if (!has_const) {
1577:         data[i - first] = 0.;
1578:       } else {
1579:         data[2 * i - first]     = 0.;
1580:         data[2 * i - first + 1] = 0.;
1581:       }
1582:       PetscCall(VecRestoreArray(quad_vecs[i], &data));
1583:     }
1584:     PetscCall(PetscObjectStateIncrease((PetscObject)quad_vecs[i]));
1585:     PetscCall(VecLockReadPush(quad_vecs[i]));
1586:   }
1587:   PetscFunctionReturn(PETSC_SUCCESS);
1588: }

1590: PetscErrorCode PCBDDCComputeNoNetFlux(Mat A, Mat divudotp, PetscBool transpose, IS vl2l, PCBDDCGraph graph, MatNullSpace *nnsp)
1591: {
1592:   Mat                    loc_divudotp;
1593:   Vec                    p, v, quad_vec;
1594:   ISLocalToGlobalMapping map;
1595:   PetscScalar           *array;

1597:   PetscFunctionBegin;
1598:   PetscCall(MatCreateVecs(A, &quad_vec, NULL));
1599:   if (!transpose) {
1600:     PetscCall(MatISGetLocalToGlobalMapping(A, &map, NULL));
1601:   } else {
1602:     PetscCall(MatISGetLocalToGlobalMapping(A, NULL, &map));
1603:   }
1604:   PetscCall(PCBDDCNullSpaceCreate(PetscObjectComm((PetscObject)A), PETSC_FALSE, 1, &quad_vec, nnsp));
1605:   PetscCall(VecLockReadPop(quad_vec));
1606:   PetscCall(VecSetLocalToGlobalMapping(quad_vec, map));

1608:   /* compute local quad vec */
1609:   PetscCall(MatISGetLocalMat(divudotp, &loc_divudotp));
1610:   if (!transpose) {
1611:     PetscCall(MatCreateVecs(loc_divudotp, &v, &p));
1612:   } else {
1613:     PetscCall(MatCreateVecs(loc_divudotp, &p, &v));
1614:   }
1615:   /* the assumption here is that the constant vector interpolates the constant on the L2 conforming space */
1616:   PetscCall(VecSet(p, 1.));
1617:   if (!transpose) {
1618:     PetscCall(MatMultTranspose(loc_divudotp, p, v));
1619:   } else {
1620:     PetscCall(MatMult(loc_divudotp, p, v));
1621:   }
1622:   PetscCall(VecDestroy(&p));
1623:   if (vl2l) {
1624:     Mat        lA;
1625:     VecScatter sc;
1626:     Vec        vins;

1628:     PetscCall(MatISGetLocalMat(A, &lA));
1629:     PetscCall(MatCreateVecs(lA, &vins, NULL));
1630:     PetscCall(VecScatterCreate(v, NULL, vins, vl2l, &sc));
1631:     PetscCall(VecScatterBegin(sc, v, vins, INSERT_VALUES, SCATTER_FORWARD));
1632:     PetscCall(VecScatterEnd(sc, v, vins, INSERT_VALUES, SCATTER_FORWARD));
1633:     PetscCall(VecScatterDestroy(&sc));
1634:     PetscCall(VecDestroy(&v));
1635:     v = vins;
1636:   }

1638:   /* mask summation of interface values */
1639:   PetscInt        n, *mmask, *mask, *idxs, nmr, nr;
1640:   const PetscInt *degree;
1641:   PetscSF         msf;

1643:   PetscCall(VecGetLocalSize(v, &n));
1644:   PetscCall(PetscSFGetGraph(graph->interface_subset_sf, &nr, NULL, NULL, NULL));
1645:   PetscCall(PetscSFGetMultiSF(graph->interface_subset_sf, &msf));
1646:   PetscCall(PetscSFGetGraph(msf, &nmr, NULL, NULL, NULL));
1647:   PetscCall(PetscCalloc3(nmr, &mmask, n, &mask, n, &idxs));
1648:   PetscCall(PetscSFComputeDegreeBegin(graph->interface_subset_sf, &degree));
1649:   PetscCall(PetscSFComputeDegreeEnd(graph->interface_subset_sf, &degree));
1650:   for (PetscInt i = 0, c = 0; i < nr; i++) {
1651:     mmask[c] = 1;
1652:     c += degree[i];
1653:   }
1654:   PetscCall(PetscSFScatterBegin(graph->interface_subset_sf, MPIU_INT, mmask, mask));
1655:   PetscCall(PetscSFScatterEnd(graph->interface_subset_sf, MPIU_INT, mmask, mask));
1656:   PetscCall(VecGetArray(v, &array));
1657:   for (PetscInt i = 0; i < n; i++) {
1658:     array[i] *= mask[i];
1659:     idxs[i] = i;
1660:   }
1661:   PetscCall(VecSetValuesLocal(quad_vec, n, idxs, array, ADD_VALUES));
1662:   PetscCall(VecRestoreArray(v, &array));
1663:   PetscCall(PetscFree3(mmask, mask, idxs));
1664:   PetscCall(VecDestroy(&v));
1665:   PetscCall(VecAssemblyBegin(quad_vec));
1666:   PetscCall(VecAssemblyEnd(quad_vec));
1667:   PetscCall(VecViewFromOptions(quad_vec, NULL, "-pc_bddc_quad_vec_view"));
1668:   PetscCall(VecLockReadPush(quad_vec));
1669:   PetscCall(VecDestroy(&quad_vec));
1670:   PetscFunctionReturn(PETSC_SUCCESS);
1671: }

1673: PetscErrorCode PCBDDCAddPrimalVerticesLocalIS(PC pc, IS primalv)
1674: {
1675:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;

1677:   PetscFunctionBegin;
1678:   if (primalv) {
1679:     if (pcbddc->user_primal_vertices_local) {
1680:       IS list[2], newp;

1682:       list[0] = primalv;
1683:       list[1] = pcbddc->user_primal_vertices_local;
1684:       PetscCall(ISConcatenate(PetscObjectComm((PetscObject)pc), 2, list, &newp));
1685:       PetscCall(ISSortRemoveDups(newp));
1686:       PetscCall(ISDestroy(&list[1]));
1687:       pcbddc->user_primal_vertices_local = newp;
1688:     } else {
1689:       PetscCall(PCBDDCSetPrimalVerticesLocalIS(pc, primalv));
1690:     }
1691:   }
1692:   PetscFunctionReturn(PETSC_SUCCESS);
1693: }

1695: static PetscErrorCode func_coords_private(PetscInt dim, PetscReal t, const PetscReal X[], PetscInt Nf, PetscScalar *out, void *ctx)
1696: {
1697:   PetscInt f, *comp = (PetscInt *)ctx;

1699:   PetscFunctionBegin;
1700:   for (f = 0; f < Nf; f++) out[f] = X[*comp];
1701:   PetscFunctionReturn(PETSC_SUCCESS);
1702: }

1704: PetscErrorCode PCBDDCComputeLocalTopologyInfo(PC pc)
1705: {
1706:   Vec       local, global;
1707:   PC_BDDC  *pcbddc     = (PC_BDDC *)pc->data;
1708:   Mat_IS   *matis      = (Mat_IS *)pc->pmat->data;
1709:   PetscBool monolithic = PETSC_FALSE;

1711:   PetscFunctionBegin;
1712:   PetscOptionsBegin(PetscObjectComm((PetscObject)pc), ((PetscObject)pc)->prefix, "BDDC topology options", "PC");
1713:   PetscCall(PetscOptionsBool("-pc_bddc_monolithic", "Discard any information on dofs splitting", NULL, monolithic, &monolithic, NULL));
1714:   PetscOptionsEnd();
1715:   /* need to convert from global to local topology information and remove references to information in global ordering */
1716:   PetscCall(MatCreateVecs(pc->pmat, &global, NULL));
1717:   PetscCall(MatCreateVecs(matis->A, &local, NULL));
1718:   PetscCall(VecBindToCPU(global, PETSC_TRUE));
1719:   PetscCall(VecBindToCPU(local, PETSC_TRUE));
1720:   if (monolithic) { /* just get block size to properly compute vertices */
1721:     if (pcbddc->vertex_size == 1) PetscCall(MatGetBlockSize(pc->pmat, &pcbddc->vertex_size));
1722:     goto boundary;
1723:   }

1725:   if (pcbddc->user_provided_isfordofs) {
1726:     if (pcbddc->n_ISForDofs) {
1727:       PetscInt i;

1729:       PetscCall(PetscMalloc1(pcbddc->n_ISForDofs, &pcbddc->ISForDofsLocal));
1730:       for (i = 0; i < pcbddc->n_ISForDofs; i++) {
1731:         PetscInt bs;

1733:         PetscCall(PCBDDCGlobalToLocal(matis->rctx, global, local, pcbddc->ISForDofs[i], &pcbddc->ISForDofsLocal[i]));
1734:         PetscCall(ISGetBlockSize(pcbddc->ISForDofs[i], &bs));
1735:         PetscCall(ISSetBlockSize(pcbddc->ISForDofsLocal[i], bs));
1736:         PetscCall(ISDestroy(&pcbddc->ISForDofs[i]));
1737:       }
1738:       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
1739:       pcbddc->n_ISForDofs      = 0;
1740:       PetscCall(PetscFree(pcbddc->ISForDofs));
1741:     }
1742:   } else {
1743:     if (!pcbddc->n_ISForDofsLocal) { /* field split not present */
1744:       DM dm;

1746:       PetscCall(MatGetDM(pc->pmat, &dm));
1747:       if (!dm) PetscCall(PCGetDM(pc, &dm));
1748:       if (dm) {
1749:         IS      *fields;
1750:         PetscInt nf, i;

1752:         PetscCall(DMCreateFieldDecomposition(dm, &nf, NULL, &fields, NULL));
1753:         PetscCall(PetscMalloc1(nf, &pcbddc->ISForDofsLocal));
1754:         for (i = 0; i < nf; i++) {
1755:           PetscInt bs;

1757:           PetscCall(PCBDDCGlobalToLocal(matis->rctx, global, local, fields[i], &pcbddc->ISForDofsLocal[i]));
1758:           PetscCall(ISGetBlockSize(fields[i], &bs));
1759:           PetscCall(ISSetBlockSize(pcbddc->ISForDofsLocal[i], bs));
1760:           PetscCall(ISDestroy(&fields[i]));
1761:         }
1762:         PetscCall(PetscFree(fields));
1763:         pcbddc->n_ISForDofsLocal = nf;
1764:       } else { /* See if MATIS has fields attached by the conversion from MatNest */
1765:         PetscContainer c;

1767:         PetscCall(PetscObjectQuery((PetscObject)pc->pmat, "_convert_nest_lfields", (PetscObject *)&c));
1768:         if (c) {
1769:           MatISLocalFields lf;
1770:           PetscCall(PetscContainerGetPointer(c, (void **)&lf));
1771:           PetscCall(PCBDDCSetDofsSplittingLocal(pc, lf->nr, lf->rf));
1772:         } else { /* fallback, create the default fields if bs > 1 */
1773:           PetscInt i, n = matis->A->rmap->n;
1774:           PetscCall(MatGetBlockSize(pc->pmat, &i));
1775:           if (i > 1) {
1776:             pcbddc->n_ISForDofsLocal = i;
1777:             PetscCall(PetscMalloc1(pcbddc->n_ISForDofsLocal, &pcbddc->ISForDofsLocal));
1778:             for (i = 0; i < pcbddc->n_ISForDofsLocal; i++) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), n / pcbddc->n_ISForDofsLocal, i, pcbddc->n_ISForDofsLocal, &pcbddc->ISForDofsLocal[i]));
1779:           }
1780:         }
1781:       }
1782:     } else {
1783:       PetscInt i;
1784:       for (i = 0; i < pcbddc->n_ISForDofsLocal; i++) PetscCall(PCBDDCConsistencyCheckIS(pc, MPI_LAND, &pcbddc->ISForDofsLocal[i]));
1785:     }
1786:   }

1788: boundary:
1789:   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) {
1790:     PetscCall(PCBDDCGlobalToLocal(matis->rctx, global, local, pcbddc->DirichletBoundaries, &pcbddc->DirichletBoundariesLocal));
1791:   } else if (pcbddc->DirichletBoundariesLocal) {
1792:     PetscCall(PCBDDCConsistencyCheckIS(pc, MPI_LAND, &pcbddc->DirichletBoundariesLocal));
1793:   }
1794:   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) {
1795:     PetscCall(PCBDDCGlobalToLocal(matis->rctx, global, local, pcbddc->NeumannBoundaries, &pcbddc->NeumannBoundariesLocal));
1796:   } else if (pcbddc->NeumannBoundariesLocal) {
1797:     PetscCall(PCBDDCConsistencyCheckIS(pc, MPI_LOR, &pcbddc->NeumannBoundariesLocal));
1798:   }
1799:   if (!pcbddc->user_primal_vertices_local && pcbddc->user_primal_vertices) PetscCall(PCBDDCGlobalToLocal(matis->rctx, global, local, pcbddc->user_primal_vertices, &pcbddc->user_primal_vertices_local));
1800:   PetscCall(VecDestroy(&global));
1801:   PetscCall(VecDestroy(&local));
1802:   /* detect local disconnected subdomains if requested or needed */
1803:   if (pcbddc->detect_disconnected || matis->allow_repeated) {
1804:     IS        primalv = NULL;
1805:     PetscInt  nel;
1806:     PetscBool filter = pcbddc->detect_disconnected_filter;

1808:     for (PetscInt i = 0; i < pcbddc->n_local_subs; i++) PetscCall(ISDestroy(&pcbddc->local_subs[i]));
1809:     PetscCall(PetscFree(pcbddc->local_subs));
1810:     PetscCall(MatGetVariableBlockSizes(matis->A, &nel, NULL));
1811:     if (matis->allow_repeated && nel) {
1812:       const PetscInt *elsizes;

1814:       pcbddc->n_local_subs = nel;
1815:       PetscCall(MatGetVariableBlockSizes(matis->A, NULL, &elsizes));
1816:       PetscCall(PetscMalloc1(nel, &pcbddc->local_subs));
1817:       for (PetscInt i = 0, c = 0; i < nel; i++) {
1818:         PetscCall(ISCreateStride(PETSC_COMM_SELF, elsizes[i], c, 1, &pcbddc->local_subs[i]));
1819:         c += elsizes[i];
1820:       }
1821:     } else {
1822:       PetscCall(PCBDDCDetectDisconnectedComponents(pc, filter, &pcbddc->n_local_subs, &pcbddc->local_subs, &primalv));
1823:     }
1824:     PetscCall(PCBDDCAddPrimalVerticesLocalIS(pc, primalv));
1825:     PetscCall(ISDestroy(&primalv));
1826:   }
1827:   /* early stage corner detection */
1828:   {
1829:     DM dm;

1831:     PetscCall(MatGetDM(pc->pmat, &dm));
1832:     if (!dm) PetscCall(PCGetDM(pc, &dm));
1833:     if (dm) {
1834:       PetscBool isda;

1836:       PetscCall(PetscObjectTypeCompare((PetscObject)dm, DMDA, &isda));
1837:       if (isda) {
1838:         ISLocalToGlobalMapping l2l;
1839:         IS                     corners;
1840:         Mat                    lA;
1841:         PetscBool              gl, lo;

1843:         {
1844:           Vec                cvec;
1845:           const PetscScalar *coords;
1846:           PetscInt           dof, n, cdim;
1847:           PetscBool          memc = PETSC_TRUE;

1849:           PetscCall(DMDAGetInfo(dm, NULL, NULL, NULL, NULL, NULL, NULL, NULL, &dof, NULL, NULL, NULL, NULL, NULL));
1850:           PetscCall(DMGetCoordinates(dm, &cvec));
1851:           PetscCall(VecGetLocalSize(cvec, &n));
1852:           PetscCall(VecGetBlockSize(cvec, &cdim));
1853:           n /= cdim;
1854:           PetscCall(PetscFree(pcbddc->mat_graph->coords));
1855:           PetscCall(PetscMalloc1(dof * n * cdim, &pcbddc->mat_graph->coords));
1856:           PetscCall(VecGetArrayRead(cvec, &coords));
1857: #if defined(PETSC_USE_COMPLEX)
1858:           memc = PETSC_FALSE;
1859: #endif
1860:           if (dof != 1) memc = PETSC_FALSE;
1861:           if (memc) {
1862:             PetscCall(PetscArraycpy(pcbddc->mat_graph->coords, coords, cdim * n * dof));
1863:           } else { /* BDDC graph does not use any blocked information, we need to replicate the data */
1864:             PetscReal *bcoords = pcbddc->mat_graph->coords;
1865:             PetscInt   i, b, d;

1867:             for (i = 0; i < n; i++) {
1868:               for (b = 0; b < dof; b++) {
1869:                 for (d = 0; d < cdim; d++) bcoords[i * dof * cdim + b * cdim + d] = PetscRealPart(coords[i * cdim + d]);
1870:               }
1871:             }
1872:           }
1873:           PetscCall(VecRestoreArrayRead(cvec, &coords));
1874:           pcbddc->mat_graph->cdim  = cdim;
1875:           pcbddc->mat_graph->cnloc = dof * n;
1876:           pcbddc->mat_graph->cloc  = PETSC_FALSE;
1877:         }
1878:         PetscCall(DMDAGetSubdomainCornersIS(dm, &corners));
1879:         PetscCall(MatISGetLocalMat(pc->pmat, &lA));
1880:         PetscCall(MatGetLocalToGlobalMapping(lA, &l2l, NULL));
1881:         PetscCall(MatISRestoreLocalMat(pc->pmat, &lA));
1882:         lo = (PetscBool)(l2l && corners);
1883:         PetscCallMPI(MPIU_Allreduce(&lo, &gl, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)pc)));
1884:         if (gl) { /* From PETSc's DMDA */
1885:           const PetscInt *idx;
1886:           PetscInt        dof, bs, *idxout, n;

1888:           PetscCall(DMDAGetInfo(dm, NULL, NULL, NULL, NULL, NULL, NULL, NULL, &dof, NULL, NULL, NULL, NULL, NULL));
1889:           PetscCall(ISLocalToGlobalMappingGetBlockSize(l2l, &bs));
1890:           PetscCall(ISGetLocalSize(corners, &n));
1891:           PetscCall(ISGetIndices(corners, &idx));
1892:           if (bs == dof) {
1893:             PetscCall(PetscMalloc1(n, &idxout));
1894:             PetscCall(ISLocalToGlobalMappingApplyBlock(l2l, n, idx, idxout));
1895:           } else { /* the original DMDA local-to-local map have been modified */
1896:             PetscInt i, d;

1898:             PetscCall(PetscMalloc1(dof * n, &idxout));
1899:             for (i = 0; i < n; i++)
1900:               for (d = 0; d < dof; d++) idxout[dof * i + d] = dof * idx[i] + d;
1901:             PetscCall(ISLocalToGlobalMappingApply(l2l, dof * n, idxout, idxout));

1903:             bs = 1;
1904:             n *= dof;
1905:           }
1906:           PetscCall(ISRestoreIndices(corners, &idx));
1907:           PetscCall(DMDARestoreSubdomainCornersIS(dm, &corners));
1908:           PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)pc), bs, n, idxout, PETSC_OWN_POINTER, &corners));
1909:           PetscCall(PCBDDCAddPrimalVerticesLocalIS(pc, corners));
1910:           PetscCall(ISDestroy(&corners));
1911:           pcbddc->corner_selected  = PETSC_TRUE;
1912:           pcbddc->corner_selection = PETSC_TRUE;
1913:         }
1914:         if (corners) PetscCall(DMDARestoreSubdomainCornersIS(dm, &corners));
1915:       }
1916:     }
1917:   }
1918:   if (pcbddc->corner_selection && !pcbddc->mat_graph->cdim) {
1919:     DM dm;

1921:     PetscCall(MatGetDM(pc->pmat, &dm));
1922:     if (!dm) PetscCall(PCGetDM(pc, &dm));
1923:     if (dm) { /* this can get very expensive, I need to find a faster alternative */
1924:       Vec          vcoords;
1925:       PetscSection section;
1926:       PetscReal   *coords;
1927:       PetscInt     d, cdim, nl, nf, **ctxs;
1928:       PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *);
1929:       /* debug coordinates */
1930:       PetscViewer       viewer;
1931:       PetscBool         flg;
1932:       PetscViewerFormat format;
1933:       const char       *prefix;

1935:       PetscCall(DMGetCoordinateDim(dm, &cdim));
1936:       PetscCall(DMGetLocalSection(dm, &section));
1937:       PetscCall(PetscSectionGetNumFields(section, &nf));
1938:       PetscCall(DMCreateGlobalVector(dm, &vcoords));
1939:       PetscCall(VecGetLocalSize(vcoords, &nl));
1940:       PetscCall(PetscMalloc1(nl * cdim, &coords));
1941:       PetscCall(PetscMalloc2(nf, &funcs, nf, &ctxs));
1942:       PetscCall(PetscMalloc1(nf, &ctxs[0]));
1943:       for (d = 0; d < nf; d++) funcs[d] = func_coords_private;
1944:       for (d = 1; d < nf; d++) ctxs[d] = ctxs[d - 1] + 1;

1946:       /* debug coordinates */
1947:       PetscCall(PCGetOptionsPrefix(pc, &prefix));
1948:       PetscCall(PetscOptionsCreateViewer(PetscObjectComm((PetscObject)vcoords), ((PetscObject)vcoords)->options, prefix, "-pc_bddc_coords_vec_view", &viewer, &format, &flg));
1949:       if (flg) PetscCall(PetscViewerPushFormat(viewer, format));
1950:       for (d = 0; d < cdim; d++) {
1951:         PetscInt           i;
1952:         const PetscScalar *v;
1953:         char               name[16];

1955:         for (i = 0; i < nf; i++) ctxs[i][0] = d;
1956:         PetscCall(PetscSNPrintf(name, sizeof(name), "bddc_coords_%" PetscInt_FMT, d));
1957:         PetscCall(PetscObjectSetName((PetscObject)vcoords, name));
1958:         PetscCall(DMProjectFunction(dm, 0.0, funcs, (void **)ctxs, INSERT_VALUES, vcoords));
1959:         if (flg) PetscCall(VecView(vcoords, viewer));
1960:         PetscCall(VecGetArrayRead(vcoords, &v));
1961:         for (i = 0; i < nl; i++) coords[i * cdim + d] = PetscRealPart(v[i]);
1962:         PetscCall(VecRestoreArrayRead(vcoords, &v));
1963:       }
1964:       PetscCall(VecDestroy(&vcoords));
1965:       PetscCall(PCSetCoordinates(pc, cdim, nl, coords));
1966:       PetscCall(PetscFree(coords));
1967:       PetscCall(PetscFree(ctxs[0]));
1968:       PetscCall(PetscFree2(funcs, ctxs));
1969:       if (flg) {
1970:         PetscCall(PetscViewerPopFormat(viewer));
1971:         PetscCall(PetscViewerDestroy(&viewer));
1972:       }
1973:     }
1974:   }
1975:   PetscFunctionReturn(PETSC_SUCCESS);
1976: }

1978: PetscErrorCode PCBDDCConsistencyCheckIS(PC pc, MPI_Op mop, IS *is)
1979: {
1980:   Mat_IS         *matis = (Mat_IS *)pc->pmat->data;
1981:   IS              nis;
1982:   const PetscInt *idxs;
1983:   PetscInt        i, nd, n = matis->A->rmap->n, *nidxs, nnd;

1985:   PetscFunctionBegin;
1986:   PetscCheck(mop == MPI_LAND || mop == MPI_LOR, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Supported are MPI_LAND and MPI_LOR");
1987:   if (mop == MPI_LAND) {
1988:     /* init rootdata with true */
1989:     for (i = 0; i < pc->pmat->rmap->n; i++) matis->sf_rootdata[i] = 1;
1990:   } else {
1991:     PetscCall(PetscArrayzero(matis->sf_rootdata, pc->pmat->rmap->n));
1992:   }
1993:   PetscCall(PetscArrayzero(matis->sf_leafdata, n));
1994:   PetscCall(ISGetLocalSize(*is, &nd));
1995:   PetscCall(ISGetIndices(*is, &idxs));
1996:   for (i = 0; i < nd; i++)
1997:     if (-1 < idxs[i] && idxs[i] < n) matis->sf_leafdata[idxs[i]] = 1;
1998:   PetscCall(ISRestoreIndices(*is, &idxs));
1999:   PetscCall(PetscSFReduceBegin(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, mop));
2000:   PetscCall(PetscSFReduceEnd(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, mop));
2001:   PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
2002:   PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
2003:   if (mop == MPI_LAND) {
2004:     PetscCall(PetscMalloc1(nd, &nidxs));
2005:   } else {
2006:     PetscCall(PetscMalloc1(n, &nidxs));
2007:   }
2008:   for (i = 0, nnd = 0; i < n; i++)
2009:     if (matis->sf_leafdata[i]) nidxs[nnd++] = i;
2010:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)*is), nnd, nidxs, PETSC_OWN_POINTER, &nis));
2011:   PetscCall(ISDestroy(is));
2012:   *is = nis;
2013:   PetscFunctionReturn(PETSC_SUCCESS);
2014: }

2016: PetscErrorCode PCBDDCBenignRemoveInterior(PC pc, Vec r, Vec z)
2017: {
2018:   PC_IS   *pcis   = (PC_IS *)pc->data;
2019:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;

2021:   PetscFunctionBegin;
2022:   if (!pcbddc->benign_have_null) PetscFunctionReturn(PETSC_SUCCESS);
2023:   if (pcbddc->ChangeOfBasisMatrix) {
2024:     Vec swap;

2026:     PetscCall(MatMultTranspose(pcbddc->ChangeOfBasisMatrix, r, pcbddc->work_change));
2027:     swap                = pcbddc->work_change;
2028:     pcbddc->work_change = r;
2029:     r                   = swap;
2030:   }
2031:   PetscCall(VecScatterBegin(pcis->global_to_D, r, pcis->vec1_D, INSERT_VALUES, SCATTER_FORWARD));
2032:   PetscCall(VecScatterEnd(pcis->global_to_D, r, pcis->vec1_D, INSERT_VALUES, SCATTER_FORWARD));
2033:   PetscCall(PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][0], pc, 0, 0, 0));
2034:   PetscCall(KSPSolve(pcbddc->ksp_D, pcis->vec1_D, pcis->vec2_D));
2035:   PetscCall(PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][0], pc, 0, 0, 0));
2036:   PetscCall(KSPCheckSolve(pcbddc->ksp_D, pc, pcis->vec2_D));
2037:   PetscCall(VecSet(z, 0.));
2038:   PetscCall(VecScatterBegin(pcis->global_to_D, pcis->vec2_D, z, INSERT_VALUES, SCATTER_REVERSE));
2039:   PetscCall(VecScatterEnd(pcis->global_to_D, pcis->vec2_D, z, INSERT_VALUES, SCATTER_REVERSE));
2040:   if (pcbddc->ChangeOfBasisMatrix) {
2041:     pcbddc->work_change = r;
2042:     PetscCall(VecCopy(z, pcbddc->work_change));
2043:     PetscCall(MatMult(pcbddc->ChangeOfBasisMatrix, pcbddc->work_change, z));
2044:   }
2045:   PetscFunctionReturn(PETSC_SUCCESS);
2046: }

2048: static PetscErrorCode PCBDDCBenignMatMult_Private_Private(Mat A, Vec x, Vec y, PetscBool transpose)
2049: {
2050:   PCBDDCBenignMatMult_ctx ctx;
2051:   PetscBool               apply_right, apply_left, reset_x;

2053:   PetscFunctionBegin;
2054:   PetscCall(MatShellGetContext(A, &ctx));
2055:   if (transpose) {
2056:     apply_right = ctx->apply_left;
2057:     apply_left  = ctx->apply_right;
2058:   } else {
2059:     apply_right = ctx->apply_right;
2060:     apply_left  = ctx->apply_left;
2061:   }
2062:   reset_x = PETSC_FALSE;
2063:   if (apply_right) {
2064:     const PetscScalar *ax;
2065:     PetscInt           nl, i;

2067:     PetscCall(VecGetLocalSize(x, &nl));
2068:     PetscCall(VecGetArrayRead(x, &ax));
2069:     PetscCall(PetscArraycpy(ctx->work, ax, nl));
2070:     PetscCall(VecRestoreArrayRead(x, &ax));
2071:     for (i = 0; i < ctx->benign_n; i++) {
2072:       PetscScalar     sum, val;
2073:       const PetscInt *idxs;
2074:       PetscInt        nz, j;
2075:       PetscCall(ISGetLocalSize(ctx->benign_zerodiag_subs[i], &nz));
2076:       PetscCall(ISGetIndices(ctx->benign_zerodiag_subs[i], &idxs));
2077:       sum = 0.;
2078:       if (ctx->apply_p0) {
2079:         val = ctx->work[idxs[nz - 1]];
2080:         for (j = 0; j < nz - 1; j++) {
2081:           sum += ctx->work[idxs[j]];
2082:           ctx->work[idxs[j]] += val;
2083:         }
2084:       } else {
2085:         for (j = 0; j < nz - 1; j++) sum += ctx->work[idxs[j]];
2086:       }
2087:       ctx->work[idxs[nz - 1]] -= sum;
2088:       PetscCall(ISRestoreIndices(ctx->benign_zerodiag_subs[i], &idxs));
2089:     }
2090:     PetscCall(VecPlaceArray(x, ctx->work));
2091:     reset_x = PETSC_TRUE;
2092:   }
2093:   if (transpose) {
2094:     PetscCall(MatMultTranspose(ctx->A, x, y));
2095:   } else {
2096:     PetscCall(MatMult(ctx->A, x, y));
2097:   }
2098:   if (reset_x) PetscCall(VecResetArray(x));
2099:   if (apply_left) {
2100:     PetscScalar *ay;
2101:     PetscInt     i;

2103:     PetscCall(VecGetArray(y, &ay));
2104:     for (i = 0; i < ctx->benign_n; i++) {
2105:       PetscScalar     sum, val;
2106:       const PetscInt *idxs;
2107:       PetscInt        nz, j;
2108:       PetscCall(ISGetLocalSize(ctx->benign_zerodiag_subs[i], &nz));
2109:       PetscCall(ISGetIndices(ctx->benign_zerodiag_subs[i], &idxs));
2110:       val = -ay[idxs[nz - 1]];
2111:       if (ctx->apply_p0) {
2112:         sum = 0.;
2113:         for (j = 0; j < nz - 1; j++) {
2114:           sum += ay[idxs[j]];
2115:           ay[idxs[j]] += val;
2116:         }
2117:         ay[idxs[nz - 1]] += sum;
2118:       } else {
2119:         for (j = 0; j < nz - 1; j++) ay[idxs[j]] += val;
2120:         ay[idxs[nz - 1]] = 0.;
2121:       }
2122:       PetscCall(ISRestoreIndices(ctx->benign_zerodiag_subs[i], &idxs));
2123:     }
2124:     PetscCall(VecRestoreArray(y, &ay));
2125:   }
2126:   PetscFunctionReturn(PETSC_SUCCESS);
2127: }

2129: static PetscErrorCode PCBDDCBenignMatMultTranspose_Private(Mat A, Vec x, Vec y)
2130: {
2131:   PetscFunctionBegin;
2132:   PetscCall(PCBDDCBenignMatMult_Private_Private(A, x, y, PETSC_TRUE));
2133:   PetscFunctionReturn(PETSC_SUCCESS);
2134: }

2136: static PetscErrorCode PCBDDCBenignMatMult_Private(Mat A, Vec x, Vec y)
2137: {
2138:   PetscFunctionBegin;
2139:   PetscCall(PCBDDCBenignMatMult_Private_Private(A, x, y, PETSC_FALSE));
2140:   PetscFunctionReturn(PETSC_SUCCESS);
2141: }

2143: PetscErrorCode PCBDDCBenignShellMat(PC pc, PetscBool restore)
2144: {
2145:   PC_IS                  *pcis   = (PC_IS *)pc->data;
2146:   PC_BDDC                *pcbddc = (PC_BDDC *)pc->data;
2147:   PCBDDCBenignMatMult_ctx ctx;

2149:   PetscFunctionBegin;
2150:   if (!restore) {
2151:     Mat                A_IB, A_BI;
2152:     PetscScalar       *work;
2153:     PCBDDCReuseSolvers reuse = pcbddc->sub_schurs ? pcbddc->sub_schurs->reuse_solver : NULL;

2155:     PetscCheck(!pcbddc->benign_original_mat, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Benign original mat has not been restored");
2156:     if (!pcbddc->benign_change || !pcbddc->benign_n || pcbddc->benign_change_explicit) PetscFunctionReturn(PETSC_SUCCESS);
2157:     PetscCall(PetscMalloc1(pcis->n, &work));
2158:     PetscCall(MatCreate(PETSC_COMM_SELF, &A_IB));
2159:     PetscCall(MatSetSizes(A_IB, pcis->n - pcis->n_B, pcis->n_B, PETSC_DECIDE, PETSC_DECIDE));
2160:     PetscCall(MatSetType(A_IB, MATSHELL));
2161:     PetscCall(MatShellSetOperation(A_IB, MATOP_MULT, (void (*)(void))PCBDDCBenignMatMult_Private));
2162:     PetscCall(MatShellSetOperation(A_IB, MATOP_MULT_TRANSPOSE, (void (*)(void))PCBDDCBenignMatMultTranspose_Private));
2163:     PetscCall(PetscNew(&ctx));
2164:     PetscCall(MatShellSetContext(A_IB, ctx));
2165:     ctx->apply_left  = PETSC_TRUE;
2166:     ctx->apply_right = PETSC_FALSE;
2167:     ctx->apply_p0    = PETSC_FALSE;
2168:     ctx->benign_n    = pcbddc->benign_n;
2169:     if (reuse) {
2170:       ctx->benign_zerodiag_subs = reuse->benign_zerodiag_subs;
2171:       ctx->free                 = PETSC_FALSE;
2172:     } else { /* TODO: could be optimized for successive solves */
2173:       ISLocalToGlobalMapping N_to_D;
2174:       PetscInt               i;

2176:       PetscCall(ISLocalToGlobalMappingCreateIS(pcis->is_I_local, &N_to_D));
2177:       PetscCall(PetscMalloc1(pcbddc->benign_n, &ctx->benign_zerodiag_subs));
2178:       for (i = 0; i < pcbddc->benign_n; i++) PetscCall(ISGlobalToLocalMappingApplyIS(N_to_D, IS_GTOLM_DROP, pcbddc->benign_zerodiag_subs[i], &ctx->benign_zerodiag_subs[i]));
2179:       PetscCall(ISLocalToGlobalMappingDestroy(&N_to_D));
2180:       ctx->free = PETSC_TRUE;
2181:     }
2182:     ctx->A    = pcis->A_IB;
2183:     ctx->work = work;
2184:     PetscCall(MatSetUp(A_IB));
2185:     PetscCall(MatAssemblyBegin(A_IB, MAT_FINAL_ASSEMBLY));
2186:     PetscCall(MatAssemblyEnd(A_IB, MAT_FINAL_ASSEMBLY));
2187:     pcis->A_IB = A_IB;

2189:     /* A_BI as A_IB^T */
2190:     PetscCall(MatCreateTranspose(A_IB, &A_BI));
2191:     pcbddc->benign_original_mat = pcis->A_BI;
2192:     pcis->A_BI                  = A_BI;
2193:   } else {
2194:     if (!pcbddc->benign_original_mat) PetscFunctionReturn(PETSC_SUCCESS);
2195:     PetscCall(MatShellGetContext(pcis->A_IB, &ctx));
2196:     PetscCall(MatDestroy(&pcis->A_IB));
2197:     pcis->A_IB = ctx->A;
2198:     ctx->A     = NULL;
2199:     PetscCall(MatDestroy(&pcis->A_BI));
2200:     pcis->A_BI                  = pcbddc->benign_original_mat;
2201:     pcbddc->benign_original_mat = NULL;
2202:     if (ctx->free) {
2203:       PetscInt i;
2204:       for (i = 0; i < ctx->benign_n; i++) PetscCall(ISDestroy(&ctx->benign_zerodiag_subs[i]));
2205:       PetscCall(PetscFree(ctx->benign_zerodiag_subs));
2206:     }
2207:     PetscCall(PetscFree(ctx->work));
2208:     PetscCall(PetscFree(ctx));
2209:   }
2210:   PetscFunctionReturn(PETSC_SUCCESS);
2211: }

2213: /* used just in bddc debug mode */
2214: static PetscErrorCode PCBDDCBenignProject(PC pc, IS is1, IS is2, Mat *B)
2215: {
2216:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;
2217:   Mat_IS  *matis  = (Mat_IS *)pc->pmat->data;
2218:   Mat      An;

2220:   PetscFunctionBegin;
2221:   PetscCall(MatPtAP(matis->A, pcbddc->benign_change, MAT_INITIAL_MATRIX, 2.0, &An));
2222:   PetscCall(MatZeroRowsColumns(An, pcbddc->benign_n, pcbddc->benign_p0_lidx, 1.0, NULL, NULL));
2223:   if (is1) {
2224:     PetscCall(MatCreateSubMatrix(An, is1, is2, MAT_INITIAL_MATRIX, B));
2225:     PetscCall(MatDestroy(&An));
2226:   } else {
2227:     *B = An;
2228:   }
2229:   PetscFunctionReturn(PETSC_SUCCESS);
2230: }

2232: /* TODO: add reuse flag */
2233: PetscErrorCode MatSeqAIJCompress(Mat A, Mat *B)
2234: {
2235:   Mat             Bt;
2236:   PetscScalar    *a, *bdata;
2237:   const PetscInt *ii, *ij;
2238:   PetscInt        m, n, i, nnz, *bii, *bij;
2239:   PetscBool       flg_row;

2241:   PetscFunctionBegin;
2242:   PetscCall(MatGetSize(A, &n, &m));
2243:   PetscCall(MatGetRowIJ(A, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, &ij, &flg_row));
2244:   PetscCall(MatSeqAIJGetArray(A, &a));
2245:   nnz = n;
2246:   for (i = 0; i < ii[n]; i++) {
2247:     if (PetscLikely(PetscAbsScalar(a[i]) > PETSC_SMALL)) nnz++;
2248:   }
2249:   PetscCall(PetscMalloc1(n + 1, &bii));
2250:   PetscCall(PetscMalloc1(nnz, &bij));
2251:   PetscCall(PetscMalloc1(nnz, &bdata));
2252:   nnz    = 0;
2253:   bii[0] = 0;
2254:   for (i = 0; i < n; i++) {
2255:     PetscInt j;
2256:     for (j = ii[i]; j < ii[i + 1]; j++) {
2257:       PetscScalar entry = a[j];
2258:       if (PetscLikely(PetscAbsScalar(entry) > PETSC_SMALL) || (n == m && ij[j] == i)) {
2259:         bij[nnz]   = ij[j];
2260:         bdata[nnz] = entry;
2261:         nnz++;
2262:       }
2263:     }
2264:     bii[i + 1] = nnz;
2265:   }
2266:   PetscCall(MatSeqAIJRestoreArray(A, &a));
2267:   PetscCall(MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A), n, m, bii, bij, bdata, &Bt));
2268:   PetscCall(MatRestoreRowIJ(A, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, &ij, &flg_row));
2269:   {
2270:     Mat_SeqAIJ *b = (Mat_SeqAIJ *)Bt->data;
2271:     b->free_a     = PETSC_TRUE;
2272:     b->free_ij    = PETSC_TRUE;
2273:   }
2274:   if (*B == A) PetscCall(MatDestroy(&A));
2275:   *B = Bt;
2276:   PetscFunctionReturn(PETSC_SUCCESS);
2277: }

2279: PetscErrorCode PCBDDCDetectDisconnectedComponents(PC pc, PetscBool filter, PetscInt *ncc, IS *cc[], IS *primalv)
2280: {
2281:   Mat                    B = NULL;
2282:   DM                     dm;
2283:   IS                     is_dummy, *cc_n;
2284:   ISLocalToGlobalMapping l2gmap_dummy;
2285:   PCBDDCGraph            graph;
2286:   PetscInt              *xadj_filtered = NULL, *adjncy_filtered = NULL;
2287:   PetscInt               i, n;
2288:   PetscInt              *xadj, *adjncy;
2289:   PetscBool              isplex = PETSC_FALSE;

2291:   PetscFunctionBegin;
2292:   if (ncc) *ncc = 0;
2293:   if (cc) *cc = NULL;
2294:   if (primalv) *primalv = NULL;
2295:   PetscCall(PCBDDCGraphCreate(&graph));
2296:   PetscCall(MatGetDM(pc->pmat, &dm));
2297:   if (!dm) PetscCall(PCGetDM(pc, &dm));
2298:   if (dm) PetscCall(PetscObjectTypeCompareAny((PetscObject)dm, &isplex, DMPLEX, DMP4EST, DMP8EST, ""));
2299:   if (filter) isplex = PETSC_FALSE;

2301:   if (isplex) { /* this code has been modified from plexpartition.c */
2302:     PetscInt        p, pStart, pEnd, a, adjSize, idx, size, nroots;
2303:     PetscInt       *adj = NULL;
2304:     IS              cellNumbering;
2305:     const PetscInt *cellNum;
2306:     PetscBool       useCone, useClosure;
2307:     PetscSection    section;
2308:     PetscSegBuffer  adjBuffer;
2309:     PetscSF         sfPoint;

2311:     PetscCall(DMConvert(dm, DMPLEX, &dm));
2312:     PetscCall(DMPlexGetHeightStratum(dm, 0, &pStart, &pEnd));
2313:     PetscCall(DMGetPointSF(dm, &sfPoint));
2314:     PetscCall(PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL));
2315:     /* Build adjacency graph via a section/segbuffer */
2316:     PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &section));
2317:     PetscCall(PetscSectionSetChart(section, pStart, pEnd));
2318:     PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 1000, &adjBuffer));
2319:     /* Always use FVM adjacency to create partitioner graph */
2320:     PetscCall(DMGetBasicAdjacency(dm, &useCone, &useClosure));
2321:     PetscCall(DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE));
2322:     PetscCall(DMPlexGetCellNumbering(dm, &cellNumbering));
2323:     PetscCall(ISGetIndices(cellNumbering, &cellNum));
2324:     for (n = 0, p = pStart; p < pEnd; p++) {
2325:       /* Skip non-owned cells in parallel (ParMetis expects no overlap) */
2326:       if (nroots > 0) {
2327:         if (cellNum[p] < 0) continue;
2328:       }
2329:       adjSize = PETSC_DETERMINE;
2330:       PetscCall(DMPlexGetAdjacency(dm, p, &adjSize, &adj));
2331:       for (a = 0; a < adjSize; ++a) {
2332:         const PetscInt point = adj[a];
2333:         if (pStart <= point && point < pEnd) {
2334:           PetscInt *PETSC_RESTRICT pBuf;
2335:           PetscCall(PetscSectionAddDof(section, p, 1));
2336:           PetscCall(PetscSegBufferGetInts(adjBuffer, 1, &pBuf));
2337:           *pBuf = point;
2338:         }
2339:       }
2340:       n++;
2341:     }
2342:     PetscCall(DMSetBasicAdjacency(dm, useCone, useClosure));
2343:     /* Derive CSR graph from section/segbuffer */
2344:     PetscCall(PetscSectionSetUp(section));
2345:     PetscCall(PetscSectionGetStorageSize(section, &size));
2346:     PetscCall(PetscMalloc1(n + 1, &xadj));
2347:     for (idx = 0, p = pStart; p < pEnd; p++) {
2348:       if (nroots > 0) {
2349:         if (cellNum[p] < 0) continue;
2350:       }
2351:       PetscCall(PetscSectionGetOffset(section, p, &xadj[idx++]));
2352:     }
2353:     xadj[n] = size;
2354:     PetscCall(PetscSegBufferExtractAlloc(adjBuffer, &adjncy));
2355:     /* Clean up */
2356:     PetscCall(PetscSegBufferDestroy(&adjBuffer));
2357:     PetscCall(PetscSectionDestroy(&section));
2358:     PetscCall(PetscFree(adj));
2359:     graph->xadj   = xadj;
2360:     graph->adjncy = adjncy;
2361:   } else {
2362:     Mat       A;
2363:     PetscBool isseqaij, flg_row;

2365:     PetscCall(MatISGetLocalMat(pc->pmat, &A));
2366:     if (!A->rmap->N || !A->cmap->N) {
2367:       PetscCall(PCBDDCGraphDestroy(&graph));
2368:       PetscFunctionReturn(PETSC_SUCCESS);
2369:     }
2370:     PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQAIJ, &isseqaij));
2371:     if (!isseqaij && filter) {
2372:       PetscBool isseqdense;

2374:       PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQDENSE, &isseqdense));
2375:       if (!isseqdense) {
2376:         PetscCall(MatConvert(A, MATSEQAIJ, MAT_INITIAL_MATRIX, &B));
2377:       } else { /* TODO: rectangular case and LDA */
2378:         PetscScalar *array;
2379:         PetscReal    chop = 1.e-6;

2381:         PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &B));
2382:         PetscCall(MatDenseGetArray(B, &array));
2383:         PetscCall(MatGetSize(B, &n, NULL));
2384:         for (i = 0; i < n; i++) {
2385:           PetscInt j;
2386:           for (j = i + 1; j < n; j++) {
2387:             PetscReal thresh = chop * (PetscAbsScalar(array[i * (n + 1)]) + PetscAbsScalar(array[j * (n + 1)]));
2388:             if (PetscAbsScalar(array[i * n + j]) < thresh) array[i * n + j] = 0.;
2389:             if (PetscAbsScalar(array[j * n + i]) < thresh) array[j * n + i] = 0.;
2390:           }
2391:         }
2392:         PetscCall(MatDenseRestoreArray(B, &array));
2393:         PetscCall(MatConvert(B, MATSEQAIJ, MAT_INPLACE_MATRIX, &B));
2394:       }
2395:     } else {
2396:       PetscCall(PetscObjectReference((PetscObject)A));
2397:       B = A;
2398:     }
2399:     PetscCall(MatGetRowIJ(B, 0, PETSC_TRUE, PETSC_FALSE, &n, (const PetscInt **)&xadj, (const PetscInt **)&adjncy, &flg_row));

2401:     /* if filter is true, then removes entries lower than PETSC_SMALL in magnitude */
2402:     if (filter) {
2403:       PetscScalar *data;
2404:       PetscInt     j, cum;

2406:       PetscCall(PetscCalloc2(n + 1, &xadj_filtered, xadj[n], &adjncy_filtered));
2407:       PetscCall(MatSeqAIJGetArray(B, &data));
2408:       cum = 0;
2409:       for (i = 0; i < n; i++) {
2410:         PetscInt t;

2412:         for (j = xadj[i]; j < xadj[i + 1]; j++) {
2413:           if (PetscUnlikely(PetscAbsScalar(data[j]) < PETSC_SMALL)) continue;
2414:           adjncy_filtered[cum + xadj_filtered[i]++] = adjncy[j];
2415:         }
2416:         t                = xadj_filtered[i];
2417:         xadj_filtered[i] = cum;
2418:         cum += t;
2419:       }
2420:       PetscCall(MatSeqAIJRestoreArray(B, &data));
2421:       graph->xadj   = xadj_filtered;
2422:       graph->adjncy = adjncy_filtered;
2423:     } else {
2424:       graph->xadj   = xadj;
2425:       graph->adjncy = adjncy;
2426:     }
2427:   }
2428:   /* compute local connected components using PCBDDCGraph */
2429:   graph->seq_graph = PETSC_TRUE; /* analyze local connected components (i.e. disconnected subdomains) irrespective of dofs count */
2430:   PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &is_dummy));
2431:   PetscCall(ISLocalToGlobalMappingCreateIS(is_dummy, &l2gmap_dummy));
2432:   PetscCall(ISDestroy(&is_dummy));
2433:   PetscCall(PCBDDCGraphInit(graph, l2gmap_dummy, n, PETSC_INT_MAX));
2434:   PetscCall(ISLocalToGlobalMappingDestroy(&l2gmap_dummy));
2435:   PetscCall(PCBDDCGraphSetUp(graph, 1, NULL, NULL, 0, NULL, NULL));
2436:   PetscCall(PCBDDCGraphComputeConnectedComponents(graph));

2438:   /* partial clean up */
2439:   PetscCall(PetscFree2(xadj_filtered, adjncy_filtered));
2440:   if (B) {
2441:     PetscBool flg_row;
2442:     PetscCall(MatRestoreRowIJ(B, 0, PETSC_TRUE, PETSC_FALSE, &n, (const PetscInt **)&xadj, (const PetscInt **)&adjncy, &flg_row));
2443:     PetscCall(MatDestroy(&B));
2444:   }
2445:   if (isplex) {
2446:     PetscCall(PetscFree(xadj));
2447:     PetscCall(PetscFree(adjncy));
2448:   }

2450:   /* get back data */
2451:   if (isplex) {
2452:     if (ncc) *ncc = graph->ncc;
2453:     if (cc || primalv) {
2454:       Mat          A;
2455:       PetscBT      btv, btvt, btvc;
2456:       PetscSection subSection;
2457:       PetscInt    *ids, cum, cump, *cids, *pids;
2458:       PetscInt     dim, cStart, cEnd, fStart, fEnd, vStart, vEnd, pStart, pEnd;

2460:       PetscCall(DMGetDimension(dm, &dim));
2461:       PetscCall(DMPlexGetSubdomainSection(dm, &subSection));
2462:       PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
2463:       PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2464:       PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
2465:       PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
2466:       PetscCall(MatISGetLocalMat(pc->pmat, &A));
2467:       PetscCall(PetscMalloc3(A->rmap->n, &ids, graph->ncc + 1, &cids, A->rmap->n, &pids));
2468:       PetscCall(PetscBTCreate(A->rmap->n, &btv));
2469:       PetscCall(PetscBTCreate(A->rmap->n, &btvt));
2470:       PetscCall(PetscBTCreate(pEnd - pStart, &btvc));

2472:       /* First see if we find corners for the subdomains, i.e. a vertex
2473:          shared by at least dim subdomain boundary faces. This does not
2474:          cover all the possible cases with simplices but it is enough
2475:          for tensor cells */
2476:       if (vStart != fStart && dim <= 3) {
2477:         for (PetscInt c = cStart; c < cEnd; c++) {
2478:           PetscInt        nf, cnt = 0, mcnt = dim, *cfaces;
2479:           const PetscInt *faces;

2481:           PetscCall(DMPlexGetConeSize(dm, c, &nf));
2482:           PetscCall(DMGetWorkArray(dm, nf, MPIU_INT, &cfaces));
2483:           PetscCall(DMPlexGetCone(dm, c, &faces));
2484:           for (PetscInt f = 0; f < nf; f++) {
2485:             PetscInt nc, ff;

2487:             PetscCall(DMPlexGetSupportSize(dm, faces[f], &nc));
2488:             PetscCall(DMPlexGetTreeParent(dm, faces[f], &ff, NULL));
2489:             if (nc == 1 && faces[f] == ff) cfaces[cnt++] = faces[f];
2490:           }
2491:           if (cnt >= mcnt) {
2492:             PetscInt size, *closure = NULL;

2494:             PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &size, &closure));
2495:             for (PetscInt k = 0; k < 2 * size; k += 2) {
2496:               PetscInt v = closure[k];
2497:               if (v >= vStart && v < vEnd) {
2498:                 PetscInt vsize, *vclosure = NULL;

2500:                 cnt = 0;
2501:                 PetscCall(DMPlexGetTransitiveClosure(dm, v, PETSC_FALSE, &vsize, &vclosure));
2502:                 for (PetscInt vk = 0; vk < 2 * vsize; vk += 2) {
2503:                   PetscInt f = vclosure[vk];
2504:                   if (f >= fStart && f < fEnd) {
2505:                     PetscInt  nc, ff;
2506:                     PetscBool valid = PETSC_FALSE;

2508:                     for (PetscInt fk = 0; fk < nf; fk++)
2509:                       if (f == cfaces[fk]) valid = PETSC_TRUE;
2510:                     if (!valid) continue;
2511:                     PetscCall(DMPlexGetSupportSize(dm, f, &nc));
2512:                     PetscCall(DMPlexGetTreeParent(dm, f, &ff, NULL));
2513:                     if (nc == 1 && f == ff) cnt++;
2514:                   }
2515:                 }
2516:                 if (cnt >= mcnt) PetscCall(PetscBTSet(btvc, v - pStart));
2517:                 PetscCall(DMPlexRestoreTransitiveClosure(dm, v, PETSC_FALSE, &vsize, &vclosure));
2518:               }
2519:             }
2520:             PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &size, &closure));
2521:           }
2522:           PetscCall(DMRestoreWorkArray(dm, nf, MPIU_INT, &cfaces));
2523:         }
2524:       }

2526:       cids[0] = 0;
2527:       for (i = 0, cump = 0, cum = 0; i < graph->ncc; i++) {
2528:         PetscInt j;

2530:         PetscCall(PetscBTMemzero(A->rmap->n, btvt));
2531:         for (j = graph->cptr[i]; j < graph->cptr[i + 1]; j++) {
2532:           PetscInt k, size, *closure = NULL, cell = graph->queue[j];

2534:           PetscCall(DMPlexGetTransitiveClosure(dm, cell, PETSC_TRUE, &size, &closure));
2535:           for (k = 0; k < 2 * size; k += 2) {
2536:             PetscInt s, pp, p = closure[k], off, dof, cdof;

2538:             PetscCall(PetscSectionGetConstraintDof(subSection, p, &cdof));
2539:             PetscCall(PetscSectionGetOffset(subSection, p, &off));
2540:             PetscCall(PetscSectionGetDof(subSection, p, &dof));
2541:             for (s = 0; s < dof - cdof; s++) {
2542:               if (PetscBTLookupSet(btvt, off + s)) continue;
2543:               if (PetscBTLookup(btvc, p - pStart)) pids[cump++] = off + s; /* subdomain corner */
2544:               else if (!PetscBTLookup(btv, off + s)) ids[cum++] = off + s;
2545:               else pids[cump++] = off + s; /* cross-vertex */
2546:             }
2547:             PetscCall(DMPlexGetTreeParent(dm, p, &pp, NULL));
2548:             if (pp != p) {
2549:               PetscCall(PetscSectionGetConstraintDof(subSection, pp, &cdof));
2550:               PetscCall(PetscSectionGetOffset(subSection, pp, &off));
2551:               PetscCall(PetscSectionGetDof(subSection, pp, &dof));
2552:               for (s = 0; s < dof - cdof; s++) {
2553:                 if (PetscBTLookupSet(btvt, off + s)) continue;
2554:                 if (PetscBTLookup(btvc, pp - pStart)) pids[cump++] = off + s; /* subdomain corner */
2555:                 else if (!PetscBTLookup(btv, off + s)) ids[cum++] = off + s;
2556:                 else pids[cump++] = off + s; /* cross-vertex */
2557:               }
2558:             }
2559:           }
2560:           PetscCall(DMPlexRestoreTransitiveClosure(dm, cell, PETSC_TRUE, &size, &closure));
2561:         }
2562:         cids[i + 1] = cum;
2563:         /* mark dofs as already assigned */
2564:         for (j = cids[i]; j < cids[i + 1]; j++) PetscCall(PetscBTSet(btv, ids[j]));
2565:       }
2566:       if (cc) {
2567:         PetscCall(PetscMalloc1(graph->ncc, &cc_n));
2568:         for (i = 0; i < graph->ncc; i++) PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cids[i + 1] - cids[i], ids + cids[i], PETSC_COPY_VALUES, &cc_n[i]));
2569:         *cc = cc_n;
2570:       }
2571:       if (primalv) PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), cump, pids, PETSC_COPY_VALUES, primalv));
2572:       PetscCall(PetscFree3(ids, cids, pids));
2573:       PetscCall(PetscBTDestroy(&btv));
2574:       PetscCall(PetscBTDestroy(&btvt));
2575:       PetscCall(PetscBTDestroy(&btvc));
2576:       PetscCall(DMDestroy(&dm));
2577:     }
2578:   } else {
2579:     if (ncc) *ncc = graph->ncc;
2580:     if (cc) {
2581:       PetscCall(PetscMalloc1(graph->ncc, &cc_n));
2582:       for (i = 0; i < graph->ncc; i++) PetscCall(ISCreateGeneral(PETSC_COMM_SELF, graph->cptr[i + 1] - graph->cptr[i], graph->queue + graph->cptr[i], PETSC_COPY_VALUES, &cc_n[i]));
2583:       *cc = cc_n;
2584:     }
2585:   }
2586:   /* clean up graph */
2587:   graph->xadj   = NULL;
2588:   graph->adjncy = NULL;
2589:   PetscCall(PCBDDCGraphDestroy(&graph));
2590:   PetscFunctionReturn(PETSC_SUCCESS);
2591: }

2593: PetscErrorCode PCBDDCBenignCheck(PC pc, IS zerodiag)
2594: {
2595:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;
2596:   PC_IS   *pcis   = (PC_IS *)pc->data;
2597:   IS       dirIS  = NULL;
2598:   PetscInt i;

2600:   PetscFunctionBegin;
2601:   PetscCall(PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph, &dirIS));
2602:   if (zerodiag) {
2603:     Mat             A;
2604:     Vec             vec3_N;
2605:     PetscScalar    *vals;
2606:     const PetscInt *idxs;
2607:     PetscInt        nz, *count;

2609:     /* p0 */
2610:     PetscCall(VecSet(pcis->vec1_N, 0.));
2611:     PetscCall(PetscMalloc1(pcis->n, &vals));
2612:     PetscCall(ISGetLocalSize(zerodiag, &nz));
2613:     PetscCall(ISGetIndices(zerodiag, &idxs));
2614:     for (i = 0; i < nz; i++) vals[i] = 1.;
2615:     PetscCall(VecSetValues(pcis->vec1_N, nz, idxs, vals, INSERT_VALUES));
2616:     PetscCall(VecAssemblyBegin(pcis->vec1_N));
2617:     PetscCall(VecAssemblyEnd(pcis->vec1_N));
2618:     /* v_I */
2619:     PetscCall(VecSetRandom(pcis->vec2_N, NULL));
2620:     for (i = 0; i < nz; i++) vals[i] = 0.;
2621:     PetscCall(VecSetValues(pcis->vec2_N, nz, idxs, vals, INSERT_VALUES));
2622:     PetscCall(ISRestoreIndices(zerodiag, &idxs));
2623:     PetscCall(ISGetIndices(pcis->is_B_local, &idxs));
2624:     for (i = 0; i < pcis->n_B; i++) vals[i] = 0.;
2625:     PetscCall(VecSetValues(pcis->vec2_N, pcis->n_B, idxs, vals, INSERT_VALUES));
2626:     PetscCall(ISRestoreIndices(pcis->is_B_local, &idxs));
2627:     if (dirIS) {
2628:       PetscInt n;

2630:       PetscCall(ISGetLocalSize(dirIS, &n));
2631:       PetscCall(ISGetIndices(dirIS, &idxs));
2632:       for (i = 0; i < n; i++) vals[i] = 0.;
2633:       PetscCall(VecSetValues(pcis->vec2_N, n, idxs, vals, INSERT_VALUES));
2634:       PetscCall(ISRestoreIndices(dirIS, &idxs));
2635:     }
2636:     PetscCall(VecAssemblyBegin(pcis->vec2_N));
2637:     PetscCall(VecAssemblyEnd(pcis->vec2_N));
2638:     PetscCall(VecDuplicate(pcis->vec1_N, &vec3_N));
2639:     PetscCall(VecSet(vec3_N, 0.));
2640:     PetscCall(MatISGetLocalMat(pc->pmat, &A));
2641:     PetscCall(MatMult(A, pcis->vec1_N, vec3_N));
2642:     PetscCall(VecDot(vec3_N, pcis->vec2_N, &vals[0]));
2643:     PetscCheck(PetscAbsScalar(vals[0]) <= 1.e-1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Benign trick can not be applied! b(v_I,p_0) = %1.6e (should be numerically 0.)", (double)PetscAbsScalar(vals[0]));
2644:     PetscCall(PetscFree(vals));
2645:     PetscCall(VecDestroy(&vec3_N));

2647:     /* there should not be any pressure dofs lying on the interface */
2648:     PetscCall(PetscCalloc1(pcis->n, &count));
2649:     PetscCall(ISGetIndices(pcis->is_B_local, &idxs));
2650:     for (i = 0; i < pcis->n_B; i++) count[idxs[i]]++;
2651:     PetscCall(ISRestoreIndices(pcis->is_B_local, &idxs));
2652:     PetscCall(ISGetIndices(zerodiag, &idxs));
2653:     for (i = 0; i < nz; i++) PetscCheck(!count[idxs[i]], PETSC_COMM_SELF, PETSC_ERR_SUP, "Benign trick can not be applied! pressure dof %" PetscInt_FMT " is an interface dof", idxs[i]);
2654:     PetscCall(ISRestoreIndices(zerodiag, &idxs));
2655:     PetscCall(PetscFree(count));
2656:   }
2657:   PetscCall(ISDestroy(&dirIS));

2659:   /* check PCBDDCBenignGetOrSetP0 */
2660:   PetscCall(VecSetRandom(pcis->vec1_global, NULL));
2661:   for (i = 0; i < pcbddc->benign_n; i++) pcbddc->benign_p0[i] = -PetscGlobalRank - i;
2662:   PetscCall(PCBDDCBenignGetOrSetP0(pc, pcis->vec1_global, PETSC_FALSE));
2663:   for (i = 0; i < pcbddc->benign_n; i++) pcbddc->benign_p0[i] = 1;
2664:   PetscCall(PCBDDCBenignGetOrSetP0(pc, pcis->vec1_global, PETSC_TRUE));
2665:   for (i = 0; i < pcbddc->benign_n; i++) {
2666:     PetscInt val = PetscRealPart(pcbddc->benign_p0[i]);
2667:     PetscCheck(val == -PetscGlobalRank - i, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error testing PCBDDCBenignGetOrSetP0! Found %g at %" PetscInt_FMT " instead of %g", (double)PetscRealPart(pcbddc->benign_p0[i]), i, (double)(-PetscGlobalRank - i));
2668:   }
2669:   PetscFunctionReturn(PETSC_SUCCESS);
2670: }

2672: PetscErrorCode PCBDDCBenignDetectSaddlePoint(PC pc, PetscBool reuse, IS *zerodiaglocal)
2673: {
2674:   PC_BDDC  *pcbddc    = (PC_BDDC *)pc->data;
2675:   Mat_IS   *matis     = (Mat_IS *)pc->pmat->data;
2676:   IS        pressures = NULL, zerodiag = NULL, *bzerodiag = NULL, zerodiag_save, *zerodiag_subs;
2677:   PetscInt  nz, n, benign_n, bsp = 1;
2678:   PetscInt *interior_dofs, n_interior_dofs, nneu;
2679:   PetscBool sorted, have_null, has_null_pressures, recompute_zerodiag, checkb;

2681:   PetscFunctionBegin;
2682:   if (reuse) goto project_b0;
2683:   PetscCall(PetscSFDestroy(&pcbddc->benign_sf));
2684:   PetscCall(MatDestroy(&pcbddc->benign_B0));
2685:   for (n = 0; n < pcbddc->benign_n; n++) PetscCall(ISDestroy(&pcbddc->benign_zerodiag_subs[n]));
2686:   PetscCall(PetscFree(pcbddc->benign_zerodiag_subs));
2687:   has_null_pressures = PETSC_TRUE;
2688:   have_null          = PETSC_TRUE;
2689:   /* if a local information on dofs is present, gets pressure dofs from command line (uses the last field is not provided)
2690:      Without local information, it uses only the zerodiagonal dofs (ok if the pressure block is all zero and it is a scalar field)
2691:      Checks if all the pressure dofs in each subdomain have a zero diagonal
2692:      If not, a change of basis on pressures is not needed
2693:      since the local Schur complements are already SPD
2694:   */
2695:   if (pcbddc->n_ISForDofsLocal) {
2696:     IS        iP = NULL;
2697:     PetscInt  p, *pp;
2698:     PetscBool flg, blocked = PETSC_FALSE;

2700:     PetscCall(PetscMalloc1(pcbddc->n_ISForDofsLocal, &pp));
2701:     n = pcbddc->n_ISForDofsLocal;
2702:     PetscOptionsBegin(PetscObjectComm((PetscObject)pc), ((PetscObject)pc)->prefix, "BDDC benign options", "PC");
2703:     PetscCall(PetscOptionsIntArray("-pc_bddc_pressure_field", "Field id for pressures", NULL, pp, &n, &flg));
2704:     PetscCall(PetscOptionsBool("-pc_bddc_pressure_blocked", "Use blocked pressure fields", NULL, blocked, &blocked, NULL));
2705:     PetscOptionsEnd();
2706:     if (!flg) {
2707:       n     = 1;
2708:       pp[0] = pcbddc->n_ISForDofsLocal - 1;
2709:     }

2711:     bsp = 0;
2712:     for (p = 0; p < n; p++) {
2713:       PetscInt bs = 1;

2715:       PetscCheck(pp[p] >= 0 && pp[p] < pcbddc->n_ISForDofsLocal, PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "Invalid field id for pressures %" PetscInt_FMT, pp[p]);
2716:       if (blocked) PetscCall(ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]], &bs));
2717:       bsp += bs;
2718:     }
2719:     PetscCall(PetscMalloc1(bsp, &bzerodiag));
2720:     bsp = 0;
2721:     for (p = 0; p < n; p++) {
2722:       const PetscInt *idxs;
2723:       PetscInt        b, bs = 1, npl, *bidxs;

2725:       if (blocked) PetscCall(ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]], &bs));
2726:       PetscCall(ISGetLocalSize(pcbddc->ISForDofsLocal[pp[p]], &npl));
2727:       PetscCall(ISGetIndices(pcbddc->ISForDofsLocal[pp[p]], &idxs));
2728:       PetscCall(PetscMalloc1(npl / bs, &bidxs));
2729:       for (b = 0; b < bs; b++) {
2730:         PetscInt i;

2732:         for (i = 0; i < npl / bs; i++) bidxs[i] = idxs[bs * i + b];
2733:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, npl / bs, bidxs, PETSC_COPY_VALUES, &bzerodiag[bsp]));
2734:         bsp++;
2735:       }
2736:       PetscCall(PetscFree(bidxs));
2737:       PetscCall(ISRestoreIndices(pcbddc->ISForDofsLocal[pp[p]], &idxs));
2738:     }
2739:     PetscCall(ISConcatenate(PETSC_COMM_SELF, bsp, bzerodiag, &pressures));

2741:     /* remove zeroed out pressures if we are setting up a BDDC solver for a saddle-point FETI-DP */
2742:     PetscCall(PetscObjectQuery((PetscObject)pc, "__KSPFETIDP_lP", (PetscObject *)&iP));
2743:     if (iP) {
2744:       IS newpressures;

2746:       PetscCall(ISDifference(pressures, iP, &newpressures));
2747:       PetscCall(ISDestroy(&pressures));
2748:       pressures = newpressures;
2749:     }
2750:     PetscCall(ISSorted(pressures, &sorted));
2751:     if (!sorted) PetscCall(ISSort(pressures));
2752:     PetscCall(PetscFree(pp));
2753:   }

2755:   /* pcis has not been setup yet, so get the local size from the subdomain matrix */
2756:   PetscCall(MatGetLocalSize(pcbddc->local_mat, &n, NULL));
2757:   if (!n) pcbddc->benign_change_explicit = PETSC_TRUE;
2758:   PetscCall(MatFindZeroDiagonals(pcbddc->local_mat, &zerodiag));
2759:   PetscCall(ISSorted(zerodiag, &sorted));
2760:   if (!sorted) PetscCall(ISSort(zerodiag));
2761:   PetscCall(PetscObjectReference((PetscObject)zerodiag));
2762:   zerodiag_save = zerodiag;
2763:   PetscCall(ISGetLocalSize(zerodiag, &nz));
2764:   if (!nz) {
2765:     if (n) have_null = PETSC_FALSE;
2766:     has_null_pressures = PETSC_FALSE;
2767:     PetscCall(ISDestroy(&zerodiag));
2768:   }
2769:   recompute_zerodiag = PETSC_FALSE;

2771:   /* in case disconnected subdomains info is present, split the pressures accordingly (otherwise the benign trick could fail) */
2772:   zerodiag_subs   = NULL;
2773:   benign_n        = 0;
2774:   n_interior_dofs = 0;
2775:   interior_dofs   = NULL;
2776:   nneu            = 0;
2777:   if (pcbddc->NeumannBoundariesLocal) PetscCall(ISGetLocalSize(pcbddc->NeumannBoundariesLocal, &nneu));
2778:   checkb = (PetscBool)(!pcbddc->NeumannBoundariesLocal || pcbddc->current_level);
2779:   if (checkb) { /* need to compute interior nodes */
2780:     PetscInt               n, i;
2781:     PetscInt              *count;
2782:     ISLocalToGlobalMapping mapping;

2784:     PetscCall(MatISGetLocalToGlobalMapping(pc->pmat, &mapping, NULL));
2785:     PetscCall(ISLocalToGlobalMappingGetNodeInfo(mapping, &n, &count, NULL));
2786:     PetscCall(PetscMalloc1(n, &interior_dofs));
2787:     for (i = 0; i < n; i++)
2788:       if (count[i] < 2) interior_dofs[n_interior_dofs++] = i;
2789:     PetscCall(ISLocalToGlobalMappingRestoreNodeInfo(mapping, &n, &count, NULL));
2790:   }
2791:   if (has_null_pressures) {
2792:     IS             *subs;
2793:     PetscInt        nsubs, i, j, nl;
2794:     const PetscInt *idxs;
2795:     PetscScalar    *array;
2796:     Vec            *work;

2798:     subs  = pcbddc->local_subs;
2799:     nsubs = pcbddc->n_local_subs;
2800:     /* these vectors are needed to check if the constant on pressures is in the kernel of the local operator B (i.e. B(v_I,p0) should be zero) */
2801:     if (checkb) {
2802:       PetscCall(VecDuplicateVecs(matis->y, 2, &work));
2803:       PetscCall(ISGetLocalSize(zerodiag, &nl));
2804:       PetscCall(ISGetIndices(zerodiag, &idxs));
2805:       /* work[0] = 1_p */
2806:       PetscCall(VecSet(work[0], 0.));
2807:       PetscCall(VecGetArray(work[0], &array));
2808:       for (j = 0; j < nl; j++) array[idxs[j]] = 1.;
2809:       PetscCall(VecRestoreArray(work[0], &array));
2810:       /* work[0] = 1_v */
2811:       PetscCall(VecSet(work[1], 1.));
2812:       PetscCall(VecGetArray(work[1], &array));
2813:       for (j = 0; j < nl; j++) array[idxs[j]] = 0.;
2814:       PetscCall(VecRestoreArray(work[1], &array));
2815:       PetscCall(ISRestoreIndices(zerodiag, &idxs));
2816:     }

2818:     if (nsubs > 1 || bsp > 1) {
2819:       IS      *is;
2820:       PetscInt b, totb;

2822:       totb  = bsp;
2823:       is    = bsp > 1 ? bzerodiag : &zerodiag;
2824:       nsubs = PetscMax(nsubs, 1);
2825:       PetscCall(PetscCalloc1(nsubs * totb, &zerodiag_subs));
2826:       for (b = 0; b < totb; b++) {
2827:         for (i = 0; i < nsubs; i++) {
2828:           ISLocalToGlobalMapping l2g;
2829:           IS                     t_zerodiag_subs;
2830:           PetscInt               nl;

2832:           if (subs) {
2833:             PetscCall(ISLocalToGlobalMappingCreateIS(subs[i], &l2g));
2834:           } else {
2835:             IS tis;

2837:             PetscCall(MatGetLocalSize(pcbddc->local_mat, &nl, NULL));
2838:             PetscCall(ISCreateStride(PETSC_COMM_SELF, nl, 0, 1, &tis));
2839:             PetscCall(ISLocalToGlobalMappingCreateIS(tis, &l2g));
2840:             PetscCall(ISDestroy(&tis));
2841:           }
2842:           PetscCall(ISGlobalToLocalMappingApplyIS(l2g, IS_GTOLM_DROP, is[b], &t_zerodiag_subs));
2843:           PetscCall(ISGetLocalSize(t_zerodiag_subs, &nl));
2844:           if (nl) {
2845:             PetscBool valid = PETSC_TRUE;

2847:             if (checkb) {
2848:               PetscCall(VecSet(matis->x, 0));
2849:               PetscCall(ISGetLocalSize(subs[i], &nl));
2850:               PetscCall(ISGetIndices(subs[i], &idxs));
2851:               PetscCall(VecGetArray(matis->x, &array));
2852:               for (j = 0; j < nl; j++) array[idxs[j]] = 1.;
2853:               PetscCall(VecRestoreArray(matis->x, &array));
2854:               PetscCall(ISRestoreIndices(subs[i], &idxs));
2855:               PetscCall(VecPointwiseMult(matis->x, work[0], matis->x));
2856:               PetscCall(MatMult(matis->A, matis->x, matis->y));
2857:               PetscCall(VecPointwiseMult(matis->y, work[1], matis->y));
2858:               PetscCall(VecGetArray(matis->y, &array));
2859:               for (j = 0; j < n_interior_dofs; j++) {
2860:                 if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
2861:                   valid = PETSC_FALSE;
2862:                   break;
2863:                 }
2864:               }
2865:               PetscCall(VecRestoreArray(matis->y, &array));
2866:             }
2867:             if (valid && nneu) {
2868:               const PetscInt *idxs;
2869:               PetscInt        nzb;

2871:               PetscCall(ISGetIndices(pcbddc->NeumannBoundariesLocal, &idxs));
2872:               PetscCall(ISGlobalToLocalMappingApply(l2g, IS_GTOLM_DROP, nneu, idxs, &nzb, NULL));
2873:               PetscCall(ISRestoreIndices(pcbddc->NeumannBoundariesLocal, &idxs));
2874:               if (nzb) valid = PETSC_FALSE;
2875:             }
2876:             if (valid && pressures) {
2877:               IS       t_pressure_subs, tmp;
2878:               PetscInt i1, i2;

2880:               PetscCall(ISGlobalToLocalMappingApplyIS(l2g, IS_GTOLM_DROP, pressures, &t_pressure_subs));
2881:               PetscCall(ISEmbed(t_zerodiag_subs, t_pressure_subs, PETSC_TRUE, &tmp));
2882:               PetscCall(ISGetLocalSize(tmp, &i1));
2883:               PetscCall(ISGetLocalSize(t_zerodiag_subs, &i2));
2884:               if (i2 != i1) valid = PETSC_FALSE;
2885:               PetscCall(ISDestroy(&t_pressure_subs));
2886:               PetscCall(ISDestroy(&tmp));
2887:             }
2888:             if (valid) {
2889:               PetscCall(ISLocalToGlobalMappingApplyIS(l2g, t_zerodiag_subs, &zerodiag_subs[benign_n]));
2890:               benign_n++;
2891:             } else recompute_zerodiag = PETSC_TRUE;
2892:           }
2893:           PetscCall(ISDestroy(&t_zerodiag_subs));
2894:           PetscCall(ISLocalToGlobalMappingDestroy(&l2g));
2895:         }
2896:       }
2897:     } else { /* there's just one subdomain (or zero if they have not been detected */
2898:       PetscBool valid = PETSC_TRUE;

2900:       if (nneu) valid = PETSC_FALSE;
2901:       if (valid && pressures) PetscCall(ISEqual(pressures, zerodiag, &valid));
2902:       if (valid && checkb) {
2903:         PetscCall(MatMult(matis->A, work[0], matis->x));
2904:         PetscCall(VecPointwiseMult(matis->x, work[1], matis->x));
2905:         PetscCall(VecGetArray(matis->x, &array));
2906:         for (j = 0; j < n_interior_dofs; j++) {
2907:           if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
2908:             valid = PETSC_FALSE;
2909:             break;
2910:           }
2911:         }
2912:         PetscCall(VecRestoreArray(matis->x, &array));
2913:       }
2914:       if (valid) {
2915:         benign_n = 1;
2916:         PetscCall(PetscMalloc1(benign_n, &zerodiag_subs));
2917:         PetscCall(PetscObjectReference((PetscObject)zerodiag));
2918:         zerodiag_subs[0] = zerodiag;
2919:       }
2920:     }
2921:     if (checkb) PetscCall(VecDestroyVecs(2, &work));
2922:   }
2923:   PetscCall(PetscFree(interior_dofs));

2925:   if (!benign_n) {
2926:     PetscInt n;

2928:     PetscCall(ISDestroy(&zerodiag));
2929:     recompute_zerodiag = PETSC_FALSE;
2930:     PetscCall(MatGetLocalSize(pcbddc->local_mat, &n, NULL));
2931:     if (n) have_null = PETSC_FALSE;
2932:   }

2934:   /* final check for null pressures */
2935:   if (zerodiag && pressures) PetscCall(ISEqual(pressures, zerodiag, &have_null));

2937:   if (recompute_zerodiag) {
2938:     PetscCall(ISDestroy(&zerodiag));
2939:     if (benign_n == 1) {
2940:       PetscCall(PetscObjectReference((PetscObject)zerodiag_subs[0]));
2941:       zerodiag = zerodiag_subs[0];
2942:     } else {
2943:       PetscInt i, nzn, *new_idxs;

2945:       nzn = 0;
2946:       for (i = 0; i < benign_n; i++) {
2947:         PetscInt ns;
2948:         PetscCall(ISGetLocalSize(zerodiag_subs[i], &ns));
2949:         nzn += ns;
2950:       }
2951:       PetscCall(PetscMalloc1(nzn, &new_idxs));
2952:       nzn = 0;
2953:       for (i = 0; i < benign_n; i++) {
2954:         PetscInt ns, *idxs;
2955:         PetscCall(ISGetLocalSize(zerodiag_subs[i], &ns));
2956:         PetscCall(ISGetIndices(zerodiag_subs[i], (const PetscInt **)&idxs));
2957:         PetscCall(PetscArraycpy(new_idxs + nzn, idxs, ns));
2958:         PetscCall(ISRestoreIndices(zerodiag_subs[i], (const PetscInt **)&idxs));
2959:         nzn += ns;
2960:       }
2961:       PetscCall(PetscSortInt(nzn, new_idxs));
2962:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nzn, new_idxs, PETSC_OWN_POINTER, &zerodiag));
2963:     }
2964:     have_null = PETSC_FALSE;
2965:   }

2967:   /* determines if the coarse solver will be singular or not */
2968:   PetscCallMPI(MPIU_Allreduce(&have_null, &pcbddc->benign_null, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)pc)));

2970:   /* Prepare matrix to compute no-net-flux */
2971:   if (pcbddc->compute_nonetflux && !pcbddc->divudotp) {
2972:     Mat                    A, loc_divudotp;
2973:     ISLocalToGlobalMapping rl2g, cl2g, l2gmap;
2974:     IS                     row, col, isused = NULL;
2975:     PetscInt               M, N, n, st, n_isused;

2977:     if (pressures) {
2978:       isused = pressures;
2979:     } else {
2980:       isused = zerodiag_save;
2981:     }
2982:     PetscCall(MatISGetLocalToGlobalMapping(pc->pmat, &l2gmap, NULL));
2983:     PetscCall(MatISGetLocalMat(pc->pmat, &A));
2984:     PetscCall(MatGetLocalSize(A, &n, NULL));
2985:     PetscCheck(isused || (n == 0), PETSC_COMM_SELF, PETSC_ERR_USER, "Don't know how to extract div u dot p! Please provide the pressure field");
2986:     n_isused = 0;
2987:     if (isused) PetscCall(ISGetLocalSize(isused, &n_isused));
2988:     PetscCallMPI(MPI_Scan(&n_isused, &st, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)pc)));
2989:     st = st - n_isused;
2990:     if (n) {
2991:       const PetscInt *gidxs;

2993:       PetscCall(MatCreateSubMatrix(A, isused, NULL, MAT_INITIAL_MATRIX, &loc_divudotp));
2994:       PetscCall(ISLocalToGlobalMappingGetIndices(l2gmap, &gidxs));
2995:       /* TODO: extend ISCreateStride with st = PETSC_DECIDE */
2996:       PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), n_isused, st, 1, &row));
2997:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), n, gidxs, PETSC_COPY_VALUES, &col));
2998:       PetscCall(ISLocalToGlobalMappingRestoreIndices(l2gmap, &gidxs));
2999:     } else {
3000:       PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, 0, 0, 1, NULL, &loc_divudotp));
3001:       PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), n_isused, st, 1, &row));
3002:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), 0, NULL, PETSC_COPY_VALUES, &col));
3003:     }
3004:     PetscCall(MatGetSize(pc->pmat, NULL, &N));
3005:     PetscCall(ISGetSize(row, &M));
3006:     PetscCall(ISLocalToGlobalMappingCreateIS(row, &rl2g));
3007:     PetscCall(ISLocalToGlobalMappingCreateIS(col, &cl2g));
3008:     PetscCall(ISDestroy(&row));
3009:     PetscCall(ISDestroy(&col));
3010:     PetscCall(MatCreate(PetscObjectComm((PetscObject)pc), &pcbddc->divudotp));
3011:     PetscCall(MatSetType(pcbddc->divudotp, MATIS));
3012:     PetscCall(MatSetSizes(pcbddc->divudotp, PETSC_DECIDE, PETSC_DECIDE, M, N));
3013:     PetscCall(MatSetLocalToGlobalMapping(pcbddc->divudotp, rl2g, cl2g));
3014:     PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
3015:     PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));
3016:     PetscCall(MatISSetLocalMat(pcbddc->divudotp, loc_divudotp));
3017:     PetscCall(MatDestroy(&loc_divudotp));
3018:     PetscCall(MatAssemblyBegin(pcbddc->divudotp, MAT_FINAL_ASSEMBLY));
3019:     PetscCall(MatAssemblyEnd(pcbddc->divudotp, MAT_FINAL_ASSEMBLY));
3020:   }
3021:   PetscCall(ISDestroy(&zerodiag_save));
3022:   PetscCall(ISDestroy(&pressures));
3023:   if (bzerodiag) {
3024:     PetscInt i;

3026:     for (i = 0; i < bsp; i++) PetscCall(ISDestroy(&bzerodiag[i]));
3027:     PetscCall(PetscFree(bzerodiag));
3028:   }
3029:   pcbddc->benign_n             = benign_n;
3030:   pcbddc->benign_zerodiag_subs = zerodiag_subs;

3032:   /* determines if the problem has subdomains with 0 pressure block */
3033:   have_null = (PetscBool)(!!pcbddc->benign_n);
3034:   PetscCallMPI(MPIU_Allreduce(&have_null, &pcbddc->benign_have_null, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)pc)));

3036: project_b0:
3037:   PetscCall(MatGetLocalSize(pcbddc->local_mat, &n, NULL));
3038:   /* change of basis and p0 dofs */
3039:   if (pcbddc->benign_n) {
3040:     PetscInt i, s, *nnz;

3042:     /* local change of basis for pressures */
3043:     PetscCall(MatDestroy(&pcbddc->benign_change));
3044:     PetscCall(MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat), &pcbddc->benign_change));
3045:     PetscCall(MatSetType(pcbddc->benign_change, MATAIJ));
3046:     PetscCall(MatSetSizes(pcbddc->benign_change, n, n, PETSC_DECIDE, PETSC_DECIDE));
3047:     PetscCall(PetscMalloc1(n, &nnz));
3048:     for (i = 0; i < n; i++) nnz[i] = 1; /* defaults to identity */
3049:     for (i = 0; i < pcbddc->benign_n; i++) {
3050:       const PetscInt *idxs;
3051:       PetscInt        nzs, j;

3053:       PetscCall(ISGetLocalSize(pcbddc->benign_zerodiag_subs[i], &nzs));
3054:       PetscCall(ISGetIndices(pcbddc->benign_zerodiag_subs[i], &idxs));
3055:       for (j = 0; j < nzs - 1; j++) nnz[idxs[j]] = 2; /* change on pressures */
3056:       nnz[idxs[nzs - 1]] = nzs;                       /* last local pressure dof in subdomain */
3057:       PetscCall(ISRestoreIndices(pcbddc->benign_zerodiag_subs[i], &idxs));
3058:     }
3059:     PetscCall(MatSeqAIJSetPreallocation(pcbddc->benign_change, 0, nnz));
3060:     PetscCall(MatSetOption(pcbddc->benign_change, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
3061:     PetscCall(PetscFree(nnz));
3062:     /* set identity by default */
3063:     for (i = 0; i < n; i++) PetscCall(MatSetValue(pcbddc->benign_change, i, i, 1., INSERT_VALUES));
3064:     PetscCall(PetscFree3(pcbddc->benign_p0_lidx, pcbddc->benign_p0_gidx, pcbddc->benign_p0));
3065:     PetscCall(PetscMalloc3(pcbddc->benign_n, &pcbddc->benign_p0_lidx, pcbddc->benign_n, &pcbddc->benign_p0_gidx, pcbddc->benign_n, &pcbddc->benign_p0));
3066:     /* set change on pressures */
3067:     for (s = 0; s < pcbddc->benign_n; s++) {
3068:       PetscScalar    *array;
3069:       const PetscInt *idxs;
3070:       PetscInt        nzs;

3072:       PetscCall(ISGetLocalSize(pcbddc->benign_zerodiag_subs[s], &nzs));
3073:       PetscCall(ISGetIndices(pcbddc->benign_zerodiag_subs[s], &idxs));
3074:       for (i = 0; i < nzs - 1; i++) {
3075:         PetscScalar vals[2];
3076:         PetscInt    cols[2];

3078:         cols[0] = idxs[i];
3079:         cols[1] = idxs[nzs - 1];
3080:         vals[0] = 1.;
3081:         vals[1] = 1.;
3082:         PetscCall(MatSetValues(pcbddc->benign_change, 1, cols, 2, cols, vals, INSERT_VALUES));
3083:       }
3084:       PetscCall(PetscMalloc1(nzs, &array));
3085:       for (i = 0; i < nzs - 1; i++) array[i] = -1.;
3086:       array[nzs - 1] = 1.;
3087:       PetscCall(MatSetValues(pcbddc->benign_change, 1, idxs + nzs - 1, nzs, idxs, array, INSERT_VALUES));
3088:       /* store local idxs for p0 */
3089:       pcbddc->benign_p0_lidx[s] = idxs[nzs - 1];
3090:       PetscCall(ISRestoreIndices(pcbddc->benign_zerodiag_subs[s], &idxs));
3091:       PetscCall(PetscFree(array));
3092:     }
3093:     PetscCall(MatAssemblyBegin(pcbddc->benign_change, MAT_FINAL_ASSEMBLY));
3094:     PetscCall(MatAssemblyEnd(pcbddc->benign_change, MAT_FINAL_ASSEMBLY));

3096:     /* project if needed */
3097:     if (pcbddc->benign_change_explicit) {
3098:       Mat M;

3100:       PetscCall(MatPtAP(pcbddc->local_mat, pcbddc->benign_change, MAT_INITIAL_MATRIX, 2.0, &M));
3101:       PetscCall(MatDestroy(&pcbddc->local_mat));
3102:       PetscCall(MatSeqAIJCompress(M, &pcbddc->local_mat));
3103:       PetscCall(MatDestroy(&M));
3104:     }
3105:     /* store global idxs for p0 */
3106:     PetscCall(ISLocalToGlobalMappingApply(matis->rmapping, pcbddc->benign_n, pcbddc->benign_p0_lidx, pcbddc->benign_p0_gidx));
3107:   }
3108:   *zerodiaglocal = zerodiag;
3109:   PetscFunctionReturn(PETSC_SUCCESS);
3110: }

3112: PetscErrorCode PCBDDCBenignGetOrSetP0(PC pc, Vec v, PetscBool get)
3113: {
3114:   PC_BDDC     *pcbddc = (PC_BDDC *)pc->data;
3115:   PetscScalar *array;

3117:   PetscFunctionBegin;
3118:   if (!pcbddc->benign_sf) {
3119:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)pc), &pcbddc->benign_sf));
3120:     PetscCall(PetscSFSetGraphLayout(pcbddc->benign_sf, pc->pmat->rmap, pcbddc->benign_n, NULL, PETSC_OWN_POINTER, pcbddc->benign_p0_gidx));
3121:   }
3122:   if (get) {
3123:     PetscCall(VecGetArrayRead(v, (const PetscScalar **)&array));
3124:     PetscCall(PetscSFBcastBegin(pcbddc->benign_sf, MPIU_SCALAR, array, pcbddc->benign_p0, MPI_REPLACE));
3125:     PetscCall(PetscSFBcastEnd(pcbddc->benign_sf, MPIU_SCALAR, array, pcbddc->benign_p0, MPI_REPLACE));
3126:     PetscCall(VecRestoreArrayRead(v, (const PetscScalar **)&array));
3127:   } else {
3128:     PetscCall(VecGetArray(v, &array));
3129:     PetscCall(PetscSFReduceBegin(pcbddc->benign_sf, MPIU_SCALAR, pcbddc->benign_p0, array, MPI_REPLACE));
3130:     PetscCall(PetscSFReduceEnd(pcbddc->benign_sf, MPIU_SCALAR, pcbddc->benign_p0, array, MPI_REPLACE));
3131:     PetscCall(VecRestoreArray(v, &array));
3132:   }
3133:   PetscFunctionReturn(PETSC_SUCCESS);
3134: }

3136: PetscErrorCode PCBDDCBenignPopOrPushB0(PC pc, PetscBool pop)
3137: {
3138:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;

3140:   PetscFunctionBegin;
3141:   /* TODO: add error checking
3142:     - avoid nested pop (or push) calls.
3143:     - cannot push before pop.
3144:     - cannot call this if pcbddc->local_mat is NULL
3145:   */
3146:   if (!pcbddc->benign_n) PetscFunctionReturn(PETSC_SUCCESS);
3147:   if (pop) {
3148:     if (pcbddc->benign_change_explicit) {
3149:       IS       is_p0;
3150:       MatReuse reuse;

3152:       /* extract B_0 */
3153:       reuse = MAT_INITIAL_MATRIX;
3154:       if (pcbddc->benign_B0) reuse = MAT_REUSE_MATRIX;
3155:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, pcbddc->benign_n, pcbddc->benign_p0_lidx, PETSC_COPY_VALUES, &is_p0));
3156:       PetscCall(MatCreateSubMatrix(pcbddc->local_mat, is_p0, NULL, reuse, &pcbddc->benign_B0));
3157:       /* remove rows and cols from local problem */
3158:       PetscCall(MatSetOption(pcbddc->local_mat, MAT_KEEP_NONZERO_PATTERN, PETSC_TRUE));
3159:       PetscCall(MatSetOption(pcbddc->local_mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
3160:       PetscCall(MatZeroRowsColumnsIS(pcbddc->local_mat, is_p0, 1.0, NULL, NULL));
3161:       PetscCall(ISDestroy(&is_p0));
3162:     } else {
3163:       Mat_IS      *matis = (Mat_IS *)pc->pmat->data;
3164:       PetscScalar *vals;
3165:       PetscInt     i, n, *idxs_ins;

3167:       PetscCall(VecGetLocalSize(matis->y, &n));
3168:       PetscCall(PetscMalloc2(n, &idxs_ins, n, &vals));
3169:       if (!pcbddc->benign_B0) {
3170:         PetscInt *nnz;
3171:         PetscCall(MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat), &pcbddc->benign_B0));
3172:         PetscCall(MatSetType(pcbddc->benign_B0, MATAIJ));
3173:         PetscCall(MatSetSizes(pcbddc->benign_B0, pcbddc->benign_n, n, PETSC_DECIDE, PETSC_DECIDE));
3174:         PetscCall(PetscMalloc1(pcbddc->benign_n, &nnz));
3175:         for (i = 0; i < pcbddc->benign_n; i++) {
3176:           PetscCall(ISGetLocalSize(pcbddc->benign_zerodiag_subs[i], &nnz[i]));
3177:           nnz[i] = n - nnz[i];
3178:         }
3179:         PetscCall(MatSeqAIJSetPreallocation(pcbddc->benign_B0, 0, nnz));
3180:         PetscCall(MatSetOption(pcbddc->benign_B0, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
3181:         PetscCall(PetscFree(nnz));
3182:       }

3184:       for (i = 0; i < pcbddc->benign_n; i++) {
3185:         PetscScalar *array;
3186:         PetscInt    *idxs, j, nz, cum;

3188:         PetscCall(VecSet(matis->x, 0.));
3189:         PetscCall(ISGetLocalSize(pcbddc->benign_zerodiag_subs[i], &nz));
3190:         PetscCall(ISGetIndices(pcbddc->benign_zerodiag_subs[i], (const PetscInt **)&idxs));
3191:         for (j = 0; j < nz; j++) vals[j] = 1.;
3192:         PetscCall(VecSetValues(matis->x, nz, idxs, vals, INSERT_VALUES));
3193:         PetscCall(VecAssemblyBegin(matis->x));
3194:         PetscCall(VecAssemblyEnd(matis->x));
3195:         PetscCall(VecSet(matis->y, 0.));
3196:         PetscCall(MatMult(matis->A, matis->x, matis->y));
3197:         PetscCall(VecGetArray(matis->y, &array));
3198:         cum = 0;
3199:         for (j = 0; j < n; j++) {
3200:           if (PetscUnlikely(PetscAbsScalar(array[j]) > PETSC_SMALL)) {
3201:             vals[cum]     = array[j];
3202:             idxs_ins[cum] = j;
3203:             cum++;
3204:           }
3205:         }
3206:         PetscCall(MatSetValues(pcbddc->benign_B0, 1, &i, cum, idxs_ins, vals, INSERT_VALUES));
3207:         PetscCall(VecRestoreArray(matis->y, &array));
3208:         PetscCall(ISRestoreIndices(pcbddc->benign_zerodiag_subs[i], (const PetscInt **)&idxs));
3209:       }
3210:       PetscCall(MatAssemblyBegin(pcbddc->benign_B0, MAT_FINAL_ASSEMBLY));
3211:       PetscCall(MatAssemblyEnd(pcbddc->benign_B0, MAT_FINAL_ASSEMBLY));
3212:       PetscCall(PetscFree2(idxs_ins, vals));
3213:     }
3214:   } else { /* push */

3216:     PetscCheck(pcbddc->benign_change_explicit, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot push B0!");
3217:     for (PetscInt i = 0; i < pcbddc->benign_n; i++) {
3218:       PetscScalar *B0_vals;
3219:       PetscInt    *B0_cols, B0_ncol;

3221:       PetscCall(MatGetRow(pcbddc->benign_B0, i, &B0_ncol, (const PetscInt **)&B0_cols, (const PetscScalar **)&B0_vals));
3222:       PetscCall(MatSetValues(pcbddc->local_mat, 1, pcbddc->benign_p0_lidx + i, B0_ncol, B0_cols, B0_vals, INSERT_VALUES));
3223:       PetscCall(MatSetValues(pcbddc->local_mat, B0_ncol, B0_cols, 1, pcbddc->benign_p0_lidx + i, B0_vals, INSERT_VALUES));
3224:       PetscCall(MatSetValue(pcbddc->local_mat, pcbddc->benign_p0_lidx[i], pcbddc->benign_p0_lidx[i], 0.0, INSERT_VALUES));
3225:       PetscCall(MatRestoreRow(pcbddc->benign_B0, i, &B0_ncol, (const PetscInt **)&B0_cols, (const PetscScalar **)&B0_vals));
3226:     }
3227:     PetscCall(MatAssemblyBegin(pcbddc->local_mat, MAT_FINAL_ASSEMBLY));
3228:     PetscCall(MatAssemblyEnd(pcbddc->local_mat, MAT_FINAL_ASSEMBLY));
3229:   }
3230:   PetscFunctionReturn(PETSC_SUCCESS);
3231: }

3233: PetscErrorCode PCBDDCAdaptiveSelection(PC pc)
3234: {
3235:   PC_BDDC        *pcbddc     = (PC_BDDC *)pc->data;
3236:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
3237:   PetscBLASInt    B_dummyint, B_neigs, B_ierr, B_lwork;
3238:   PetscBLASInt   *B_iwork, *B_ifail;
3239:   PetscScalar    *work, lwork;
3240:   PetscScalar    *St, *S, *eigv;
3241:   PetscScalar    *Sarray, *Starray;
3242:   PetscReal      *eigs, thresh, lthresh, uthresh;
3243:   PetscInt        i, nmax, nmin, nv, cum, mss, cum2, cumarray, maxneigs;
3244:   PetscBool       allocated_S_St, upart;
3245: #if defined(PETSC_USE_COMPLEX)
3246:   PetscReal *rwork;
3247: #endif

3249:   PetscFunctionBegin;
3250:   if (!pcbddc->adaptive_selection) PetscFunctionReturn(PETSC_SUCCESS);
3251:   PetscCheck(sub_schurs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Adaptive selection of constraints requires SubSchurs data");
3252:   PetscCheck(sub_schurs->schur_explicit || !sub_schurs->n_subs, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Adaptive selection of constraints requires MUMPS and/or MKL_CPARDISO");
3253:   PetscCheck(!sub_schurs->n_subs || sub_schurs->is_symmetric, PETSC_COMM_SELF, PETSC_ERR_SUP, "Adaptive selection not yet implemented for this matrix pencil (herm %d, symm %d, posdef %d)", sub_schurs->is_hermitian, sub_schurs->is_symmetric,
3254:              sub_schurs->is_posdef);
3255:   PetscCall(PetscLogEventBegin(PC_BDDC_AdaptiveSetUp[pcbddc->current_level], pc, 0, 0, 0));

3257:   if (pcbddc->dbg_flag) {
3258:     if (!pcbddc->dbg_viewer) pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
3259:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
3260:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "--------------------------------------------------\n"));
3261:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "Check adaptive selection of constraints\n"));
3262:     PetscCall(PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer));
3263:   }

3265:   if (pcbddc->dbg_flag) PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d cc %" PetscInt_FMT " (%d,%d).\n", PetscGlobalRank, sub_schurs->n_subs, sub_schurs->is_hermitian, sub_schurs->is_posdef));

3267:   /* max size of subsets */
3268:   mss = 0;
3269:   for (i = 0; i < sub_schurs->n_subs; i++) {
3270:     PetscInt subset_size;

3272:     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
3273:     mss = PetscMax(mss, subset_size);
3274:   }

3276:   /* min/max and threshold */
3277:   nmax           = pcbddc->adaptive_nmax > 0 ? pcbddc->adaptive_nmax : mss;
3278:   nmin           = pcbddc->adaptive_nmin > 0 ? pcbddc->adaptive_nmin : 0;
3279:   nmax           = PetscMax(nmin, nmax);
3280:   allocated_S_St = PETSC_FALSE;
3281:   if (nmin || !sub_schurs->is_posdef) { /* XXX */
3282:     allocated_S_St = PETSC_TRUE;
3283:   }

3285:   /* allocate lapack workspace */
3286:   cum = cum2 = 0;
3287:   maxneigs   = 0;
3288:   for (i = 0; i < sub_schurs->n_subs; i++) {
3289:     PetscInt n, subset_size;

3291:     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
3292:     n = PetscMin(subset_size, nmax);
3293:     cum += subset_size;
3294:     cum2 += subset_size * n;
3295:     maxneigs = PetscMax(maxneigs, n);
3296:   }
3297:   lwork = 0;
3298:   if (mss) {
3299:     PetscScalar  sdummy  = 0.;
3300:     PetscBLASInt B_itype = 1;
3301:     PetscBLASInt B_N, idummy = 0;
3302:     PetscReal    rdummy = 0., zero = 0.0;
3303:     PetscReal    eps = 0.0; /* dlamch? */

3305:     PetscCheck(sub_schurs->is_symmetric, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented");
3306:     PetscCall(PetscBLASIntCast(mss, &B_N));
3307:     B_lwork = -1;
3308:     /* some implementations may complain about NULL pointers, even if we are querying */
3309:     S       = &sdummy;
3310:     St      = &sdummy;
3311:     eigs    = &rdummy;
3312:     eigv    = &sdummy;
3313:     B_iwork = &idummy;
3314:     B_ifail = &idummy;
3315: #if defined(PETSC_USE_COMPLEX)
3316:     rwork = &rdummy;
3317: #endif
3318:     thresh = 1.0;
3319:     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
3320: #if defined(PETSC_USE_COMPLEX)
3321:     PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &zero, &thresh, &B_dummyint, &B_dummyint, &eps, &B_neigs, eigs, eigv, &B_N, &lwork, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3322: #else
3323:     PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &zero, &thresh, &B_dummyint, &B_dummyint, &eps, &B_neigs, eigs, eigv, &B_N, &lwork, &B_lwork, B_iwork, B_ifail, &B_ierr));
3324: #endif
3325:     PetscCheck(B_ierr == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to SYGVX Lapack routine %" PetscBLASInt_FMT, B_ierr);
3326:     PetscCall(PetscFPTrapPop());
3327:   }

3329:   nv = 0;
3330:   if (sub_schurs->is_vertices && pcbddc->use_vertices) { /* complement set of active subsets, each entry is a vertex (boundary made by active subsets, vertices and dirichlet dofs) */
3331:     PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &nv));
3332:   }
3333:   PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(lwork), &B_lwork));
3334:   if (allocated_S_St) PetscCall(PetscMalloc2(mss * mss, &S, mss * mss, &St));
3335:   PetscCall(PetscMalloc5(mss * mss, &eigv, mss, &eigs, B_lwork, &work, 5 * mss, &B_iwork, mss, &B_ifail));
3336: #if defined(PETSC_USE_COMPLEX)
3337:   PetscCall(PetscMalloc1(7 * mss, &rwork));
3338: #endif
3339:   PetscCall(PetscMalloc5(nv + sub_schurs->n_subs, &pcbddc->adaptive_constraints_n, nv + sub_schurs->n_subs + 1, &pcbddc->adaptive_constraints_idxs_ptr, nv + sub_schurs->n_subs + 1, &pcbddc->adaptive_constraints_data_ptr, nv + cum, &pcbddc->adaptive_constraints_idxs, nv + cum2,
3340:                          &pcbddc->adaptive_constraints_data));
3341:   PetscCall(PetscArrayzero(pcbddc->adaptive_constraints_n, nv + sub_schurs->n_subs));

3343:   maxneigs = 0;
3344:   cum = cumarray                           = 0;
3345:   pcbddc->adaptive_constraints_idxs_ptr[0] = 0;
3346:   pcbddc->adaptive_constraints_data_ptr[0] = 0;
3347:   if (sub_schurs->is_vertices && pcbddc->use_vertices) {
3348:     const PetscInt *idxs;

3350:     PetscCall(ISGetIndices(sub_schurs->is_vertices, &idxs));
3351:     for (cum = 0; cum < nv; cum++) {
3352:       pcbddc->adaptive_constraints_n[cum]            = 1;
3353:       pcbddc->adaptive_constraints_idxs[cum]         = idxs[cum];
3354:       pcbddc->adaptive_constraints_data[cum]         = 1.0;
3355:       pcbddc->adaptive_constraints_idxs_ptr[cum + 1] = pcbddc->adaptive_constraints_idxs_ptr[cum] + 1;
3356:       pcbddc->adaptive_constraints_data_ptr[cum + 1] = pcbddc->adaptive_constraints_data_ptr[cum] + 1;
3357:     }
3358:     PetscCall(ISRestoreIndices(sub_schurs->is_vertices, &idxs));
3359:   }

3361:   if (mss) { /* multilevel */
3362:     if (sub_schurs->gdsw) {
3363:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all, &Sarray));
3364:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &Starray));
3365:     } else {
3366:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all, &Sarray));
3367:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &Starray));
3368:     }
3369:   }

3371:   lthresh = pcbddc->adaptive_threshold[0];
3372:   uthresh = pcbddc->adaptive_threshold[1];
3373:   upart   = pcbddc->use_deluxe_scaling;
3374:   for (i = 0; i < sub_schurs->n_subs; i++) {
3375:     const PetscInt *idxs;
3376:     PetscReal       upper, lower;
3377:     PetscInt        j, subset_size, eigs_start = 0;
3378:     PetscBLASInt    B_N;
3379:     PetscBool       same_data = PETSC_FALSE;
3380:     PetscBool       scal      = PETSC_FALSE;

3382:     if (upart) {
3383:       upper = PETSC_MAX_REAL;
3384:       lower = uthresh;
3385:     } else {
3386:       if (sub_schurs->gdsw) {
3387:         upper = uthresh;
3388:         lower = PETSC_MIN_REAL;
3389:       } else {
3390:         PetscCheck(sub_schurs->is_posdef, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented without deluxe scaling");
3391:         upper = 1. / uthresh;
3392:         lower = 0.;
3393:       }
3394:     }
3395:     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
3396:     PetscCall(ISGetIndices(sub_schurs->is_subs[i], &idxs));
3397:     PetscCall(PetscBLASIntCast(subset_size, &B_N));
3398:     /* this is experimental: we assume the dofs have been properly grouped to have
3399:        the diagonal blocks Schur complements either positive or negative definite (true for Stokes) */
3400:     if (!sub_schurs->is_posdef) {
3401:       Mat T;

3403:       for (j = 0; j < subset_size; j++) {
3404:         if (PetscRealPart(*(Sarray + cumarray + j * (subset_size + 1))) < 0.0) {
3405:           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, Sarray + cumarray, &T));
3406:           PetscCall(MatScale(T, -1.0));
3407:           PetscCall(MatDestroy(&T));
3408:           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, Starray + cumarray, &T));
3409:           PetscCall(MatScale(T, -1.0));
3410:           PetscCall(MatDestroy(&T));
3411:           if (sub_schurs->change_primal_sub) {
3412:             PetscInt        nz, k;
3413:             const PetscInt *idxs;

3415:             PetscCall(ISGetLocalSize(sub_schurs->change_primal_sub[i], &nz));
3416:             PetscCall(ISGetIndices(sub_schurs->change_primal_sub[i], &idxs));
3417:             for (k = 0; k < nz; k++) {
3418:               *(Sarray + cumarray + idxs[k] * (subset_size + 1)) *= -1.0;
3419:               *(Starray + cumarray + idxs[k] * (subset_size + 1)) = 0.0;
3420:             }
3421:             PetscCall(ISRestoreIndices(sub_schurs->change_primal_sub[i], &idxs));
3422:           }
3423:           scal = PETSC_TRUE;
3424:           break;
3425:         }
3426:       }
3427:     }

3429:     if (allocated_S_St) { /* S and S_t should be copied since we could need them later */
3430:       if (sub_schurs->is_symmetric) {
3431:         PetscInt j, k;
3432:         if (sub_schurs->n_subs == 1) { /* zeroing memory to use PetscArraycmp() later */
3433:           PetscCall(PetscArrayzero(S, subset_size * subset_size));
3434:           PetscCall(PetscArrayzero(St, subset_size * subset_size));
3435:         }
3436:         for (j = 0; j < subset_size; j++) {
3437:           for (k = j; k < subset_size; k++) {
3438:             S[j * subset_size + k]  = Sarray[cumarray + j * subset_size + k];
3439:             St[j * subset_size + k] = Starray[cumarray + j * subset_size + k];
3440:           }
3441:         }
3442:       } else {
3443:         PetscCall(PetscArraycpy(S, Sarray + cumarray, subset_size * subset_size));
3444:         PetscCall(PetscArraycpy(St, Starray + cumarray, subset_size * subset_size));
3445:       }
3446:     } else {
3447:       S  = Sarray + cumarray;
3448:       St = Starray + cumarray;
3449:     }
3450:     /* see if we can save some work */
3451:     if (sub_schurs->n_subs == 1 && pcbddc->use_deluxe_scaling) PetscCall(PetscArraycmp(S, St, subset_size * subset_size, &same_data));

3453:     if (same_data && !sub_schurs->change) { /* there's no need of constraints here */
3454:       B_neigs = 0;
3455:     } else {
3456:       PetscBLASInt B_itype = 1;
3457:       PetscBLASInt B_IL, B_IU;
3458:       PetscReal    eps = -1.0; /* dlamch? */
3459:       PetscInt     nmin_s;
3460:       PetscBool    compute_range;

3462:       PetscCheck(sub_schurs->is_symmetric, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented");
3463:       B_neigs       = 0;
3464:       compute_range = (PetscBool)!same_data;
3465:       if (nmin >= subset_size) compute_range = PETSC_FALSE;

3467:       if (pcbddc->dbg_flag) {
3468:         PetscInt nc = 0, c = pcbddc->mat_graph->nodes[idxs[0]].count, w = pcbddc->mat_graph->nodes[idxs[0]].which_dof;

3470:         if (sub_schurs->change_primal_sub) PetscCall(ISGetLocalSize(sub_schurs->change_primal_sub[i], &nc));
3471:         PetscCall(
3472:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Computing for sub %" PetscInt_FMT "/%" PetscInt_FMT " size %" PetscInt_FMT " count %" PetscInt_FMT " fid %" PetscInt_FMT " (range %d) (change %" PetscInt_FMT ").\n", i, sub_schurs->n_subs, subset_size, c, w, compute_range, nc));
3473:       }

3475:       PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
3476:       if (compute_range) {
3477:         /* ask for eigenvalues larger than thresh */
3478:         if (sub_schurs->is_posdef) {
3479: #if defined(PETSC_USE_COMPLEX)
3480:           PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3481: #else
3482:           PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3483: #endif
3484:           PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3485:         } else { /* no theory so far, but it works nicely */
3486:           PetscInt  recipe = 0, recipe_m = 1;
3487:           PetscReal bb[2];

3489:           PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)pc)->prefix, "-pc_bddc_adaptive_recipe", &recipe, NULL));
3490:           switch (recipe) {
3491:           case 0:
3492:             if (scal) {
3493:               bb[0] = PETSC_MIN_REAL;
3494:               bb[1] = lthresh;
3495:             } else {
3496:               bb[0] = uthresh;
3497:               bb[1] = PETSC_MAX_REAL;
3498:             }
3499: #if defined(PETSC_USE_COMPLEX)
3500:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3501: #else
3502:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3503: #endif
3504:             PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3505:             break;
3506:           case 1:
3507:             bb[0] = PETSC_MIN_REAL;
3508:             bb[1] = lthresh * lthresh;
3509: #if defined(PETSC_USE_COMPLEX)
3510:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3511: #else
3512:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3513: #endif
3514:             PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3515:             if (!scal) {
3516:               PetscBLASInt B_neigs2 = 0;

3518:               bb[0] = PetscMax(lthresh * lthresh, uthresh);
3519:               bb[1] = PETSC_MAX_REAL;
3520:               PetscCall(PetscArraycpy(S, Sarray + cumarray, subset_size * subset_size));
3521:               PetscCall(PetscArraycpy(St, Starray + cumarray, subset_size * subset_size));
3522: #if defined(PETSC_USE_COMPLEX)
3523:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3524: #else
3525:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3526: #endif
3527:               PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3528:               B_neigs += B_neigs2;
3529:             }
3530:             break;
3531:           case 2:
3532:             if (scal) {
3533:               bb[0] = PETSC_MIN_REAL;
3534:               bb[1] = 0;
3535: #if defined(PETSC_USE_COMPLEX)
3536:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3537: #else
3538:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3539: #endif
3540:               PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3541:             } else {
3542:               PetscBLASInt B_neigs2 = 0;
3543:               PetscBool    do_copy  = PETSC_FALSE;

3545:               lthresh = PetscMax(lthresh, 0.0);
3546:               if (lthresh > 0.0) {
3547:                 bb[0] = PETSC_MIN_REAL;
3548:                 bb[1] = lthresh * lthresh;

3550:                 do_copy = PETSC_TRUE;
3551: #if defined(PETSC_USE_COMPLEX)
3552:                 PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3553: #else
3554:                 PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3555: #endif
3556:                 PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3557:               }
3558:               bb[0] = PetscMax(lthresh * lthresh, uthresh);
3559:               bb[1] = PETSC_MAX_REAL;
3560:               if (do_copy) {
3561:                 PetscCall(PetscArraycpy(S, Sarray + cumarray, subset_size * subset_size));
3562:                 PetscCall(PetscArraycpy(St, Starray + cumarray, subset_size * subset_size));
3563:               }
3564: #if defined(PETSC_USE_COMPLEX)
3565:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3566: #else
3567:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3568: #endif
3569:               PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3570:               B_neigs += B_neigs2;
3571:             }
3572:             break;
3573:           case 3:
3574:             if (scal) {
3575:               PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)pc)->prefix, "-pc_bddc_adaptive_recipe3_min_scal", &recipe_m, NULL));
3576:             } else {
3577:               PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)pc)->prefix, "-pc_bddc_adaptive_recipe3_min", &recipe_m, NULL));
3578:             }
3579:             if (!scal) {
3580:               bb[0] = uthresh;
3581:               bb[1] = PETSC_MAX_REAL;
3582: #if defined(PETSC_USE_COMPLEX)
3583:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3584: #else
3585:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3586: #endif
3587:               PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3588:             }
3589:             if (recipe_m > 0 && B_N - B_neigs > 0) {
3590:               PetscBLASInt B_neigs2 = 0;

3592:               B_IL = 1;
3593:               PetscCall(PetscBLASIntCast(PetscMin(recipe_m, B_N - B_neigs), &B_IU));
3594:               PetscCall(PetscArraycpy(S, Sarray + cumarray, subset_size * subset_size));
3595:               PetscCall(PetscArraycpy(St, Starray + cumarray, subset_size * subset_size));
3596: #if defined(PETSC_USE_COMPLEX)
3597:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "I", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3598: #else
3599:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "I", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3600: #endif
3601:               PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3602:               B_neigs += B_neigs2;
3603:             }
3604:             break;
3605:           case 4:
3606:             bb[0] = PETSC_MIN_REAL;
3607:             bb[1] = lthresh;
3608: #if defined(PETSC_USE_COMPLEX)
3609:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3610: #else
3611:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3612: #endif
3613:             PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3614:             {
3615:               PetscBLASInt B_neigs2 = 0;

3617:               bb[0] = PetscMax(lthresh + PETSC_SMALL, uthresh);
3618:               bb[1] = PETSC_MAX_REAL;
3619:               PetscCall(PetscArraycpy(S, Sarray + cumarray, subset_size * subset_size));
3620:               PetscCall(PetscArraycpy(St, Starray + cumarray, subset_size * subset_size));
3621: #if defined(PETSC_USE_COMPLEX)
3622:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3623: #else
3624:               PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "V", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * B_N, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3625: #endif
3626:               PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3627:               B_neigs += B_neigs2;
3628:             }
3629:             break;
3630:           case 5: /* same as before: first compute all eigenvalues, then filter */
3631: #if defined(PETSC_USE_COMPLEX)
3632:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "A", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3633: #else
3634:             PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "A", "L", &B_N, St, &B_N, S, &B_N, &bb[0], &bb[1], &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3635: #endif
3636:             PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3637:             {
3638:               PetscInt e, k, ne;
3639:               for (e = 0, ne = 0; e < B_neigs; e++) {
3640:                 if (eigs[e] < lthresh || eigs[e] > uthresh) {
3641:                   for (k = 0; k < B_N; k++) S[ne * B_N + k] = eigv[e * B_N + k];
3642:                   eigs[ne] = eigs[e];
3643:                   ne++;
3644:                 }
3645:               }
3646:               PetscCall(PetscArraycpy(eigv, S, B_N * ne));
3647:               PetscCall(PetscBLASIntCast(ne, &B_neigs));
3648:             }
3649:             break;
3650:           default:
3651:             SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unknown recipe %" PetscInt_FMT, recipe);
3652:           }
3653:         }
3654:       } else if (!same_data) { /* this is just to see all the eigenvalues */
3655:         PetscCall(PetscBLASIntCast(PetscMax(1, PetscMin(B_N, nmax)), &B_IU));
3656:         B_IL = 1;
3657: #if defined(PETSC_USE_COMPLEX)
3658:         PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "I", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3659: #else
3660:         PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "I", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs, eigs, eigv, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3661: #endif
3662:         PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3663:       } else { /* same_data is true, so just get the adaptive functional requested by the user */
3664:         PetscInt k;
3665:         PetscCheck(sub_schurs->change_primal_sub, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
3666:         PetscCall(ISGetLocalSize(sub_schurs->change_primal_sub[i], &nmax));
3667:         PetscCall(PetscBLASIntCast(nmax, &B_neigs));
3668:         nmin = nmax;
3669:         PetscCall(PetscArrayzero(eigv, subset_size * nmax));
3670:         for (k = 0; k < nmax; k++) {
3671:           eigs[k]                     = 1. / PETSC_SMALL;
3672:           eigv[k * (subset_size + 1)] = 1.0;
3673:         }
3674:       }
3675:       PetscCall(PetscFPTrapPop());
3676:       if (B_ierr) {
3677:         PetscCheck(B_ierr >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYGVX Lapack routine: illegal value for argument %" PetscBLASInt_FMT, -B_ierr);
3678:         PetscCheck(B_ierr > B_N, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYGVX Lapack routine: %" PetscBLASInt_FMT " eigenvalues failed to converge", B_ierr);
3679:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYGVX Lapack routine: leading minor of order %" PetscBLASInt_FMT " is not positive definite", B_ierr - B_N - 1);
3680:       }

3682:       if (B_neigs > nmax) {
3683:         if (pcbddc->dbg_flag) PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "   found %" PetscBLASInt_FMT " eigs, more than maximum required %" PetscInt_FMT ".\n", B_neigs, nmax));
3684:         if (upart) eigs_start = scal ? 0 : B_neigs - nmax;
3685:         PetscCall(PetscBLASIntCast(nmax, &B_neigs));
3686:       }

3688:       nmin_s = PetscMin(nmin, B_N);
3689:       if (B_neigs < nmin_s) {
3690:         PetscBLASInt B_neigs2 = 0;

3692:         if (upart) {
3693:           if (scal) {
3694:             PetscCall(PetscBLASIntCast(nmin_s, &B_IU));
3695:             B_IL = B_neigs + 1;
3696:           } else {
3697:             PetscCall(PetscBLASIntCast(B_N - nmin_s + 1, &B_IL));
3698:             B_IU = B_N - B_neigs;
3699:           }
3700:         } else {
3701:           B_IL = B_neigs + 1;
3702:           PetscCall(PetscBLASIntCast(nmin_s, &B_IU));
3703:         }
3704:         if (pcbddc->dbg_flag) {
3705:           PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "   found %" PetscBLASInt_FMT " eigs, less than minimum required %" PetscInt_FMT ". Asking for %" PetscBLASInt_FMT " to %" PetscBLASInt_FMT " incl (fortran like)\n", B_neigs, nmin, B_IL, B_IU));
3706:         }
3707:         if (sub_schurs->is_symmetric) {
3708:           PetscInt j, k;
3709:           for (j = 0; j < subset_size; j++) {
3710:             for (k = j; k < subset_size; k++) {
3711:               S[j * subset_size + k]  = Sarray[cumarray + j * subset_size + k];
3712:               St[j * subset_size + k] = Starray[cumarray + j * subset_size + k];
3713:             }
3714:           }
3715:         } else {
3716:           PetscCall(PetscArraycpy(S, Sarray + cumarray, subset_size * subset_size));
3717:           PetscCall(PetscArraycpy(St, Starray + cumarray, subset_size * subset_size));
3718:         }
3719:         PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
3720: #if defined(PETSC_USE_COMPLEX)
3721:         PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "I", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * subset_size, &B_N, work, &B_lwork, rwork, B_iwork, B_ifail, &B_ierr));
3722: #else
3723:         PetscCallBLAS("LAPACKsygvx", LAPACKsygvx_(&B_itype, "V", "I", "L", &B_N, St, &B_N, S, &B_N, &lower, &upper, &B_IL, &B_IU, &eps, &B_neigs2, eigs + B_neigs, eigv + B_neigs * subset_size, &B_N, work, &B_lwork, B_iwork, B_ifail, &B_ierr));
3724: #endif
3725:         PetscCall(PetscLogFlops((4.0 * subset_size * subset_size * subset_size) / 3.0));
3726:         PetscCall(PetscFPTrapPop());
3727:         B_neigs += B_neigs2;
3728:       }
3729:       if (B_ierr) {
3730:         PetscCheck(B_ierr >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYGVX Lapack routine: illegal value for argument %" PetscBLASInt_FMT, -B_ierr);
3731:         PetscCheck(B_ierr > B_N, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYGVX Lapack routine: %" PetscBLASInt_FMT " eigenvalues failed to converge", B_ierr);
3732:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYGVX Lapack routine: leading minor of order %" PetscBLASInt_FMT " is not positive definite", B_ierr - B_N - 1);
3733:       }
3734:       if (pcbddc->dbg_flag) {
3735:         PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "   -> Got %" PetscBLASInt_FMT " eigs\n", B_neigs));
3736:         for (j = 0; j < B_neigs; j++) {
3737:           if (!sub_schurs->gdsw) {
3738:             if (eigs[j] == 0.0) {
3739:               PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "     Inf\n"));
3740:             } else {
3741:               if (upart) {
3742:                 PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "     %1.6e\n", (double)eigs[j + eigs_start]));
3743:               } else {
3744:                 PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "     %1.6e\n", (double)(1 / eigs[j + eigs_start])));
3745:               }
3746:             }
3747:           } else {
3748:             double pg = (double)eigs[j + eigs_start];
3749:             if (pg < 2 * PETSC_SMALL) pg = 0.0;
3750:             PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "     %1.6e\n", pg));
3751:           }
3752:         }
3753:       }
3754:     }
3755:     /* change the basis back to the original one */
3756:     if (sub_schurs->change) {
3757:       Mat change, phi, phit;

3759:       if (pcbddc->dbg_flag > 2) {
3760:         PetscInt ii;
3761:         for (ii = 0; ii < B_neigs; ii++) {
3762:           PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "   -> Eigenvector (old basis) %" PetscInt_FMT "/%" PetscBLASInt_FMT " (%" PetscBLASInt_FMT ")\n", ii, B_neigs, B_N));
3763:           for (j = 0; j < B_N; j++) {
3764: #if defined(PETSC_USE_COMPLEX)
3765:             PetscReal r = PetscRealPart(eigv[(ii + eigs_start) * subset_size + j]);
3766:             PetscReal c = PetscImaginaryPart(eigv[(ii + eigs_start) * subset_size + j]);
3767:             PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "       %1.4e + %1.4e i\n", (double)r, (double)c));
3768: #else
3769:             PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "       %1.4e\n", (double)(eigv[(ii + eigs_start) * subset_size + j])));
3770: #endif
3771:           }
3772:         }
3773:       }
3774:       PetscCall(KSPGetOperators(sub_schurs->change[i], &change, NULL));
3775:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, B_neigs, eigv + eigs_start * subset_size, &phit));
3776:       PetscCall(MatMatMult(change, phit, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &phi));
3777:       PetscCall(MatCopy(phi, phit, SAME_NONZERO_PATTERN));
3778:       PetscCall(MatDestroy(&phit));
3779:       PetscCall(MatDestroy(&phi));
3780:     }
3781:     maxneigs                               = PetscMax(B_neigs, maxneigs);
3782:     pcbddc->adaptive_constraints_n[i + nv] = B_neigs;
3783:     if (B_neigs) {
3784:       PetscCall(PetscArraycpy(pcbddc->adaptive_constraints_data + pcbddc->adaptive_constraints_data_ptr[cum], eigv + eigs_start * subset_size, B_neigs * subset_size));

3786:       if (pcbddc->dbg_flag > 1) {
3787:         PetscInt ii;
3788:         for (ii = 0; ii < B_neigs; ii++) {
3789:           PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "   -> Eigenvector %" PetscInt_FMT "/%" PetscBLASInt_FMT " (%" PetscBLASInt_FMT ")\n", ii, B_neigs, B_N));
3790:           for (j = 0; j < B_N; j++) {
3791: #if defined(PETSC_USE_COMPLEX)
3792:             PetscReal r = PetscRealPart(pcbddc->adaptive_constraints_data[ii * subset_size + j + pcbddc->adaptive_constraints_data_ptr[cum]]);
3793:             PetscReal c = PetscImaginaryPart(pcbddc->adaptive_constraints_data[ii * subset_size + j + pcbddc->adaptive_constraints_data_ptr[cum]]);
3794:             PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "       %1.4e + %1.4e i\n", (double)r, (double)c));
3795: #else
3796:             PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "       %1.4e\n", (double)PetscRealPart(pcbddc->adaptive_constraints_data[ii * subset_size + j + pcbddc->adaptive_constraints_data_ptr[cum]])));
3797: #endif
3798:           }
3799:         }
3800:       }
3801:       PetscCall(PetscArraycpy(pcbddc->adaptive_constraints_idxs + pcbddc->adaptive_constraints_idxs_ptr[cum], idxs, subset_size));
3802:       pcbddc->adaptive_constraints_idxs_ptr[cum + 1] = pcbddc->adaptive_constraints_idxs_ptr[cum] + subset_size;
3803:       pcbddc->adaptive_constraints_data_ptr[cum + 1] = pcbddc->adaptive_constraints_data_ptr[cum] + subset_size * B_neigs;
3804:       cum++;
3805:     }
3806:     PetscCall(ISRestoreIndices(sub_schurs->is_subs[i], &idxs));
3807:     /* shift for next computation */
3808:     cumarray += subset_size * subset_size;
3809:   }
3810:   if (pcbddc->dbg_flag) PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));

3812:   if (mss) {
3813:     if (sub_schurs->gdsw) {
3814:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all, &Sarray));
3815:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &Starray));
3816:     } else {
3817:       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all, &Sarray));
3818:       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &Starray));
3819:       /* destroy matrices (junk) */
3820:       PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_inv_all));
3821:       PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_tilda_all));
3822:     }
3823:   }
3824:   if (allocated_S_St) PetscCall(PetscFree2(S, St));
3825:   PetscCall(PetscFree5(eigv, eigs, work, B_iwork, B_ifail));
3826: #if defined(PETSC_USE_COMPLEX)
3827:   PetscCall(PetscFree(rwork));
3828: #endif
3829:   if (pcbddc->dbg_flag) {
3830:     PetscInt maxneigs_r;
3831:     PetscCallMPI(MPIU_Allreduce(&maxneigs, &maxneigs_r, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)pc)));
3832:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "Maximum number of constraints per cc %" PetscInt_FMT "\n", maxneigs_r));
3833:   }
3834:   PetscCall(PetscLogEventEnd(PC_BDDC_AdaptiveSetUp[pcbddc->current_level], pc, 0, 0, 0));
3835:   PetscFunctionReturn(PETSC_SUCCESS);
3836: }

3838: PetscErrorCode PCBDDCSetUpSolvers(PC pc)
3839: {
3840:   Mat coarse_submat;

3842:   PetscFunctionBegin;
3843:   /* Setup local scatters R_to_B and (optionally) R_to_D */
3844:   /* PCBDDCSetUpLocalWorkVectors should be called first! */
3845:   PetscCall(PCBDDCSetUpLocalScatters(pc));

3847:   /* Setup local neumann solver ksp_R */
3848:   /* PCBDDCSetUpLocalScatters should be called first! */
3849:   PetscCall(PCBDDCSetUpLocalSolvers(pc, PETSC_FALSE, PETSC_TRUE));

3851:   /*
3852:      Setup local correction and local part of coarse basis.
3853:      Gives back the dense local part of the coarse matrix in column major ordering
3854:   */
3855:   PetscCall(PCBDDCSetUpCorrection(pc, &coarse_submat));

3857:   /* Compute total number of coarse nodes and setup coarse solver */
3858:   PetscCall(PCBDDCSetUpCoarseSolver(pc, coarse_submat));
3859:   PetscCall(MatDestroy(&coarse_submat));
3860:   PetscFunctionReturn(PETSC_SUCCESS);
3861: }

3863: PetscErrorCode PCBDDCResetCustomization(PC pc)
3864: {
3865:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;

3867:   PetscFunctionBegin;
3868:   PetscCall(ISDestroy(&pcbddc->user_primal_vertices));
3869:   PetscCall(ISDestroy(&pcbddc->user_primal_vertices_local));
3870:   PetscCall(ISDestroy(&pcbddc->NeumannBoundaries));
3871:   PetscCall(ISDestroy(&pcbddc->NeumannBoundariesLocal));
3872:   PetscCall(ISDestroy(&pcbddc->DirichletBoundaries));
3873:   PetscCall(MatNullSpaceDestroy(&pcbddc->onearnullspace));
3874:   PetscCall(PetscFree(pcbddc->onearnullvecs_state));
3875:   PetscCall(ISDestroy(&pcbddc->DirichletBoundariesLocal));
3876:   PetscCall(PCBDDCSetDofsSplitting(pc, 0, NULL));
3877:   PetscCall(PCBDDCSetDofsSplittingLocal(pc, 0, NULL));
3878:   PetscFunctionReturn(PETSC_SUCCESS);
3879: }

3881: PetscErrorCode PCBDDCResetTopography(PC pc)
3882: {
3883:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;
3884:   PetscInt i;

3886:   PetscFunctionBegin;
3887:   PetscCall(MatDestroy(&pcbddc->nedcG));
3888:   PetscCall(ISDestroy(&pcbddc->nedclocal));
3889:   PetscCall(MatDestroy(&pcbddc->discretegradient));
3890:   PetscCall(MatDestroy(&pcbddc->user_ChangeOfBasisMatrix));
3891:   PetscCall(MatDestroy(&pcbddc->ChangeOfBasisMatrix));
3892:   PetscCall(MatDestroy(&pcbddc->switch_static_change));
3893:   PetscCall(VecDestroy(&pcbddc->work_change));
3894:   PetscCall(MatDestroy(&pcbddc->ConstraintMatrix));
3895:   PetscCall(MatDestroy(&pcbddc->divudotp));
3896:   PetscCall(ISDestroy(&pcbddc->divudotp_vl2l));
3897:   PetscCall(PCBDDCGraphDestroy(&pcbddc->mat_graph));
3898:   for (i = 0; i < pcbddc->n_local_subs; i++) PetscCall(ISDestroy(&pcbddc->local_subs[i]));
3899:   pcbddc->n_local_subs = 0;
3900:   PetscCall(PetscFree(pcbddc->local_subs));
3901:   PetscCall(PCBDDCSubSchursDestroy(&pcbddc->sub_schurs));
3902:   pcbddc->graphanalyzed        = PETSC_FALSE;
3903:   pcbddc->recompute_topography = PETSC_TRUE;
3904:   pcbddc->corner_selected      = PETSC_FALSE;
3905:   PetscFunctionReturn(PETSC_SUCCESS);
3906: }

3908: PetscErrorCode PCBDDCResetSolvers(PC pc)
3909: {
3910:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;

3912:   PetscFunctionBegin;
3913:   PetscCall(VecDestroy(&pcbddc->coarse_vec));
3914:   PetscCall(MatDestroy(&pcbddc->coarse_phi_B));
3915:   PetscCall(MatDestroy(&pcbddc->coarse_phi_D));
3916:   PetscCall(MatDestroy(&pcbddc->coarse_psi_B));
3917:   PetscCall(MatDestroy(&pcbddc->coarse_psi_D));
3918:   PetscCall(VecDestroy(&pcbddc->vec1_P));
3919:   PetscCall(VecDestroy(&pcbddc->vec1_C));
3920:   PetscCall(MatDestroy(&pcbddc->local_auxmat2));
3921:   PetscCall(MatDestroy(&pcbddc->local_auxmat1));
3922:   PetscCall(VecDestroy(&pcbddc->vec1_R));
3923:   PetscCall(VecDestroy(&pcbddc->vec2_R));
3924:   PetscCall(ISDestroy(&pcbddc->is_R_local));
3925:   PetscCall(VecScatterDestroy(&pcbddc->R_to_B));
3926:   PetscCall(VecScatterDestroy(&pcbddc->R_to_D));
3927:   PetscCall(VecScatterDestroy(&pcbddc->coarse_loc_to_glob));
3928:   PetscCall(KSPReset(pcbddc->ksp_D));
3929:   PetscCall(KSPReset(pcbddc->ksp_R));
3930:   PetscCall(KSPReset(pcbddc->coarse_ksp));
3931:   PetscCall(MatDestroy(&pcbddc->local_mat));
3932:   PetscCall(PetscFree(pcbddc->primal_indices_local_idxs));
3933:   PetscCall(PetscFree2(pcbddc->local_primal_ref_node, pcbddc->local_primal_ref_mult));
3934:   PetscCall(PetscFree(pcbddc->global_primal_indices));
3935:   PetscCall(ISDestroy(&pcbddc->coarse_subassembling));
3936:   PetscCall(MatDestroy(&pcbddc->benign_change));
3937:   PetscCall(VecDestroy(&pcbddc->benign_vec));
3938:   PetscCall(PCBDDCBenignShellMat(pc, PETSC_TRUE));
3939:   PetscCall(MatDestroy(&pcbddc->benign_B0));
3940:   PetscCall(PetscSFDestroy(&pcbddc->benign_sf));
3941:   if (pcbddc->benign_zerodiag_subs) {
3942:     PetscInt i;
3943:     for (i = 0; i < pcbddc->benign_n; i++) PetscCall(ISDestroy(&pcbddc->benign_zerodiag_subs[i]));
3944:     PetscCall(PetscFree(pcbddc->benign_zerodiag_subs));
3945:   }
3946:   PetscCall(PetscFree3(pcbddc->benign_p0_lidx, pcbddc->benign_p0_gidx, pcbddc->benign_p0));
3947:   PetscFunctionReturn(PETSC_SUCCESS);
3948: }

3950: PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
3951: {
3952:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;
3953:   PC_IS   *pcis   = (PC_IS *)pc->data;
3954:   VecType  impVecType;
3955:   PetscInt n_constraints, n_R, old_size;

3957:   PetscFunctionBegin;
3958:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - pcbddc->n_vertices;
3959:   n_R           = pcis->n - pcbddc->n_vertices;
3960:   PetscCall(VecGetType(pcis->vec1_N, &impVecType));
3961:   /* local work vectors (try to avoid unneeded work)*/
3962:   /* R nodes */
3963:   old_size = -1;
3964:   if (pcbddc->vec1_R) PetscCall(VecGetSize(pcbddc->vec1_R, &old_size));
3965:   if (n_R != old_size) {
3966:     PetscCall(VecDestroy(&pcbddc->vec1_R));
3967:     PetscCall(VecDestroy(&pcbddc->vec2_R));
3968:     PetscCall(VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N), &pcbddc->vec1_R));
3969:     PetscCall(VecSetSizes(pcbddc->vec1_R, PETSC_DECIDE, n_R));
3970:     PetscCall(VecSetType(pcbddc->vec1_R, impVecType));
3971:     PetscCall(VecDuplicate(pcbddc->vec1_R, &pcbddc->vec2_R));
3972:   }
3973:   /* local primal dofs */
3974:   old_size = -1;
3975:   if (pcbddc->vec1_P) PetscCall(VecGetSize(pcbddc->vec1_P, &old_size));
3976:   if (pcbddc->local_primal_size != old_size) {
3977:     PetscCall(VecDestroy(&pcbddc->vec1_P));
3978:     PetscCall(VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N), &pcbddc->vec1_P));
3979:     PetscCall(VecSetSizes(pcbddc->vec1_P, PETSC_DECIDE, pcbddc->local_primal_size));
3980:     PetscCall(VecSetType(pcbddc->vec1_P, impVecType));
3981:   }
3982:   /* local explicit constraints */
3983:   old_size = -1;
3984:   if (pcbddc->vec1_C) PetscCall(VecGetSize(pcbddc->vec1_C, &old_size));
3985:   if (n_constraints && n_constraints != old_size) {
3986:     PetscCall(VecDestroy(&pcbddc->vec1_C));
3987:     PetscCall(VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N), &pcbddc->vec1_C));
3988:     PetscCall(VecSetSizes(pcbddc->vec1_C, PETSC_DECIDE, n_constraints));
3989:     PetscCall(VecSetType(pcbddc->vec1_C, impVecType));
3990:   }
3991:   PetscFunctionReturn(PETSC_SUCCESS);
3992: }

3994: static PetscErrorCode MatSetValuesSubMat(Mat A, Mat S, PetscInt nr, const PetscInt rows[], PetscInt nc, const PetscInt cols[], InsertMode imode)
3995: {
3996:   PetscBool          flg;
3997:   const PetscScalar *a;

3999:   PetscFunctionBegin;
4000:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)S, MATSEQDENSE, &flg));
4001:   if (flg) {
4002:     PetscCall(MatDenseGetArrayRead(S, &a));
4003:     PetscCall(MatSetOption(A, MAT_ROW_ORIENTED, PETSC_FALSE));
4004:     PetscCall(MatSetValues(A, nr, rows, nc, cols, a, imode));
4005:     PetscCall(MatSetOption(A, MAT_ROW_ORIENTED, PETSC_TRUE));
4006:     PetscCall(MatDenseRestoreArrayRead(S, &a));
4007:   } else {
4008:     const PetscInt *ii, *jj;
4009:     PetscInt        n;
4010:     PetscInt        buf[8192], *bufc = NULL;
4011:     PetscBool       freeb = PETSC_FALSE;
4012:     Mat             Sm    = S;

4014:     PetscCall(PetscObjectBaseTypeCompare((PetscObject)S, MATSEQAIJ, &flg));
4015:     if (!flg) PetscCall(MatConvert(S, MATSEQAIJ, MAT_INITIAL_MATRIX, &Sm));
4016:     else PetscCall(PetscObjectReference((PetscObject)S));
4017:     PetscCall(MatSeqAIJGetArrayRead(Sm, &a));
4018:     PetscCall(MatGetRowIJ(Sm, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, &jj, &flg));
4019:     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot get IJ structure");
4020:     if (nc <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
4021:       bufc = buf;
4022:     } else {
4023:       PetscCall(PetscMalloc1(nc, &bufc));
4024:       freeb = PETSC_TRUE;
4025:     }

4027:     for (PetscInt i = 0; i < n; i++) {
4028:       const PetscInt nci = ii[i + 1] - ii[i];

4030:       for (PetscInt j = 0; j < nci; j++) bufc[j] = cols[jj[ii[i] + j]];
4031:       PetscCall(MatSetValues(A, 1, rows + i, nci, bufc, a + ii[i], imode));
4032:     }
4033:     PetscCall(MatRestoreRowIJ(Sm, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, &jj, &flg));
4034:     PetscCall(MatSeqAIJRestoreArrayRead(Sm, &a));
4035:     PetscCall(MatDestroy(&Sm));
4036:     if (freeb) PetscCall(PetscFree(bufc));
4037:   }
4038:   PetscCall(MatAssemblyBegin(A, MAT_FLUSH_ASSEMBLY));
4039:   PetscCall(MatAssemblyEnd(A, MAT_FLUSH_ASSEMBLY));
4040:   PetscFunctionReturn(PETSC_SUCCESS);
4041: }

4043: static PetscErrorCode MatCreateSeqAIJFromDenseExpand(Mat D, PetscInt n, const PetscInt j[], Mat *mat)
4044: {
4045:   Mat_SeqAIJ        *aij;
4046:   PetscInt          *ii, *jj;
4047:   PetscScalar       *aa;
4048:   PetscInt           nnz = 0, m, nc;
4049:   const PetscScalar *a;
4050:   const PetscScalar  zero = 0.0;

4052:   PetscFunctionBegin;
4053:   PetscCall(MatGetLocalSize(D, &m, &nc));
4054:   PetscCall(MatDenseGetArrayRead(D, &a));
4055:   PetscCall(PetscMalloc1(m + 1, &ii));
4056:   PetscCall(PetscMalloc1(m * nc, &jj));
4057:   PetscCall(PetscMalloc1(m * nc, &aa));
4058:   ii[0] = 0;
4059:   for (PetscInt k = 0; k < m; k++) {
4060:     for (PetscInt s = 0; s < nc; s++) {
4061:       const PetscInt    c = s + k * nc;
4062:       const PetscScalar v = a[k + s * m];

4064:       if (PetscUnlikely(j[c] < 0 || v == zero)) continue;
4065:       jj[nnz] = j[c];
4066:       aa[nnz] = a[k + s * m];
4067:       nnz++;
4068:     }
4069:     ii[k + 1] = nnz;
4070:   }

4072:   PetscCall(MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)D), m, n, ii, jj, aa, mat));
4073:   PetscCall(MatDenseRestoreArrayRead(D, &a));

4075:   aij          = (Mat_SeqAIJ *)(*mat)->data;
4076:   aij->free_a  = PETSC_TRUE;
4077:   aij->free_ij = PETSC_TRUE;
4078:   PetscFunctionReturn(PETSC_SUCCESS);
4079: }

4081: /* adapted from MatInvertVariableBlockDiagonal_SeqAIJ */
4082: static PetscErrorCode MatSeqAIJInvertVariableBlockDiagonalMat(Mat A, PetscInt nblocks, const PetscInt *bsizes, Mat *B)
4083: {
4084:   PetscInt        n = A->rmap->n, ncnt = 0, ncnt2 = 0, bsizemax = 0, *v_pivots = NULL;
4085:   const PetscBool allowzeropivot    = PETSC_FALSE;
4086:   PetscBool       zeropivotdetected = PETSC_FALSE;
4087:   const PetscReal shift             = 0.0;
4088:   PetscInt        ipvt[5], *ii, *jj, *indi, *indj;
4089:   PetscScalar     work[25], *v_work = NULL, *aa, *diag;
4090:   PetscLogDouble  flops = 0.0;

4092:   PetscFunctionBegin;
4093:   PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Not for rectangular matrices");
4094:   for (PetscInt i = 0; i < nblocks; i++) {
4095:     ncnt += bsizes[i];
4096:     ncnt2 += PetscSqr(bsizes[i]);
4097:   }
4098:   PetscCheck(ncnt == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Total blocksizes %" PetscInt_FMT " doesn't match number matrix rows %" PetscInt_FMT, ncnt, n);
4099:   for (PetscInt i = 0; i < nblocks; i++) bsizemax = PetscMax(bsizemax, bsizes[i]);
4100:   if (bsizemax > 7) PetscCall(PetscMalloc2(bsizemax, &v_work, bsizemax, &v_pivots));

4102:   PetscCall(PetscMalloc1(n + 1, &ii));
4103:   PetscCall(PetscMalloc1(ncnt2, &jj));
4104:   PetscCall(PetscCalloc1(ncnt2, &aa));

4106:   ncnt  = 0;
4107:   ii[0] = 0;
4108:   indi  = ii;
4109:   indj  = jj;
4110:   diag  = aa;
4111:   for (PetscInt i = 0; i < nblocks; i++) {
4112:     const PetscInt bs = bsizes[i];

4114:     for (PetscInt k = 0; k < bs; k++) {
4115:       indi[k + 1] = indi[k] + bs;
4116:       for (PetscInt j = 0; j < bs; j++) indj[k * bs + j] = ncnt + j;
4117:     }
4118:     PetscCall(MatGetValues(A, bs, indj, bs, indj, diag));
4119:     switch (bs) {
4120:     case 1:
4121:       *diag = 1.0 / (*diag);
4122:       break;
4123:     case 2:
4124:       PetscCall(PetscKernel_A_gets_inverse_A_2(diag, shift, allowzeropivot, &zeropivotdetected));
4125:       break;
4126:     case 3:
4127:       PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
4128:       break;
4129:     case 4:
4130:       PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
4131:       break;
4132:     case 5:
4133:       PetscCall(PetscKernel_A_gets_inverse_A_5(diag, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
4134:       break;
4135:     case 6:
4136:       PetscCall(PetscKernel_A_gets_inverse_A_6(diag, shift, allowzeropivot, &zeropivotdetected));
4137:       break;
4138:     case 7:
4139:       PetscCall(PetscKernel_A_gets_inverse_A_7(diag, shift, allowzeropivot, &zeropivotdetected));
4140:       break;
4141:     default:
4142:       PetscCall(PetscKernel_A_gets_inverse_A(bs, diag, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
4143:     }
4144:     ncnt += bs;
4145:     flops += 2.0 * PetscPowInt(bs, 3) / 3.0;
4146:     diag += bs * bs;
4147:     indj += bs * bs;
4148:     indi += bs;
4149:   }
4150:   PetscCall(PetscLogFlops(flops));
4151:   PetscCall(PetscFree2(v_work, v_pivots));
4152:   PetscCall(MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A), n, n, ii, jj, aa, B));
4153:   {
4154:     Mat_SeqAIJ *aij = (Mat_SeqAIJ *)(*B)->data;
4155:     aij->free_a     = PETSC_TRUE;
4156:     aij->free_ij    = PETSC_TRUE;
4157:   }
4158:   PetscFunctionReturn(PETSC_SUCCESS);
4159: }

4161: static PetscErrorCode MatDenseScatter(Mat A, PetscSF sf, Mat B)
4162: {
4163:   const PetscScalar *rarr;
4164:   PetscScalar       *larr;
4165:   PetscSF            vsf;
4166:   PetscInt           n, rld, lld;

4168:   PetscFunctionBegin;
4169:   PetscCall(MatGetSize(A, NULL, &n));
4170:   PetscCall(MatDenseGetLDA(A, &rld));
4171:   PetscCall(MatDenseGetLDA(B, &lld));
4172:   PetscCall(MatDenseGetArrayRead(A, &rarr));
4173:   PetscCall(MatDenseGetArrayWrite(B, &larr));
4174:   PetscCall(PetscSFCreateStridedSF(sf, n, rld, lld, &vsf));
4175:   PetscCall(PetscSFBcastBegin(vsf, MPIU_SCALAR, rarr, larr, MPI_REPLACE));
4176:   PetscCall(PetscSFBcastEnd(vsf, MPIU_SCALAR, rarr, larr, MPI_REPLACE));
4177:   PetscCall(MatDenseRestoreArrayRead(A, &rarr));
4178:   PetscCall(MatDenseRestoreArrayWrite(B, &larr));
4179:   PetscCall(PetscSFDestroy(&vsf));
4180:   PetscFunctionReturn(PETSC_SUCCESS);
4181: }

4183: PetscErrorCode PCBDDCSetUpCorrection(PC pc, Mat *coarse_submat)
4184: {
4185:   PC_IS          *pcis       = (PC_IS *)pc->data;
4186:   PC_BDDC        *pcbddc     = (PC_BDDC *)pc->data;
4187:   PCBDDCGraph     graph      = pcbddc->mat_graph;
4188:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
4189:   /* submatrices of local problem */
4190:   Mat A_RV = NULL, A_VR, A_VV, local_auxmat2_R = NULL;
4191:   /* submatrices of local coarse problem */
4192:   Mat S_CV = NULL, S_VC = NULL, S_CC = NULL;
4193:   /* working matrices */
4194:   Mat C_CR;

4196:   /* additional working stuff */
4197:   PC              pc_R;
4198:   IS              is_R, is_V, is_C;
4199:   const PetscInt *idx_V, *idx_C;
4200:   Mat             F, Brhs = NULL;
4201:   Vec             dummy_vec;
4202:   PetscBool       isLU, isCHOL, need_benign_correction, sparserhs;
4203:   PetscInt       *idx_V_B;
4204:   PetscInt        lda_rhs, n_vertices, n_constraints, *p0_lidx_I;
4205:   PetscInt        n_eff_vertices, n_eff_constraints;
4206:   PetscInt        i, n_R, n_D, n_B;
4207:   PetscScalar     one = 1.0, m_one = -1.0;

4209:   /* Multi-element support */
4210:   PetscBool multi_element = graph->multi_element;
4211:   PetscInt *V_to_eff_V = NULL, *C_to_eff_C = NULL;
4212:   PetscInt *B_eff_V_J = NULL, *R_eff_V_J = NULL, *B_eff_C_J = NULL, *R_eff_C_J = NULL;
4213:   IS        is_C_perm = NULL;
4214:   PetscInt  n_C_bss = 0, *C_bss = NULL;
4215:   Mat       coarse_phi_multi;

4217:   PetscFunctionBegin;
4218:   PetscCheck(pcbddc->symmetric_primal || !pcbddc->benign_n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Non-symmetric primal basis computation with benign trick not yet implemented");
4219:   PetscCall(PetscLogEventBegin(PC_BDDC_CorrectionSetUp[pcbddc->current_level], pc, 0, 0, 0));

4221:   /* Set Non-overlapping dimensions */
4222:   n_vertices    = pcbddc->n_vertices;
4223:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - n_vertices;
4224:   n_B           = pcis->n_B;
4225:   n_D           = pcis->n - n_B;
4226:   n_R           = pcis->n - n_vertices;

4228:   /* vertices in boundary numbering */
4229:   PetscCall(PetscMalloc1(n_vertices, &idx_V_B));
4230:   PetscCall(ISGlobalToLocalMappingApply(pcis->BtoNmap, IS_GTOLM_DROP, n_vertices, pcbddc->local_primal_ref_node, &i, idx_V_B));
4231:   PetscCheck(i == n_vertices, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error in boundary numbering for BDDC vertices! %" PetscInt_FMT " != %" PetscInt_FMT, n_vertices, i);

4233:   /* these two cases still need to be optimized */
4234:   if (pcbddc->benign_saddle_point || !pcbddc->symmetric_primal) multi_element = PETSC_FALSE;

4236:   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
4237:   if (multi_element) {
4238:     PetscCheck(!pcbddc->benign_n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented");

4240:     PetscCall(MatCreate(PETSC_COMM_SELF, coarse_submat));
4241:     PetscCall(MatSetSizes(*coarse_submat, pcbddc->local_primal_size, pcbddc->local_primal_size, pcbddc->local_primal_size, pcbddc->local_primal_size));
4242:     PetscCall(MatSetType(*coarse_submat, MATSEQAIJ));
4243:     PetscCall(MatSetOption(*coarse_submat, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
4244:     PetscCall(MatSetOption(*coarse_submat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

4246:     /* group vertices and constraints by subdomain id */
4247:     const PetscInt *vidxs = pcbddc->primal_indices_local_idxs;
4248:     const PetscInt *cidxs = pcbddc->primal_indices_local_idxs + n_vertices;
4249:     PetscInt       *count_eff, *V_eff_to_V, *C_eff_to_C, *nnz;
4250:     PetscInt        n_el = PetscMax(graph->n_local_subs, 1);

4252:     PetscCall(PetscCalloc1(2 * n_el, &count_eff));
4253:     PetscCall(PetscMalloc1(n_vertices, &V_to_eff_V));
4254:     PetscCall(PetscMalloc1(n_constraints, &C_to_eff_C));
4255:     for (PetscInt i = 0; i < n_vertices; i++) {
4256:       PetscInt s = 2 * graph->nodes[vidxs[i]].local_sub;

4258:       V_to_eff_V[i] = count_eff[s];
4259:       count_eff[s] += 1;
4260:     }
4261:     for (PetscInt i = 0; i < n_constraints; i++) {
4262:       PetscInt s = 2 * graph->nodes[cidxs[i]].local_sub + 1;

4264:       C_to_eff_C[i] = count_eff[s];
4265:       count_eff[s] += 1;
4266:     }

4268:     /* preallocation */
4269:     PetscCall(PetscMalloc1(n_vertices + n_constraints, &nnz));
4270:     for (PetscInt i = 0; i < n_vertices; i++) {
4271:       PetscInt s = 2 * graph->nodes[vidxs[i]].local_sub;

4273:       nnz[i] = count_eff[s] + count_eff[s + 1];
4274:     }
4275:     for (PetscInt i = 0; i < n_constraints; i++) {
4276:       PetscInt s = 2 * graph->nodes[cidxs[i]].local_sub;

4278:       nnz[i + n_vertices] = count_eff[s] + count_eff[s + 1];
4279:     }
4280:     PetscCall(MatSeqAIJSetPreallocation(*coarse_submat, 0, nnz));
4281:     PetscCall(PetscFree(nnz));

4283:     n_eff_vertices    = 0;
4284:     n_eff_constraints = 0;
4285:     for (PetscInt i = 0; i < n_el; i++) {
4286:       n_eff_vertices       = PetscMax(n_eff_vertices, count_eff[2 * i]);
4287:       n_eff_constraints    = PetscMax(n_eff_constraints, count_eff[2 * i + 1]);
4288:       count_eff[2 * i]     = 0;
4289:       count_eff[2 * i + 1] = 0;
4290:     }

4292:     const PetscInt *idx;
4293:     PetscCall(PetscMalloc2(n_el * n_eff_vertices, &V_eff_to_V, n_el * n_eff_constraints, &C_eff_to_C));

4295:     for (PetscInt i = 0; i < n_vertices; i++) {
4296:       const PetscInt e = graph->nodes[vidxs[i]].local_sub;
4297:       const PetscInt s = 2 * e;

4299:       V_eff_to_V[e * n_eff_vertices + count_eff[s]] = i;
4300:       count_eff[s] += 1;
4301:     }
4302:     for (PetscInt i = 0; i < n_constraints; i++) {
4303:       const PetscInt e = graph->nodes[cidxs[i]].local_sub;
4304:       const PetscInt s = 2 * e + 1;

4306:       C_eff_to_C[e * n_eff_constraints + count_eff[s]] = i;
4307:       count_eff[s] += 1;
4308:     }

4310:     PetscCall(PetscMalloc1(n_R * n_eff_vertices, &R_eff_V_J));
4311:     PetscCall(PetscMalloc1(n_R * n_eff_constraints, &R_eff_C_J));
4312:     PetscCall(PetscMalloc1(n_B * n_eff_vertices, &B_eff_V_J));
4313:     PetscCall(PetscMalloc1(n_B * n_eff_constraints, &B_eff_C_J));
4314:     for (PetscInt i = 0; i < n_R * n_eff_vertices; i++) R_eff_V_J[i] = -1;
4315:     for (PetscInt i = 0; i < n_R * n_eff_constraints; i++) R_eff_C_J[i] = -1;
4316:     for (PetscInt i = 0; i < n_B * n_eff_vertices; i++) B_eff_V_J[i] = -1;
4317:     for (PetscInt i = 0; i < n_B * n_eff_constraints; i++) B_eff_C_J[i] = -1;

4319:     PetscCall(ISGetIndices(pcbddc->is_R_local, &idx));
4320:     for (PetscInt i = 0; i < n_R; i++) {
4321:       const PetscInt e = graph->nodes[idx[i]].local_sub;
4322:       const PetscInt s = 2 * e;
4323:       PetscInt       j;

4325:       for (j = 0; j < count_eff[s]; j++) R_eff_V_J[i * n_eff_vertices + j] = V_eff_to_V[e * n_eff_vertices + j];
4326:       for (j = 0; j < count_eff[s + 1]; j++) R_eff_C_J[i * n_eff_constraints + j] = C_eff_to_C[e * n_eff_constraints + j];
4327:     }
4328:     PetscCall(ISRestoreIndices(pcbddc->is_R_local, &idx));
4329:     PetscCall(ISGetIndices(pcis->is_B_local, &idx));
4330:     for (PetscInt i = 0; i < n_B; i++) {
4331:       const PetscInt e = graph->nodes[idx[i]].local_sub;
4332:       const PetscInt s = 2 * e;
4333:       PetscInt       j;

4335:       for (j = 0; j < count_eff[s]; j++) B_eff_V_J[i * n_eff_vertices + j] = V_eff_to_V[e * n_eff_vertices + j];
4336:       for (j = 0; j < count_eff[s + 1]; j++) B_eff_C_J[i * n_eff_constraints + j] = C_eff_to_C[e * n_eff_constraints + j];
4337:     }
4338:     PetscCall(ISRestoreIndices(pcis->is_B_local, &idx));

4340:     /* permutation and blocksizes for block invert of S_CC */
4341:     PetscInt *idxp;

4343:     PetscCall(PetscMalloc1(n_constraints, &idxp));
4344:     PetscCall(PetscMalloc1(n_el, &C_bss));
4345:     n_C_bss = 0;
4346:     for (PetscInt e = 0, cnt = 0; e < n_el; e++) {
4347:       const PetscInt nc = count_eff[2 * e + 1];

4349:       if (nc) C_bss[n_C_bss++] = nc;
4350:       for (PetscInt c = 0; c < nc; c++) { idxp[cnt + c] = C_eff_to_C[e * n_eff_constraints + c]; }
4351:       cnt += nc;
4352:     }

4354:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n_constraints, idxp, PETSC_OWN_POINTER, &is_C_perm));

4356:     PetscCall(PetscFree2(V_eff_to_V, C_eff_to_C));
4357:     PetscCall(PetscFree(count_eff));
4358:   } else {
4359:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pcbddc->local_primal_size, pcbddc->local_primal_size, NULL, coarse_submat));
4360:     n_eff_constraints = n_constraints;
4361:     n_eff_vertices    = n_vertices;
4362:   }

4364:   /* determine if can use MatSolve routines instead of calling KSPSolve on ksp_R */
4365:   PetscCall(KSPGetPC(pcbddc->ksp_R, &pc_R));
4366:   PetscCall(PCSetUp(pc_R));
4367:   PetscCall(PetscObjectTypeCompare((PetscObject)pc_R, PCLU, &isLU));
4368:   PetscCall(PetscObjectTypeCompare((PetscObject)pc_R, PCCHOLESKY, &isCHOL));
4369:   lda_rhs                = n_R;
4370:   need_benign_correction = PETSC_FALSE;
4371:   if (isLU || isCHOL) {
4372:     PetscCall(PCFactorGetMatrix(pc_R, &F));
4373:   } else if (sub_schurs && sub_schurs->reuse_solver) {
4374:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4375:     MatFactorType      type;

4377:     F = reuse_solver->F;
4378:     PetscCall(MatGetFactorType(F, &type));
4379:     if (type == MAT_FACTOR_CHOLESKY) isCHOL = PETSC_TRUE;
4380:     if (type == MAT_FACTOR_LU) isLU = PETSC_TRUE;
4381:     PetscCall(MatGetSize(F, &lda_rhs, NULL));
4382:     need_benign_correction = (PetscBool)(!!reuse_solver->benign_n);
4383:   } else F = NULL;

4385:   /* determine if we can use a sparse right-hand side */
4386:   sparserhs = PETSC_FALSE;
4387:   if (F && !multi_element) {
4388:     MatSolverType solver;

4390:     PetscCall(MatFactorGetSolverType(F, &solver));
4391:     PetscCall(PetscStrcmp(solver, MATSOLVERMUMPS, &sparserhs));
4392:   }

4394:   /* create dummy vector to modify rhs and sol of MatMatSolve (work array will never be used) */
4395:   dummy_vec = NULL;
4396:   if (need_benign_correction && lda_rhs != n_R && F) {
4397:     PetscCall(VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N), &dummy_vec));
4398:     PetscCall(VecSetSizes(dummy_vec, lda_rhs, PETSC_DECIDE));
4399:     PetscCall(VecSetType(dummy_vec, ((PetscObject)pcis->vec1_N)->type_name));
4400:   }

4402:   PetscCall(MatDestroy(&pcbddc->local_auxmat1));
4403:   PetscCall(MatDestroy(&pcbddc->local_auxmat2));

4405:   PetscCall(ISCreateStride(PETSC_COMM_SELF, n_R, 0, 1, &is_R));
4406:   PetscCall(ISCreateStride(PETSC_COMM_SELF, n_vertices, 0, 1, &is_V));
4407:   PetscCall(ISCreateStride(PETSC_COMM_SELF, n_constraints, n_vertices, 1, &is_C));
4408:   PetscCall(ISGetIndices(is_V, &idx_V));
4409:   PetscCall(ISGetIndices(is_C, &idx_C));

4411:   /* Precompute stuffs needed for preprocessing and application of BDDC*/
4412:   if (n_constraints) {
4413:     Mat C_B;

4415:     /* Extract constraints on R nodes: C_{CR}  */
4416:     PetscCall(MatCreateSubMatrix(pcbddc->ConstraintMatrix, is_C, pcbddc->is_R_local, MAT_INITIAL_MATRIX, &C_CR));
4417:     PetscCall(MatCreateSubMatrix(pcbddc->ConstraintMatrix, is_C, pcis->is_B_local, MAT_INITIAL_MATRIX, &C_B));

4419:     /* Assemble         local_auxmat2_R =        (- A_{RR}^{-1} C^T_{CR}) needed by BDDC setup */
4420:     /* Assemble pcbddc->local_auxmat2   = R_to_B (- A_{RR}^{-1} C^T_{CR}) needed by BDDC application */
4421:     if (!sparserhs) {
4422:       PetscScalar *marr;

4424:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, lda_rhs, n_eff_constraints, NULL, &Brhs));
4425:       PetscCall(MatDenseGetArrayWrite(Brhs, &marr));
4426:       for (i = 0; i < n_constraints; i++) {
4427:         const PetscScalar *row_cmat_values;
4428:         const PetscInt    *row_cmat_indices;
4429:         PetscInt           size_of_constraint, j, col = C_to_eff_C ? C_to_eff_C[i] : i;

4431:         PetscCall(MatGetRow(C_CR, i, &size_of_constraint, &row_cmat_indices, &row_cmat_values));
4432:         for (j = 0; j < size_of_constraint; j++) marr[row_cmat_indices[j] + col * lda_rhs] = -row_cmat_values[j];
4433:         PetscCall(MatRestoreRow(C_CR, i, &size_of_constraint, &row_cmat_indices, &row_cmat_values));
4434:       }
4435:       PetscCall(MatDenseRestoreArrayWrite(Brhs, &marr));
4436:     } else {
4437:       Mat tC_CR;

4439:       PetscCall(MatScale(C_CR, -1.0));
4440:       if (lda_rhs != n_R) {
4441:         PetscScalar *aa;
4442:         PetscInt     r, *ii, *jj;
4443:         PetscBool    done;

4445:         PetscCall(MatGetRowIJ(C_CR, 0, PETSC_FALSE, PETSC_FALSE, &r, (const PetscInt **)&ii, (const PetscInt **)&jj, &done));
4446:         PetscCheck(done, PETSC_COMM_SELF, PETSC_ERR_PLIB, "GetRowIJ failed");
4447:         PetscCall(MatSeqAIJGetArray(C_CR, &aa));
4448:         PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, n_constraints, lda_rhs, ii, jj, aa, &tC_CR));
4449:         PetscCall(MatRestoreRowIJ(C_CR, 0, PETSC_FALSE, PETSC_FALSE, &r, (const PetscInt **)&ii, (const PetscInt **)&jj, &done));
4450:         PetscCheck(done, PETSC_COMM_SELF, PETSC_ERR_PLIB, "RestoreRowIJ failed");
4451:       } else {
4452:         PetscCall(PetscObjectReference((PetscObject)C_CR));
4453:         tC_CR = C_CR;
4454:       }
4455:       PetscCall(MatCreateTranspose(tC_CR, &Brhs));
4456:       PetscCall(MatDestroy(&tC_CR));
4457:     }
4458:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, lda_rhs, n_eff_constraints, NULL, &local_auxmat2_R));
4459:     if (F) {
4460:       if (need_benign_correction) {
4461:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

4463:         /* rhs is already zero on interior dofs, no need to change the rhs */
4464:         PetscCall(PetscArrayzero(reuse_solver->benign_save_vals, pcbddc->benign_n));
4465:       }
4466:       PetscCall(MatMatSolve(F, Brhs, local_auxmat2_R));
4467:       if (need_benign_correction) {
4468:         PetscScalar       *marr;
4469:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

4471:         /* XXX multi_element? */
4472:         PetscCall(MatDenseGetArray(local_auxmat2_R, &marr));
4473:         if (lda_rhs != n_R) {
4474:           for (i = 0; i < n_eff_constraints; i++) {
4475:             PetscCall(VecPlaceArray(dummy_vec, marr + i * lda_rhs));
4476:             PetscCall(PCBDDCReuseSolversBenignAdapt(reuse_solver, dummy_vec, NULL, PETSC_TRUE, PETSC_TRUE));
4477:             PetscCall(VecResetArray(dummy_vec));
4478:           }
4479:         } else {
4480:           for (i = 0; i < n_eff_constraints; i++) {
4481:             PetscCall(VecPlaceArray(pcbddc->vec1_R, marr + i * lda_rhs));
4482:             PetscCall(PCBDDCReuseSolversBenignAdapt(reuse_solver, pcbddc->vec1_R, NULL, PETSC_TRUE, PETSC_TRUE));
4483:             PetscCall(VecResetArray(pcbddc->vec1_R));
4484:           }
4485:         }
4486:         PetscCall(MatDenseRestoreArray(local_auxmat2_R, &marr));
4487:       }
4488:     } else {
4489:       const PetscScalar *barr;
4490:       PetscScalar       *marr;

4492:       PetscCall(MatDenseGetArrayRead(Brhs, &barr));
4493:       PetscCall(MatDenseGetArray(local_auxmat2_R, &marr));
4494:       for (i = 0; i < n_eff_constraints; i++) {
4495:         PetscCall(VecPlaceArray(pcbddc->vec1_R, barr + i * lda_rhs));
4496:         PetscCall(VecPlaceArray(pcbddc->vec2_R, marr + i * lda_rhs));
4497:         PetscCall(KSPSolve(pcbddc->ksp_R, pcbddc->vec1_R, pcbddc->vec2_R));
4498:         PetscCall(KSPCheckSolve(pcbddc->ksp_R, pc, pcbddc->vec2_R));
4499:         PetscCall(VecResetArray(pcbddc->vec1_R));
4500:         PetscCall(VecResetArray(pcbddc->vec2_R));
4501:       }
4502:       PetscCall(MatDenseRestoreArrayRead(Brhs, &barr));
4503:       PetscCall(MatDenseRestoreArray(local_auxmat2_R, &marr));
4504:     }
4505:     if (sparserhs) PetscCall(MatScale(C_CR, -1.0));
4506:     PetscCall(MatDestroy(&Brhs));
4507:     /* Assemble explicitly S_CC = ( C_{CR} A_{RR}^{-1} C^T_{CR})^{-1}  */
4508:     if (!pcbddc->switch_static) {
4509:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n_B, n_eff_constraints, NULL, &pcbddc->local_auxmat2));
4510:       for (i = 0; i < n_eff_constraints; i++) {
4511:         Vec r, b;
4512:         PetscCall(MatDenseGetColumnVecRead(local_auxmat2_R, i, &r));
4513:         PetscCall(MatDenseGetColumnVec(pcbddc->local_auxmat2, i, &b));
4514:         PetscCall(VecScatterBegin(pcbddc->R_to_B, r, b, INSERT_VALUES, SCATTER_FORWARD));
4515:         PetscCall(VecScatterEnd(pcbddc->R_to_B, r, b, INSERT_VALUES, SCATTER_FORWARD));
4516:         PetscCall(MatDenseRestoreColumnVec(pcbddc->local_auxmat2, i, &b));
4517:         PetscCall(MatDenseRestoreColumnVecRead(local_auxmat2_R, i, &r));
4518:       }
4519:       if (multi_element) {
4520:         Mat T;

4522:         PetscCall(MatCreateSeqAIJFromDenseExpand(local_auxmat2_R, n_constraints, R_eff_C_J, &T));
4523:         PetscCall(MatDestroy(&local_auxmat2_R));
4524:         local_auxmat2_R = T;
4525:         PetscCall(MatCreateSeqAIJFromDenseExpand(pcbddc->local_auxmat2, n_constraints, B_eff_C_J, &T));
4526:         PetscCall(MatDestroy(&pcbddc->local_auxmat2));
4527:         pcbddc->local_auxmat2 = T;
4528:       }
4529:       PetscCall(MatMatMult(C_B, pcbddc->local_auxmat2, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &S_CC));
4530:     } else {
4531:       if (multi_element) {
4532:         Mat T;

4534:         PetscCall(MatCreateSeqAIJFromDenseExpand(local_auxmat2_R, n_constraints, R_eff_C_J, &T));
4535:         PetscCall(MatDestroy(&local_auxmat2_R));
4536:         local_auxmat2_R = T;
4537:       }
4538:       if (lda_rhs != n_R) {
4539:         PetscCall(MatCreateSubMatrix(local_auxmat2_R, is_R, NULL, MAT_INITIAL_MATRIX, &pcbddc->local_auxmat2));
4540:       } else {
4541:         PetscCall(PetscObjectReference((PetscObject)local_auxmat2_R));
4542:         pcbddc->local_auxmat2 = local_auxmat2_R;
4543:       }
4544:       PetscCall(MatMatMult(C_CR, pcbddc->local_auxmat2, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &S_CC));
4545:     }
4546:     PetscCall(MatScale(S_CC, m_one));
4547:     if (multi_element) {
4548:       Mat T, T2;
4549:       IS  isp, ispi;

4551:       isp = is_C_perm;

4553:       PetscCall(ISInvertPermutation(isp, PETSC_DECIDE, &ispi));
4554:       PetscCall(MatPermute(S_CC, isp, isp, &T));
4555:       PetscCall(MatSeqAIJInvertVariableBlockDiagonalMat(T, n_C_bss, C_bss, &T2));
4556:       PetscCall(MatDestroy(&T));
4557:       PetscCall(MatDestroy(&S_CC));
4558:       PetscCall(MatPermute(T2, ispi, ispi, &S_CC));
4559:       PetscCall(MatDestroy(&T2));
4560:       PetscCall(ISDestroy(&ispi));
4561:     } else {
4562:       if (isCHOL) {
4563:         PetscCall(MatCholeskyFactor(S_CC, NULL, NULL));
4564:       } else {
4565:         PetscCall(MatLUFactor(S_CC, NULL, NULL, NULL));
4566:       }
4567:       PetscCall(MatSeqDenseInvertFactors_Private(S_CC));
4568:     }
4569:     /* Assemble local_auxmat1 = S_CC*C_{CB} needed by BDDC application in KSP and in preproc */
4570:     PetscCall(MatMatMult(S_CC, C_B, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &pcbddc->local_auxmat1));
4571:     PetscCall(MatDestroy(&C_B));
4572:     PetscCall(MatSetValuesSubMat(*coarse_submat, S_CC, n_constraints, idx_C, n_constraints, idx_C, INSERT_VALUES));
4573:   }

4575:   /* Get submatrices from subdomain matrix */
4576:   if (n_vertices) {
4577: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4578:     PetscBool oldpin;
4579: #endif
4580:     IS is_aux;

4582:     if (sub_schurs && sub_schurs->reuse_solver) { /* is_R_local is not sorted, ISComplement doesn't like it */
4583:       IS tis;

4585:       PetscCall(ISDuplicate(pcbddc->is_R_local, &tis));
4586:       PetscCall(ISSort(tis));
4587:       PetscCall(ISComplement(tis, 0, pcis->n, &is_aux));
4588:       PetscCall(ISDestroy(&tis));
4589:     } else {
4590:       PetscCall(ISComplement(pcbddc->is_R_local, 0, pcis->n, &is_aux));
4591:     }
4592: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4593:     oldpin = pcbddc->local_mat->boundtocpu;
4594: #endif
4595:     PetscCall(MatBindToCPU(pcbddc->local_mat, PETSC_TRUE));
4596:     PetscCall(MatCreateSubMatrix(pcbddc->local_mat, pcbddc->is_R_local, is_aux, MAT_INITIAL_MATRIX, &A_RV));
4597:     PetscCall(MatCreateSubMatrix(pcbddc->local_mat, is_aux, pcbddc->is_R_local, MAT_INITIAL_MATRIX, &A_VR));
4598:     /* TODO REMOVE: MatMatMult(A_VR,A_RRmA_RV) below may raise an error */
4599:     PetscCall(MatConvert(A_VR, MATSEQAIJ, MAT_INPLACE_MATRIX, &A_VR));
4600:     PetscCall(MatCreateSubMatrix(pcbddc->local_mat, is_aux, is_aux, MAT_INITIAL_MATRIX, &A_VV));
4601: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4602:     PetscCall(MatBindToCPU(pcbddc->local_mat, oldpin));
4603: #endif
4604:     PetscCall(ISDestroy(&is_aux));
4605:   }
4606:   PetscCall(ISDestroy(&is_C_perm));
4607:   PetscCall(PetscFree(C_bss));

4609:   p0_lidx_I = NULL;
4610:   if (pcbddc->benign_n && (pcbddc->switch_static || pcbddc->dbg_flag)) {
4611:     const PetscInt *idxs;

4613:     PetscCall(ISGetIndices(pcis->is_I_local, &idxs));
4614:     PetscCall(PetscMalloc1(pcbddc->benign_n, &p0_lidx_I));
4615:     for (i = 0; i < pcbddc->benign_n; i++) PetscCall(PetscFindInt(pcbddc->benign_p0_lidx[i], pcis->n - pcis->n_B, idxs, &p0_lidx_I[i]));
4616:     PetscCall(ISRestoreIndices(pcis->is_I_local, &idxs));
4617:   }

4619:   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */

4621:   /* Matrices of coarse basis functions (local) */
4622:   PetscCall(MatDestroy(&pcbddc->coarse_phi_B));
4623:   PetscCall(MatDestroy(&pcbddc->coarse_psi_B));
4624:   PetscCall(MatDestroy(&pcbddc->coarse_phi_D));
4625:   PetscCall(MatDestroy(&pcbddc->coarse_psi_D));
4626:   if (!multi_element) {
4627:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n_B, pcbddc->local_primal_size, NULL, &pcbddc->coarse_phi_B));
4628:     if (pcbddc->switch_static || pcbddc->dbg_flag) PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n_D, pcbddc->local_primal_size, NULL, &pcbddc->coarse_phi_D));
4629:     coarse_phi_multi = NULL;
4630:   } else { /* Create temporary NEST matrix to hold coarse basis functions blocks */
4631:     IS is_rows[2] = {pcbddc->is_R_local, NULL};
4632:     IS is_cols[2] = {is_V, is_C};

4634:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n_vertices, pcbddc->local_primal_ref_node, PETSC_USE_POINTER, &is_rows[1]));
4635:     PetscCall(MatCreateNest(PETSC_COMM_SELF, 2, is_rows, 2, is_cols, NULL, &coarse_phi_multi));
4636:     PetscCall(ISDestroy(&is_rows[1]));
4637:   }

4639:   /* vertices */
4640:   if (n_vertices) {
4641:     PetscBool restoreavr = PETSC_FALSE;
4642:     Mat       A_RRmA_RV  = NULL;

4644:     PetscCall(MatSetValuesSubMat(*coarse_submat, A_VV, n_vertices, idx_V, n_vertices, idx_V, ADD_VALUES));
4645:     PetscCall(MatDestroy(&A_VV));

4647:     if (n_R) {
4648:       Mat A_RV_bcorr = NULL, S_VV;

4650:       PetscCall(MatScale(A_RV, m_one));
4651:       if (need_benign_correction) {
4652:         ISLocalToGlobalMapping RtoN;
4653:         IS                     is_p0;
4654:         PetscInt              *idxs_p0, n;

4656:         PetscCall(PetscMalloc1(pcbddc->benign_n, &idxs_p0));
4657:         PetscCall(ISLocalToGlobalMappingCreateIS(pcbddc->is_R_local, &RtoN));
4658:         PetscCall(ISGlobalToLocalMappingApply(RtoN, IS_GTOLM_DROP, pcbddc->benign_n, pcbddc->benign_p0_lidx, &n, idxs_p0));
4659:         PetscCheck(n == pcbddc->benign_n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error in R numbering for benign p0! %" PetscInt_FMT " != %" PetscInt_FMT, n, pcbddc->benign_n);
4660:         PetscCall(ISLocalToGlobalMappingDestroy(&RtoN));
4661:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, idxs_p0, PETSC_OWN_POINTER, &is_p0));
4662:         PetscCall(MatCreateSubMatrix(A_RV, is_p0, NULL, MAT_INITIAL_MATRIX, &A_RV_bcorr));
4663:         PetscCall(ISDestroy(&is_p0));
4664:       }

4666:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, lda_rhs, n_eff_vertices, NULL, &A_RRmA_RV));
4667:       if (!sparserhs || need_benign_correction) {
4668:         if (lda_rhs == n_R && !multi_element) {
4669:           PetscCall(MatConvert(A_RV, MATDENSE, MAT_INPLACE_MATRIX, &A_RV));
4670:         } else {
4671:           Mat             T;
4672:           PetscScalar    *av, *array;
4673:           const PetscInt *xadj, *adjncy;
4674:           PetscInt        n;
4675:           PetscBool       flg_row;

4677:           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, lda_rhs, n_eff_vertices, NULL, &T));
4678:           PetscCall(MatDenseGetArrayWrite(T, &array));
4679:           PetscCall(MatConvert(A_RV, MATSEQAIJ, MAT_INPLACE_MATRIX, &A_RV));
4680:           PetscCall(MatGetRowIJ(A_RV, 0, PETSC_FALSE, PETSC_FALSE, &n, &xadj, &adjncy, &flg_row));
4681:           PetscCall(MatSeqAIJGetArray(A_RV, &av));
4682:           for (i = 0; i < n; i++) {
4683:             PetscInt j;
4684:             for (j = xadj[i]; j < xadj[i + 1]; j++) array[lda_rhs * (V_to_eff_V ? V_to_eff_V[adjncy[j]] : adjncy[j]) + i] = av[j];
4685:           }
4686:           PetscCall(MatRestoreRowIJ(A_RV, 0, PETSC_FALSE, PETSC_FALSE, &n, &xadj, &adjncy, &flg_row));
4687:           PetscCall(MatDenseRestoreArrayWrite(T, &array));
4688:           PetscCall(MatDestroy(&A_RV));
4689:           A_RV = T;
4690:         }
4691:         if (need_benign_correction) {
4692:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4693:           PetscScalar       *marr;

4695:           /* XXX multi_element */
4696:           PetscCall(MatDenseGetArray(A_RV, &marr));
4697:           /* need \Phi^T A_RV = (I+L)A_RV, L given by

4699:                  | 0 0  0 | (V)
4700:              L = | 0 0 -1 | (P-p0)
4701:                  | 0 0 -1 | (p0)

4703:           */
4704:           for (i = 0; i < reuse_solver->benign_n; i++) {
4705:             const PetscScalar *vals;
4706:             const PetscInt    *idxs, *idxs_zero;
4707:             PetscInt           n, j, nz;

4709:             PetscCall(ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i], &nz));
4710:             PetscCall(ISGetIndices(reuse_solver->benign_zerodiag_subs[i], &idxs_zero));
4711:             PetscCall(MatGetRow(A_RV_bcorr, i, &n, &idxs, &vals));
4712:             for (j = 0; j < n; j++) {
4713:               PetscScalar val = vals[j];
4714:               PetscInt    k, col = idxs[j];
4715:               for (k = 0; k < nz; k++) marr[idxs_zero[k] + lda_rhs * col] -= val;
4716:             }
4717:             PetscCall(MatRestoreRow(A_RV_bcorr, i, &n, &idxs, &vals));
4718:             PetscCall(ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i], &idxs_zero));
4719:           }
4720:           PetscCall(MatDenseRestoreArray(A_RV, &marr));
4721:         }
4722:         PetscCall(PetscObjectReference((PetscObject)A_RV));
4723:         Brhs = A_RV;
4724:       } else {
4725:         Mat tA_RVT, A_RVT;

4727:         if (!pcbddc->symmetric_primal) {
4728:           /* A_RV already scaled by -1 */
4729:           PetscCall(MatTranspose(A_RV, MAT_INITIAL_MATRIX, &A_RVT));
4730:         } else {
4731:           restoreavr = PETSC_TRUE;
4732:           PetscCall(MatScale(A_VR, -1.0));
4733:           PetscCall(PetscObjectReference((PetscObject)A_VR));
4734:           A_RVT = A_VR;
4735:         }
4736:         if (lda_rhs != n_R) {
4737:           PetscScalar *aa;
4738:           PetscInt     r, *ii, *jj;
4739:           PetscBool    done;

4741:           PetscCall(MatGetRowIJ(A_RVT, 0, PETSC_FALSE, PETSC_FALSE, &r, (const PetscInt **)&ii, (const PetscInt **)&jj, &done));
4742:           PetscCheck(done, PETSC_COMM_SELF, PETSC_ERR_PLIB, "GetRowIJ failed");
4743:           PetscCall(MatSeqAIJGetArray(A_RVT, &aa));
4744:           PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, n_vertices, lda_rhs, ii, jj, aa, &tA_RVT));
4745:           PetscCall(MatRestoreRowIJ(A_RVT, 0, PETSC_FALSE, PETSC_FALSE, &r, (const PetscInt **)&ii, (const PetscInt **)&jj, &done));
4746:           PetscCheck(done, PETSC_COMM_SELF, PETSC_ERR_PLIB, "RestoreRowIJ failed");
4747:         } else {
4748:           PetscCall(PetscObjectReference((PetscObject)A_RVT));
4749:           tA_RVT = A_RVT;
4750:         }
4751:         PetscCall(MatCreateTranspose(tA_RVT, &Brhs));
4752:         PetscCall(MatDestroy(&tA_RVT));
4753:         PetscCall(MatDestroy(&A_RVT));
4754:       }
4755:       if (F) {
4756:         /* need to correct the rhs */
4757:         if (need_benign_correction) {
4758:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4759:           PetscScalar       *marr;

4761:           PetscCall(MatDenseGetArray(Brhs, &marr));
4762:           if (lda_rhs != n_R) {
4763:             for (i = 0; i < n_eff_vertices; i++) {
4764:               PetscCall(VecPlaceArray(dummy_vec, marr + i * lda_rhs));
4765:               PetscCall(PCBDDCReuseSolversBenignAdapt(reuse_solver, dummy_vec, NULL, PETSC_FALSE, PETSC_TRUE));
4766:               PetscCall(VecResetArray(dummy_vec));
4767:             }
4768:           } else {
4769:             for (i = 0; i < n_eff_vertices; i++) {
4770:               PetscCall(VecPlaceArray(pcbddc->vec1_R, marr + i * lda_rhs));
4771:               PetscCall(PCBDDCReuseSolversBenignAdapt(reuse_solver, pcbddc->vec1_R, NULL, PETSC_FALSE, PETSC_TRUE));
4772:               PetscCall(VecResetArray(pcbddc->vec1_R));
4773:             }
4774:           }
4775:           PetscCall(MatDenseRestoreArray(Brhs, &marr));
4776:         }
4777:         PetscCall(MatMatSolve(F, Brhs, A_RRmA_RV));
4778:         if (restoreavr) PetscCall(MatScale(A_VR, -1.0));
4779:         /* need to correct the solution */
4780:         if (need_benign_correction) {
4781:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4782:           PetscScalar       *marr;

4784:           PetscCall(MatDenseGetArray(A_RRmA_RV, &marr));
4785:           if (lda_rhs != n_R) {
4786:             for (i = 0; i < n_eff_vertices; i++) {
4787:               PetscCall(VecPlaceArray(dummy_vec, marr + i * lda_rhs));
4788:               PetscCall(PCBDDCReuseSolversBenignAdapt(reuse_solver, dummy_vec, NULL, PETSC_TRUE, PETSC_TRUE));
4789:               PetscCall(VecResetArray(dummy_vec));
4790:             }
4791:           } else {
4792:             for (i = 0; i < n_eff_vertices; i++) {
4793:               PetscCall(VecPlaceArray(pcbddc->vec1_R, marr + i * lda_rhs));
4794:               PetscCall(PCBDDCReuseSolversBenignAdapt(reuse_solver, pcbddc->vec1_R, NULL, PETSC_TRUE, PETSC_TRUE));
4795:               PetscCall(VecResetArray(pcbddc->vec1_R));
4796:             }
4797:           }
4798:           PetscCall(MatDenseRestoreArray(A_RRmA_RV, &marr));
4799:         }
4800:       } else {
4801:         const PetscScalar *barr;
4802:         PetscScalar       *marr;

4804:         PetscCall(MatDenseGetArrayRead(Brhs, &barr));
4805:         PetscCall(MatDenseGetArray(A_RRmA_RV, &marr));
4806:         for (i = 0; i < n_eff_vertices; i++) {
4807:           PetscCall(VecPlaceArray(pcbddc->vec1_R, barr + i * lda_rhs));
4808:           PetscCall(VecPlaceArray(pcbddc->vec2_R, marr + i * lda_rhs));
4809:           PetscCall(KSPSolve(pcbddc->ksp_R, pcbddc->vec1_R, pcbddc->vec2_R));
4810:           PetscCall(KSPCheckSolve(pcbddc->ksp_R, pc, pcbddc->vec2_R));
4811:           PetscCall(VecResetArray(pcbddc->vec1_R));
4812:           PetscCall(VecResetArray(pcbddc->vec2_R));
4813:         }
4814:         PetscCall(MatDenseRestoreArrayRead(Brhs, &barr));
4815:         PetscCall(MatDenseRestoreArray(A_RRmA_RV, &marr));
4816:       }
4817:       PetscCall(MatDestroy(&A_RV));
4818:       PetscCall(MatDestroy(&Brhs));
4819:       /* S_VV and S_CV */
4820:       if (n_constraints) {
4821:         Mat B;

4823:         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n_B, n_eff_vertices, NULL, &B));
4824:         PetscCall(MatDenseScatter(A_RRmA_RV, pcbddc->R_to_B, B));

4826:         /* S_CV = pcbddc->local_auxmat1 * B */
4827:         if (multi_element) {
4828:           Mat T;

4830:           PetscCall(MatCreateSeqAIJFromDenseExpand(B, n_vertices, B_eff_V_J, &T));
4831:           PetscCall(MatDestroy(&B));
4832:           B = T;
4833:         }
4834:         PetscCall(MatProductCreate(pcbddc->local_auxmat1, B, NULL, &S_CV));
4835:         PetscCall(MatProductSetType(S_CV, MATPRODUCT_AB));
4836:         PetscCall(MatProductSetFromOptions(S_CV));
4837:         PetscCall(MatProductSymbolic(S_CV));
4838:         PetscCall(MatProductNumeric(S_CV));
4839:         PetscCall(MatProductClear(S_CV));
4840:         PetscCall(MatDestroy(&B));

4842:         /* B = local_auxmat2_R * S_CV */
4843:         PetscCall(MatProductCreate(local_auxmat2_R, S_CV, NULL, &B));
4844:         PetscCall(MatProductSetType(B, MATPRODUCT_AB));
4845:         PetscCall(MatProductSetFromOptions(B));
4846:         PetscCall(MatProductSymbolic(B));
4847:         PetscCall(MatProductNumeric(B));

4849:         PetscCall(MatScale(S_CV, m_one));
4850:         PetscCall(MatSetValuesSubMat(*coarse_submat, S_CV, n_constraints, idx_C, n_vertices, idx_V, INSERT_VALUES));

4852:         if (multi_element) {
4853:           Mat T;

4855:           PetscCall(MatCreateSeqAIJFromDenseExpand(A_RRmA_RV, n_vertices, R_eff_V_J, &T));
4856:           PetscCall(MatDestroy(&A_RRmA_RV));
4857:           A_RRmA_RV = T;
4858:         }
4859:         PetscCall(MatAXPY(A_RRmA_RV, 1.0, B, UNKNOWN_NONZERO_PATTERN)); /* XXX ? */
4860:         PetscCall(MatDestroy(&B));
4861:       } else if (multi_element) {
4862:         Mat T;

4864:         PetscCall(MatCreateSeqAIJFromDenseExpand(A_RRmA_RV, n_vertices, R_eff_V_J, &T));
4865:         PetscCall(MatDestroy(&A_RRmA_RV));
4866:         A_RRmA_RV = T;
4867:       }

4869:       if (lda_rhs != n_R) {
4870:         Mat T;

4872:         PetscCall(MatCreateSubMatrix(A_RRmA_RV, is_R, NULL, MAT_INITIAL_MATRIX, &T));
4873:         PetscCall(MatDestroy(&A_RRmA_RV));
4874:         A_RRmA_RV = T;
4875:       }

4877:       /* need A_VR * \Phi * A_RRmA_RV = A_VR * (I+L)^T * A_RRmA_RV, L given as before */
4878:       if (need_benign_correction) { /* XXX SPARSE */
4879:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4880:         PetscScalar       *sums;
4881:         const PetscScalar *marr;

4883:         PetscCall(MatDenseGetArrayRead(A_RRmA_RV, &marr));
4884:         PetscCall(PetscMalloc1(n_vertices, &sums));
4885:         for (i = 0; i < reuse_solver->benign_n; i++) {
4886:           const PetscScalar *vals;
4887:           const PetscInt    *idxs, *idxs_zero;
4888:           PetscInt           n, j, nz;

4890:           PetscCall(ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i], &nz));
4891:           PetscCall(ISGetIndices(reuse_solver->benign_zerodiag_subs[i], &idxs_zero));
4892:           for (j = 0; j < n_vertices; j++) {
4893:             sums[j] = 0.;
4894:             for (PetscInt k = 0; k < nz; k++) sums[j] += marr[idxs_zero[k] + j * n_R];
4895:           }
4896:           PetscCall(MatGetRow(A_RV_bcorr, i, &n, &idxs, &vals));
4897:           for (j = 0; j < n; j++) {
4898:             PetscScalar val = vals[j];
4899:             for (PetscInt k = 0; k < n_vertices; k++) PetscCall(MatSetValue(*coarse_submat, idx_V[idxs[j]], idx_V[k], val * sums[k], ADD_VALUES));
4900:           }
4901:           PetscCall(MatRestoreRow(A_RV_bcorr, i, &n, &idxs, &vals));
4902:           PetscCall(ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i], &idxs_zero));
4903:         }
4904:         PetscCall(PetscFree(sums));
4905:         PetscCall(MatDestroy(&A_RV_bcorr));
4906:         PetscCall(MatDenseRestoreArrayRead(A_RRmA_RV, &marr));
4907:       }

4909:       PetscCall(MatMatMult(A_VR, A_RRmA_RV, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &S_VV));
4910:       PetscCall(MatSetValuesSubMat(*coarse_submat, S_VV, n_vertices, idx_V, n_vertices, idx_V, ADD_VALUES));
4911:       PetscCall(MatDestroy(&S_VV));
4912:     }

4914:     /* coarse basis functions */
4915:     if (coarse_phi_multi) {
4916:       Mat Vid;

4918:       PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, n_vertices, n_vertices, 1, NULL, &Vid));
4919:       PetscCall(MatShift_Basic(Vid, 1.0));
4920:       PetscCall(MatNestSetSubMat(coarse_phi_multi, 0, 0, A_RRmA_RV));
4921:       PetscCall(MatNestSetSubMat(coarse_phi_multi, 1, 0, Vid));
4922:       PetscCall(MatDestroy(&Vid));
4923:     } else {
4924:       if (A_RRmA_RV) {
4925:         PetscCall(MatDenseScatter(A_RRmA_RV, pcbddc->R_to_B, pcbddc->coarse_phi_B));
4926:         if (pcbddc->switch_static || pcbddc->dbg_flag) {
4927:           PetscCall(MatDenseScatter(A_RRmA_RV, pcbddc->R_to_D, pcbddc->coarse_phi_D));
4928:           if (pcbddc->benign_n) {
4929:             for (i = 0; i < n_vertices; i++) { PetscCall(MatSetValues(pcbddc->coarse_phi_D, pcbddc->benign_n, p0_lidx_I, 1, &i, NULL, INSERT_VALUES)); }
4930:             PetscCall(MatAssemblyBegin(pcbddc->coarse_phi_D, MAT_FINAL_ASSEMBLY));
4931:             PetscCall(MatAssemblyEnd(pcbddc->coarse_phi_D, MAT_FINAL_ASSEMBLY));
4932:           }
4933:         }
4934:       }
4935:       for (i = 0; i < n_vertices; i++) PetscCall(MatSetValues(pcbddc->coarse_phi_B, 1, &idx_V_B[i], 1, &i, &one, INSERT_VALUES));
4936:       PetscCall(MatAssemblyBegin(pcbddc->coarse_phi_B, MAT_FINAL_ASSEMBLY));
4937:       PetscCall(MatAssemblyEnd(pcbddc->coarse_phi_B, MAT_FINAL_ASSEMBLY));
4938:     }
4939:     PetscCall(MatDestroy(&A_RRmA_RV));
4940:   }
4941:   PetscCall(MatDestroy(&A_RV));
4942:   PetscCall(VecDestroy(&dummy_vec));

4944:   if (n_constraints) {
4945:     Mat B, B2;

4947:     PetscCall(MatScale(S_CC, m_one));
4948:     PetscCall(MatProductCreate(local_auxmat2_R, S_CC, NULL, &B));
4949:     PetscCall(MatProductSetType(B, MATPRODUCT_AB));
4950:     PetscCall(MatProductSetFromOptions(B));
4951:     PetscCall(MatProductSymbolic(B));
4952:     PetscCall(MatProductNumeric(B));

4954:     if (n_vertices) {
4955:       if (isCHOL || need_benign_correction) { /* if we can solve the interior problem with cholesky, we should also be fine with transposing here */
4956:         PetscCall(MatTranspose(S_CV, MAT_INITIAL_MATRIX, &S_VC));
4957:       } else {
4958:         if (lda_rhs != n_R) {
4959:           Mat tB;

4961:           PetscCall(MatCreateSubMatrix(B, is_R, NULL, MAT_INITIAL_MATRIX, &tB));
4962:           PetscCall(MatDestroy(&B));
4963:           B = tB;
4964:         }
4965:         PetscCall(MatMatMult(A_VR, B, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &S_VC));
4966:       }
4967:       PetscCall(MatSetValuesSubMat(*coarse_submat, S_VC, n_vertices, idx_V, n_constraints, idx_C, INSERT_VALUES));
4968:     }

4970:     /* coarse basis functions */
4971:     if (coarse_phi_multi) {
4972:       PetscCall(MatNestSetSubMat(coarse_phi_multi, 0, 1, B));
4973:     } else {
4974:       PetscCall(MatDenseGetSubMatrix(pcbddc->coarse_phi_B, PETSC_DECIDE, PETSC_DECIDE, n_vertices, n_vertices + n_constraints, &B2));
4975:       PetscCall(MatDenseScatter(B, pcbddc->R_to_B, B2));
4976:       PetscCall(MatDenseRestoreSubMatrix(pcbddc->coarse_phi_B, &B2));
4977:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4978:         PetscCall(MatDenseGetSubMatrix(pcbddc->coarse_phi_D, PETSC_DECIDE, PETSC_DECIDE, n_vertices, n_vertices + n_constraints, &B2));
4979:         PetscCall(MatDenseScatter(B, pcbddc->R_to_D, B2));
4980:         if (pcbddc->benign_n) {
4981:           for (i = 0; i < n_constraints; i++) { PetscCall(MatSetValues(B2, pcbddc->benign_n, p0_lidx_I, 1, &i, NULL, INSERT_VALUES)); }
4982:         }
4983:         PetscCall(MatDenseRestoreSubMatrix(pcbddc->coarse_phi_D, &B2));
4984:       }
4985:     }
4986:     PetscCall(MatDestroy(&B));
4987:   }

4989:   /* assemble sparse coarse basis functions */
4990:   if (coarse_phi_multi) {
4991:     Mat T;

4993:     PetscCall(MatConvert(coarse_phi_multi, MATSEQAIJ, MAT_INITIAL_MATRIX, &T));
4994:     PetscCall(MatDestroy(&coarse_phi_multi));
4995:     PetscCall(MatCreateSubMatrix(T, pcis->is_B_local, NULL, MAT_INITIAL_MATRIX, &pcbddc->coarse_phi_B));
4996:     if (pcbddc->switch_static || pcbddc->dbg_flag) { PetscCall(MatCreateSubMatrix(T, pcis->is_I_local, NULL, MAT_INITIAL_MATRIX, &pcbddc->coarse_phi_D)); }
4997:     PetscCall(MatDestroy(&T));
4998:   }
4999:   PetscCall(MatDestroy(&local_auxmat2_R));
5000:   PetscCall(PetscFree(p0_lidx_I));

5002:   /* coarse matrix entries relative to B_0 */
5003:   if (pcbddc->benign_n) {
5004:     Mat                B0_B, B0_BPHI;
5005:     IS                 is_dummy;
5006:     const PetscScalar *data;
5007:     PetscInt           j;

5009:     PetscCall(ISCreateStride(PETSC_COMM_SELF, pcbddc->benign_n, 0, 1, &is_dummy));
5010:     PetscCall(MatCreateSubMatrix(pcbddc->benign_B0, is_dummy, pcis->is_B_local, MAT_INITIAL_MATRIX, &B0_B));
5011:     PetscCall(ISDestroy(&is_dummy));
5012:     PetscCall(MatMatMult(B0_B, pcbddc->coarse_phi_B, MAT_INITIAL_MATRIX, 1.0, &B0_BPHI));
5013:     PetscCall(MatConvert(B0_BPHI, MATSEQDENSE, MAT_INPLACE_MATRIX, &B0_BPHI));
5014:     PetscCall(MatDenseGetArrayRead(B0_BPHI, &data));
5015:     for (j = 0; j < pcbddc->benign_n; j++) {
5016:       PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
5017:       for (i = 0; i < pcbddc->local_primal_size; i++) {
5018:         PetscCall(MatSetValue(*coarse_submat, primal_idx, i, data[i * pcbddc->benign_n + j], INSERT_VALUES));
5019:         PetscCall(MatSetValue(*coarse_submat, i, primal_idx, data[i * pcbddc->benign_n + j], INSERT_VALUES));
5020:       }
5021:     }
5022:     PetscCall(MatDenseRestoreArrayRead(B0_BPHI, &data));
5023:     PetscCall(MatDestroy(&B0_B));
5024:     PetscCall(MatDestroy(&B0_BPHI));
5025:   }

5027:   /* compute other basis functions for non-symmetric problems */
5028:   if (!pcbddc->symmetric_primal) {
5029:     Mat          B_V = NULL, B_C = NULL;
5030:     PetscScalar *marray, *work;

5032:     /* TODO multi_element MatDenseScatter */
5033:     if (n_constraints) {
5034:       Mat S_CCT, C_CRT;

5036:       PetscCall(MatScale(S_CC, m_one));
5037:       PetscCall(MatTranspose(C_CR, MAT_INITIAL_MATRIX, &C_CRT));
5038:       PetscCall(MatTranspose(S_CC, MAT_INITIAL_MATRIX, &S_CCT));
5039:       PetscCall(MatMatMult(C_CRT, S_CCT, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &B_C));
5040:       PetscCall(MatConvert(B_C, MATDENSE, MAT_INPLACE_MATRIX, &B_C));
5041:       PetscCall(MatDestroy(&S_CCT));
5042:       if (n_vertices) {
5043:         Mat S_VCT;

5045:         PetscCall(MatTranspose(S_VC, MAT_INITIAL_MATRIX, &S_VCT));
5046:         PetscCall(MatMatMult(C_CRT, S_VCT, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &B_V));
5047:         PetscCall(MatDestroy(&S_VCT));
5048:         PetscCall(MatConvert(B_V, MATDENSE, MAT_INPLACE_MATRIX, &B_V));
5049:       }
5050:       PetscCall(MatDestroy(&C_CRT));
5051:     } else {
5052:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n_R, n_vertices, NULL, &B_V));
5053:     }
5054:     if (n_vertices && n_R) {
5055:       PetscScalar    *av, *marray;
5056:       const PetscInt *xadj, *adjncy;
5057:       PetscInt        n;
5058:       PetscBool       flg_row;

5060:       /* B_V = B_V - A_VR^T */
5061:       PetscCall(MatConvert(A_VR, MATSEQAIJ, MAT_INPLACE_MATRIX, &A_VR));
5062:       PetscCall(MatGetRowIJ(A_VR, 0, PETSC_FALSE, PETSC_FALSE, &n, &xadj, &adjncy, &flg_row));
5063:       PetscCall(MatSeqAIJGetArray(A_VR, &av));
5064:       PetscCall(MatDenseGetArray(B_V, &marray));
5065:       for (i = 0; i < n; i++) {
5066:         PetscInt j;
5067:         for (j = xadj[i]; j < xadj[i + 1]; j++) marray[i * n_R + adjncy[j]] -= av[j];
5068:       }
5069:       PetscCall(MatDenseRestoreArray(B_V, &marray));
5070:       PetscCall(MatRestoreRowIJ(A_VR, 0, PETSC_FALSE, PETSC_FALSE, &n, &xadj, &adjncy, &flg_row));
5071:       PetscCall(MatDestroy(&A_VR));
5072:     }

5074:     /* currently there's no support for MatTransposeMatSolve(F,B,X) */
5075:     PetscCall(PetscMalloc1(n_R * pcbddc->local_primal_size, &work));
5076:     if (n_vertices) {
5077:       PetscCall(MatDenseGetArray(B_V, &marray));
5078:       for (i = 0; i < n_vertices; i++) {
5079:         PetscCall(VecPlaceArray(pcbddc->vec1_R, marray + i * n_R));
5080:         PetscCall(VecPlaceArray(pcbddc->vec2_R, work + i * n_R));
5081:         PetscCall(KSPSolveTranspose(pcbddc->ksp_R, pcbddc->vec1_R, pcbddc->vec2_R));
5082:         PetscCall(KSPCheckSolve(pcbddc->ksp_R, pc, pcbddc->vec2_R));
5083:         PetscCall(VecResetArray(pcbddc->vec1_R));
5084:         PetscCall(VecResetArray(pcbddc->vec2_R));
5085:       }
5086:       PetscCall(MatDenseRestoreArray(B_V, &marray));
5087:     }
5088:     if (B_C) {
5089:       PetscCall(MatDenseGetArray(B_C, &marray));
5090:       for (i = n_vertices; i < n_constraints + n_vertices; i++) {
5091:         PetscCall(VecPlaceArray(pcbddc->vec1_R, marray + (i - n_vertices) * n_R));
5092:         PetscCall(VecPlaceArray(pcbddc->vec2_R, work + i * n_R));
5093:         PetscCall(KSPSolveTranspose(pcbddc->ksp_R, pcbddc->vec1_R, pcbddc->vec2_R));
5094:         PetscCall(KSPCheckSolve(pcbddc->ksp_R, pc, pcbddc->vec2_R));
5095:         PetscCall(VecResetArray(pcbddc->vec1_R));
5096:         PetscCall(VecResetArray(pcbddc->vec2_R));
5097:       }
5098:       PetscCall(MatDenseRestoreArray(B_C, &marray));
5099:     }
5100:     /* coarse basis functions */
5101:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n_B, pcbddc->local_primal_size, NULL, &pcbddc->coarse_psi_B));
5102:     if (pcbddc->switch_static || pcbddc->dbg_flag) PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, n_D, pcbddc->local_primal_size, NULL, &pcbddc->coarse_psi_D));
5103:     for (i = 0; i < pcbddc->local_primal_size; i++) {
5104:       Vec v;

5106:       PetscCall(VecPlaceArray(pcbddc->vec1_R, work + i * n_R));
5107:       PetscCall(MatDenseGetColumnVec(pcbddc->coarse_psi_B, i, &v));
5108:       PetscCall(VecScatterBegin(pcbddc->R_to_B, pcbddc->vec1_R, v, INSERT_VALUES, SCATTER_FORWARD));
5109:       PetscCall(VecScatterEnd(pcbddc->R_to_B, pcbddc->vec1_R, v, INSERT_VALUES, SCATTER_FORWARD));
5110:       if (i < n_vertices) {
5111:         PetscScalar one = 1.0;
5112:         PetscCall(VecSetValues(v, 1, &idx_V_B[i], &one, INSERT_VALUES));
5113:         PetscCall(VecAssemblyBegin(v));
5114:         PetscCall(VecAssemblyEnd(v));
5115:       }
5116:       PetscCall(MatDenseRestoreColumnVec(pcbddc->coarse_psi_B, i, &v));

5118:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
5119:         PetscCall(MatDenseGetColumnVec(pcbddc->coarse_psi_D, i, &v));
5120:         PetscCall(VecScatterBegin(pcbddc->R_to_D, pcbddc->vec1_R, v, INSERT_VALUES, SCATTER_FORWARD));
5121:         PetscCall(VecScatterEnd(pcbddc->R_to_D, pcbddc->vec1_R, v, INSERT_VALUES, SCATTER_FORWARD));
5122:         PetscCall(MatDenseRestoreColumnVec(pcbddc->coarse_psi_D, i, &v));
5123:       }
5124:       PetscCall(VecResetArray(pcbddc->vec1_R));
5125:     }
5126:     PetscCall(MatDestroy(&B_V));
5127:     PetscCall(MatDestroy(&B_C));
5128:     PetscCall(PetscFree(work));
5129:   } else {
5130:     PetscCall(PetscObjectReference((PetscObject)pcbddc->coarse_phi_B));
5131:     pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
5132:     PetscCall(PetscObjectReference((PetscObject)pcbddc->coarse_phi_D));
5133:     pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
5134:   }
5135:   PetscCall(MatAssemblyBegin(*coarse_submat, MAT_FINAL_ASSEMBLY));
5136:   PetscCall(MatAssemblyEnd(*coarse_submat, MAT_FINAL_ASSEMBLY));

5138:   /* free memory */
5139:   PetscCall(PetscFree(V_to_eff_V));
5140:   PetscCall(PetscFree(C_to_eff_C));
5141:   PetscCall(PetscFree(R_eff_V_J));
5142:   PetscCall(PetscFree(R_eff_C_J));
5143:   PetscCall(PetscFree(B_eff_V_J));
5144:   PetscCall(PetscFree(B_eff_C_J));
5145:   PetscCall(ISDestroy(&is_R));
5146:   PetscCall(ISRestoreIndices(is_V, &idx_V));
5147:   PetscCall(ISRestoreIndices(is_C, &idx_C));
5148:   PetscCall(ISDestroy(&is_V));
5149:   PetscCall(ISDestroy(&is_C));
5150:   PetscCall(PetscFree(idx_V_B));
5151:   PetscCall(MatDestroy(&S_CV));
5152:   PetscCall(MatDestroy(&S_VC));
5153:   PetscCall(MatDestroy(&S_CC));
5154:   if (n_vertices) PetscCall(MatDestroy(&A_VR));
5155:   if (n_constraints) PetscCall(MatDestroy(&C_CR));
5156:   PetscCall(PetscLogEventEnd(PC_BDDC_CorrectionSetUp[pcbddc->current_level], pc, 0, 0, 0));

5158:   /* Checking coarse_sub_mat and coarse basis functions */
5159:   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
5160:   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
5161:   if (pcbddc->dbg_flag) {
5162:     Mat       AUXMAT, TM1, TM2, TM3, TM4;
5163:     Mat       coarse_phi_D, coarse_phi_B;
5164:     Mat       coarse_psi_D, coarse_psi_B;
5165:     Mat       A_II, A_BB, A_IB, A_BI;
5166:     Mat       C_B, CPHI;
5167:     IS        is_dummy;
5168:     Vec       mones;
5169:     MatType   checkmattype = MATSEQAIJ;
5170:     PetscReal real_value;

5172:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
5173:       Mat A;
5174:       PetscCall(PCBDDCBenignProject(pc, NULL, NULL, &A));
5175:       PetscCall(MatCreateSubMatrix(A, pcis->is_I_local, pcis->is_I_local, MAT_INITIAL_MATRIX, &A_II));
5176:       PetscCall(MatCreateSubMatrix(A, pcis->is_I_local, pcis->is_B_local, MAT_INITIAL_MATRIX, &A_IB));
5177:       PetscCall(MatCreateSubMatrix(A, pcis->is_B_local, pcis->is_I_local, MAT_INITIAL_MATRIX, &A_BI));
5178:       PetscCall(MatCreateSubMatrix(A, pcis->is_B_local, pcis->is_B_local, MAT_INITIAL_MATRIX, &A_BB));
5179:       PetscCall(MatDestroy(&A));
5180:     } else {
5181:       PetscCall(MatConvert(pcis->A_II, checkmattype, MAT_INITIAL_MATRIX, &A_II));
5182:       PetscCall(MatConvert(pcis->A_IB, checkmattype, MAT_INITIAL_MATRIX, &A_IB));
5183:       PetscCall(MatConvert(pcis->A_BI, checkmattype, MAT_INITIAL_MATRIX, &A_BI));
5184:       PetscCall(MatConvert(pcis->A_BB, checkmattype, MAT_INITIAL_MATRIX, &A_BB));
5185:     }
5186:     PetscCall(MatConvert(pcbddc->coarse_phi_D, checkmattype, MAT_INITIAL_MATRIX, &coarse_phi_D));
5187:     PetscCall(MatConvert(pcbddc->coarse_phi_B, checkmattype, MAT_INITIAL_MATRIX, &coarse_phi_B));
5188:     if (!pcbddc->symmetric_primal) {
5189:       PetscCall(MatConvert(pcbddc->coarse_psi_D, checkmattype, MAT_INITIAL_MATRIX, &coarse_psi_D));
5190:       PetscCall(MatConvert(pcbddc->coarse_psi_B, checkmattype, MAT_INITIAL_MATRIX, &coarse_psi_B));
5191:     }
5192:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "--------------------------------------------------\n"));
5193:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "Check coarse sub mat computation (symmetric %d)\n", pcbddc->symmetric_primal));
5194:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
5195:     if (!pcbddc->symmetric_primal) {
5196:       PetscCall(MatMatMult(A_II, coarse_phi_D, MAT_INITIAL_MATRIX, 1.0, &AUXMAT));
5197:       PetscCall(MatTransposeMatMult(coarse_psi_D, AUXMAT, MAT_INITIAL_MATRIX, 1.0, &TM1));
5198:       PetscCall(MatDestroy(&AUXMAT));
5199:       PetscCall(MatMatMult(A_BB, coarse_phi_B, MAT_INITIAL_MATRIX, 1.0, &AUXMAT));
5200:       PetscCall(MatTransposeMatMult(coarse_psi_B, AUXMAT, MAT_INITIAL_MATRIX, 1.0, &TM2));
5201:       PetscCall(MatDestroy(&AUXMAT));
5202:       PetscCall(MatMatMult(A_IB, coarse_phi_B, MAT_INITIAL_MATRIX, 1.0, &AUXMAT));
5203:       PetscCall(MatTransposeMatMult(coarse_psi_D, AUXMAT, MAT_INITIAL_MATRIX, 1.0, &TM3));
5204:       PetscCall(MatDestroy(&AUXMAT));
5205:       PetscCall(MatMatMult(A_BI, coarse_phi_D, MAT_INITIAL_MATRIX, 1.0, &AUXMAT));
5206:       PetscCall(MatTransposeMatMult(coarse_psi_B, AUXMAT, MAT_INITIAL_MATRIX, 1.0, &TM4));
5207:       PetscCall(MatDestroy(&AUXMAT));
5208:     } else {
5209:       PetscCall(MatPtAP(A_II, coarse_phi_D, MAT_INITIAL_MATRIX, 1.0, &TM1));
5210:       PetscCall(MatPtAP(A_BB, coarse_phi_B, MAT_INITIAL_MATRIX, 1.0, &TM2));
5211:       PetscCall(MatMatMult(A_IB, coarse_phi_B, MAT_INITIAL_MATRIX, 1.0, &AUXMAT));
5212:       PetscCall(MatTransposeMatMult(coarse_phi_D, AUXMAT, MAT_INITIAL_MATRIX, 1.0, &TM3));
5213:       PetscCall(MatDestroy(&AUXMAT));
5214:       PetscCall(MatMatMult(A_BI, coarse_phi_D, MAT_INITIAL_MATRIX, 1.0, &AUXMAT));
5215:       PetscCall(MatTransposeMatMult(coarse_phi_B, AUXMAT, MAT_INITIAL_MATRIX, 1.0, &TM4));
5216:       PetscCall(MatDestroy(&AUXMAT));
5217:     }
5218:     PetscCall(MatAXPY(TM1, one, TM2, DIFFERENT_NONZERO_PATTERN));
5219:     PetscCall(MatAXPY(TM1, one, TM3, DIFFERENT_NONZERO_PATTERN));
5220:     PetscCall(MatAXPY(TM1, one, TM4, DIFFERENT_NONZERO_PATTERN));
5221:     PetscCall(MatConvert(TM1, MATSEQDENSE, MAT_INPLACE_MATRIX, &TM1));
5222:     if (pcbddc->benign_n) {
5223:       Mat                B0_B, B0_BPHI;
5224:       const PetscScalar *data2;
5225:       PetscScalar       *data;
5226:       PetscInt           j;

5228:       PetscCall(ISCreateStride(PETSC_COMM_SELF, pcbddc->benign_n, 0, 1, &is_dummy));
5229:       PetscCall(MatCreateSubMatrix(pcbddc->benign_B0, is_dummy, pcis->is_B_local, MAT_INITIAL_MATRIX, &B0_B));
5230:       PetscCall(MatMatMult(B0_B, coarse_phi_B, MAT_INITIAL_MATRIX, 1.0, &B0_BPHI));
5231:       PetscCall(MatConvert(B0_BPHI, MATSEQDENSE, MAT_INPLACE_MATRIX, &B0_BPHI));
5232:       PetscCall(MatDenseGetArray(TM1, &data));
5233:       PetscCall(MatDenseGetArrayRead(B0_BPHI, &data2));
5234:       for (j = 0; j < pcbddc->benign_n; j++) {
5235:         PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
5236:         for (i = 0; i < pcbddc->local_primal_size; i++) {
5237:           data[primal_idx * pcbddc->local_primal_size + i] += data2[i * pcbddc->benign_n + j];
5238:           data[i * pcbddc->local_primal_size + primal_idx] += data2[i * pcbddc->benign_n + j];
5239:         }
5240:       }
5241:       PetscCall(MatDenseRestoreArray(TM1, &data));
5242:       PetscCall(MatDenseRestoreArrayRead(B0_BPHI, &data2));
5243:       PetscCall(MatDestroy(&B0_B));
5244:       PetscCall(ISDestroy(&is_dummy));
5245:       PetscCall(MatDestroy(&B0_BPHI));
5246:     }
5247:     PetscCall(MatAXPY(TM1, m_one, *coarse_submat, DIFFERENT_NONZERO_PATTERN));
5248:     PetscCall(MatNorm(TM1, NORM_FROBENIUS, &real_value));
5249:     PetscCall(PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer));
5250:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d          matrix error % 1.14e\n", PetscGlobalRank, (double)real_value));

5252:     /* check constraints */
5253:     PetscCall(ISCreateStride(PETSC_COMM_SELF, pcbddc->local_primal_size - pcbddc->benign_n, 0, 1, &is_dummy));
5254:     PetscCall(MatCreateSubMatrix(pcbddc->ConstraintMatrix, is_dummy, pcis->is_B_local, MAT_INITIAL_MATRIX, &C_B));
5255:     if (!pcbddc->benign_n) { /* TODO: add benign case */
5256:       PetscCall(MatMatMult(C_B, coarse_phi_B, MAT_INITIAL_MATRIX, 1.0, &CPHI));
5257:     } else {
5258:       PetscScalar *data;
5259:       Mat          tmat;
5260:       PetscCall(MatDenseGetArray(pcbddc->coarse_phi_B, &data));
5261:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, pcis->n_B, pcbddc->local_primal_size - pcbddc->benign_n, data, &tmat));
5262:       PetscCall(MatDenseRestoreArray(pcbddc->coarse_phi_B, &data));
5263:       PetscCall(MatMatMult(C_B, tmat, MAT_INITIAL_MATRIX, 1.0, &CPHI));
5264:       PetscCall(MatDestroy(&tmat));
5265:     }
5266:     PetscCall(MatCreateVecs(CPHI, &mones, NULL));
5267:     PetscCall(VecSet(mones, -1.0));
5268:     PetscCall(MatDiagonalSet(CPHI, mones, ADD_VALUES));
5269:     PetscCall(MatNorm(CPHI, NORM_FROBENIUS, &real_value));
5270:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d phi constraints error % 1.14e\n", PetscGlobalRank, (double)real_value));
5271:     if (!pcbddc->symmetric_primal) {
5272:       PetscCall(MatMatMult(C_B, coarse_psi_B, MAT_REUSE_MATRIX, 1.0, &CPHI));
5273:       PetscCall(VecSet(mones, -1.0));
5274:       PetscCall(MatDiagonalSet(CPHI, mones, ADD_VALUES));
5275:       PetscCall(MatNorm(CPHI, NORM_FROBENIUS, &real_value));
5276:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d psi constraints error % 1.14e\n", PetscGlobalRank, (double)real_value));
5277:     }
5278:     PetscCall(MatDestroy(&C_B));
5279:     PetscCall(MatDestroy(&CPHI));
5280:     PetscCall(ISDestroy(&is_dummy));
5281:     PetscCall(VecDestroy(&mones));
5282:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
5283:     PetscCall(MatDestroy(&A_II));
5284:     PetscCall(MatDestroy(&A_BB));
5285:     PetscCall(MatDestroy(&A_IB));
5286:     PetscCall(MatDestroy(&A_BI));
5287:     PetscCall(MatDestroy(&TM1));
5288:     PetscCall(MatDestroy(&TM2));
5289:     PetscCall(MatDestroy(&TM3));
5290:     PetscCall(MatDestroy(&TM4));
5291:     PetscCall(MatDestroy(&coarse_phi_D));
5292:     PetscCall(MatDestroy(&coarse_phi_B));
5293:     if (!pcbddc->symmetric_primal) {
5294:       PetscCall(MatDestroy(&coarse_psi_D));
5295:       PetscCall(MatDestroy(&coarse_psi_B));
5296:     }
5297:   }

5299: #if 0
5300:   {
5301:     PetscViewer viewer;
5302:     char filename[256];

5304:     PetscCall(PetscSNPrintf(filename, PETSC_STATIC_ARRAY_LENGTH(filename), "details_local_coarse_mat%d_level%d.m",PetscGlobalRank,pcbddc->current_level));
5305:     PetscCall(PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer));
5306:     PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
5307:     PetscCall(PetscObjectSetName((PetscObject)*coarse_submat,"coarse submat"));
5308:     PetscCall(MatView(*coarse_submat,viewer));
5309:     if (pcbddc->coarse_phi_B) {
5310:       PetscCall(PetscObjectSetName((PetscObject)pcbddc->coarse_phi_B,"phi_B"));
5311:       PetscCall(MatView(pcbddc->coarse_phi_B,viewer));
5312:     }
5313:     if (pcbddc->coarse_phi_D) {
5314:       PetscCall(PetscObjectSetName((PetscObject)pcbddc->coarse_phi_D,"phi_D"));
5315:       PetscCall(MatView(pcbddc->coarse_phi_D,viewer));
5316:     }
5317:     if (pcbddc->coarse_psi_B) {
5318:       PetscCall(PetscObjectSetName((PetscObject)pcbddc->coarse_psi_B,"psi_B"));
5319:       PetscCall(MatView(pcbddc->coarse_psi_B,viewer));
5320:     }
5321:     if (pcbddc->coarse_psi_D) {
5322:       PetscCall(PetscObjectSetName((PetscObject)pcbddc->coarse_psi_D,"psi_D"));
5323:       PetscCall(MatView(pcbddc->coarse_psi_D,viewer));
5324:     }
5325:     PetscCall(PetscObjectSetName((PetscObject)pcbddc->local_mat,"A"));
5326:     PetscCall(MatView(pcbddc->local_mat,viewer));
5327:     PetscCall(PetscObjectSetName((PetscObject)pcbddc->ConstraintMatrix,"C"));
5328:     PetscCall(MatView(pcbddc->ConstraintMatrix,viewer));
5329:     PetscCall(PetscObjectSetName((PetscObject)pcis->is_I_local,"I"));
5330:     PetscCall(ISView(pcis->is_I_local,viewer));
5331:     PetscCall(PetscObjectSetName((PetscObject)pcis->is_B_local,"B"));
5332:     PetscCall(ISView(pcis->is_B_local,viewer));
5333:     PetscCall(PetscObjectSetName((PetscObject)pcbddc->is_R_local,"R"));
5334:     PetscCall(ISView(pcbddc->is_R_local,viewer));
5335:     PetscCall(PetscViewerDestroy(&viewer));
5336:   }
5337: #endif

5339:   /* device support */
5340:   {
5341:     PetscBool iscuda, iship, iskokkos;
5342:     MatType   mtype = NULL;

5344:     PetscCall(PetscObjectTypeCompareAny((PetscObject)pcis->vec1_N, &iscuda, VECCUDA, VECMPICUDA, VECSEQCUDA, ""));
5345:     PetscCall(PetscObjectTypeCompareAny((PetscObject)pcis->vec1_N, &iship, VECHIP, VECMPIHIP, VECSEQHIP, ""));
5346:     PetscCall(PetscObjectTypeCompareAny((PetscObject)pcis->vec1_N, &iskokkos, VECKOKKOS, VECMPIKOKKOS, VECSEQKOKKOS, ""));
5347:     if (iskokkos) {
5348:       if (PetscDefined(HAVE_MACRO_KOKKOS_ENABLE_CUDA)) iscuda = PETSC_TRUE;
5349:       else if (PetscDefined(HAVE_MACRO_KOKKOS_ENABLE_HIP)) iship = PETSC_TRUE;
5350:     }
5351:     if (iskokkos) mtype = multi_element ? MATSEQAIJKOKKOS : (iscuda ? MATSEQDENSECUDA : MATSEQDENSEHIP);
5352:     else if (iship) mtype = multi_element ? MATSEQAIJHIPSPARSE : MATSEQDENSEHIP;
5353:     else if (iscuda) mtype = multi_element ? MATSEQAIJCUSPARSE : MATSEQDENSECUDA;
5354:     if (mtype) {
5355:       if (pcbddc->local_auxmat1) PetscCall(MatConvert(pcbddc->local_auxmat1, mtype, MAT_INPLACE_MATRIX, &pcbddc->local_auxmat1));
5356:       if (pcbddc->local_auxmat2) PetscCall(MatConvert(pcbddc->local_auxmat2, mtype, MAT_INPLACE_MATRIX, &pcbddc->local_auxmat2));
5357:       if (pcbddc->coarse_phi_B) PetscCall(MatConvert(pcbddc->coarse_phi_B, mtype, MAT_INPLACE_MATRIX, &pcbddc->coarse_phi_B));
5358:       if (pcbddc->coarse_phi_D) PetscCall(MatConvert(pcbddc->coarse_phi_D, mtype, MAT_INPLACE_MATRIX, &pcbddc->coarse_phi_D));
5359:       if (pcbddc->coarse_psi_B) PetscCall(MatConvert(pcbddc->coarse_psi_B, mtype, MAT_INPLACE_MATRIX, &pcbddc->coarse_psi_B));
5360:       if (pcbddc->coarse_psi_D) PetscCall(MatConvert(pcbddc->coarse_psi_D, mtype, MAT_INPLACE_MATRIX, &pcbddc->coarse_psi_D));
5361:     }
5362:   }
5363:   PetscFunctionReturn(PETSC_SUCCESS);
5364: }

5366: PetscErrorCode MatCreateSubMatrixUnsorted(Mat A, IS isrow, IS iscol, Mat *B)
5367: {
5368:   Mat      *work_mat;
5369:   IS        isrow_s, iscol_s;
5370:   PetscBool rsorted, csorted;
5371:   PetscInt  rsize, *idxs_perm_r = NULL, csize, *idxs_perm_c = NULL;

5373:   PetscFunctionBegin;
5374:   PetscCall(ISSorted(isrow, &rsorted));
5375:   PetscCall(ISSorted(iscol, &csorted));
5376:   PetscCall(ISGetLocalSize(isrow, &rsize));
5377:   PetscCall(ISGetLocalSize(iscol, &csize));

5379:   if (!rsorted) {
5380:     const PetscInt *idxs;
5381:     PetscInt       *idxs_sorted, i;

5383:     PetscCall(PetscMalloc1(rsize, &idxs_perm_r));
5384:     PetscCall(PetscMalloc1(rsize, &idxs_sorted));
5385:     for (i = 0; i < rsize; i++) idxs_perm_r[i] = i;
5386:     PetscCall(ISGetIndices(isrow, &idxs));
5387:     PetscCall(PetscSortIntWithPermutation(rsize, idxs, idxs_perm_r));
5388:     for (i = 0; i < rsize; i++) idxs_sorted[i] = idxs[idxs_perm_r[i]];
5389:     PetscCall(ISRestoreIndices(isrow, &idxs));
5390:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, rsize, idxs_sorted, PETSC_OWN_POINTER, &isrow_s));
5391:   } else {
5392:     PetscCall(PetscObjectReference((PetscObject)isrow));
5393:     isrow_s = isrow;
5394:   }

5396:   if (!csorted) {
5397:     if (isrow == iscol) {
5398:       PetscCall(PetscObjectReference((PetscObject)isrow_s));
5399:       iscol_s = isrow_s;
5400:     } else {
5401:       const PetscInt *idxs;
5402:       PetscInt       *idxs_sorted, i;

5404:       PetscCall(PetscMalloc1(csize, &idxs_perm_c));
5405:       PetscCall(PetscMalloc1(csize, &idxs_sorted));
5406:       for (i = 0; i < csize; i++) idxs_perm_c[i] = i;
5407:       PetscCall(ISGetIndices(iscol, &idxs));
5408:       PetscCall(PetscSortIntWithPermutation(csize, idxs, idxs_perm_c));
5409:       for (i = 0; i < csize; i++) idxs_sorted[i] = idxs[idxs_perm_c[i]];
5410:       PetscCall(ISRestoreIndices(iscol, &idxs));
5411:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, csize, idxs_sorted, PETSC_OWN_POINTER, &iscol_s));
5412:     }
5413:   } else {
5414:     PetscCall(PetscObjectReference((PetscObject)iscol));
5415:     iscol_s = iscol;
5416:   }

5418:   PetscCall(MatCreateSubMatrices(A, 1, &isrow_s, &iscol_s, MAT_INITIAL_MATRIX, &work_mat));

5420:   if (!rsorted || !csorted) {
5421:     Mat new_mat;
5422:     IS  is_perm_r, is_perm_c;

5424:     if (!rsorted) {
5425:       PetscInt *idxs_r, i;
5426:       PetscCall(PetscMalloc1(rsize, &idxs_r));
5427:       for (i = 0; i < rsize; i++) idxs_r[idxs_perm_r[i]] = i;
5428:       PetscCall(PetscFree(idxs_perm_r));
5429:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, rsize, idxs_r, PETSC_OWN_POINTER, &is_perm_r));
5430:     } else {
5431:       PetscCall(ISCreateStride(PETSC_COMM_SELF, rsize, 0, 1, &is_perm_r));
5432:     }
5433:     PetscCall(ISSetPermutation(is_perm_r));

5435:     if (!csorted) {
5436:       if (isrow_s == iscol_s) {
5437:         PetscCall(PetscObjectReference((PetscObject)is_perm_r));
5438:         is_perm_c = is_perm_r;
5439:       } else {
5440:         PetscInt *idxs_c, i;
5441:         PetscCheck(idxs_perm_c, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Permutation array not present");
5442:         PetscCall(PetscMalloc1(csize, &idxs_c));
5443:         for (i = 0; i < csize; i++) idxs_c[idxs_perm_c[i]] = i;
5444:         PetscCall(PetscFree(idxs_perm_c));
5445:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, csize, idxs_c, PETSC_OWN_POINTER, &is_perm_c));
5446:       }
5447:     } else {
5448:       PetscCall(ISCreateStride(PETSC_COMM_SELF, csize, 0, 1, &is_perm_c));
5449:     }
5450:     PetscCall(ISSetPermutation(is_perm_c));

5452:     PetscCall(MatPermute(work_mat[0], is_perm_r, is_perm_c, &new_mat));
5453:     PetscCall(MatDestroy(&work_mat[0]));
5454:     work_mat[0] = new_mat;
5455:     PetscCall(ISDestroy(&is_perm_r));
5456:     PetscCall(ISDestroy(&is_perm_c));
5457:   }

5459:   PetscCall(PetscObjectReference((PetscObject)work_mat[0]));
5460:   *B = work_mat[0];
5461:   PetscCall(MatDestroyMatrices(1, &work_mat));
5462:   PetscCall(ISDestroy(&isrow_s));
5463:   PetscCall(ISDestroy(&iscol_s));
5464:   PetscFunctionReturn(PETSC_SUCCESS);
5465: }

5467: PetscErrorCode PCBDDCComputeLocalMatrix(PC pc, Mat ChangeOfBasisMatrix)
5468: {
5469:   Mat_IS   *matis  = (Mat_IS *)pc->pmat->data;
5470:   PC_BDDC  *pcbddc = (PC_BDDC *)pc->data;
5471:   Mat       new_mat, lA;
5472:   IS        is_local, is_global;
5473:   PetscInt  local_size;
5474:   PetscBool isseqaij, issym, isset;

5476:   PetscFunctionBegin;
5477:   PetscCall(MatDestroy(&pcbddc->local_mat));
5478:   PetscCall(MatGetSize(matis->A, &local_size, NULL));
5479:   if (pcbddc->mat_graph->multi_element) {
5480:     Mat     *mats, *bdiags;
5481:     IS      *gsubs;
5482:     PetscInt nsubs = pcbddc->n_local_subs;

5484:     PetscCall(PetscCalloc1(nsubs * nsubs, &mats));
5485:     PetscCall(PetscMalloc1(nsubs, &gsubs));
5486:     for (PetscInt i = 0; i < nsubs; i++) PetscCall(ISLocalToGlobalMappingApplyIS(matis->rmapping, pcbddc->local_subs[i], &gsubs[i]));
5487:     PetscCall(MatCreateSubMatrices(ChangeOfBasisMatrix, nsubs, gsubs, gsubs, MAT_INITIAL_MATRIX, &bdiags));
5488:     for (PetscInt i = 0; i < nsubs; i++) PetscCall(ISDestroy(&gsubs[i]));
5489:     PetscCall(PetscFree(gsubs));

5491:     for (PetscInt i = 0; i < nsubs; i++) mats[i * (1 + nsubs)] = bdiags[i];
5492:     PetscCall(MatCreateNest(PETSC_COMM_SELF, nsubs, pcbddc->local_subs, nsubs, pcbddc->local_subs, mats, &new_mat));
5493:     PetscCall(MatConvert(new_mat, MATSEQAIJ, MAT_INPLACE_MATRIX, &new_mat));
5494:     PetscCall(MatDestroySubMatrices(nsubs, &bdiags));
5495:     PetscCall(PetscFree(mats));
5496:   } else {
5497:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)matis->A), local_size, 0, 1, &is_local));
5498:     PetscCall(ISLocalToGlobalMappingApplyIS(matis->rmapping, is_local, &is_global));
5499:     PetscCall(ISDestroy(&is_local));
5500:     PetscCall(MatCreateSubMatrixUnsorted(ChangeOfBasisMatrix, is_global, is_global, &new_mat));
5501:     PetscCall(ISDestroy(&is_global));
5502:   }
5503:   if (pcbddc->dbg_flag) {
5504:     Vec       x, x_change;
5505:     PetscReal error;

5507:     PetscCall(MatCreateVecs(ChangeOfBasisMatrix, &x, &x_change));
5508:     PetscCall(VecSetRandom(x, NULL));
5509:     PetscCall(MatMult(ChangeOfBasisMatrix, x, x_change));
5510:     PetscCall(VecScatterBegin(matis->cctx, x, matis->x, INSERT_VALUES, SCATTER_FORWARD));
5511:     PetscCall(VecScatterEnd(matis->cctx, x, matis->x, INSERT_VALUES, SCATTER_FORWARD));
5512:     PetscCall(MatMult(new_mat, matis->x, matis->y));
5513:     if (!pcbddc->change_interior) {
5514:       const PetscScalar *x, *y, *v;
5515:       PetscReal          lerror = 0.;
5516:       PetscInt           i;

5518:       PetscCall(VecGetArrayRead(matis->x, &x));
5519:       PetscCall(VecGetArrayRead(matis->y, &y));
5520:       PetscCall(VecGetArrayRead(matis->counter, &v));
5521:       for (i = 0; i < local_size; i++)
5522:         if (PetscRealPart(v[i]) < 1.5 && PetscAbsScalar(x[i] - y[i]) > lerror) lerror = PetscAbsScalar(x[i] - y[i]);
5523:       PetscCall(VecRestoreArrayRead(matis->x, &x));
5524:       PetscCall(VecRestoreArrayRead(matis->y, &y));
5525:       PetscCall(VecRestoreArrayRead(matis->counter, &v));
5526:       PetscCallMPI(MPIU_Allreduce(&lerror, &error, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)pc)));
5527:       if (error > PETSC_SMALL) {
5528:         if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
5529:           SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Error global vs local change on I: %1.6e", (double)error);
5530:         } else {
5531:           SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "Error global vs local change on I: %1.6e", (double)error);
5532:         }
5533:       }
5534:     }
5535:     PetscCall(VecScatterBegin(matis->rctx, matis->y, x, INSERT_VALUES, SCATTER_REVERSE));
5536:     PetscCall(VecScatterEnd(matis->rctx, matis->y, x, INSERT_VALUES, SCATTER_REVERSE));
5537:     PetscCall(VecAXPY(x, -1.0, x_change));
5538:     PetscCall(VecNorm(x, NORM_INFINITY, &error));
5539:     if (error > PETSC_SMALL) {
5540:       if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
5541:         SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Error global vs local change on N: %1.6e", (double)error);
5542:       } else {
5543:         SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "Error global vs local change on N: %1.6e", (double)error);
5544:       }
5545:     }
5546:     PetscCall(VecDestroy(&x));
5547:     PetscCall(VecDestroy(&x_change));
5548:   }

5550:   /* lA is present if we are setting up an inner BDDC for a saddle point FETI-DP */
5551:   PetscCall(PetscObjectQuery((PetscObject)pc, "__KSPFETIDP_lA", (PetscObject *)&lA));

5553:   /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
5554:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)matis->A, MATSEQAIJ, &isseqaij));
5555:   if (isseqaij) {
5556:     PetscCall(MatDestroy(&pcbddc->local_mat));
5557:     PetscCall(MatPtAP(matis->A, new_mat, MAT_INITIAL_MATRIX, 2.0, &pcbddc->local_mat));
5558:     if (lA) {
5559:       Mat work;
5560:       PetscCall(MatPtAP(lA, new_mat, MAT_INITIAL_MATRIX, 2.0, &work));
5561:       PetscCall(PetscObjectCompose((PetscObject)pc, "__KSPFETIDP_lA", (PetscObject)work));
5562:       PetscCall(MatDestroy(&work));
5563:     }
5564:   } else {
5565:     Mat work_mat;

5567:     PetscCall(MatDestroy(&pcbddc->local_mat));
5568:     PetscCall(MatConvert(matis->A, MATSEQAIJ, MAT_INITIAL_MATRIX, &work_mat));
5569:     PetscCall(MatPtAP(work_mat, new_mat, MAT_INITIAL_MATRIX, 2.0, &pcbddc->local_mat));
5570:     PetscCall(MatDestroy(&work_mat));
5571:     if (lA) {
5572:       Mat work;
5573:       PetscCall(MatConvert(lA, MATSEQAIJ, MAT_INITIAL_MATRIX, &work_mat));
5574:       PetscCall(MatPtAP(work_mat, new_mat, MAT_INITIAL_MATRIX, 2.0, &work));
5575:       PetscCall(PetscObjectCompose((PetscObject)pc, "__KSPFETIDP_lA", (PetscObject)work));
5576:       PetscCall(MatDestroy(&work));
5577:     }
5578:   }
5579:   PetscCall(MatIsSymmetricKnown(matis->A, &isset, &issym));
5580:   if (isset) PetscCall(MatSetOption(pcbddc->local_mat, MAT_SYMMETRIC, issym));
5581:   PetscCall(MatDestroy(&new_mat));
5582:   PetscFunctionReturn(PETSC_SUCCESS);
5583: }

5585: PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
5586: {
5587:   PC_IS          *pcis        = (PC_IS *)pc->data;
5588:   PC_BDDC        *pcbddc      = (PC_BDDC *)pc->data;
5589:   PCBDDCSubSchurs sub_schurs  = pcbddc->sub_schurs;
5590:   PetscInt       *idx_R_local = NULL;
5591:   PetscInt        n_vertices, i, j, n_R, n_D, n_B;
5592:   PetscInt        vbs, bs;
5593:   PetscBT         bitmask = NULL;

5595:   PetscFunctionBegin;
5596:   /*
5597:     No need to setup local scatters if
5598:       - primal space is unchanged
5599:         AND
5600:       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
5601:         AND
5602:       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
5603:   */
5604:   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) PetscFunctionReturn(PETSC_SUCCESS);
5605:   /* destroy old objects */
5606:   PetscCall(ISDestroy(&pcbddc->is_R_local));
5607:   PetscCall(VecScatterDestroy(&pcbddc->R_to_B));
5608:   PetscCall(VecScatterDestroy(&pcbddc->R_to_D));
5609:   /* Set Non-overlapping dimensions */
5610:   n_B        = pcis->n_B;
5611:   n_D        = pcis->n - n_B;
5612:   n_vertices = pcbddc->n_vertices;

5614:   /* Dohrmann's notation: dofs split in R (Remaining: all dofs but the vertices) and V (Vertices) */

5616:   /* create auxiliary bitmask and allocate workspace */
5617:   if (!sub_schurs || !sub_schurs->reuse_solver) {
5618:     PetscCall(PetscMalloc1(pcis->n - n_vertices, &idx_R_local));
5619:     PetscCall(PetscBTCreate(pcis->n, &bitmask));
5620:     for (i = 0; i < n_vertices; i++) PetscCall(PetscBTSet(bitmask, pcbddc->local_primal_ref_node[i]));

5622:     for (i = 0, n_R = 0; i < pcis->n; i++) {
5623:       if (!PetscBTLookup(bitmask, i)) idx_R_local[n_R++] = i;
5624:     }
5625:   } else { /* A different ordering (already computed) is present if we are reusing the Schur solver */
5626:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5628:     PetscCall(ISGetIndices(reuse_solver->is_R, (const PetscInt **)&idx_R_local));
5629:     PetscCall(ISGetLocalSize(reuse_solver->is_R, &n_R));
5630:   }

5632:   /* Block code */
5633:   vbs = 1;
5634:   PetscCall(MatGetBlockSize(pcbddc->local_mat, &bs));
5635:   if (bs > 1 && !(n_vertices % bs)) {
5636:     PetscBool is_blocked = PETSC_TRUE;
5637:     PetscInt *vary;
5638:     if (!sub_schurs || !sub_schurs->reuse_solver) {
5639:       PetscCall(PetscMalloc1(pcis->n / bs, &vary));
5640:       PetscCall(PetscArrayzero(vary, pcis->n / bs));
5641:       /* Verify that the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
5642:       /* it is ok to check this way since local_primal_ref_node are always sorted by local numbering and idx_R_local is obtained as a complement */
5643:       for (i = 0; i < n_vertices; i++) vary[pcbddc->local_primal_ref_node[i] / bs]++;
5644:       for (i = 0; i < pcis->n / bs; i++) {
5645:         if (vary[i] != 0 && vary[i] != bs) {
5646:           is_blocked = PETSC_FALSE;
5647:           break;
5648:         }
5649:       }
5650:       PetscCall(PetscFree(vary));
5651:     } else {
5652:       /* Verify directly the R set */
5653:       for (i = 0; i < n_R / bs; i++) {
5654:         PetscInt j, node = idx_R_local[bs * i];
5655:         for (j = 1; j < bs; j++) {
5656:           if (node != idx_R_local[bs * i + j] - j) {
5657:             is_blocked = PETSC_FALSE;
5658:             break;
5659:           }
5660:         }
5661:       }
5662:     }
5663:     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
5664:       vbs = bs;
5665:       for (i = 0; i < n_R / vbs; i++) idx_R_local[i] = idx_R_local[vbs * i] / vbs;
5666:     }
5667:   }
5668:   PetscCall(ISCreateBlock(PETSC_COMM_SELF, vbs, n_R / vbs, idx_R_local, PETSC_COPY_VALUES, &pcbddc->is_R_local));
5669:   if (sub_schurs && sub_schurs->reuse_solver) {
5670:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5672:     PetscCall(ISRestoreIndices(reuse_solver->is_R, (const PetscInt **)&idx_R_local));
5673:     PetscCall(ISDestroy(&reuse_solver->is_R));
5674:     PetscCall(PetscObjectReference((PetscObject)pcbddc->is_R_local));
5675:     reuse_solver->is_R = pcbddc->is_R_local;
5676:   } else {
5677:     PetscCall(PetscFree(idx_R_local));
5678:   }

5680:   /* print some info if requested */
5681:   if (pcbddc->dbg_flag) {
5682:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "--------------------------------------------------\n"));
5683:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
5684:     PetscCall(PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer));
5685:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d local dimensions\n", PetscGlobalRank));
5686:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "local_size = %" PetscInt_FMT ", dirichlet_size = %" PetscInt_FMT ", boundary_size = %" PetscInt_FMT "\n", pcis->n, n_D, n_B));
5687:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "r_size = %" PetscInt_FMT ", v_size = %" PetscInt_FMT ", constraints = %" PetscInt_FMT ", local_primal_size = %" PetscInt_FMT "\n", n_R, n_vertices,
5688:                                                  pcbddc->local_primal_size - n_vertices - pcbddc->benign_n, pcbddc->local_primal_size));
5689:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
5690:   }

5692:   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
5693:   if (!sub_schurs || !sub_schurs->reuse_solver) {
5694:     IS        is_aux1, is_aux2;
5695:     PetscInt *aux_array1, *aux_array2, *is_indices, *idx_R_local;

5697:     PetscCall(ISGetIndices(pcbddc->is_R_local, (const PetscInt **)&idx_R_local));
5698:     PetscCall(PetscMalloc1(pcis->n_B - n_vertices, &aux_array1));
5699:     PetscCall(PetscMalloc1(pcis->n_B - n_vertices, &aux_array2));
5700:     PetscCall(ISGetIndices(pcis->is_I_local, (const PetscInt **)&is_indices));
5701:     for (i = 0; i < n_D; i++) PetscCall(PetscBTSet(bitmask, is_indices[i]));
5702:     PetscCall(ISRestoreIndices(pcis->is_I_local, (const PetscInt **)&is_indices));
5703:     for (i = 0, j = 0; i < n_R; i++) {
5704:       if (!PetscBTLookup(bitmask, idx_R_local[i])) aux_array1[j++] = i;
5705:     }
5706:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, j, aux_array1, PETSC_OWN_POINTER, &is_aux1));
5707:     PetscCall(ISGetIndices(pcis->is_B_local, (const PetscInt **)&is_indices));
5708:     for (i = 0, j = 0; i < n_B; i++) {
5709:       if (!PetscBTLookup(bitmask, is_indices[i])) aux_array2[j++] = i;
5710:     }
5711:     PetscCall(ISRestoreIndices(pcis->is_B_local, (const PetscInt **)&is_indices));
5712:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, j, aux_array2, PETSC_OWN_POINTER, &is_aux2));
5713:     PetscCall(VecScatterCreate(pcbddc->vec1_R, is_aux1, pcis->vec1_B, is_aux2, &pcbddc->R_to_B));
5714:     PetscCall(ISDestroy(&is_aux1));
5715:     PetscCall(ISDestroy(&is_aux2));

5717:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
5718:       PetscCall(PetscMalloc1(n_D, &aux_array1));
5719:       for (i = 0, j = 0; i < n_R; i++) {
5720:         if (PetscBTLookup(bitmask, idx_R_local[i])) aux_array1[j++] = i;
5721:       }
5722:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, j, aux_array1, PETSC_OWN_POINTER, &is_aux1));
5723:       PetscCall(VecScatterCreate(pcbddc->vec1_R, is_aux1, pcis->vec1_D, (IS)0, &pcbddc->R_to_D));
5724:       PetscCall(ISDestroy(&is_aux1));
5725:     }
5726:     PetscCall(PetscBTDestroy(&bitmask));
5727:     PetscCall(ISRestoreIndices(pcbddc->is_R_local, (const PetscInt **)&idx_R_local));
5728:   } else {
5729:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
5730:     IS                 tis;
5731:     PetscInt           schur_size;

5733:     PetscCall(ISGetLocalSize(reuse_solver->is_B, &schur_size));
5734:     PetscCall(ISCreateStride(PETSC_COMM_SELF, schur_size, n_D, 1, &tis));
5735:     PetscCall(VecScatterCreate(pcbddc->vec1_R, tis, pcis->vec1_B, reuse_solver->is_B, &pcbddc->R_to_B));
5736:     PetscCall(ISDestroy(&tis));
5737:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
5738:       PetscCall(ISCreateStride(PETSC_COMM_SELF, n_D, 0, 1, &tis));
5739:       PetscCall(VecScatterCreate(pcbddc->vec1_R, tis, pcis->vec1_D, (IS)0, &pcbddc->R_to_D));
5740:       PetscCall(ISDestroy(&tis));
5741:     }
5742:   }
5743:   PetscFunctionReturn(PETSC_SUCCESS);
5744: }

5746: PetscErrorCode MatNullSpacePropagateAny_Private(Mat A, IS is, Mat B)
5747: {
5748:   MatNullSpace NullSpace;
5749:   Mat          dmat;
5750:   const Vec   *nullvecs;
5751:   Vec          v, v2, *nullvecs2;
5752:   VecScatter   sct = NULL;
5753:   PetscScalar *ddata;
5754:   PetscInt     k, nnsp_size, bsiz, bsiz2, n, N, bs;
5755:   PetscBool    nnsp_has_cnst;

5757:   PetscFunctionBegin;
5758:   if (!is && !B) { /* MATIS */
5759:     Mat_IS *matis = (Mat_IS *)A->data;

5761:     if (!B) PetscCall(MatISGetLocalMat(A, &B));
5762:     sct = matis->cctx;
5763:     PetscCall(PetscObjectReference((PetscObject)sct));
5764:   } else {
5765:     PetscCall(MatGetNullSpace(B, &NullSpace));
5766:     if (!NullSpace) PetscCall(MatGetNearNullSpace(B, &NullSpace));
5767:     if (NullSpace) PetscFunctionReturn(PETSC_SUCCESS);
5768:   }
5769:   PetscCall(MatGetNullSpace(A, &NullSpace));
5770:   if (!NullSpace) PetscCall(MatGetNearNullSpace(A, &NullSpace));
5771:   if (!NullSpace) PetscFunctionReturn(PETSC_SUCCESS);

5773:   PetscCall(MatCreateVecs(A, &v, NULL));
5774:   PetscCall(MatCreateVecs(B, &v2, NULL));
5775:   if (!sct) PetscCall(VecScatterCreate(v, is, v2, NULL, &sct));
5776:   PetscCall(MatNullSpaceGetVecs(NullSpace, &nnsp_has_cnst, &nnsp_size, &nullvecs));
5777:   bsiz = bsiz2 = nnsp_size + !!nnsp_has_cnst;
5778:   PetscCall(PetscMalloc1(bsiz, &nullvecs2));
5779:   PetscCall(VecGetBlockSize(v2, &bs));
5780:   PetscCall(VecGetSize(v2, &N));
5781:   PetscCall(VecGetLocalSize(v2, &n));
5782:   PetscCall(PetscMalloc1(n * bsiz, &ddata));
5783:   for (k = 0; k < nnsp_size; k++) {
5784:     PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), bs, n, N, ddata + n * k, &nullvecs2[k]));
5785:     PetscCall(VecScatterBegin(sct, nullvecs[k], nullvecs2[k], INSERT_VALUES, SCATTER_FORWARD));
5786:     PetscCall(VecScatterEnd(sct, nullvecs[k], nullvecs2[k], INSERT_VALUES, SCATTER_FORWARD));
5787:   }
5788:   if (nnsp_has_cnst) {
5789:     PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)B), bs, n, N, ddata + n * nnsp_size, &nullvecs2[nnsp_size]));
5790:     PetscCall(VecSet(nullvecs2[nnsp_size], 1.0));
5791:   }
5792:   PetscCall(PCBDDCOrthonormalizeVecs(&bsiz2, nullvecs2));
5793:   PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)B), PETSC_FALSE, bsiz2, nullvecs2, &NullSpace));

5795:   PetscCall(MatCreateDense(PetscObjectComm((PetscObject)B), n, PETSC_DECIDE, N, bsiz2, ddata, &dmat));
5796:   PetscCall(PetscObjectContainerCompose((PetscObject)dmat, "_PBDDC_Null_dmat_arr", ddata, PetscCtxDestroyDefault));
5797:   PetscCall(PetscObjectCompose((PetscObject)NullSpace, "_PBDDC_Null_dmat", (PetscObject)dmat));
5798:   PetscCall(MatDestroy(&dmat));

5800:   for (k = 0; k < bsiz; k++) PetscCall(VecDestroy(&nullvecs2[k]));
5801:   PetscCall(PetscFree(nullvecs2));
5802:   PetscCall(MatSetNearNullSpace(B, NullSpace));
5803:   PetscCall(MatNullSpaceDestroy(&NullSpace));
5804:   PetscCall(VecDestroy(&v));
5805:   PetscCall(VecDestroy(&v2));
5806:   PetscCall(VecScatterDestroy(&sct));
5807:   PetscFunctionReturn(PETSC_SUCCESS);
5808: }

5810: PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, PetscBool dirichlet, PetscBool neumann)
5811: {
5812:   PC_BDDC     *pcbddc = (PC_BDDC *)pc->data;
5813:   PC_IS       *pcis   = (PC_IS *)pc->data;
5814:   PC           pc_temp;
5815:   Mat          A_RR;
5816:   MatNullSpace nnsp;
5817:   MatReuse     reuse;
5818:   PetscScalar  m_one = -1.0;
5819:   PetscReal    value;
5820:   PetscInt     n_D, n_R;
5821:   PetscBool    issbaij, opts, isset, issym;
5822:   PetscBool    f = PETSC_FALSE;
5823:   char         dir_prefix[256], neu_prefix[256], str_level[16];
5824:   size_t       len;

5826:   PetscFunctionBegin;
5827:   PetscCall(PetscLogEventBegin(PC_BDDC_LocalSolvers[pcbddc->current_level], pc, 0, 0, 0));
5828:   /* approximate solver, propagate NearNullSpace if needed */
5829:   if (!pc->setupcalled && (pcbddc->NullSpace_corr[0] || pcbddc->NullSpace_corr[2])) {
5830:     MatNullSpace gnnsp1, gnnsp2;
5831:     PetscBool    lhas, ghas;

5833:     PetscCall(MatGetNearNullSpace(pcbddc->local_mat, &nnsp));
5834:     PetscCall(MatGetNearNullSpace(pc->pmat, &gnnsp1));
5835:     PetscCall(MatGetNullSpace(pc->pmat, &gnnsp2));
5836:     lhas = nnsp ? PETSC_TRUE : PETSC_FALSE;
5837:     PetscCallMPI(MPIU_Allreduce(&lhas, &ghas, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)pc)));
5838:     if (!ghas && (gnnsp1 || gnnsp2)) PetscCall(MatNullSpacePropagateAny_Private(pc->pmat, NULL, NULL));
5839:   }

5841:   /* compute prefixes */
5842:   PetscCall(PetscStrncpy(dir_prefix, "", sizeof(dir_prefix)));
5843:   PetscCall(PetscStrncpy(neu_prefix, "", sizeof(neu_prefix)));
5844:   if (!pcbddc->current_level) {
5845:     PetscCall(PetscStrncpy(dir_prefix, ((PetscObject)pc)->prefix, sizeof(dir_prefix)));
5846:     PetscCall(PetscStrncpy(neu_prefix, ((PetscObject)pc)->prefix, sizeof(neu_prefix)));
5847:     PetscCall(PetscStrlcat(dir_prefix, "pc_bddc_dirichlet_", sizeof(dir_prefix)));
5848:     PetscCall(PetscStrlcat(neu_prefix, "pc_bddc_neumann_", sizeof(neu_prefix)));
5849:   } else {
5850:     PetscCall(PetscSNPrintf(str_level, sizeof(str_level), "l%" PetscInt_FMT "_", pcbddc->current_level));
5851:     PetscCall(PetscStrlen(((PetscObject)pc)->prefix, &len));
5852:     len -= 15;                                /* remove "pc_bddc_coarse_" */
5853:     if (pcbddc->current_level > 1) len -= 3;  /* remove "lX_" with X level number */
5854:     if (pcbddc->current_level > 10) len -= 1; /* remove another char from level number */
5855:     /* Nonstandard use of PetscStrncpy() to only copy a portion of the input string */
5856:     PetscCall(PetscStrncpy(dir_prefix, ((PetscObject)pc)->prefix, len + 1));
5857:     PetscCall(PetscStrncpy(neu_prefix, ((PetscObject)pc)->prefix, len + 1));
5858:     PetscCall(PetscStrlcat(dir_prefix, "pc_bddc_dirichlet_", sizeof(dir_prefix)));
5859:     PetscCall(PetscStrlcat(neu_prefix, "pc_bddc_neumann_", sizeof(neu_prefix)));
5860:     PetscCall(PetscStrlcat(dir_prefix, str_level, sizeof(dir_prefix)));
5861:     PetscCall(PetscStrlcat(neu_prefix, str_level, sizeof(neu_prefix)));
5862:   }

5864:   /* DIRICHLET PROBLEM */
5865:   if (dirichlet) {
5866:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5867:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
5868:       PetscCheck(sub_schurs && sub_schurs->reuse_solver, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented");
5869:       if (pcbddc->dbg_flag) {
5870:         Mat A_IIn;

5872:         PetscCall(PCBDDCBenignProject(pc, pcis->is_I_local, pcis->is_I_local, &A_IIn));
5873:         PetscCall(MatDestroy(&pcis->A_II));
5874:         pcis->A_II = A_IIn;
5875:       }
5876:     }
5877:     PetscCall(MatIsSymmetricKnown(pcbddc->local_mat, &isset, &issym));
5878:     if (isset) PetscCall(MatSetOption(pcis->A_II, MAT_SYMMETRIC, issym));

5880:     /* Matrix for Dirichlet problem is pcis->A_II */
5881:     n_D  = pcis->n - pcis->n_B;
5882:     opts = PETSC_FALSE;
5883:     if (!pcbddc->ksp_D) { /* create object if not yet build */
5884:       opts = PETSC_TRUE;
5885:       PetscCall(KSPCreate(PETSC_COMM_SELF, &pcbddc->ksp_D));
5886:       PetscCall(KSPSetNestLevel(pcbddc->ksp_D, pc->kspnestlevel));
5887:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D, (PetscObject)pc, 1));
5888:       /* default */
5889:       PetscCall(KSPSetType(pcbddc->ksp_D, KSPPREONLY));
5890:       PetscCall(KSPSetOptionsPrefix(pcbddc->ksp_D, dir_prefix));
5891:       PetscCall(PetscObjectTypeCompare((PetscObject)pcis->pA_II, MATSEQSBAIJ, &issbaij));
5892:       PetscCall(KSPGetPC(pcbddc->ksp_D, &pc_temp));
5893:       if (issbaij) {
5894:         PetscCall(PCSetType(pc_temp, PCCHOLESKY));
5895:       } else {
5896:         PetscCall(PCSetType(pc_temp, PCLU));
5897:       }
5898:       PetscCall(KSPSetErrorIfNotConverged(pcbddc->ksp_D, pc->erroriffailure));
5899:     }
5900:     PetscCall(MatSetOptionsPrefix(pcis->pA_II, ((PetscObject)pcbddc->ksp_D)->prefix));
5901:     PetscCall(MatViewFromOptions(pcis->pA_II, NULL, "-mat_view"));
5902:     PetscCall(KSPSetOperators(pcbddc->ksp_D, pcis->A_II, pcis->pA_II));
5903:     /* Allow user's customization */
5904:     if (opts) PetscCall(KSPSetFromOptions(pcbddc->ksp_D));
5905:     PetscCall(MatGetNearNullSpace(pcis->pA_II, &nnsp));
5906:     if (pcbddc->NullSpace_corr[0] && !nnsp) { /* approximate solver, propagate NearNullSpace */
5907:       PetscCall(MatNullSpacePropagateAny_Private(pcbddc->local_mat, pcis->is_I_local, pcis->pA_II));
5908:     }
5909:     PetscCall(MatGetNearNullSpace(pcis->pA_II, &nnsp));
5910:     PetscCall(KSPGetPC(pcbddc->ksp_D, &pc_temp));
5911:     PetscCall(PetscObjectHasFunction((PetscObject)pc_temp, "PCSetCoordinates_C", &f));
5912:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
5913:       PetscReal      *coords = pcbddc->mat_graph->coords, *scoords;
5914:       const PetscInt *idxs;
5915:       PetscInt        cdim = pcbddc->mat_graph->cdim, nl, i, d;

5917:       PetscCall(ISGetLocalSize(pcis->is_I_local, &nl));
5918:       PetscCall(ISGetIndices(pcis->is_I_local, &idxs));
5919:       PetscCall(PetscMalloc1(nl * cdim, &scoords));
5920:       for (i = 0; i < nl; i++) {
5921:         for (d = 0; d < cdim; d++) scoords[i * cdim + d] = coords[idxs[i] * cdim + d];
5922:       }
5923:       PetscCall(ISRestoreIndices(pcis->is_I_local, &idxs));
5924:       PetscCall(PCSetCoordinates(pc_temp, cdim, nl, scoords));
5925:       PetscCall(PetscFree(scoords));
5926:     }
5927:     if (sub_schurs && sub_schurs->reuse_solver) {
5928:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5930:       PetscCall(KSPSetPC(pcbddc->ksp_D, reuse_solver->interior_solver));
5931:     }

5933:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
5934:     if (!n_D) {
5935:       PetscCall(KSPGetPC(pcbddc->ksp_D, &pc_temp));
5936:       PetscCall(PCSetType(pc_temp, PCNONE));
5937:     }
5938:     PetscCall(KSPSetUp(pcbddc->ksp_D));
5939:     /* set ksp_D into pcis data */
5940:     PetscCall(PetscObjectReference((PetscObject)pcbddc->ksp_D));
5941:     PetscCall(KSPDestroy(&pcis->ksp_D));
5942:     pcis->ksp_D = pcbddc->ksp_D;
5943:   }

5945:   /* NEUMANN PROBLEM */
5946:   A_RR = NULL;
5947:   if (neumann) {
5948:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5949:     PetscInt        ibs, mbs;
5950:     PetscBool       issbaij, reuse_neumann_solver, isset, issym;
5951:     Mat_IS         *matis = (Mat_IS *)pc->pmat->data;

5953:     reuse_neumann_solver = PETSC_FALSE;
5954:     if (sub_schurs && sub_schurs->reuse_solver) {
5955:       IS iP;

5957:       reuse_neumann_solver = PETSC_TRUE;
5958:       PetscCall(PetscObjectQuery((PetscObject)sub_schurs->A, "__KSPFETIDP_iP", (PetscObject *)&iP));
5959:       if (iP) reuse_neumann_solver = PETSC_FALSE;
5960:     }
5961:     /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
5962:     PetscCall(ISGetSize(pcbddc->is_R_local, &n_R));
5963:     if (pcbddc->ksp_R) { /* already created ksp */
5964:       PetscInt nn_R;
5965:       PetscCall(KSPGetOperators(pcbddc->ksp_R, NULL, &A_RR));
5966:       PetscCall(PetscObjectReference((PetscObject)A_RR));
5967:       PetscCall(MatGetSize(A_RR, &nn_R, NULL));
5968:       if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
5969:         PetscCall(KSPReset(pcbddc->ksp_R));
5970:         PetscCall(MatDestroy(&A_RR));
5971:         reuse = MAT_INITIAL_MATRIX;
5972:       } else {                                /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
5973:         if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
5974:           PetscCall(MatDestroy(&A_RR));
5975:           reuse = MAT_INITIAL_MATRIX;
5976:         } else { /* safe to reuse the matrix */
5977:           reuse = MAT_REUSE_MATRIX;
5978:         }
5979:       }
5980:       /* last check */
5981:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
5982:         PetscCall(MatDestroy(&A_RR));
5983:         reuse = MAT_INITIAL_MATRIX;
5984:       }
5985:     } else { /* first time, so we need to create the matrix */
5986:       reuse = MAT_INITIAL_MATRIX;
5987:     }
5988:     /* convert pcbddc->local_mat if needed later in PCBDDCSetUpCorrection
5989:        TODO: Get Rid of these conversions */
5990:     PetscCall(MatGetBlockSize(pcbddc->local_mat, &mbs));
5991:     PetscCall(ISGetBlockSize(pcbddc->is_R_local, &ibs));
5992:     PetscCall(PetscObjectTypeCompare((PetscObject)pcbddc->local_mat, MATSEQSBAIJ, &issbaij));
5993:     if (ibs != mbs) { /* need to convert to SEQAIJ to extract any submatrix with is_R_local */
5994:       if (matis->A == pcbddc->local_mat) {
5995:         PetscCall(MatDestroy(&pcbddc->local_mat));
5996:         PetscCall(MatConvert(matis->A, MATSEQAIJ, MAT_INITIAL_MATRIX, &pcbddc->local_mat));
5997:       } else {
5998:         PetscCall(MatConvert(pcbddc->local_mat, MATSEQAIJ, MAT_INPLACE_MATRIX, &pcbddc->local_mat));
5999:       }
6000:     } else if (issbaij) { /* need to convert to BAIJ to get off-diagonal blocks */
6001:       if (matis->A == pcbddc->local_mat) {
6002:         PetscCall(MatDestroy(&pcbddc->local_mat));
6003:         PetscCall(MatConvert(matis->A, mbs > 1 ? MATSEQBAIJ : MATSEQAIJ, MAT_INITIAL_MATRIX, &pcbddc->local_mat));
6004:       } else {
6005:         PetscCall(MatConvert(pcbddc->local_mat, mbs > 1 ? MATSEQBAIJ : MATSEQAIJ, MAT_INPLACE_MATRIX, &pcbddc->local_mat));
6006:       }
6007:     }
6008:     /* extract A_RR */
6009:     if (reuse_neumann_solver) {
6010:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

6012:       if (pcbddc->dbg_flag) { /* we need A_RR to test the solver later */
6013:         PetscCall(MatDestroy(&A_RR));
6014:         if (reuse_solver->benign_n) { /* we are not using the explicit change of basis on the pressures */
6015:           PetscCall(PCBDDCBenignProject(pc, pcbddc->is_R_local, pcbddc->is_R_local, &A_RR));
6016:         } else {
6017:           PetscCall(MatCreateSubMatrix(pcbddc->local_mat, pcbddc->is_R_local, pcbddc->is_R_local, MAT_INITIAL_MATRIX, &A_RR));
6018:         }
6019:       } else {
6020:         PetscCall(MatDestroy(&A_RR));
6021:         PetscCall(PCGetOperators(reuse_solver->correction_solver, &A_RR, NULL));
6022:         PetscCall(PetscObjectReference((PetscObject)A_RR));
6023:       }
6024:     } else { /* we have to build the neumann solver, so we need to extract the relevant matrix */
6025:       PetscCall(MatCreateSubMatrix(pcbddc->local_mat, pcbddc->is_R_local, pcbddc->is_R_local, reuse, &A_RR));
6026:     }
6027:     PetscCall(MatIsSymmetricKnown(pcbddc->local_mat, &isset, &issym));
6028:     if (isset) PetscCall(MatSetOption(A_RR, MAT_SYMMETRIC, issym));
6029:     opts = PETSC_FALSE;
6030:     if (!pcbddc->ksp_R) { /* create object if not present */
6031:       opts = PETSC_TRUE;
6032:       PetscCall(KSPCreate(PETSC_COMM_SELF, &pcbddc->ksp_R));
6033:       PetscCall(KSPSetNestLevel(pcbddc->ksp_R, pc->kspnestlevel));
6034:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R, (PetscObject)pc, 1));
6035:       /* default */
6036:       PetscCall(KSPSetType(pcbddc->ksp_R, KSPPREONLY));
6037:       PetscCall(KSPSetOptionsPrefix(pcbddc->ksp_R, neu_prefix));
6038:       PetscCall(KSPGetPC(pcbddc->ksp_R, &pc_temp));
6039:       PetscCall(PetscObjectTypeCompare((PetscObject)A_RR, MATSEQSBAIJ, &issbaij));
6040:       if (issbaij) {
6041:         PetscCall(PCSetType(pc_temp, PCCHOLESKY));
6042:       } else {
6043:         PetscCall(PCSetType(pc_temp, PCLU));
6044:       }
6045:       PetscCall(KSPSetErrorIfNotConverged(pcbddc->ksp_R, pc->erroriffailure));
6046:     }
6047:     PetscCall(MatSetOptionsPrefix(A_RR, ((PetscObject)pcbddc->ksp_R)->prefix));
6048:     PetscCall(MatViewFromOptions(A_RR, NULL, "-mat_view"));
6049:     PetscCall(KSPSetOperators(pcbddc->ksp_R, A_RR, A_RR));
6050:     if (opts) { /* Allow user's customization once */
6051:       PetscCall(KSPSetFromOptions(pcbddc->ksp_R));
6052:     }
6053:     PetscCall(MatGetNearNullSpace(A_RR, &nnsp));
6054:     if (pcbddc->NullSpace_corr[2] && !nnsp) { /* approximate solver, propagate NearNullSpace */
6055:       PetscCall(MatNullSpacePropagateAny_Private(pcbddc->local_mat, pcbddc->is_R_local, A_RR));
6056:     }
6057:     PetscCall(MatGetNearNullSpace(A_RR, &nnsp));
6058:     PetscCall(KSPGetPC(pcbddc->ksp_R, &pc_temp));
6059:     PetscCall(PetscObjectHasFunction((PetscObject)pc_temp, "PCSetCoordinates_C", &f));
6060:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
6061:       PetscReal      *coords = pcbddc->mat_graph->coords, *scoords;
6062:       const PetscInt *idxs;
6063:       PetscInt        cdim = pcbddc->mat_graph->cdim, nl, i, d;

6065:       PetscCall(ISGetLocalSize(pcbddc->is_R_local, &nl));
6066:       PetscCall(ISGetIndices(pcbddc->is_R_local, &idxs));
6067:       PetscCall(PetscMalloc1(nl * cdim, &scoords));
6068:       for (i = 0; i < nl; i++) {
6069:         for (d = 0; d < cdim; d++) scoords[i * cdim + d] = coords[idxs[i] * cdim + d];
6070:       }
6071:       PetscCall(ISRestoreIndices(pcbddc->is_R_local, &idxs));
6072:       PetscCall(PCSetCoordinates(pc_temp, cdim, nl, scoords));
6073:       PetscCall(PetscFree(scoords));
6074:     }

6076:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
6077:     if (!n_R) {
6078:       PetscCall(KSPGetPC(pcbddc->ksp_R, &pc_temp));
6079:       PetscCall(PCSetType(pc_temp, PCNONE));
6080:     }
6081:     /* Reuse solver if it is present */
6082:     if (reuse_neumann_solver) {
6083:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

6085:       PetscCall(KSPSetPC(pcbddc->ksp_R, reuse_solver->correction_solver));
6086:     }
6087:     PetscCall(KSPSetUp(pcbddc->ksp_R));
6088:   }

6090:   if (pcbddc->dbg_flag) {
6091:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
6092:     PetscCall(PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer));
6093:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "--------------------------------------------------\n"));
6094:   }
6095:   PetscCall(PetscLogEventEnd(PC_BDDC_LocalSolvers[pcbddc->current_level], pc, 0, 0, 0));

6097:   /* adapt Dirichlet and Neumann solvers if a nullspace correction has been requested */
6098:   if (pcbddc->NullSpace_corr[0]) PetscCall(PCBDDCSetUseExactDirichlet(pc, PETSC_FALSE));
6099:   if (dirichlet && pcbddc->NullSpace_corr[0] && !pcbddc->switch_static) PetscCall(PCBDDCNullSpaceAssembleCorrection(pc, PETSC_TRUE, pcbddc->NullSpace_corr[1]));
6100:   if (neumann && pcbddc->NullSpace_corr[2]) PetscCall(PCBDDCNullSpaceAssembleCorrection(pc, PETSC_FALSE, pcbddc->NullSpace_corr[3]));
6101:   /* check Dirichlet and Neumann solvers */
6102:   if (pcbddc->dbg_flag) {
6103:     if (dirichlet) { /* Dirichlet */
6104:       PetscCall(VecSetRandom(pcis->vec1_D, NULL));
6105:       PetscCall(MatMult(pcis->A_II, pcis->vec1_D, pcis->vec2_D));
6106:       PetscCall(KSPSolve(pcbddc->ksp_D, pcis->vec2_D, pcis->vec2_D));
6107:       PetscCall(KSPCheckSolve(pcbddc->ksp_D, pc, pcis->vec2_D));
6108:       PetscCall(VecAXPY(pcis->vec1_D, m_one, pcis->vec2_D));
6109:       PetscCall(VecNorm(pcis->vec1_D, NORM_INFINITY, &value));
6110:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n", PetscGlobalRank, ((PetscObject)pcbddc->ksp_D)->prefix, (double)value));
6111:       PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
6112:     }
6113:     if (neumann) { /* Neumann */
6114:       PetscCall(VecSetRandom(pcbddc->vec1_R, NULL));
6115:       PetscCall(MatMult(A_RR, pcbddc->vec1_R, pcbddc->vec2_R));
6116:       PetscCall(KSPSolve(pcbddc->ksp_R, pcbddc->vec2_R, pcbddc->vec2_R));
6117:       PetscCall(KSPCheckSolve(pcbddc->ksp_R, pc, pcbddc->vec2_R));
6118:       PetscCall(VecAXPY(pcbddc->vec1_R, m_one, pcbddc->vec2_R));
6119:       PetscCall(VecNorm(pcbddc->vec1_R, NORM_INFINITY, &value));
6120:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e\n", PetscGlobalRank, ((PetscObject)pcbddc->ksp_R)->prefix, (double)value));
6121:       PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
6122:     }
6123:   }
6124:   /* free Neumann problem's matrix */
6125:   PetscCall(MatDestroy(&A_RR));
6126:   PetscFunctionReturn(PETSC_SUCCESS);
6127: }

6129: static PetscErrorCode PCBDDCSolveSubstructureCorrection(PC pc, Vec inout_B, Vec inout_D, PetscBool applytranspose)
6130: {
6131:   PC_BDDC        *pcbddc       = (PC_BDDC *)pc->data;
6132:   PCBDDCSubSchurs sub_schurs   = pcbddc->sub_schurs;
6133:   PetscBool       reuse_solver = sub_schurs ? (sub_schurs->reuse_solver ? PETSC_TRUE : PETSC_FALSE) : PETSC_FALSE;

6135:   PetscFunctionBegin;
6136:   if (!reuse_solver) PetscCall(VecSet(pcbddc->vec1_R, 0.));
6137:   if (!pcbddc->switch_static) {
6138:     if (applytranspose && pcbddc->local_auxmat1) {
6139:       PetscCall(MatMultTranspose(pcbddc->local_auxmat2, inout_B, pcbddc->vec1_C));
6140:       PetscCall(MatMultTransposeAdd(pcbddc->local_auxmat1, pcbddc->vec1_C, inout_B, inout_B));
6141:     }
6142:     if (!reuse_solver) {
6143:       PetscCall(VecScatterBegin(pcbddc->R_to_B, inout_B, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6144:       PetscCall(VecScatterEnd(pcbddc->R_to_B, inout_B, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6145:     } else {
6146:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

6148:       PetscCall(VecScatterBegin(reuse_solver->correction_scatter_B, inout_B, reuse_solver->rhs_B, INSERT_VALUES, SCATTER_FORWARD));
6149:       PetscCall(VecScatterEnd(reuse_solver->correction_scatter_B, inout_B, reuse_solver->rhs_B, INSERT_VALUES, SCATTER_FORWARD));
6150:     }
6151:   } else {
6152:     PetscCall(VecScatterBegin(pcbddc->R_to_B, inout_B, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6153:     PetscCall(VecScatterEnd(pcbddc->R_to_B, inout_B, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6154:     PetscCall(VecScatterBegin(pcbddc->R_to_D, inout_D, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6155:     PetscCall(VecScatterEnd(pcbddc->R_to_D, inout_D, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6156:     if (applytranspose && pcbddc->local_auxmat1) {
6157:       PetscCall(MatMultTranspose(pcbddc->local_auxmat2, pcbddc->vec1_R, pcbddc->vec1_C));
6158:       PetscCall(MatMultTransposeAdd(pcbddc->local_auxmat1, pcbddc->vec1_C, inout_B, inout_B));
6159:       PetscCall(VecScatterBegin(pcbddc->R_to_B, inout_B, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6160:       PetscCall(VecScatterEnd(pcbddc->R_to_B, inout_B, pcbddc->vec1_R, INSERT_VALUES, SCATTER_REVERSE));
6161:     }
6162:   }
6163:   PetscCall(PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][1], pc, 0, 0, 0));
6164:   if (!reuse_solver || pcbddc->switch_static) {
6165:     if (applytranspose) {
6166:       PetscCall(KSPSolveTranspose(pcbddc->ksp_R, pcbddc->vec1_R, pcbddc->vec1_R));
6167:     } else {
6168:       PetscCall(KSPSolve(pcbddc->ksp_R, pcbddc->vec1_R, pcbddc->vec1_R));
6169:     }
6170:     PetscCall(KSPCheckSolve(pcbddc->ksp_R, pc, pcbddc->vec1_R));
6171:   } else {
6172:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

6174:     if (applytranspose) {
6175:       PetscCall(MatFactorSolveSchurComplementTranspose(reuse_solver->F, reuse_solver->rhs_B, reuse_solver->sol_B));
6176:     } else {
6177:       PetscCall(MatFactorSolveSchurComplement(reuse_solver->F, reuse_solver->rhs_B, reuse_solver->sol_B));
6178:     }
6179:   }
6180:   PetscCall(PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][1], pc, 0, 0, 0));
6181:   PetscCall(VecSet(inout_B, 0.));
6182:   if (!pcbddc->switch_static) {
6183:     if (!reuse_solver) {
6184:       PetscCall(VecScatterBegin(pcbddc->R_to_B, pcbddc->vec1_R, inout_B, INSERT_VALUES, SCATTER_FORWARD));
6185:       PetscCall(VecScatterEnd(pcbddc->R_to_B, pcbddc->vec1_R, inout_B, INSERT_VALUES, SCATTER_FORWARD));
6186:     } else {
6187:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

6189:       PetscCall(VecScatterBegin(reuse_solver->correction_scatter_B, reuse_solver->sol_B, inout_B, INSERT_VALUES, SCATTER_REVERSE));
6190:       PetscCall(VecScatterEnd(reuse_solver->correction_scatter_B, reuse_solver->sol_B, inout_B, INSERT_VALUES, SCATTER_REVERSE));
6191:     }
6192:     if (!applytranspose && pcbddc->local_auxmat1) {
6193:       PetscCall(MatMult(pcbddc->local_auxmat1, inout_B, pcbddc->vec1_C));
6194:       PetscCall(MatMultAdd(pcbddc->local_auxmat2, pcbddc->vec1_C, inout_B, inout_B));
6195:     }
6196:   } else {
6197:     PetscCall(VecScatterBegin(pcbddc->R_to_B, pcbddc->vec1_R, inout_B, INSERT_VALUES, SCATTER_FORWARD));
6198:     PetscCall(VecScatterEnd(pcbddc->R_to_B, pcbddc->vec1_R, inout_B, INSERT_VALUES, SCATTER_FORWARD));
6199:     PetscCall(VecScatterBegin(pcbddc->R_to_D, pcbddc->vec1_R, inout_D, INSERT_VALUES, SCATTER_FORWARD));
6200:     PetscCall(VecScatterEnd(pcbddc->R_to_D, pcbddc->vec1_R, inout_D, INSERT_VALUES, SCATTER_FORWARD));
6201:     if (!applytranspose && pcbddc->local_auxmat1) {
6202:       PetscCall(MatMult(pcbddc->local_auxmat1, inout_B, pcbddc->vec1_C));
6203:       PetscCall(MatMultAdd(pcbddc->local_auxmat2, pcbddc->vec1_C, pcbddc->vec1_R, pcbddc->vec1_R));
6204:     }
6205:     PetscCall(VecScatterBegin(pcbddc->R_to_B, pcbddc->vec1_R, inout_B, INSERT_VALUES, SCATTER_FORWARD));
6206:     PetscCall(VecScatterEnd(pcbddc->R_to_B, pcbddc->vec1_R, inout_B, INSERT_VALUES, SCATTER_FORWARD));
6207:     PetscCall(VecScatterBegin(pcbddc->R_to_D, pcbddc->vec1_R, inout_D, INSERT_VALUES, SCATTER_FORWARD));
6208:     PetscCall(VecScatterEnd(pcbddc->R_to_D, pcbddc->vec1_R, inout_D, INSERT_VALUES, SCATTER_FORWARD));
6209:   }
6210:   PetscFunctionReturn(PETSC_SUCCESS);
6211: }

6213: /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
6214: PetscErrorCode PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
6215: {
6216:   PC_BDDC          *pcbddc = (PC_BDDC *)pc->data;
6217:   PC_IS            *pcis   = (PC_IS *)pc->data;
6218:   const PetscScalar zero   = 0.0;

6220:   PetscFunctionBegin;
6221:   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
6222:   if (!pcbddc->benign_apply_coarse_only) {
6223:     if (applytranspose) {
6224:       PetscCall(MatMultTranspose(pcbddc->coarse_phi_B, pcis->vec1_B, pcbddc->vec1_P));
6225:       if (pcbddc->switch_static) PetscCall(MatMultTransposeAdd(pcbddc->coarse_phi_D, pcis->vec1_D, pcbddc->vec1_P, pcbddc->vec1_P));
6226:     } else {
6227:       PetscCall(MatMultTranspose(pcbddc->coarse_psi_B, pcis->vec1_B, pcbddc->vec1_P));
6228:       if (pcbddc->switch_static) PetscCall(MatMultTransposeAdd(pcbddc->coarse_psi_D, pcis->vec1_D, pcbddc->vec1_P, pcbddc->vec1_P));
6229:     }
6230:   } else {
6231:     PetscCall(VecSet(pcbddc->vec1_P, zero));
6232:   }

6234:   /* add p0 to the last value of vec1_P holding the coarse dof relative to p0 */
6235:   if (pcbddc->benign_n) {
6236:     PetscScalar *array;
6237:     PetscInt     j;

6239:     PetscCall(VecGetArray(pcbddc->vec1_P, &array));
6240:     for (j = 0; j < pcbddc->benign_n; j++) array[pcbddc->local_primal_size - pcbddc->benign_n + j] += pcbddc->benign_p0[j];
6241:     PetscCall(VecRestoreArray(pcbddc->vec1_P, &array));
6242:   }

6244:   /* start communications from local primal nodes to rhs of coarse solver */
6245:   PetscCall(VecSet(pcbddc->coarse_vec, zero));
6246:   PetscCall(PCBDDCScatterCoarseDataBegin(pc, ADD_VALUES, SCATTER_FORWARD));
6247:   PetscCall(PCBDDCScatterCoarseDataEnd(pc, ADD_VALUES, SCATTER_FORWARD));

6249:   /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
6250:   PetscCall(PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][2], pc, 0, 0, 0));
6251:   if (pcbddc->coarse_ksp) {
6252:     Mat          coarse_mat;
6253:     Vec          rhs, sol;
6254:     MatNullSpace nullsp;
6255:     PetscBool    isbddc = PETSC_FALSE;

6257:     if (pcbddc->benign_have_null) {
6258:       PC coarse_pc;

6260:       PetscCall(KSPGetPC(pcbddc->coarse_ksp, &coarse_pc));
6261:       PetscCall(PetscObjectTypeCompare((PetscObject)coarse_pc, PCBDDC, &isbddc));
6262:       /* we need to propagate to coarser levels the need for a possible benign correction */
6263:       if (isbddc && pcbddc->benign_apply_coarse_only && !pcbddc->benign_skip_correction) {
6264:         PC_BDDC *coarsepcbddc                  = (PC_BDDC *)coarse_pc->data;
6265:         coarsepcbddc->benign_skip_correction   = PETSC_FALSE;
6266:         coarsepcbddc->benign_apply_coarse_only = PETSC_TRUE;
6267:       }
6268:     }
6269:     PetscCall(KSPGetRhs(pcbddc->coarse_ksp, &rhs));
6270:     PetscCall(KSPGetSolution(pcbddc->coarse_ksp, &sol));
6271:     PetscCall(KSPGetOperators(pcbddc->coarse_ksp, &coarse_mat, NULL));
6272:     if (applytranspose) {
6273:       PetscCheck(!pcbddc->benign_apply_coarse_only, PetscObjectComm((PetscObject)pcbddc->coarse_ksp), PETSC_ERR_SUP, "Not yet implemented");
6274:       PetscCall(KSPSolveTranspose(pcbddc->coarse_ksp, rhs, sol));
6275:       PetscCall(KSPCheckSolve(pcbddc->coarse_ksp, pc, sol));
6276:       PetscCall(MatGetTransposeNullSpace(coarse_mat, &nullsp));
6277:       if (nullsp) PetscCall(MatNullSpaceRemove(nullsp, sol));
6278:     } else {
6279:       PetscCall(MatGetNullSpace(coarse_mat, &nullsp));
6280:       if (pcbddc->benign_apply_coarse_only && isbddc) { /* need just to apply the coarse preconditioner during presolve */
6281:         PC coarse_pc;

6283:         if (nullsp) PetscCall(MatNullSpaceRemove(nullsp, rhs));
6284:         PetscCall(KSPGetPC(pcbddc->coarse_ksp, &coarse_pc));
6285:         PetscCall(PCPreSolve(coarse_pc, pcbddc->coarse_ksp));
6286:         PetscCall(PCBDDCBenignRemoveInterior(coarse_pc, rhs, sol));
6287:         PetscCall(PCPostSolve(coarse_pc, pcbddc->coarse_ksp));
6288:       } else {
6289:         PetscCall(KSPSolve(pcbddc->coarse_ksp, rhs, sol));
6290:         PetscCall(KSPCheckSolve(pcbddc->coarse_ksp, pc, sol));
6291:         if (nullsp) PetscCall(MatNullSpaceRemove(nullsp, sol));
6292:       }
6293:     }
6294:     /* we don't need the benign correction at coarser levels anymore */
6295:     if (pcbddc->benign_have_null && isbddc) {
6296:       PC       coarse_pc;
6297:       PC_BDDC *coarsepcbddc;

6299:       PetscCall(KSPGetPC(pcbddc->coarse_ksp, &coarse_pc));
6300:       coarsepcbddc                           = (PC_BDDC *)coarse_pc->data;
6301:       coarsepcbddc->benign_skip_correction   = PETSC_TRUE;
6302:       coarsepcbddc->benign_apply_coarse_only = PETSC_FALSE;
6303:     }
6304:   }
6305:   PetscCall(PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][2], pc, 0, 0, 0));

6307:   /* Local solution on R nodes */
6308:   if (!pcbddc->benign_apply_coarse_only) PetscCall(PCBDDCSolveSubstructureCorrection(pc, pcis->vec1_B, pcis->vec1_D, applytranspose));
6309:   /* communications from coarse sol to local primal nodes */
6310:   PetscCall(PCBDDCScatterCoarseDataBegin(pc, INSERT_VALUES, SCATTER_REVERSE));
6311:   PetscCall(PCBDDCScatterCoarseDataEnd(pc, INSERT_VALUES, SCATTER_REVERSE));

6313:   /* Sum contributions from the two levels */
6314:   if (!pcbddc->benign_apply_coarse_only) {
6315:     if (applytranspose) {
6316:       PetscCall(MatMultAdd(pcbddc->coarse_psi_B, pcbddc->vec1_P, pcis->vec1_B, pcis->vec1_B));
6317:       if (pcbddc->switch_static) PetscCall(MatMultAdd(pcbddc->coarse_psi_D, pcbddc->vec1_P, pcis->vec1_D, pcis->vec1_D));
6318:     } else {
6319:       PetscCall(MatMultAdd(pcbddc->coarse_phi_B, pcbddc->vec1_P, pcis->vec1_B, pcis->vec1_B));
6320:       if (pcbddc->switch_static) PetscCall(MatMultAdd(pcbddc->coarse_phi_D, pcbddc->vec1_P, pcis->vec1_D, pcis->vec1_D));
6321:     }
6322:     /* store p0 */
6323:     if (pcbddc->benign_n) {
6324:       PetscScalar *array;
6325:       PetscInt     j;

6327:       PetscCall(VecGetArray(pcbddc->vec1_P, &array));
6328:       for (j = 0; j < pcbddc->benign_n; j++) pcbddc->benign_p0[j] = array[pcbddc->local_primal_size - pcbddc->benign_n + j];
6329:       PetscCall(VecRestoreArray(pcbddc->vec1_P, &array));
6330:     }
6331:   } else { /* expand the coarse solution */
6332:     if (applytranspose) {
6333:       PetscCall(MatMult(pcbddc->coarse_psi_B, pcbddc->vec1_P, pcis->vec1_B));
6334:     } else {
6335:       PetscCall(MatMult(pcbddc->coarse_phi_B, pcbddc->vec1_P, pcis->vec1_B));
6336:     }
6337:   }
6338:   PetscFunctionReturn(PETSC_SUCCESS);
6339: }

6341: PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc, InsertMode imode, ScatterMode smode)
6342: {
6343:   PC_BDDC           *pcbddc = (PC_BDDC *)pc->data;
6344:   Vec                from, to;
6345:   const PetscScalar *array;

6347:   PetscFunctionBegin;
6348:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
6349:     from = pcbddc->coarse_vec;
6350:     to   = pcbddc->vec1_P;
6351:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
6352:       Vec tvec;

6354:       PetscCall(KSPGetRhs(pcbddc->coarse_ksp, &tvec));
6355:       PetscCall(VecResetArray(tvec));
6356:       PetscCall(KSPGetSolution(pcbddc->coarse_ksp, &tvec));
6357:       PetscCall(VecGetArrayRead(tvec, &array));
6358:       PetscCall(VecPlaceArray(from, array));
6359:       PetscCall(VecRestoreArrayRead(tvec, &array));
6360:     }
6361:   } else { /* from local to global -> put data in coarse right-hand side */
6362:     from = pcbddc->vec1_P;
6363:     to   = pcbddc->coarse_vec;
6364:   }
6365:   PetscCall(VecScatterBegin(pcbddc->coarse_loc_to_glob, from, to, imode, smode));
6366:   PetscFunctionReturn(PETSC_SUCCESS);
6367: }

6369: PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
6370: {
6371:   PC_BDDC           *pcbddc = (PC_BDDC *)pc->data;
6372:   Vec                from, to;
6373:   const PetscScalar *array;

6375:   PetscFunctionBegin;
6376:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
6377:     from = pcbddc->coarse_vec;
6378:     to   = pcbddc->vec1_P;
6379:   } else { /* from local to global -> put data in coarse right-hand side */
6380:     from = pcbddc->vec1_P;
6381:     to   = pcbddc->coarse_vec;
6382:   }
6383:   PetscCall(VecScatterEnd(pcbddc->coarse_loc_to_glob, from, to, imode, smode));
6384:   if (smode == SCATTER_FORWARD) {
6385:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
6386:       Vec tvec;

6388:       PetscCall(KSPGetRhs(pcbddc->coarse_ksp, &tvec));
6389:       PetscCall(VecGetArrayRead(to, &array));
6390:       PetscCall(VecPlaceArray(tvec, array));
6391:       PetscCall(VecRestoreArrayRead(to, &array));
6392:     }
6393:   } else {
6394:     if (pcbddc->coarse_ksp) { /* restore array of pcbddc->coarse_vec */
6395:       PetscCall(VecResetArray(from));
6396:     }
6397:   }
6398:   PetscFunctionReturn(PETSC_SUCCESS);
6399: }

6401: PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
6402: {
6403:   PC_IS   *pcis   = (PC_IS *)pc->data;
6404:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;
6405:   Mat_IS  *matis  = (Mat_IS *)pc->pmat->data;
6406:   /* one and zero */
6407:   PetscScalar one = 1.0, zero = 0.0;
6408:   /* space to store constraints and their local indices */
6409:   PetscScalar *constraints_data;
6410:   PetscInt    *constraints_idxs, *constraints_idxs_B;
6411:   PetscInt    *constraints_idxs_ptr, *constraints_data_ptr;
6412:   PetscInt    *constraints_n;
6413:   /* iterators */
6414:   PetscInt i, j, k, total_counts, total_counts_cc, cum;
6415:   /* BLAS integers */
6416:   PetscBLASInt lwork, lierr;
6417:   PetscBLASInt Blas_N, Blas_M, Blas_K, Blas_one = 1;
6418:   PetscBLASInt Blas_LDA, Blas_LDB, Blas_LDC;
6419:   /* reuse */
6420:   PetscInt  olocal_primal_size, olocal_primal_size_cc;
6421:   PetscInt *olocal_primal_ref_node, *olocal_primal_ref_mult;
6422:   /* change of basis */
6423:   PetscBool qr_needed;
6424:   PetscBT   change_basis, qr_needed_idx;
6425:   /* auxiliary stuff */
6426:   PetscInt *nnz, *is_indices;
6427:   PetscInt  ncc;
6428:   /* some quantities */
6429:   PetscInt  n_vertices, total_primal_vertices, valid_constraints;
6430:   PetscInt  size_of_constraint, max_size_of_constraint = 0, max_constraints, temp_constraints;
6431:   PetscReal tol; /* tolerance for retaining eigenmodes */

6433:   PetscFunctionBegin;
6434:   tol = PetscSqrtReal(PETSC_SMALL);
6435:   /* Destroy Mat objects computed previously */
6436:   PetscCall(MatDestroy(&pcbddc->ChangeOfBasisMatrix));
6437:   PetscCall(MatDestroy(&pcbddc->ConstraintMatrix));
6438:   PetscCall(MatDestroy(&pcbddc->switch_static_change));
6439:   /* save info on constraints from previous setup (if any) */
6440:   olocal_primal_size    = pcbddc->local_primal_size;
6441:   olocal_primal_size_cc = pcbddc->local_primal_size_cc;
6442:   PetscCall(PetscMalloc2(olocal_primal_size_cc, &olocal_primal_ref_node, olocal_primal_size_cc, &olocal_primal_ref_mult));
6443:   PetscCall(PetscArraycpy(olocal_primal_ref_node, pcbddc->local_primal_ref_node, olocal_primal_size_cc));
6444:   PetscCall(PetscArraycpy(olocal_primal_ref_mult, pcbddc->local_primal_ref_mult, olocal_primal_size_cc));
6445:   PetscCall(PetscFree2(pcbddc->local_primal_ref_node, pcbddc->local_primal_ref_mult));
6446:   PetscCall(PetscFree(pcbddc->primal_indices_local_idxs));

6448:   if (!pcbddc->adaptive_selection) {
6449:     IS           ISForVertices, *ISForFaces, *ISForEdges;
6450:     MatNullSpace nearnullsp;
6451:     const Vec   *nearnullvecs;
6452:     Vec         *localnearnullsp;
6453:     PetscScalar *array;
6454:     PetscInt     n_ISForFaces, n_ISForEdges, nnsp_size, o_nf, o_ne;
6455:     PetscBool    nnsp_has_cnst;
6456:     /* LAPACK working arrays for SVD or POD */
6457:     PetscBool    skip_lapack, boolforchange;
6458:     PetscScalar *work;
6459:     PetscReal   *singular_vals;
6460: #if defined(PETSC_USE_COMPLEX)
6461:     PetscReal *rwork;
6462: #endif
6463:     PetscScalar *temp_basis = NULL, *correlation_mat = NULL;
6464:     PetscBLASInt dummy_int    = 1;
6465:     PetscScalar  dummy_scalar = 1.;
6466:     PetscBool    use_pod      = PETSC_FALSE;

6468:     /* MKL SVD with same input gives different results on different processes! */
6469: #if defined(PETSC_MISSING_LAPACK_GESVD) || defined(PETSC_HAVE_MKL_LIBS)
6470:     use_pod = PETSC_TRUE;
6471: #endif
6472:     /* Get index sets for faces, edges and vertices from graph */
6473:     PetscCall(PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph, &n_ISForFaces, &ISForFaces, &n_ISForEdges, &ISForEdges, &ISForVertices));
6474:     o_nf       = n_ISForFaces;
6475:     o_ne       = n_ISForEdges;
6476:     n_vertices = 0;
6477:     if (ISForVertices) PetscCall(ISGetSize(ISForVertices, &n_vertices));
6478:     /* print some info */
6479:     if (pcbddc->dbg_flag && (!pcbddc->sub_schurs || pcbddc->sub_schurs_rebuild)) {
6480:       if (!pcbddc->dbg_viewer) pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
6481:       PetscCall(PCBDDCGraphASCIIView(pcbddc->mat_graph, pcbddc->dbg_flag, pcbddc->dbg_viewer));
6482:       PetscCall(PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer));
6483:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "--------------------------------------------------------------\n"));
6484:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d got %02" PetscInt_FMT " local candidate vertices (%d)\n", PetscGlobalRank, n_vertices, pcbddc->use_vertices));
6485:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d got %02" PetscInt_FMT " local candidate edges    (%d)\n", PetscGlobalRank, n_ISForEdges, pcbddc->use_edges));
6486:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d got %02" PetscInt_FMT " local candidate faces    (%d)\n", PetscGlobalRank, n_ISForFaces, pcbddc->use_faces));
6487:       PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
6488:       PetscCall(PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer));
6489:     }

6491:     if (!pcbddc->use_vertices) n_vertices = 0;
6492:     if (!pcbddc->use_edges) n_ISForEdges = 0;
6493:     if (!pcbddc->use_faces) n_ISForFaces = 0;

6495:     /* check if near null space is attached to global mat */
6496:     if (pcbddc->use_nnsp) {
6497:       PetscCall(MatGetNearNullSpace(pc->pmat, &nearnullsp));
6498:     } else nearnullsp = NULL;

6500:     if (nearnullsp) {
6501:       PetscCall(MatNullSpaceGetVecs(nearnullsp, &nnsp_has_cnst, &nnsp_size, &nearnullvecs));
6502:       /* remove any stored info */
6503:       PetscCall(MatNullSpaceDestroy(&pcbddc->onearnullspace));
6504:       PetscCall(PetscFree(pcbddc->onearnullvecs_state));
6505:       /* store information for BDDC solver reuse */
6506:       PetscCall(PetscObjectReference((PetscObject)nearnullsp));
6507:       pcbddc->onearnullspace = nearnullsp;
6508:       PetscCall(PetscMalloc1(nnsp_size, &pcbddc->onearnullvecs_state));
6509:       for (i = 0; i < nnsp_size; i++) PetscCall(PetscObjectStateGet((PetscObject)nearnullvecs[i], &pcbddc->onearnullvecs_state[i]));
6510:     } else { /* if near null space is not provided BDDC uses constants by default */
6511:       nnsp_size     = 0;
6512:       nnsp_has_cnst = PETSC_TRUE;
6513:     }
6514:     /* get max number of constraints on a single cc */
6515:     max_constraints = nnsp_size;
6516:     if (nnsp_has_cnst) max_constraints++;

6518:     /*
6519:          Evaluate maximum storage size needed by the procedure
6520:          - Indices for connected component i stored at "constraints_idxs + constraints_idxs_ptr[i]"
6521:          - Values for constraints on connected component i stored at "constraints_data + constraints_data_ptr[i]"
6522:          There can be multiple constraints per connected component
6523:                                                                                                                                                            */
6524:     ncc = n_vertices + n_ISForFaces + n_ISForEdges;
6525:     PetscCall(PetscMalloc3(ncc + 1, &constraints_idxs_ptr, ncc + 1, &constraints_data_ptr, ncc, &constraints_n));

6527:     total_counts = n_ISForFaces + n_ISForEdges;
6528:     total_counts *= max_constraints;
6529:     total_counts += n_vertices;
6530:     PetscCall(PetscBTCreate(total_counts, &change_basis));

6532:     total_counts           = 0;
6533:     max_size_of_constraint = 0;
6534:     for (i = 0; i < n_ISForEdges + n_ISForFaces; i++) {
6535:       IS used_is;
6536:       if (i < n_ISForEdges) {
6537:         used_is = ISForEdges[i];
6538:       } else {
6539:         used_is = ISForFaces[i - n_ISForEdges];
6540:       }
6541:       PetscCall(ISGetSize(used_is, &j));
6542:       total_counts += j;
6543:       max_size_of_constraint = PetscMax(j, max_size_of_constraint);
6544:     }
6545:     PetscCall(PetscMalloc3(total_counts * max_constraints + n_vertices, &constraints_data, total_counts + n_vertices, &constraints_idxs, total_counts + n_vertices, &constraints_idxs_B));

6547:     /* get local part of global near null space vectors */
6548:     PetscCall(PetscMalloc1(nnsp_size, &localnearnullsp));
6549:     for (k = 0; k < nnsp_size; k++) {
6550:       PetscCall(VecDuplicate(pcis->vec1_N, &localnearnullsp[k]));
6551:       PetscCall(VecScatterBegin(matis->rctx, nearnullvecs[k], localnearnullsp[k], INSERT_VALUES, SCATTER_FORWARD));
6552:       PetscCall(VecScatterEnd(matis->rctx, nearnullvecs[k], localnearnullsp[k], INSERT_VALUES, SCATTER_FORWARD));
6553:     }

6555:     /* whether or not to skip lapack calls */
6556:     skip_lapack = PETSC_TRUE;
6557:     if (n_ISForFaces + n_ISForEdges && max_constraints > 1 && !pcbddc->use_nnsp_true) skip_lapack = PETSC_FALSE;

6559:     /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
6560:     if (!skip_lapack) {
6561:       PetscScalar temp_work;

6563:       if (use_pod) {
6564:         /* Proper Orthogonal Decomposition (POD) using the snapshot method */
6565:         PetscCall(PetscMalloc1(max_constraints * max_constraints, &correlation_mat));
6566:         PetscCall(PetscMalloc1(max_constraints, &singular_vals));
6567:         PetscCall(PetscMalloc1(max_size_of_constraint * max_constraints, &temp_basis));
6568: #if defined(PETSC_USE_COMPLEX)
6569:         PetscCall(PetscMalloc1(3 * max_constraints, &rwork));
6570: #endif
6571:         /* now we evaluate the optimal workspace using query with lwork=-1 */
6572:         PetscCall(PetscBLASIntCast(max_constraints, &Blas_N));
6573:         PetscCall(PetscBLASIntCast(max_constraints, &Blas_LDA));
6574:         lwork = -1;
6575:         PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
6576: #if !defined(PETSC_USE_COMPLEX)
6577:         PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &Blas_N, correlation_mat, &Blas_LDA, singular_vals, &temp_work, &lwork, &lierr));
6578: #else
6579:         PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &Blas_N, correlation_mat, &Blas_LDA, singular_vals, &temp_work, &lwork, rwork, &lierr));
6580: #endif
6581:         PetscCall(PetscFPTrapPop());
6582:         PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to SYEV Lapack routine %" PetscBLASInt_FMT, lierr);
6583:       } else {
6584: #if !defined(PETSC_MISSING_LAPACK_GESVD)
6585:         /* SVD */
6586:         PetscInt max_n, min_n;
6587:         max_n = max_size_of_constraint;
6588:         min_n = max_constraints;
6589:         if (max_size_of_constraint < max_constraints) {
6590:           min_n = max_size_of_constraint;
6591:           max_n = max_constraints;
6592:         }
6593:         PetscCall(PetscMalloc1(min_n, &singular_vals));
6594:   #if defined(PETSC_USE_COMPLEX)
6595:         PetscCall(PetscMalloc1(5 * min_n, &rwork));
6596:   #endif
6597:         /* now we evaluate the optimal workspace using query with lwork=-1 */
6598:         lwork = -1;
6599:         PetscCall(PetscBLASIntCast(max_n, &Blas_M));
6600:         PetscCall(PetscBLASIntCast(min_n, &Blas_N));
6601:         PetscCall(PetscBLASIntCast(max_n, &Blas_LDA));
6602:         PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
6603:   #if !defined(PETSC_USE_COMPLEX)
6604:         PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("O", "N", &Blas_M, &Blas_N, &constraints_data[0], &Blas_LDA, singular_vals, &dummy_scalar, &dummy_int, &dummy_scalar, &dummy_int, &temp_work, &lwork, &lierr));
6605:   #else
6606:         PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("O", "N", &Blas_M, &Blas_N, &constraints_data[0], &Blas_LDA, singular_vals, &dummy_scalar, &dummy_int, &dummy_scalar, &dummy_int, &temp_work, &lwork, rwork, &lierr));
6607:   #endif
6608:         PetscCall(PetscFPTrapPop());
6609:         PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to GESVD Lapack routine %" PetscBLASInt_FMT, lierr);
6610: #else
6611:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "This should not happen");
6612: #endif /* on missing GESVD */
6613:       }
6614:       /* Allocate optimal workspace */
6615:       PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(temp_work), &lwork));
6616:       PetscCall(PetscMalloc1(lwork, &work));
6617:     }
6618:     /* Now we can loop on constraining sets */
6619:     total_counts            = 0;
6620:     constraints_idxs_ptr[0] = 0;
6621:     constraints_data_ptr[0] = 0;
6622:     /* vertices */
6623:     if (n_vertices) {
6624:       PetscCall(ISGetIndices(ISForVertices, (const PetscInt **)&is_indices));
6625:       PetscCall(PetscArraycpy(constraints_idxs, is_indices, n_vertices));
6626:       for (i = 0; i < n_vertices; i++) {
6627:         constraints_n[total_counts]            = 1;
6628:         constraints_data[total_counts]         = 1.0;
6629:         constraints_idxs_ptr[total_counts + 1] = constraints_idxs_ptr[total_counts] + 1;
6630:         constraints_data_ptr[total_counts + 1] = constraints_data_ptr[total_counts] + 1;
6631:         total_counts++;
6632:       }
6633:       PetscCall(ISRestoreIndices(ISForVertices, (const PetscInt **)&is_indices));
6634:     }

6636:     /* edges and faces */
6637:     total_counts_cc = total_counts;
6638:     for (ncc = 0; ncc < n_ISForEdges + n_ISForFaces; ncc++) {
6639:       IS        used_is;
6640:       PetscBool idxs_copied = PETSC_FALSE;

6642:       if (ncc < n_ISForEdges) {
6643:         used_is       = ISForEdges[ncc];
6644:         boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
6645:       } else {
6646:         used_is       = ISForFaces[ncc - n_ISForEdges];
6647:         boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
6648:       }
6649:       temp_constraints = 0; /* zero the number of constraints I have on this conn comp */

6651:       PetscCall(ISGetSize(used_is, &size_of_constraint));
6652:       if (!size_of_constraint) continue;
6653:       PetscCall(ISGetIndices(used_is, (const PetscInt **)&is_indices));
6654:       if (nnsp_has_cnst) {
6655:         PetscScalar quad_value;

6657:         PetscCall(PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc], is_indices, size_of_constraint));
6658:         idxs_copied = PETSC_TRUE;

6660:         if (!pcbddc->use_nnsp_true) {
6661:           quad_value = (PetscScalar)(1.0 / PetscSqrtReal((PetscReal)size_of_constraint));
6662:         } else {
6663:           quad_value = 1.0;
6664:         }
6665:         for (j = 0; j < size_of_constraint; j++) constraints_data[constraints_data_ptr[total_counts_cc] + j] = quad_value;
6666:         temp_constraints++;
6667:         total_counts++;
6668:       }
6669:       for (k = 0; k < nnsp_size; k++) {
6670:         PetscReal    real_value;
6671:         PetscScalar *ptr_to_data;

6673:         PetscCall(VecGetArrayRead(localnearnullsp[k], (const PetscScalar **)&array));
6674:         ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc] + temp_constraints * size_of_constraint];
6675:         for (j = 0; j < size_of_constraint; j++) ptr_to_data[j] = array[is_indices[j]];
6676:         PetscCall(VecRestoreArrayRead(localnearnullsp[k], (const PetscScalar **)&array));
6677:         /* check if array is null on the connected component */
6678:         PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_N));
6679:         PetscCallBLAS("BLASasum", real_value = BLASasum_(&Blas_N, ptr_to_data, &Blas_one));
6680:         if (real_value > tol * size_of_constraint) { /* keep indices and values */
6681:           temp_constraints++;
6682:           total_counts++;
6683:           if (!idxs_copied) {
6684:             PetscCall(PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc], is_indices, size_of_constraint));
6685:             idxs_copied = PETSC_TRUE;
6686:           }
6687:         }
6688:       }
6689:       PetscCall(ISRestoreIndices(used_is, (const PetscInt **)&is_indices));
6690:       valid_constraints = temp_constraints;
6691:       if (!pcbddc->use_nnsp_true && temp_constraints) {
6692:         if (temp_constraints == 1) { /* just normalize the constraint */
6693:           PetscScalar norm, *ptr_to_data;

6695:           ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];
6696:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_N));
6697:           PetscCallBLAS("BLASdot", norm = BLASdot_(&Blas_N, ptr_to_data, &Blas_one, ptr_to_data, &Blas_one));
6698:           norm = 1.0 / PetscSqrtReal(PetscRealPart(norm));
6699:           PetscCallBLAS("BLASscal", BLASscal_(&Blas_N, &norm, ptr_to_data, &Blas_one));
6700:         } else { /* perform SVD */
6701:           PetscScalar *ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];

6703:           if (use_pod) {
6704:             /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
6705:                POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
6706:                -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
6707:                   the constraints basis will differ (by a complex factor with absolute value equal to 1)
6708:                   from that computed using LAPACKgesvd
6709:                -> This is due to a different computation of eigenvectors in LAPACKheev
6710:                -> The quality of the POD-computed basis will be the same */
6711:             PetscCall(PetscArrayzero(correlation_mat, temp_constraints * temp_constraints));
6712:             /* Store upper triangular part of correlation matrix */
6713:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_N));
6714:             PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
6715:             for (j = 0; j < temp_constraints; j++) {
6716:               for (k = 0; k < j + 1; k++) PetscCallBLAS("BLASdot", correlation_mat[j * temp_constraints + k] = BLASdot_(&Blas_N, ptr_to_data + k * size_of_constraint, &Blas_one, ptr_to_data + j * size_of_constraint, &Blas_one));
6717:             }
6718:             /* compute eigenvalues and eigenvectors of correlation matrix */
6719:             PetscCall(PetscBLASIntCast(temp_constraints, &Blas_N));
6720:             PetscCall(PetscBLASIntCast(temp_constraints, &Blas_LDA));
6721: #if !defined(PETSC_USE_COMPLEX)
6722:             PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &Blas_N, correlation_mat, &Blas_LDA, singular_vals, work, &lwork, &lierr));
6723: #else
6724:             PetscCallBLAS("LAPACKsyev", LAPACKsyev_("V", "U", &Blas_N, correlation_mat, &Blas_LDA, singular_vals, work, &lwork, rwork, &lierr));
6725: #endif
6726:             PetscCall(PetscFPTrapPop());
6727:             PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYEV Lapack routine %" PetscBLASInt_FMT, lierr);
6728:             /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
6729:             j = 0;
6730:             while (j < temp_constraints && singular_vals[j] / singular_vals[temp_constraints - 1] < tol) j++;
6731:             total_counts      = total_counts - j;
6732:             valid_constraints = temp_constraints - j;
6733:             /* scale and copy POD basis into used quadrature memory */
6734:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_M));
6735:             PetscCall(PetscBLASIntCast(temp_constraints, &Blas_N));
6736:             PetscCall(PetscBLASIntCast(temp_constraints, &Blas_K));
6737:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDA));
6738:             PetscCall(PetscBLASIntCast(temp_constraints, &Blas_LDB));
6739:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDC));
6740:             if (j < temp_constraints) {
6741:               PetscInt ii;
6742:               for (k = j; k < temp_constraints; k++) singular_vals[k] = 1.0 / PetscSqrtReal(singular_vals[k]);
6743:               PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
6744:               PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &Blas_M, &Blas_N, &Blas_K, &one, ptr_to_data, &Blas_LDA, correlation_mat, &Blas_LDB, &zero, temp_basis, &Blas_LDC));
6745:               PetscCall(PetscFPTrapPop());
6746:               for (k = 0; k < temp_constraints - j; k++) {
6747:                 for (ii = 0; ii < size_of_constraint; ii++) ptr_to_data[k * size_of_constraint + ii] = singular_vals[temp_constraints - 1 - k] * temp_basis[(temp_constraints - 1 - k) * size_of_constraint + ii];
6748:               }
6749:             }
6750:           } else {
6751: #if !defined(PETSC_MISSING_LAPACK_GESVD)
6752:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_M));
6753:             PetscCall(PetscBLASIntCast(temp_constraints, &Blas_N));
6754:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDA));
6755:             PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
6756:   #if !defined(PETSC_USE_COMPLEX)
6757:             PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("O", "N", &Blas_M, &Blas_N, ptr_to_data, &Blas_LDA, singular_vals, &dummy_scalar, &dummy_int, &dummy_scalar, &dummy_int, work, &lwork, &lierr));
6758:   #else
6759:             PetscCallBLAS("LAPACKgesvd", LAPACKgesvd_("O", "N", &Blas_M, &Blas_N, ptr_to_data, &Blas_LDA, singular_vals, &dummy_scalar, &dummy_int, &dummy_scalar, &dummy_int, work, &lwork, rwork, &lierr));
6760:   #endif
6761:             PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GESVD Lapack routine %" PetscBLASInt_FMT, lierr);
6762:             PetscCall(PetscFPTrapPop());
6763:             /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
6764:             k = temp_constraints;
6765:             if (k > size_of_constraint) k = size_of_constraint;
6766:             j = 0;
6767:             while (j < k && singular_vals[k - j - 1] / singular_vals[0] < tol) j++;
6768:             valid_constraints = k - j;
6769:             total_counts      = total_counts - temp_constraints + valid_constraints;
6770: #else
6771:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "This should not happen");
6772: #endif /* on missing GESVD */
6773:           }
6774:         }
6775:       }
6776:       /* update pointers information */
6777:       if (valid_constraints) {
6778:         constraints_n[total_counts_cc]            = valid_constraints;
6779:         constraints_idxs_ptr[total_counts_cc + 1] = constraints_idxs_ptr[total_counts_cc] + size_of_constraint;
6780:         constraints_data_ptr[total_counts_cc + 1] = constraints_data_ptr[total_counts_cc] + size_of_constraint * valid_constraints;
6781:         /* set change_of_basis flag */
6782:         if (boolforchange) PetscCall(PetscBTSet(change_basis, total_counts_cc));
6783:         total_counts_cc++;
6784:       }
6785:     }
6786:     /* free workspace */
6787:     if (!skip_lapack) {
6788:       PetscCall(PetscFree(work));
6789: #if defined(PETSC_USE_COMPLEX)
6790:       PetscCall(PetscFree(rwork));
6791: #endif
6792:       PetscCall(PetscFree(singular_vals));
6793:       PetscCall(PetscFree(correlation_mat));
6794:       PetscCall(PetscFree(temp_basis));
6795:     }
6796:     for (k = 0; k < nnsp_size; k++) PetscCall(VecDestroy(&localnearnullsp[k]));
6797:     PetscCall(PetscFree(localnearnullsp));
6798:     /* free index sets of faces, edges and vertices */
6799:     PetscCall(PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph, &o_nf, &ISForFaces, &o_ne, &ISForEdges, &ISForVertices));
6800:   } else {
6801:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

6803:     total_counts = 0;
6804:     n_vertices   = 0;
6805:     if (sub_schurs->is_vertices && pcbddc->use_vertices) PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_vertices));
6806:     max_constraints = 0;
6807:     total_counts_cc = 0;
6808:     for (i = 0; i < sub_schurs->n_subs + n_vertices; i++) {
6809:       total_counts += pcbddc->adaptive_constraints_n[i];
6810:       if (pcbddc->adaptive_constraints_n[i]) total_counts_cc++;
6811:       max_constraints = PetscMax(max_constraints, pcbddc->adaptive_constraints_n[i]);
6812:     }
6813:     constraints_idxs_ptr = pcbddc->adaptive_constraints_idxs_ptr;
6814:     constraints_data_ptr = pcbddc->adaptive_constraints_data_ptr;
6815:     constraints_idxs     = pcbddc->adaptive_constraints_idxs;
6816:     constraints_data     = pcbddc->adaptive_constraints_data;
6817:     /* constraints_n differs from pcbddc->adaptive_constraints_n */
6818:     PetscCall(PetscMalloc1(total_counts_cc, &constraints_n));
6819:     total_counts_cc = 0;
6820:     for (i = 0; i < sub_schurs->n_subs + n_vertices; i++) {
6821:       if (pcbddc->adaptive_constraints_n[i]) constraints_n[total_counts_cc++] = pcbddc->adaptive_constraints_n[i];
6822:     }

6824:     max_size_of_constraint = 0;
6825:     for (i = 0; i < total_counts_cc; i++) max_size_of_constraint = PetscMax(max_size_of_constraint, constraints_idxs_ptr[i + 1] - constraints_idxs_ptr[i]);
6826:     PetscCall(PetscMalloc1(constraints_idxs_ptr[total_counts_cc], &constraints_idxs_B));
6827:     /* Change of basis */
6828:     PetscCall(PetscBTCreate(total_counts_cc, &change_basis));
6829:     if (pcbddc->use_change_of_basis) {
6830:       for (i = 0; i < sub_schurs->n_subs; i++) {
6831:         if (PetscBTLookup(sub_schurs->is_edge, i) || pcbddc->use_change_on_faces) PetscCall(PetscBTSet(change_basis, i + n_vertices));
6832:       }
6833:     }
6834:   }
6835:   pcbddc->local_primal_size = total_counts;
6836:   PetscCall(PetscMalloc1(pcbddc->local_primal_size + pcbddc->benign_n, &pcbddc->primal_indices_local_idxs));

6838:   /* map constraints_idxs in boundary numbering */
6839:   if (pcbddc->use_change_of_basis) {
6840:     PetscCall(ISGlobalToLocalMappingApply(pcis->BtoNmap, IS_GTOLM_DROP, constraints_idxs_ptr[total_counts_cc], constraints_idxs, &i, constraints_idxs_B));
6841:     PetscCheck(i == constraints_idxs_ptr[total_counts_cc], PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error in boundary numbering for constraints indices %" PetscInt_FMT " != %" PetscInt_FMT, constraints_idxs_ptr[total_counts_cc], i);
6842:   }

6844:   /* Create constraint matrix */
6845:   PetscCall(MatCreate(PETSC_COMM_SELF, &pcbddc->ConstraintMatrix));
6846:   PetscCall(MatSetType(pcbddc->ConstraintMatrix, MATAIJ));
6847:   PetscCall(MatSetSizes(pcbddc->ConstraintMatrix, pcbddc->local_primal_size, pcis->n, pcbddc->local_primal_size, pcis->n));

6849:   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
6850:   /* determine if a QR strategy is needed for change of basis */
6851:   qr_needed = pcbddc->use_qr_single;
6852:   PetscCall(PetscBTCreate(total_counts_cc, &qr_needed_idx));
6853:   total_primal_vertices        = 0;
6854:   pcbddc->local_primal_size_cc = 0;
6855:   for (i = 0; i < total_counts_cc; i++) {
6856:     size_of_constraint = constraints_idxs_ptr[i + 1] - constraints_idxs_ptr[i];
6857:     if (size_of_constraint == 1 && pcbddc->mat_graph->custom_minimal_size) {
6858:       pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]];
6859:       pcbddc->local_primal_size_cc += 1;
6860:     } else if (PetscBTLookup(change_basis, i)) {
6861:       for (k = 0; k < constraints_n[i]; k++) pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i] + k];
6862:       pcbddc->local_primal_size_cc += constraints_n[i];
6863:       if (constraints_n[i] > 1 || pcbddc->use_qr_single) {
6864:         PetscCall(PetscBTSet(qr_needed_idx, i));
6865:         qr_needed = PETSC_TRUE;
6866:       }
6867:     } else {
6868:       pcbddc->local_primal_size_cc += 1;
6869:     }
6870:   }
6871:   /* note that the local variable n_vertices used below stores the number of pointwise constraints */
6872:   pcbddc->n_vertices = total_primal_vertices;
6873:   /* permute indices in order to have a sorted set of vertices */
6874:   PetscCall(PetscSortInt(total_primal_vertices, pcbddc->primal_indices_local_idxs));
6875:   PetscCall(PetscMalloc2(pcbddc->local_primal_size_cc + pcbddc->benign_n, &pcbddc->local_primal_ref_node, pcbddc->local_primal_size_cc + pcbddc->benign_n, &pcbddc->local_primal_ref_mult));
6876:   PetscCall(PetscArraycpy(pcbddc->local_primal_ref_node, pcbddc->primal_indices_local_idxs, total_primal_vertices));
6877:   for (i = 0; i < total_primal_vertices; i++) pcbddc->local_primal_ref_mult[i] = 1;

6879:   /* nonzero structure of constraint matrix */
6880:   /* and get reference dof for local constraints */
6881:   PetscCall(PetscMalloc1(pcbddc->local_primal_size, &nnz));
6882:   for (i = 0; i < total_primal_vertices; i++) nnz[i] = 1;

6884:   j            = total_primal_vertices;
6885:   total_counts = total_primal_vertices;
6886:   cum          = total_primal_vertices;
6887:   for (i = n_vertices; i < total_counts_cc; i++) {
6888:     if (!PetscBTLookup(change_basis, i)) {
6889:       pcbddc->local_primal_ref_node[cum] = constraints_idxs[constraints_idxs_ptr[i]];
6890:       pcbddc->local_primal_ref_mult[cum] = constraints_n[i];
6891:       cum++;
6892:       size_of_constraint = constraints_idxs_ptr[i + 1] - constraints_idxs_ptr[i];
6893:       for (k = 0; k < constraints_n[i]; k++) {
6894:         pcbddc->primal_indices_local_idxs[total_counts++] = constraints_idxs[constraints_idxs_ptr[i] + k];
6895:         nnz[j + k]                                        = size_of_constraint;
6896:       }
6897:       j += constraints_n[i];
6898:     }
6899:   }
6900:   PetscCall(MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix, 0, nnz));
6901:   PetscCall(MatSetOption(pcbddc->ConstraintMatrix, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
6902:   PetscCall(PetscFree(nnz));

6904:   /* set values in constraint matrix */
6905:   for (i = 0; i < total_primal_vertices; i++) PetscCall(MatSetValue(pcbddc->ConstraintMatrix, i, pcbddc->local_primal_ref_node[i], 1.0, INSERT_VALUES));
6906:   total_counts = total_primal_vertices;
6907:   for (i = n_vertices; i < total_counts_cc; i++) {
6908:     if (!PetscBTLookup(change_basis, i)) {
6909:       PetscInt *cols;

6911:       size_of_constraint = constraints_idxs_ptr[i + 1] - constraints_idxs_ptr[i];
6912:       cols               = constraints_idxs + constraints_idxs_ptr[i];
6913:       for (k = 0; k < constraints_n[i]; k++) {
6914:         PetscInt     row = total_counts + k;
6915:         PetscScalar *vals;

6917:         vals = constraints_data + constraints_data_ptr[i] + k * size_of_constraint;
6918:         PetscCall(MatSetValues(pcbddc->ConstraintMatrix, 1, &row, size_of_constraint, cols, vals, INSERT_VALUES));
6919:       }
6920:       total_counts += constraints_n[i];
6921:     }
6922:   }
6923:   /* assembling */
6924:   PetscCall(MatAssemblyBegin(pcbddc->ConstraintMatrix, MAT_FINAL_ASSEMBLY));
6925:   PetscCall(MatAssemblyEnd(pcbddc->ConstraintMatrix, MAT_FINAL_ASSEMBLY));
6926:   PetscCall(MatViewFromOptions(pcbddc->ConstraintMatrix, (PetscObject)pc, "-pc_bddc_constraint_mat_view"));

6928:   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
6929:   if (pcbddc->use_change_of_basis) {
6930:     /* dual and primal dofs on a single cc */
6931:     PetscInt dual_dofs, primal_dofs;
6932:     /* working stuff for GEQRF */
6933:     PetscScalar *qr_basis = NULL, *qr_tau = NULL, *qr_work = NULL, lqr_work_t;
6934:     PetscBLASInt lqr_work;
6935:     /* working stuff for UNGQR */
6936:     PetscScalar *gqr_work = NULL, lgqr_work_t = 0.0;
6937:     PetscBLASInt lgqr_work;
6938:     /* working stuff for TRTRS */
6939:     PetscScalar *trs_rhs = NULL;
6940:     PetscBLASInt Blas_NRHS;
6941:     /* pointers for values insertion into change of basis matrix */
6942:     PetscInt    *start_rows, *start_cols;
6943:     PetscScalar *start_vals;
6944:     /* working stuff for values insertion */
6945:     PetscBT   is_primal;
6946:     PetscInt *aux_primal_numbering_B;
6947:     /* matrix sizes */
6948:     PetscInt global_size, local_size;
6949:     /* temporary change of basis */
6950:     Mat localChangeOfBasisMatrix;
6951:     /* extra space for debugging */
6952:     PetscScalar *dbg_work = NULL;

6954:     PetscCall(MatCreate(PETSC_COMM_SELF, &localChangeOfBasisMatrix));
6955:     PetscCall(MatSetType(localChangeOfBasisMatrix, MATAIJ));
6956:     PetscCall(MatSetSizes(localChangeOfBasisMatrix, pcis->n, pcis->n, pcis->n, pcis->n));
6957:     /* nonzeros for local mat */
6958:     PetscCall(PetscMalloc1(pcis->n, &nnz));
6959:     if (!pcbddc->benign_change || pcbddc->fake_change) {
6960:       for (i = 0; i < pcis->n; i++) nnz[i] = 1;
6961:     } else {
6962:       const PetscInt *ii;
6963:       PetscInt        n;
6964:       PetscBool       flg_row;
6965:       PetscCall(MatGetRowIJ(pcbddc->benign_change, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, NULL, &flg_row));
6966:       for (i = 0; i < n; i++) nnz[i] = ii[i + 1] - ii[i];
6967:       PetscCall(MatRestoreRowIJ(pcbddc->benign_change, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, NULL, &flg_row));
6968:     }
6969:     for (i = n_vertices; i < total_counts_cc; i++) {
6970:       if (PetscBTLookup(change_basis, i)) {
6971:         size_of_constraint = constraints_idxs_ptr[i + 1] - constraints_idxs_ptr[i];
6972:         if (PetscBTLookup(qr_needed_idx, i)) {
6973:           for (j = 0; j < size_of_constraint; j++) nnz[constraints_idxs[constraints_idxs_ptr[i] + j]] = size_of_constraint;
6974:         } else {
6975:           nnz[constraints_idxs[constraints_idxs_ptr[i]]] = size_of_constraint;
6976:           for (j = 1; j < size_of_constraint; j++) nnz[constraints_idxs[constraints_idxs_ptr[i] + j]] = 2;
6977:         }
6978:       }
6979:     }
6980:     PetscCall(MatSeqAIJSetPreallocation(localChangeOfBasisMatrix, 0, nnz));
6981:     PetscCall(MatSetOption(localChangeOfBasisMatrix, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
6982:     PetscCall(PetscFree(nnz));
6983:     /* Set interior change in the matrix */
6984:     if (!pcbddc->benign_change || pcbddc->fake_change) {
6985:       for (i = 0; i < pcis->n; i++) PetscCall(MatSetValue(localChangeOfBasisMatrix, i, i, 1.0, INSERT_VALUES));
6986:     } else {
6987:       const PetscInt *ii, *jj;
6988:       PetscScalar    *aa;
6989:       PetscInt        n;
6990:       PetscBool       flg_row;
6991:       PetscCall(MatGetRowIJ(pcbddc->benign_change, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, &jj, &flg_row));
6992:       PetscCall(MatSeqAIJGetArray(pcbddc->benign_change, &aa));
6993:       for (i = 0; i < n; i++) PetscCall(MatSetValues(localChangeOfBasisMatrix, 1, &i, ii[i + 1] - ii[i], jj + ii[i], aa + ii[i], INSERT_VALUES));
6994:       PetscCall(MatSeqAIJRestoreArray(pcbddc->benign_change, &aa));
6995:       PetscCall(MatRestoreRowIJ(pcbddc->benign_change, 0, PETSC_FALSE, PETSC_FALSE, &n, &ii, &jj, &flg_row));
6996:     }

6998:     if (pcbddc->dbg_flag) {
6999:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "--------------------------------------------------------------\n"));
7000:       PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Checking change of basis computation for subdomain %04d\n", PetscGlobalRank));
7001:     }

7003:     /* Now we loop on the constraints which need a change of basis */
7004:     /*
7005:        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
7006:        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)

7008:        Basic blocks of change of basis matrix T computed:

7010:           - By using the following block transformation if there is only a primal dof on the cc (and -pc_bddc_use_qr_single is not specified)

7012:             | 1        0   ...        0         s_1/S |
7013:             | 0        1   ...        0         s_2/S |
7014:             |              ...                        |
7015:             | 0        ...            1     s_{n-1}/S |
7016:             | -s_1/s_n ...    -s_{n-1}/s_n      s_n/S |

7018:             with S = \sum_{i=1}^n s_i^2
7019:             NOTE: in the above example, the primal dof is the last one of the edge in LOCAL ordering
7020:                   in the current implementation, the primal dof is the first one of the edge in GLOBAL ordering

7022:           - QR decomposition of constraints otherwise
7023:     */
7024:     if (qr_needed && max_size_of_constraint) {
7025:       /* space to store Q */
7026:       PetscCall(PetscMalloc1(max_size_of_constraint * max_size_of_constraint, &qr_basis));
7027:       /* array to store scaling factors for reflectors */
7028:       PetscCall(PetscMalloc1(max_constraints, &qr_tau));
7029:       /* first we issue queries for optimal work */
7030:       PetscCall(PetscBLASIntCast(max_size_of_constraint, &Blas_M));
7031:       PetscCall(PetscBLASIntCast(max_constraints, &Blas_N));
7032:       PetscCall(PetscBLASIntCast(max_size_of_constraint, &Blas_LDA));
7033:       lqr_work = -1;
7034:       PetscCallBLAS("LAPACKgeqrf", LAPACKgeqrf_(&Blas_M, &Blas_N, qr_basis, &Blas_LDA, qr_tau, &lqr_work_t, &lqr_work, &lierr));
7035:       PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to GEQRF Lapack routine %" PetscBLASInt_FMT, lierr);
7036:       PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t), &lqr_work));
7037:       PetscCall(PetscMalloc1(lqr_work, &qr_work));
7038:       lgqr_work = -1;
7039:       PetscCall(PetscBLASIntCast(max_size_of_constraint, &Blas_M));
7040:       PetscCall(PetscBLASIntCast(max_size_of_constraint, &Blas_N));
7041:       PetscCall(PetscBLASIntCast(max_constraints, &Blas_K));
7042:       PetscCall(PetscBLASIntCast(max_size_of_constraint, &Blas_LDA));
7043:       if (Blas_K > Blas_M) Blas_K = Blas_M; /* adjust just for computing optimal work */
7044:       PetscCallBLAS("LAPACKorgqr", LAPACKorgqr_(&Blas_M, &Blas_N, &Blas_K, qr_basis, &Blas_LDA, qr_tau, &lgqr_work_t, &lgqr_work, &lierr));
7045:       PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to ORGQR/UNGQR Lapack routine %" PetscBLASInt_FMT, lierr);
7046:       PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t), &lgqr_work));
7047:       PetscCall(PetscMalloc1(lgqr_work, &gqr_work));
7048:       /* array to store rhs and solution of triangular solver */
7049:       PetscCall(PetscMalloc1(max_constraints * max_constraints, &trs_rhs));
7050:       /* allocating workspace for check */
7051:       if (pcbddc->dbg_flag) PetscCall(PetscMalloc1(max_size_of_constraint * (max_constraints + max_size_of_constraint), &dbg_work));
7052:     }
7053:     /* array to store whether a node is primal or not */
7054:     PetscCall(PetscBTCreate(pcis->n_B, &is_primal));
7055:     PetscCall(PetscMalloc1(total_primal_vertices, &aux_primal_numbering_B));
7056:     PetscCall(ISGlobalToLocalMappingApply(pcis->BtoNmap, IS_GTOLM_DROP, total_primal_vertices, pcbddc->local_primal_ref_node, &i, aux_primal_numbering_B));
7057:     PetscCheck(i == total_primal_vertices, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error in boundary numbering for BDDC vertices! %" PetscInt_FMT " != %" PetscInt_FMT, total_primal_vertices, i);
7058:     for (i = 0; i < total_primal_vertices; i++) PetscCall(PetscBTSet(is_primal, aux_primal_numbering_B[i]));
7059:     PetscCall(PetscFree(aux_primal_numbering_B));

7061:     /* loop on constraints and see whether or not they need a change of basis and compute it */
7062:     for (total_counts = n_vertices; total_counts < total_counts_cc; total_counts++) {
7063:       size_of_constraint = constraints_idxs_ptr[total_counts + 1] - constraints_idxs_ptr[total_counts];
7064:       if (PetscBTLookup(change_basis, total_counts)) {
7065:         /* get constraint info */
7066:         primal_dofs = constraints_n[total_counts];
7067:         dual_dofs   = size_of_constraint - primal_dofs;

7069:         if (pcbddc->dbg_flag) PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Constraints %" PetscInt_FMT ": %" PetscInt_FMT " need a change of basis (size %" PetscInt_FMT ")\n", total_counts, primal_dofs, size_of_constraint));

7071:         if (PetscBTLookup(qr_needed_idx, total_counts)) { /* QR */

7073:           /* copy quadrature constraints for change of basis check */
7074:           if (pcbddc->dbg_flag) PetscCall(PetscArraycpy(dbg_work, &constraints_data[constraints_data_ptr[total_counts]], size_of_constraint * primal_dofs));
7075:           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
7076:           PetscCall(PetscArraycpy(qr_basis, &constraints_data[constraints_data_ptr[total_counts]], size_of_constraint * primal_dofs));

7078:           /* compute QR decomposition of constraints */
7079:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_M));
7080:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_N));
7081:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDA));
7082:           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
7083:           PetscCallBLAS("LAPACKgeqrf", LAPACKgeqrf_(&Blas_M, &Blas_N, qr_basis, &Blas_LDA, qr_tau, qr_work, &lqr_work, &lierr));
7084:           PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GEQRF Lapack routine %" PetscBLASInt_FMT, lierr);
7085:           PetscCall(PetscFPTrapPop());

7087:           /* explicitly compute R^-T */
7088:           PetscCall(PetscArrayzero(trs_rhs, primal_dofs * primal_dofs));
7089:           for (j = 0; j < primal_dofs; j++) trs_rhs[j * (primal_dofs + 1)] = 1.0;
7090:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_N));
7091:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_NRHS));
7092:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDA));
7093:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_LDB));
7094:           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
7095:           PetscCallBLAS("LAPACKtrtrs", LAPACKtrtrs_("U", "T", "N", &Blas_N, &Blas_NRHS, qr_basis, &Blas_LDA, trs_rhs, &Blas_LDB, &lierr));
7096:           PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in TRTRS Lapack routine %" PetscBLASInt_FMT, lierr);
7097:           PetscCall(PetscFPTrapPop());

7099:           /* explicitly compute all columns of Q (Q = [Q1 | Q2]) overwriting QR factorization in qr_basis */
7100:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_M));
7101:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_N));
7102:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_K));
7103:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDA));
7104:           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
7105:           PetscCallBLAS("LAPACKorgqr", LAPACKorgqr_(&Blas_M, &Blas_N, &Blas_K, qr_basis, &Blas_LDA, qr_tau, gqr_work, &lgqr_work, &lierr));
7106:           PetscCheck(!lierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in ORGQR/UNGQR Lapack routine %" PetscBLASInt_FMT, lierr);
7107:           PetscCall(PetscFPTrapPop());

7109:           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
7110:              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
7111:              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
7112:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_M));
7113:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_N));
7114:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_K));
7115:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDA));
7116:           PetscCall(PetscBLASIntCast(primal_dofs, &Blas_LDB));
7117:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDC));
7118:           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
7119:           PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &Blas_M, &Blas_N, &Blas_K, &one, qr_basis, &Blas_LDA, trs_rhs, &Blas_LDB, &zero, constraints_data + constraints_data_ptr[total_counts], &Blas_LDC));
7120:           PetscCall(PetscFPTrapPop());
7121:           PetscCall(PetscArraycpy(qr_basis, &constraints_data[constraints_data_ptr[total_counts]], size_of_constraint * primal_dofs));

7123:           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
7124:           start_rows = &constraints_idxs[constraints_idxs_ptr[total_counts]];
7125:           /* insert cols for primal dofs */
7126:           for (j = 0; j < primal_dofs; j++) {
7127:             start_vals = &qr_basis[j * size_of_constraint];
7128:             start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts] + j];
7129:             PetscCall(MatSetValues(localChangeOfBasisMatrix, size_of_constraint, start_rows, 1, start_cols, start_vals, INSERT_VALUES));
7130:           }
7131:           /* insert cols for dual dofs */
7132:           for (j = 0, k = 0; j < dual_dofs; k++) {
7133:             if (!PetscBTLookup(is_primal, constraints_idxs_B[constraints_idxs_ptr[total_counts] + k])) {
7134:               start_vals = &qr_basis[(primal_dofs + j) * size_of_constraint];
7135:               start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts] + k];
7136:               PetscCall(MatSetValues(localChangeOfBasisMatrix, size_of_constraint, start_rows, 1, start_cols, start_vals, INSERT_VALUES));
7137:               j++;
7138:             }
7139:           }

7141:           /* check change of basis */
7142:           if (pcbddc->dbg_flag) {
7143:             PetscInt  ii, jj;
7144:             PetscBool valid_qr = PETSC_TRUE;
7145:             PetscCall(PetscBLASIntCast(primal_dofs, &Blas_M));
7146:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_N));
7147:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_K));
7148:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDA));
7149:             PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_LDB));
7150:             PetscCall(PetscBLASIntCast(primal_dofs, &Blas_LDC));
7151:             PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
7152:             PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &Blas_M, &Blas_N, &Blas_K, &one, dbg_work, &Blas_LDA, qr_basis, &Blas_LDB, &zero, &dbg_work[size_of_constraint * primal_dofs], &Blas_LDC));
7153:             PetscCall(PetscFPTrapPop());
7154:             for (jj = 0; jj < size_of_constraint; jj++) {
7155:               for (ii = 0; ii < primal_dofs; ii++) {
7156:                 if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint * primal_dofs + jj * primal_dofs + ii]) > 1.e-12) valid_qr = PETSC_FALSE;
7157:                 if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint * primal_dofs + jj * primal_dofs + ii] - (PetscReal)1) > 1.e-12) valid_qr = PETSC_FALSE;
7158:               }
7159:             }
7160:             if (!valid_qr) {
7161:               PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "\t-> wrong change of basis!\n"));
7162:               for (jj = 0; jj < size_of_constraint; jj++) {
7163:                 for (ii = 0; ii < primal_dofs; ii++) {
7164:                   if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint * primal_dofs + jj * primal_dofs + ii]) > 1.e-12) {
7165:                     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "\tQr basis function %" PetscInt_FMT " is not orthogonal to constraint %" PetscInt_FMT " (%1.14e)!\n", jj, ii, (double)PetscAbsScalar(dbg_work[size_of_constraint * primal_dofs + jj * primal_dofs + ii])));
7166:                   }
7167:                   if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint * primal_dofs + jj * primal_dofs + ii] - (PetscReal)1) > 1.e-12) {
7168:                     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "\tQr basis function %" PetscInt_FMT " is not unitary w.r.t constraint %" PetscInt_FMT " (%1.14e)!\n", jj, ii, (double)PetscAbsScalar(dbg_work[size_of_constraint * primal_dofs + jj * primal_dofs + ii])));
7169:                   }
7170:                 }
7171:               }
7172:             } else {
7173:               PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "\t-> right change of basis!\n"));
7174:             }
7175:           }
7176:         } else { /* simple transformation block */
7177:           PetscInt    row, col;
7178:           PetscScalar val, norm;

7180:           PetscCall(PetscBLASIntCast(size_of_constraint, &Blas_N));
7181:           PetscCallBLAS("BLASdot", norm = BLASdot_(&Blas_N, constraints_data + constraints_data_ptr[total_counts], &Blas_one, constraints_data + constraints_data_ptr[total_counts], &Blas_one));
7182:           for (j = 0; j < size_of_constraint; j++) {
7183:             PetscInt row_B = constraints_idxs_B[constraints_idxs_ptr[total_counts] + j];
7184:             row            = constraints_idxs[constraints_idxs_ptr[total_counts] + j];
7185:             if (!PetscBTLookup(is_primal, row_B)) {
7186:               col = constraints_idxs[constraints_idxs_ptr[total_counts]];
7187:               PetscCall(MatSetValue(localChangeOfBasisMatrix, row, row, 1.0, INSERT_VALUES));
7188:               PetscCall(MatSetValue(localChangeOfBasisMatrix, row, col, constraints_data[constraints_data_ptr[total_counts] + j] / norm, INSERT_VALUES));
7189:             } else {
7190:               for (k = 0; k < size_of_constraint; k++) {
7191:                 col = constraints_idxs[constraints_idxs_ptr[total_counts] + k];
7192:                 if (row != col) {
7193:                   val = -constraints_data[constraints_data_ptr[total_counts] + k] / constraints_data[constraints_data_ptr[total_counts]];
7194:                 } else {
7195:                   val = constraints_data[constraints_data_ptr[total_counts]] / norm;
7196:                 }
7197:                 PetscCall(MatSetValue(localChangeOfBasisMatrix, row, col, val, INSERT_VALUES));
7198:               }
7199:             }
7200:           }
7201:           if (pcbddc->dbg_flag) PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "\t-> using standard change of basis\n"));
7202:         }
7203:       } else {
7204:         if (pcbddc->dbg_flag) PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Constraint %" PetscInt_FMT " does not need a change of basis (size %" PetscInt_FMT ")\n", total_counts, size_of_constraint));
7205:       }
7206:     }

7208:     /* free workspace */
7209:     if (qr_needed) {
7210:       if (pcbddc->dbg_flag) PetscCall(PetscFree(dbg_work));
7211:       PetscCall(PetscFree(trs_rhs));
7212:       PetscCall(PetscFree(qr_tau));
7213:       PetscCall(PetscFree(qr_work));
7214:       PetscCall(PetscFree(gqr_work));
7215:       PetscCall(PetscFree(qr_basis));
7216:     }
7217:     PetscCall(PetscBTDestroy(&is_primal));
7218:     PetscCall(MatAssemblyBegin(localChangeOfBasisMatrix, MAT_FINAL_ASSEMBLY));
7219:     PetscCall(MatAssemblyEnd(localChangeOfBasisMatrix, MAT_FINAL_ASSEMBLY));

7221:     /* assembling of global change of variable */
7222:     if (!pcbddc->fake_change) {
7223:       Mat      tmat;
7224:       PetscInt bs;

7226:       PetscCall(VecGetSize(pcis->vec1_global, &global_size));
7227:       PetscCall(VecGetLocalSize(pcis->vec1_global, &local_size));
7228:       PetscCall(MatDuplicate(pc->pmat, MAT_DO_NOT_COPY_VALUES, &tmat));
7229:       PetscCall(MatISSetLocalMat(tmat, localChangeOfBasisMatrix));
7230:       PetscCall(MatAssemblyBegin(tmat, MAT_FINAL_ASSEMBLY));
7231:       PetscCall(MatAssemblyEnd(tmat, MAT_FINAL_ASSEMBLY));
7232:       PetscCall(MatCreate(PetscObjectComm((PetscObject)pc), &pcbddc->ChangeOfBasisMatrix));
7233:       PetscCall(MatSetType(pcbddc->ChangeOfBasisMatrix, MATAIJ));
7234:       PetscCall(MatGetBlockSize(pc->pmat, &bs));
7235:       PetscCall(MatSetBlockSize(pcbddc->ChangeOfBasisMatrix, bs));
7236:       PetscCall(MatSetSizes(pcbddc->ChangeOfBasisMatrix, local_size, local_size, global_size, global_size));
7237:       PetscCall(MatISSetMPIXAIJPreallocation_Private(tmat, pcbddc->ChangeOfBasisMatrix, PETSC_TRUE));
7238:       PetscCall(MatConvert(tmat, MATAIJ, MAT_REUSE_MATRIX, &pcbddc->ChangeOfBasisMatrix));
7239:       PetscCall(MatDestroy(&tmat));
7240:       PetscCall(VecSet(pcis->vec1_global, 0.0));
7241:       PetscCall(VecSet(pcis->vec1_N, 1.0));
7242:       PetscCall(VecScatterBegin(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
7243:       PetscCall(VecScatterEnd(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
7244:       PetscCall(VecReciprocal(pcis->vec1_global));
7245:       PetscCall(MatDiagonalScale(pcbddc->ChangeOfBasisMatrix, pcis->vec1_global, NULL));

7247:       /* check */
7248:       if (pcbddc->dbg_flag) {
7249:         PetscReal error;
7250:         Vec       x, x_change;

7252:         PetscCall(VecDuplicate(pcis->vec1_global, &x));
7253:         PetscCall(VecDuplicate(pcis->vec1_global, &x_change));
7254:         PetscCall(VecSetRandom(x, NULL));
7255:         PetscCall(VecCopy(x, pcis->vec1_global));
7256:         PetscCall(VecScatterBegin(matis->rctx, x, pcis->vec1_N, INSERT_VALUES, SCATTER_FORWARD));
7257:         PetscCall(VecScatterEnd(matis->rctx, x, pcis->vec1_N, INSERT_VALUES, SCATTER_FORWARD));
7258:         PetscCall(MatMult(localChangeOfBasisMatrix, pcis->vec1_N, pcis->vec2_N));
7259:         PetscCall(VecScatterBegin(matis->rctx, pcis->vec2_N, x, INSERT_VALUES, SCATTER_REVERSE));
7260:         PetscCall(VecScatterEnd(matis->rctx, pcis->vec2_N, x, INSERT_VALUES, SCATTER_REVERSE));
7261:         PetscCall(MatMult(pcbddc->ChangeOfBasisMatrix, pcis->vec1_global, x_change));
7262:         PetscCall(VecAXPY(x, -1.0, x_change));
7263:         PetscCall(VecNorm(x, NORM_INFINITY, &error));
7264:         PetscCheck(error <= PETSC_SMALL, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Error global vs local change on N: %1.6e", (double)error);
7265:         PetscCall(VecDestroy(&x));
7266:         PetscCall(VecDestroy(&x_change));
7267:       }
7268:       /* adapt sub_schurs computed (if any) */
7269:       if (pcbddc->use_deluxe_scaling) {
7270:         PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

7272:         PetscCheck(!pcbddc->use_change_of_basis || !pcbddc->adaptive_userdefined, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot mix automatic change of basis, adaptive selection and user-defined constraints");
7273:         if (sub_schurs && sub_schurs->S_Ej_all) {
7274:           Mat S_new, tmat;
7275:           IS  is_all_N, is_V_Sall = NULL;

7277:           PetscCall(ISLocalToGlobalMappingApplyIS(pcis->BtoNmap, sub_schurs->is_Ej_all, &is_all_N));
7278:           PetscCall(MatCreateSubMatrix(localChangeOfBasisMatrix, is_all_N, is_all_N, MAT_INITIAL_MATRIX, &tmat));
7279:           if (pcbddc->deluxe_zerorows) {
7280:             ISLocalToGlobalMapping NtoSall;
7281:             IS                     is_V;
7282:             PetscCall(ISCreateGeneral(PETSC_COMM_SELF, pcbddc->n_vertices, pcbddc->local_primal_ref_node, PETSC_COPY_VALUES, &is_V));
7283:             PetscCall(ISLocalToGlobalMappingCreateIS(is_all_N, &NtoSall));
7284:             PetscCall(ISGlobalToLocalMappingApplyIS(NtoSall, IS_GTOLM_DROP, is_V, &is_V_Sall));
7285:             PetscCall(ISLocalToGlobalMappingDestroy(&NtoSall));
7286:             PetscCall(ISDestroy(&is_V));
7287:           }
7288:           PetscCall(ISDestroy(&is_all_N));
7289:           PetscCall(MatPtAP(sub_schurs->S_Ej_all, tmat, MAT_INITIAL_MATRIX, 1.0, &S_new));
7290:           PetscCall(MatDestroy(&sub_schurs->S_Ej_all));
7291:           PetscCall(PetscObjectReference((PetscObject)S_new));
7292:           if (pcbddc->deluxe_zerorows) {
7293:             const PetscScalar *array;
7294:             const PetscInt    *idxs_V, *idxs_all;
7295:             PetscInt           i, n_V;

7297:             PetscCall(MatZeroRowsColumnsIS(S_new, is_V_Sall, 1., NULL, NULL));
7298:             PetscCall(ISGetLocalSize(is_V_Sall, &n_V));
7299:             PetscCall(ISGetIndices(is_V_Sall, &idxs_V));
7300:             PetscCall(ISGetIndices(sub_schurs->is_Ej_all, &idxs_all));
7301:             PetscCall(VecGetArrayRead(pcis->D, &array));
7302:             for (i = 0; i < n_V; i++) {
7303:               PetscScalar val;
7304:               PetscInt    idx;

7306:               idx = idxs_V[i];
7307:               val = array[idxs_all[idxs_V[i]]];
7308:               PetscCall(MatSetValue(S_new, idx, idx, val, INSERT_VALUES));
7309:             }
7310:             PetscCall(MatAssemblyBegin(S_new, MAT_FINAL_ASSEMBLY));
7311:             PetscCall(MatAssemblyEnd(S_new, MAT_FINAL_ASSEMBLY));
7312:             PetscCall(VecRestoreArrayRead(pcis->D, &array));
7313:             PetscCall(ISRestoreIndices(sub_schurs->is_Ej_all, &idxs_all));
7314:             PetscCall(ISRestoreIndices(is_V_Sall, &idxs_V));
7315:           }
7316:           sub_schurs->S_Ej_all = S_new;
7317:           PetscCall(MatDestroy(&S_new));
7318:           if (sub_schurs->sum_S_Ej_all) {
7319:             PetscCall(MatPtAP(sub_schurs->sum_S_Ej_all, tmat, MAT_INITIAL_MATRIX, 1.0, &S_new));
7320:             PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_all));
7321:             PetscCall(PetscObjectReference((PetscObject)S_new));
7322:             if (pcbddc->deluxe_zerorows) PetscCall(MatZeroRowsColumnsIS(S_new, is_V_Sall, 1., NULL, NULL));
7323:             sub_schurs->sum_S_Ej_all = S_new;
7324:             PetscCall(MatDestroy(&S_new));
7325:           }
7326:           PetscCall(ISDestroy(&is_V_Sall));
7327:           PetscCall(MatDestroy(&tmat));
7328:         }
7329:         /* destroy any change of basis context in sub_schurs */
7330:         if (sub_schurs && sub_schurs->change) {
7331:           PetscInt i;

7333:           for (i = 0; i < sub_schurs->n_subs; i++) PetscCall(KSPDestroy(&sub_schurs->change[i]));
7334:           PetscCall(PetscFree(sub_schurs->change));
7335:         }
7336:       }
7337:       if (pcbddc->switch_static) { /* need to save the local change */
7338:         pcbddc->switch_static_change = localChangeOfBasisMatrix;
7339:       } else {
7340:         PetscCall(MatDestroy(&localChangeOfBasisMatrix));
7341:       }
7342:       /* determine if any process has changed the pressures locally */
7343:       pcbddc->change_interior = pcbddc->benign_have_null;
7344:     } else { /* fake change (get back change of basis into ConstraintMatrix and info on qr) */
7345:       PetscCall(MatDestroy(&pcbddc->ConstraintMatrix));
7346:       pcbddc->ConstraintMatrix = localChangeOfBasisMatrix;
7347:       pcbddc->use_qr_single    = qr_needed;
7348:     }
7349:   } else if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->benign_saddle_point) {
7350:     if (!pcbddc->benign_have_null && pcbddc->user_ChangeOfBasisMatrix) {
7351:       PetscCall(PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix));
7352:       pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
7353:     } else {
7354:       Mat benign_global = NULL;
7355:       if (pcbddc->benign_have_null) {
7356:         Mat M;

7358:         pcbddc->change_interior = PETSC_TRUE;
7359:         PetscCall(VecCopy(matis->counter, pcis->vec1_N));
7360:         PetscCall(VecReciprocal(pcis->vec1_N));
7361:         PetscCall(MatDuplicate(pc->pmat, MAT_DO_NOT_COPY_VALUES, &benign_global));
7362:         if (pcbddc->benign_change) {
7363:           PetscCall(MatDuplicate(pcbddc->benign_change, MAT_COPY_VALUES, &M));
7364:           PetscCall(MatDiagonalScale(M, pcis->vec1_N, NULL));
7365:         } else {
7366:           PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, pcis->n, pcis->n, 1, NULL, &M));
7367:           PetscCall(MatDiagonalSet(M, pcis->vec1_N, INSERT_VALUES));
7368:         }
7369:         PetscCall(MatISSetLocalMat(benign_global, M));
7370:         PetscCall(MatDestroy(&M));
7371:         PetscCall(MatAssemblyBegin(benign_global, MAT_FINAL_ASSEMBLY));
7372:         PetscCall(MatAssemblyEnd(benign_global, MAT_FINAL_ASSEMBLY));
7373:       }
7374:       if (pcbddc->user_ChangeOfBasisMatrix) {
7375:         PetscCall(MatMatMult(pcbddc->user_ChangeOfBasisMatrix, benign_global, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &pcbddc->ChangeOfBasisMatrix));
7376:         PetscCall(MatDestroy(&benign_global));
7377:       } else if (pcbddc->benign_have_null) {
7378:         pcbddc->ChangeOfBasisMatrix = benign_global;
7379:       }
7380:     }
7381:     if (pcbddc->switch_static && pcbddc->ChangeOfBasisMatrix) { /* need to save the local change */
7382:       IS              is_global;
7383:       const PetscInt *gidxs;

7385:       PetscCall(ISLocalToGlobalMappingGetIndices(matis->rmapping, &gidxs));
7386:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), pcis->n, gidxs, PETSC_COPY_VALUES, &is_global));
7387:       PetscCall(ISLocalToGlobalMappingRestoreIndices(matis->rmapping, &gidxs));
7388:       PetscCall(MatCreateSubMatrixUnsorted(pcbddc->ChangeOfBasisMatrix, is_global, is_global, &pcbddc->switch_static_change));
7389:       PetscCall(ISDestroy(&is_global));
7390:     }
7391:   }
7392:   if (!pcbddc->fake_change && pcbddc->ChangeOfBasisMatrix && !pcbddc->work_change) PetscCall(VecDuplicate(pcis->vec1_global, &pcbddc->work_change));

7394:   if (!pcbddc->fake_change) {
7395:     /* add pressure dofs to set of primal nodes for numbering purposes */
7396:     for (i = 0; i < pcbddc->benign_n; i++) {
7397:       pcbddc->local_primal_ref_node[pcbddc->local_primal_size_cc]  = pcbddc->benign_p0_lidx[i];
7398:       pcbddc->primal_indices_local_idxs[pcbddc->local_primal_size] = pcbddc->benign_p0_lidx[i];
7399:       pcbddc->local_primal_ref_mult[pcbddc->local_primal_size_cc]  = 1;
7400:       pcbddc->local_primal_size_cc++;
7401:       pcbddc->local_primal_size++;
7402:     }

7404:     /* check if a new primal space has been introduced (also take into account benign trick) */
7405:     pcbddc->new_primal_space_local = PETSC_TRUE;
7406:     if (olocal_primal_size == pcbddc->local_primal_size) {
7407:       PetscCall(PetscArraycmp(pcbddc->local_primal_ref_node, olocal_primal_ref_node, olocal_primal_size_cc, &pcbddc->new_primal_space_local));
7408:       pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
7409:       if (!pcbddc->new_primal_space_local) {
7410:         PetscCall(PetscArraycmp(pcbddc->local_primal_ref_mult, olocal_primal_ref_mult, olocal_primal_size_cc, &pcbddc->new_primal_space_local));
7411:         pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
7412:       }
7413:     }
7414:     /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
7415:     PetscCallMPI(MPIU_Allreduce(&pcbddc->new_primal_space_local, &pcbddc->new_primal_space, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)pc)));
7416:   }
7417:   PetscCall(PetscFree2(olocal_primal_ref_node, olocal_primal_ref_mult));

7419:   /* flush dbg viewer */
7420:   if (pcbddc->dbg_flag) PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));

7422:   /* free workspace */
7423:   PetscCall(PetscBTDestroy(&qr_needed_idx));
7424:   PetscCall(PetscBTDestroy(&change_basis));
7425:   if (!pcbddc->adaptive_selection) {
7426:     PetscCall(PetscFree3(constraints_idxs_ptr, constraints_data_ptr, constraints_n));
7427:     PetscCall(PetscFree3(constraints_data, constraints_idxs, constraints_idxs_B));
7428:   } else {
7429:     PetscCall(PetscFree5(pcbddc->adaptive_constraints_n, pcbddc->adaptive_constraints_idxs_ptr, pcbddc->adaptive_constraints_data_ptr, pcbddc->adaptive_constraints_idxs, pcbddc->adaptive_constraints_data));
7430:     PetscCall(PetscFree(constraints_n));
7431:     PetscCall(PetscFree(constraints_idxs_B));
7432:   }
7433:   PetscFunctionReturn(PETSC_SUCCESS);
7434: }

7436: PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
7437: {
7438:   ISLocalToGlobalMapping map;
7439:   PC_BDDC               *pcbddc = (PC_BDDC *)pc->data;
7440:   Mat_IS                *matis  = (Mat_IS *)pc->pmat->data;
7441:   PetscInt               i, N;
7442:   PetscBool              rcsr = PETSC_FALSE;

7444:   PetscFunctionBegin;
7445:   if (pcbddc->recompute_topography) {
7446:     pcbddc->graphanalyzed = PETSC_FALSE;
7447:     /* Reset previously computed graph */
7448:     PetscCall(PCBDDCGraphReset(pcbddc->mat_graph));
7449:     /* Init local Graph struct */
7450:     PetscCall(MatGetSize(pc->pmat, &N, NULL));
7451:     PetscCall(MatISGetLocalToGlobalMapping(pc->pmat, &map, NULL));
7452:     PetscCall(PCBDDCGraphInit(pcbddc->mat_graph, map, N, pcbddc->graphmaxcount));

7454:     if (pcbddc->user_primal_vertices_local && !pcbddc->user_primal_vertices) PetscCall(PCBDDCConsistencyCheckIS(pc, MPI_LOR, &pcbddc->user_primal_vertices_local));
7455:     /* Check validity of the csr graph passed in by the user */
7456:     PetscCheck(!pcbddc->mat_graph->nvtxs_csr || pcbddc->mat_graph->nvtxs_csr == pcbddc->mat_graph->nvtxs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid size of local CSR graph! Found %" PetscInt_FMT ", expected %" PetscInt_FMT, pcbddc->mat_graph->nvtxs_csr,
7457:                pcbddc->mat_graph->nvtxs);

7459:     /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
7460:     if (!pcbddc->mat_graph->xadj && pcbddc->use_local_adj) {
7461:       PetscInt *xadj, *adjncy;
7462:       PetscInt  nvtxs;
7463:       PetscBool flg_row;
7464:       Mat       A;

7466:       PetscCall(PetscObjectReference((PetscObject)matis->A));
7467:       A = matis->A;
7468:       for (PetscInt i = 0; i < pcbddc->local_adj_square; i++) {
7469:         Mat AtA;

7471:         PetscCall(MatProductCreate(A, A, NULL, &AtA));
7472:         PetscCall(MatSetOptionsPrefix(AtA, "pc_bddc_graph_"));
7473:         PetscCall(MatProductSetType(AtA, MATPRODUCT_AtB));
7474:         PetscCall(MatProductSetFromOptions(AtA));
7475:         PetscCall(MatProductSymbolic(AtA));
7476:         PetscCall(MatProductClear(AtA));
7477:         /* we only need the sparsity, cheat and tell PETSc the matrix has been assembled */
7478:         AtA->assembled = PETSC_TRUE;
7479:         PetscCall(MatDestroy(&A));
7480:         A = AtA;
7481:       }
7482:       PetscCall(MatGetRowIJ(A, 0, PETSC_TRUE, PETSC_FALSE, &nvtxs, (const PetscInt **)&xadj, (const PetscInt **)&adjncy, &flg_row));
7483:       if (flg_row) {
7484:         PetscCall(PCBDDCSetLocalAdjacencyGraph(pc, nvtxs, xadj, adjncy, PETSC_COPY_VALUES));
7485:         pcbddc->computed_rowadj = PETSC_TRUE;
7486:         PetscCall(MatRestoreRowIJ(A, 0, PETSC_TRUE, PETSC_FALSE, &nvtxs, (const PetscInt **)&xadj, (const PetscInt **)&adjncy, &flg_row));
7487:         rcsr = PETSC_TRUE;
7488:       }
7489:       PetscCall(MatDestroy(&A));
7490:     }
7491:     if (pcbddc->dbg_flag) PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));

7493:     if (pcbddc->mat_graph->cdim && !pcbddc->mat_graph->cloc) {
7494:       PetscReal   *lcoords;
7495:       PetscInt     n;
7496:       MPI_Datatype dimrealtype;
7497:       PetscMPIInt  cdimi;

7499:       /* TODO: support for blocked */
7500:       PetscCheck(pcbddc->mat_graph->cnloc == pc->pmat->rmap->n, PETSC_COMM_SELF, PETSC_ERR_USER, "Invalid number of local coordinates! Got %" PetscInt_FMT ", expected %" PetscInt_FMT, pcbddc->mat_graph->cnloc, pc->pmat->rmap->n);
7501:       PetscCall(MatGetLocalSize(matis->A, &n, NULL));
7502:       PetscCall(PetscMalloc1(pcbddc->mat_graph->cdim * n, &lcoords));
7503:       PetscCall(PetscMPIIntCast(pcbddc->mat_graph->cdim, &cdimi));
7504:       PetscCallMPI(MPI_Type_contiguous(cdimi, MPIU_REAL, &dimrealtype));
7505:       PetscCallMPI(MPI_Type_commit(&dimrealtype));
7506:       PetscCall(PetscSFBcastBegin(matis->sf, dimrealtype, pcbddc->mat_graph->coords, lcoords, MPI_REPLACE));
7507:       PetscCall(PetscSFBcastEnd(matis->sf, dimrealtype, pcbddc->mat_graph->coords, lcoords, MPI_REPLACE));
7508:       PetscCallMPI(MPI_Type_free(&dimrealtype));
7509:       PetscCall(PetscFree(pcbddc->mat_graph->coords));

7511:       pcbddc->mat_graph->coords = lcoords;
7512:       pcbddc->mat_graph->cloc   = PETSC_TRUE;
7513:       pcbddc->mat_graph->cnloc  = n;
7514:     }
7515:     PetscCheck(!pcbddc->mat_graph->cnloc || pcbddc->mat_graph->cnloc == pcbddc->mat_graph->nvtxs, PETSC_COMM_SELF, PETSC_ERR_USER, "Invalid number of local subdomain coordinates! Got %" PetscInt_FMT ", expected %" PetscInt_FMT, pcbddc->mat_graph->cnloc,
7516:                pcbddc->mat_graph->nvtxs);
7517:     pcbddc->mat_graph->active_coords = (PetscBool)(pcbddc->corner_selection && pcbddc->mat_graph->cdim && !pcbddc->corner_selected);

7519:     /* attach info on disconnected subdomains if present */
7520:     if (pcbddc->n_local_subs) {
7521:       PetscInt *local_subs, n, totn;

7523:       PetscCall(MatGetLocalSize(matis->A, &n, NULL));
7524:       PetscCall(PetscMalloc1(n, &local_subs));
7525:       for (i = 0; i < n; i++) local_subs[i] = pcbddc->n_local_subs;
7526:       for (i = 0; i < pcbddc->n_local_subs; i++) {
7527:         const PetscInt *idxs;
7528:         PetscInt        nl, j;

7530:         PetscCall(ISGetLocalSize(pcbddc->local_subs[i], &nl));
7531:         PetscCall(ISGetIndices(pcbddc->local_subs[i], &idxs));
7532:         for (j = 0; j < nl; j++) local_subs[idxs[j]] = i;
7533:         PetscCall(ISRestoreIndices(pcbddc->local_subs[i], &idxs));
7534:       }
7535:       for (i = 0, totn = 0; i < n; i++) totn = PetscMax(totn, local_subs[i]);
7536:       pcbddc->mat_graph->n_local_subs = totn + 1;
7537:       pcbddc->mat_graph->local_subs   = local_subs;
7538:     }

7540:     /* Setup of Graph */
7541:     PetscCall(PCBDDCGraphSetUp(pcbddc->mat_graph, pcbddc->vertex_size, pcbddc->NeumannBoundariesLocal, pcbddc->DirichletBoundariesLocal, pcbddc->n_ISForDofsLocal, pcbddc->ISForDofsLocal, pcbddc->user_primal_vertices_local));
7542:   }

7544:   if (!pcbddc->graphanalyzed) {
7545:     /* Graph's connected components analysis */
7546:     PetscCall(PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph));
7547:     pcbddc->graphanalyzed   = PETSC_TRUE;
7548:     pcbddc->corner_selected = pcbddc->corner_selection;
7549:   }
7550:   if (rcsr) pcbddc->mat_graph->nvtxs_csr = 0;
7551:   PetscFunctionReturn(PETSC_SUCCESS);
7552: }

7554: PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt *nio, Vec vecs[])
7555: {
7556:   PetscInt     i, j, n;
7557:   PetscScalar *alphas;
7558:   PetscReal    norm, *onorms;

7560:   PetscFunctionBegin;
7561:   n = *nio;
7562:   if (!n) PetscFunctionReturn(PETSC_SUCCESS);
7563:   PetscCall(PetscMalloc2(n, &alphas, n, &onorms));
7564:   PetscCall(VecNormalize(vecs[0], &norm));
7565:   if (norm < PETSC_SMALL) {
7566:     onorms[0] = 0.0;
7567:     PetscCall(VecSet(vecs[0], 0.0));
7568:   } else {
7569:     onorms[0] = norm;
7570:   }

7572:   for (i = 1; i < n; i++) {
7573:     PetscCall(VecMDot(vecs[i], i, vecs, alphas));
7574:     for (j = 0; j < i; j++) alphas[j] = PetscConj(-alphas[j]);
7575:     PetscCall(VecMAXPY(vecs[i], i, alphas, vecs));
7576:     PetscCall(VecNormalize(vecs[i], &norm));
7577:     if (norm < PETSC_SMALL) {
7578:       onorms[i] = 0.0;
7579:       PetscCall(VecSet(vecs[i], 0.0));
7580:     } else {
7581:       onorms[i] = norm;
7582:     }
7583:   }
7584:   /* push nonzero vectors at the beginning */
7585:   for (i = 0; i < n; i++) {
7586:     if (onorms[i] == 0.0) {
7587:       for (j = i + 1; j < n; j++) {
7588:         if (onorms[j] != 0.0) {
7589:           PetscCall(VecCopy(vecs[j], vecs[i]));
7590:           onorms[i] = onorms[j];
7591:           onorms[j] = 0.0;
7592:           break;
7593:         }
7594:       }
7595:     }
7596:   }
7597:   for (i = 0, *nio = 0; i < n; i++) *nio += onorms[i] != 0.0 ? 1 : 0;
7598:   PetscCall(PetscFree2(alphas, onorms));
7599:   PetscFunctionReturn(PETSC_SUCCESS);
7600: }

7602: static PetscErrorCode PCBDDCMatISGetSubassemblingPattern(Mat mat, PetscInt *n_subdomains, PetscInt redprocs, IS *is_sends, PetscBool *have_void)
7603: {
7604:   ISLocalToGlobalMapping mapping;
7605:   Mat                    A;
7606:   PetscInt               n_neighs, *neighs, *n_shared, **shared;
7607:   PetscMPIInt            size, rank, color;
7608:   PetscInt              *xadj, *adjncy;
7609:   PetscInt              *adjncy_wgt, *v_wgt, *ranks_send_to_idx;
7610:   PetscInt               im_active, active_procs, N, n, i, j, threshold = 2;
7611:   PetscInt               void_procs, *procs_candidates = NULL;
7612:   PetscInt               xadj_count, *count;
7613:   PetscBool              ismatis, use_vwgt = PETSC_FALSE;
7614:   PetscSubcomm           psubcomm;
7615:   MPI_Comm               subcomm;

7617:   PetscFunctionBegin;
7619:   PetscCall(PetscObjectTypeCompare((PetscObject)mat, MATIS, &ismatis));
7620:   PetscCheck(ismatis, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot use %s on a matrix object which is not of type MATIS", PETSC_FUNCTION_NAME);
7623:   PetscCheck(*n_subdomains > 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Invalid number of subdomains requested %" PetscInt_FMT, *n_subdomains);

7625:   if (have_void) *have_void = PETSC_FALSE;
7626:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
7627:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
7628:   PetscCall(MatISGetLocalMat(mat, &A));
7629:   PetscCall(MatGetLocalSize(A, &n, NULL));
7630:   im_active = !!n;
7631:   PetscCallMPI(MPIU_Allreduce(&im_active, &active_procs, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)mat)));
7632:   void_procs = size - active_procs;
7633:   /* get ranks of non-active processes in mat communicator */
7634:   if (void_procs) {
7635:     PetscInt ncand;

7637:     if (have_void) *have_void = PETSC_TRUE;
7638:     PetscCall(PetscMalloc1(size, &procs_candidates));
7639:     PetscCallMPI(MPI_Allgather(&im_active, 1, MPIU_INT, procs_candidates, 1, MPIU_INT, PetscObjectComm((PetscObject)mat)));
7640:     for (i = 0, ncand = 0; i < size; i++) {
7641:       if (!procs_candidates[i]) procs_candidates[ncand++] = i;
7642:     }
7643:     /* force n_subdomains to be not greater that the number of non-active processes */
7644:     *n_subdomains = PetscMin(void_procs, *n_subdomains);
7645:   }

7647:   /* number of subdomains requested greater than active processes or matrix size -> just shift the matrix
7648:      number of subdomains requested 1 -> send to rank-0 or first candidate in voids  */
7649:   PetscCall(MatGetSize(mat, &N, NULL));
7650:   if (active_procs < *n_subdomains || *n_subdomains == 1 || N <= *n_subdomains) {
7651:     PetscInt issize, isidx, dest;
7652:     if (*n_subdomains == 1) dest = 0;
7653:     else dest = rank;
7654:     if (im_active) {
7655:       issize = 1;
7656:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7657:         isidx = procs_candidates[dest];
7658:       } else {
7659:         isidx = dest;
7660:       }
7661:     } else {
7662:       issize = 0;
7663:       isidx  = -1;
7664:     }
7665:     if (*n_subdomains != 1) *n_subdomains = active_procs;
7666:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), issize, &isidx, PETSC_COPY_VALUES, is_sends));
7667:     PetscCall(PetscFree(procs_candidates));
7668:     PetscFunctionReturn(PETSC_SUCCESS);
7669:   }
7670:   PetscCall(PetscOptionsGetBool(NULL, ((PetscObject)A)->prefix, "-mat_is_partitioning_use_vwgt", &use_vwgt, NULL));
7671:   PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)A)->prefix, "-mat_is_partitioning_threshold", &threshold, NULL));
7672:   threshold = PetscMax(threshold, 2);

7674:   /* Get info on mapping */
7675:   PetscCall(MatISGetLocalToGlobalMapping(mat, &mapping, NULL));
7676:   PetscCall(ISLocalToGlobalMappingGetInfo(mapping, &n_neighs, &neighs, &n_shared, &shared));

7678:   /* build local CSR graph of subdomains' connectivity */
7679:   PetscCall(PetscMalloc1(2, &xadj));
7680:   xadj[0] = 0;
7681:   xadj[1] = PetscMax(n_neighs - 1, 0);
7682:   PetscCall(PetscMalloc1(xadj[1], &adjncy));
7683:   PetscCall(PetscMalloc1(xadj[1], &adjncy_wgt));
7684:   PetscCall(PetscCalloc1(n, &count));
7685:   for (i = 1; i < n_neighs; i++)
7686:     for (j = 0; j < n_shared[i]; j++) count[shared[i][j]] += 1;

7688:   xadj_count = 0;
7689:   for (i = 1; i < n_neighs; i++) {
7690:     for (j = 0; j < n_shared[i]; j++) {
7691:       if (count[shared[i][j]] < threshold) {
7692:         adjncy[xadj_count]     = neighs[i];
7693:         adjncy_wgt[xadj_count] = n_shared[i];
7694:         xadj_count++;
7695:         break;
7696:       }
7697:     }
7698:   }
7699:   xadj[1] = xadj_count;
7700:   PetscCall(PetscFree(count));
7701:   PetscCall(ISLocalToGlobalMappingRestoreInfo(mapping, &n_neighs, &neighs, &n_shared, &shared));
7702:   PetscCall(PetscSortIntWithArray(xadj[1], adjncy, adjncy_wgt));

7704:   PetscCall(PetscMalloc1(1, &ranks_send_to_idx));

7706:   /* Restrict work on active processes only */
7707:   PetscCall(PetscMPIIntCast(im_active, &color));
7708:   if (void_procs) {
7709:     PetscCall(PetscSubcommCreate(PetscObjectComm((PetscObject)mat), &psubcomm));
7710:     PetscCall(PetscSubcommSetNumber(psubcomm, 2)); /* 2 groups, active process and not active processes */
7711:     PetscCall(PetscSubcommSetTypeGeneral(psubcomm, color, rank));
7712:     subcomm = PetscSubcommChild(psubcomm);
7713:   } else {
7714:     psubcomm = NULL;
7715:     subcomm  = PetscObjectComm((PetscObject)mat);
7716:   }

7718:   v_wgt = NULL;
7719:   if (!color) {
7720:     PetscCall(PetscFree(xadj));
7721:     PetscCall(PetscFree(adjncy));
7722:     PetscCall(PetscFree(adjncy_wgt));
7723:   } else {
7724:     Mat             subdomain_adj;
7725:     IS              new_ranks, new_ranks_contig;
7726:     MatPartitioning partitioner;
7727:     PetscInt        rstart, rend;
7728:     PetscMPIInt     irstart = 0, irend = 0;
7729:     PetscInt       *is_indices, *oldranks;
7730:     PetscMPIInt     size;
7731:     PetscBool       aggregate;

7733:     PetscCallMPI(MPI_Comm_size(subcomm, &size));
7734:     if (void_procs) {
7735:       PetscInt prank = rank;
7736:       PetscCall(PetscMalloc1(size, &oldranks));
7737:       PetscCallMPI(MPI_Allgather(&prank, 1, MPIU_INT, oldranks, 1, MPIU_INT, subcomm));
7738:       for (i = 0; i < xadj[1]; i++) PetscCall(PetscFindInt(adjncy[i], size, oldranks, &adjncy[i]));
7739:       PetscCall(PetscSortIntWithArray(xadj[1], adjncy, adjncy_wgt));
7740:     } else {
7741:       oldranks = NULL;
7742:     }
7743:     aggregate = ((redprocs > 0 && redprocs < size) ? PETSC_TRUE : PETSC_FALSE);
7744:     if (aggregate) { /* TODO: all this part could be made more efficient */
7745:       PetscInt     lrows, row, ncols, *cols;
7746:       PetscMPIInt  nrank;
7747:       PetscScalar *vals;

7749:       PetscCallMPI(MPI_Comm_rank(subcomm, &nrank));
7750:       lrows = 0;
7751:       if (nrank < redprocs) {
7752:         lrows = size / redprocs;
7753:         if (nrank < size % redprocs) lrows++;
7754:       }
7755:       PetscCall(MatCreateAIJ(subcomm, lrows, lrows, size, size, 50, NULL, 50, NULL, &subdomain_adj));
7756:       PetscCall(MatGetOwnershipRange(subdomain_adj, &rstart, &rend));
7757:       PetscCall(PetscMPIIntCast(rstart, &irstart));
7758:       PetscCall(PetscMPIIntCast(rend, &irend));
7759:       PetscCall(MatSetOption(subdomain_adj, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
7760:       PetscCall(MatSetOption(subdomain_adj, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
7761:       row   = nrank;
7762:       ncols = xadj[1] - xadj[0];
7763:       cols  = adjncy;
7764:       PetscCall(PetscMalloc1(ncols, &vals));
7765:       for (i = 0; i < ncols; i++) vals[i] = adjncy_wgt[i];
7766:       PetscCall(MatSetValues(subdomain_adj, 1, &row, ncols, cols, vals, INSERT_VALUES));
7767:       PetscCall(MatAssemblyBegin(subdomain_adj, MAT_FINAL_ASSEMBLY));
7768:       PetscCall(MatAssemblyEnd(subdomain_adj, MAT_FINAL_ASSEMBLY));
7769:       PetscCall(PetscFree(xadj));
7770:       PetscCall(PetscFree(adjncy));
7771:       PetscCall(PetscFree(adjncy_wgt));
7772:       PetscCall(PetscFree(vals));
7773:       if (use_vwgt) {
7774:         Vec                v;
7775:         const PetscScalar *array;
7776:         PetscInt           nl;

7778:         PetscCall(MatCreateVecs(subdomain_adj, &v, NULL));
7779:         PetscCall(VecSetValue(v, row, (PetscScalar)n, INSERT_VALUES));
7780:         PetscCall(VecAssemblyBegin(v));
7781:         PetscCall(VecAssemblyEnd(v));
7782:         PetscCall(VecGetLocalSize(v, &nl));
7783:         PetscCall(VecGetArrayRead(v, &array));
7784:         PetscCall(PetscMalloc1(nl, &v_wgt));
7785:         for (i = 0; i < nl; i++) v_wgt[i] = (PetscInt)PetscRealPart(array[i]);
7786:         PetscCall(VecRestoreArrayRead(v, &array));
7787:         PetscCall(VecDestroy(&v));
7788:       }
7789:     } else {
7790:       PetscCall(MatCreateMPIAdj(subcomm, 1, size, xadj, adjncy, adjncy_wgt, &subdomain_adj));
7791:       if (use_vwgt) {
7792:         PetscCall(PetscMalloc1(1, &v_wgt));
7793:         v_wgt[0] = n;
7794:       }
7795:     }
7796:     /* PetscCall(MatView(subdomain_adj,0)); */

7798:     /* Partition */
7799:     PetscCall(MatPartitioningCreate(subcomm, &partitioner));
7800: #if defined(PETSC_HAVE_PTSCOTCH)
7801:     PetscCall(MatPartitioningSetType(partitioner, MATPARTITIONINGPTSCOTCH));
7802: #elif defined(PETSC_HAVE_PARMETIS)
7803:     PetscCall(MatPartitioningSetType(partitioner, MATPARTITIONINGPARMETIS));
7804: #else
7805:     PetscCall(MatPartitioningSetType(partitioner, MATPARTITIONINGAVERAGE));
7806: #endif
7807:     PetscCall(MatPartitioningSetAdjacency(partitioner, subdomain_adj));
7808:     if (v_wgt) PetscCall(MatPartitioningSetVertexWeights(partitioner, v_wgt));
7809:     *n_subdomains = PetscMin(size, *n_subdomains);
7810:     PetscCall(MatPartitioningSetNParts(partitioner, *n_subdomains));
7811:     PetscCall(MatPartitioningSetFromOptions(partitioner));
7812:     PetscCall(MatPartitioningApply(partitioner, &new_ranks));
7813:     /* PetscCall(MatPartitioningView(partitioner,0)); */

7815:     /* renumber new_ranks to avoid "holes" in new set of processors */
7816:     PetscCall(ISRenumber(new_ranks, NULL, NULL, &new_ranks_contig));
7817:     PetscCall(ISDestroy(&new_ranks));
7818:     PetscCall(ISGetIndices(new_ranks_contig, (const PetscInt **)&is_indices));
7819:     if (!aggregate) {
7820:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7821:         PetscAssert(oldranks, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
7822:         ranks_send_to_idx[0] = procs_candidates[oldranks[is_indices[0]]];
7823:       } else if (oldranks) {
7824:         ranks_send_to_idx[0] = oldranks[is_indices[0]];
7825:       } else {
7826:         ranks_send_to_idx[0] = is_indices[0];
7827:       }
7828:     } else {
7829:       PetscInt     idx = 0;
7830:       PetscMPIInt  tag;
7831:       MPI_Request *reqs;

7833:       PetscCall(PetscObjectGetNewTag((PetscObject)subdomain_adj, &tag));
7834:       PetscCall(PetscMalloc1(rend - rstart, &reqs));
7835:       for (PetscMPIInt i = irstart; i < irend; i++) PetscCallMPI(MPIU_Isend(is_indices + i - rstart, 1, MPIU_INT, i, tag, subcomm, &reqs[i - rstart]));
7836:       PetscCallMPI(MPIU_Recv(&idx, 1, MPIU_INT, MPI_ANY_SOURCE, tag, subcomm, MPI_STATUS_IGNORE));
7837:       PetscCallMPI(MPI_Waitall(irend - irstart, reqs, MPI_STATUSES_IGNORE));
7838:       PetscCall(PetscFree(reqs));
7839:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7840:         PetscAssert(oldranks, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
7841:         ranks_send_to_idx[0] = procs_candidates[oldranks[idx]];
7842:       } else if (oldranks) {
7843:         ranks_send_to_idx[0] = oldranks[idx];
7844:       } else {
7845:         ranks_send_to_idx[0] = idx;
7846:       }
7847:     }
7848:     PetscCall(ISRestoreIndices(new_ranks_contig, (const PetscInt **)&is_indices));
7849:     /* clean up */
7850:     PetscCall(PetscFree(oldranks));
7851:     PetscCall(ISDestroy(&new_ranks_contig));
7852:     PetscCall(MatDestroy(&subdomain_adj));
7853:     PetscCall(MatPartitioningDestroy(&partitioner));
7854:   }
7855:   PetscCall(PetscSubcommDestroy(&psubcomm));
7856:   PetscCall(PetscFree(procs_candidates));

7858:   /* assemble parallel IS for sends */
7859:   i = 1;
7860:   if (!color) i = 0;
7861:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), i, ranks_send_to_idx, PETSC_OWN_POINTER, is_sends));
7862:   PetscFunctionReturn(PETSC_SUCCESS);
7863: }

7865: typedef enum {
7866:   MATDENSE_PRIVATE = 0,
7867:   MATAIJ_PRIVATE,
7868:   MATBAIJ_PRIVATE,
7869:   MATSBAIJ_PRIVATE
7870: } MatTypePrivate;

7872: static PetscErrorCode PCBDDCMatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, PetscBool restrict_full, PetscBool reuse, Mat *mat_n, PetscInt nis, IS isarray[], PetscInt nvecs, Vec nnsp_vec[])
7873: {
7874:   Mat                    local_mat;
7875:   IS                     is_sends_internal;
7876:   PetscInt               rows, cols, new_local_rows;
7877:   PetscInt               i, bs, buf_size_idxs, buf_size_idxs_is, buf_size_vals, buf_size_vecs;
7878:   PetscBool              ismatis, isdense, newisdense, destroy_mat;
7879:   ISLocalToGlobalMapping l2gmap;
7880:   PetscInt              *l2gmap_indices;
7881:   const PetscInt        *is_indices;
7882:   MatType                new_local_type;
7883:   /* buffers */
7884:   PetscInt          *ptr_idxs, *send_buffer_idxs, *recv_buffer_idxs;
7885:   PetscInt          *ptr_idxs_is, *send_buffer_idxs_is, *recv_buffer_idxs_is;
7886:   PetscInt          *recv_buffer_idxs_local;
7887:   PetscScalar       *ptr_vals, *recv_buffer_vals;
7888:   const PetscScalar *send_buffer_vals;
7889:   PetscScalar       *ptr_vecs, *send_buffer_vecs, *recv_buffer_vecs;
7890:   /* MPI */
7891:   MPI_Comm     comm, comm_n;
7892:   PetscSubcomm subcomm;
7893:   PetscMPIInt  n_sends, n_recvs, size;
7894:   PetscMPIInt *iflags, *ilengths_idxs, *ilengths_vals, *ilengths_idxs_is;
7895:   PetscMPIInt *onodes, *onodes_is, *olengths_idxs, *olengths_idxs_is, *olengths_vals;
7896:   PetscMPIInt  len, tag_idxs, tag_idxs_is, tag_vals, tag_vecs, source_dest;
7897:   MPI_Request *send_req_idxs, *send_req_idxs_is, *send_req_vals, *send_req_vecs;
7898:   MPI_Request *recv_req_idxs, *recv_req_idxs_is, *recv_req_vals, *recv_req_vecs;

7900:   PetscFunctionBegin;
7902:   PetscCall(PetscObjectTypeCompare((PetscObject)mat, MATIS, &ismatis));
7903:   PetscCheck(ismatis, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot use %s on a matrix object which is not of type MATIS", PETSC_FUNCTION_NAME);
7910:   if (nvecs) {
7911:     PetscCheck(nvecs <= 1, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Just 1 vector supported");
7913:   }
7914:   /* further checks */
7915:   PetscCall(MatISGetLocalMat(mat, &local_mat));
7916:   PetscCall(PetscObjectTypeCompare((PetscObject)local_mat, MATSEQDENSE, &isdense));
7917:   /* XXX hack for multi_element */
7918:   if (!isdense) PetscCall(MatConvert(local_mat, MATDENSE, MAT_INPLACE_MATRIX, &local_mat));
7919:   PetscCall(PetscObjectTypeCompare((PetscObject)local_mat, MATSEQDENSE, &isdense));
7920:   PetscCheck(isdense, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");

7922:   PetscCall(MatGetSize(local_mat, &rows, &cols));
7923:   PetscCheck(rows == cols, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Local MATIS matrices should be square");
7924:   if (reuse && *mat_n) {
7925:     PetscInt mrows, mcols, mnrows, mncols;
7927:     PetscCall(PetscObjectTypeCompare((PetscObject)*mat_n, MATIS, &ismatis));
7928:     PetscCheck(ismatis, PetscObjectComm((PetscObject)*mat_n), PETSC_ERR_SUP, "Cannot reuse a matrix which is not of type MATIS");
7929:     PetscCall(MatGetSize(mat, &mrows, &mcols));
7930:     PetscCall(MatGetSize(*mat_n, &mnrows, &mncols));
7931:     PetscCheck(mrows == mnrows, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix! Wrong number of rows %" PetscInt_FMT " != %" PetscInt_FMT, mrows, mnrows);
7932:     PetscCheck(mcols == mncols, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix! Wrong number of cols %" PetscInt_FMT " != %" PetscInt_FMT, mcols, mncols);
7933:   }
7934:   PetscCall(MatGetBlockSize(local_mat, &bs));

7937:   /* prepare IS for sending if not provided */
7938:   if (!is_sends) {
7939:     PetscCheck(n_subdomains, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "You should specify either an IS or a target number of subdomains");
7940:     PetscCall(PCBDDCMatISGetSubassemblingPattern(mat, &n_subdomains, 0, &is_sends_internal, NULL));
7941:   } else {
7942:     PetscCall(PetscObjectReference((PetscObject)is_sends));
7943:     is_sends_internal = is_sends;
7944:   }

7946:   /* get comm */
7947:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));

7949:   /* compute number of sends */
7950:   PetscCall(ISGetLocalSize(is_sends_internal, &i));
7951:   PetscCall(PetscMPIIntCast(i, &n_sends));

7953:   /* compute number of receives */
7954:   PetscCallMPI(MPI_Comm_size(comm, &size));
7955:   PetscCall(PetscMalloc1(size, &iflags));
7956:   PetscCall(PetscArrayzero(iflags, size));
7957:   PetscCall(ISGetIndices(is_sends_internal, &is_indices));
7958:   for (i = 0; i < n_sends; i++) iflags[is_indices[i]] = 1;
7959:   PetscCall(PetscGatherNumberOfMessages(comm, iflags, NULL, &n_recvs));
7960:   PetscCall(PetscFree(iflags));

7962:   /* restrict comm if requested */
7963:   subcomm     = NULL;
7964:   destroy_mat = PETSC_FALSE;
7965:   if (restrict_comm) {
7966:     PetscMPIInt color, subcommsize;

7968:     color = 0;
7969:     if (restrict_full) {
7970:       if (!n_recvs) color = 1; /* processes not receiving anything will not participate in new comm (full restriction) */
7971:     } else {
7972:       if (!n_recvs && n_sends) color = 1; /* just those processes that are sending but not receiving anything will not participate in new comm */
7973:     }
7974:     PetscCallMPI(MPIU_Allreduce(&color, &subcommsize, 1, MPI_INT, MPI_SUM, comm));
7975:     subcommsize = size - subcommsize;
7976:     /* check if reuse has been requested */
7977:     if (reuse) {
7978:       if (*mat_n) {
7979:         PetscMPIInt subcommsize2;
7980:         PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n), &subcommsize2));
7981:         PetscCheck(subcommsize == subcommsize2, PetscObjectComm((PetscObject)*mat_n), PETSC_ERR_PLIB, "Cannot reuse matrix! wrong subcomm size %d != %d", subcommsize, subcommsize2);
7982:         comm_n = PetscObjectComm((PetscObject)*mat_n);
7983:       } else {
7984:         comm_n = PETSC_COMM_SELF;
7985:       }
7986:     } else { /* MAT_INITIAL_MATRIX */
7987:       PetscMPIInt rank;

7989:       PetscCallMPI(MPI_Comm_rank(comm, &rank));
7990:       PetscCall(PetscSubcommCreate(comm, &subcomm));
7991:       PetscCall(PetscSubcommSetNumber(subcomm, 2));
7992:       PetscCall(PetscSubcommSetTypeGeneral(subcomm, color, rank));
7993:       comm_n = PetscSubcommChild(subcomm);
7994:     }
7995:     /* flag to destroy *mat_n if not significative */
7996:     if (color) destroy_mat = PETSC_TRUE;
7997:   } else {
7998:     comm_n = comm;
7999:   }

8001:   /* prepare send/receive buffers */
8002:   PetscCall(PetscMalloc1(size, &ilengths_idxs));
8003:   PetscCall(PetscArrayzero(ilengths_idxs, size));
8004:   PetscCall(PetscMalloc1(size, &ilengths_vals));
8005:   PetscCall(PetscArrayzero(ilengths_vals, size));
8006:   if (nis) PetscCall(PetscCalloc1(size, &ilengths_idxs_is));

8008:   /* Get data from local matrices */
8009:   PetscCheck(isdense, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Subassembling of AIJ local matrices not yet implemented");
8010:   /* TODO: See below some guidelines on how to prepare the local buffers */
8011:   /*
8012:        send_buffer_vals should contain the raw values of the local matrix
8013:        send_buffer_idxs should contain:
8014:        - MatType_PRIVATE type
8015:        - PetscInt        size_of_l2gmap
8016:        - PetscInt        global_row_indices[size_of_l2gmap]
8017:        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
8018:     */
8019:   {
8020:     ISLocalToGlobalMapping mapping;

8022:     PetscCall(MatISGetLocalToGlobalMapping(mat, &mapping, NULL));
8023:     PetscCall(MatDenseGetArrayRead(local_mat, &send_buffer_vals));
8024:     PetscCall(ISLocalToGlobalMappingGetSize(mapping, &i));
8025:     PetscCall(PetscMalloc1(i + 2, &send_buffer_idxs));
8026:     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
8027:     send_buffer_idxs[1] = i;
8028:     PetscCall(ISLocalToGlobalMappingGetIndices(mapping, (const PetscInt **)&ptr_idxs));
8029:     PetscCall(PetscArraycpy(&send_buffer_idxs[2], ptr_idxs, i));
8030:     PetscCall(ISLocalToGlobalMappingRestoreIndices(mapping, (const PetscInt **)&ptr_idxs));
8031:     PetscCall(PetscMPIIntCast(i, &len));
8032:     for (i = 0; i < n_sends; i++) {
8033:       ilengths_vals[is_indices[i]] = len * len;
8034:       ilengths_idxs[is_indices[i]] = len + 2;
8035:     }
8036:   }
8037:   PetscCall(PetscGatherMessageLengths2(comm, n_sends, n_recvs, ilengths_idxs, ilengths_vals, &onodes, &olengths_idxs, &olengths_vals));
8038:   /* additional is (if any) */
8039:   if (nis) {
8040:     PetscMPIInt psum;
8041:     PetscInt    j;
8042:     for (j = 0, psum = 0; j < nis; j++) {
8043:       PetscInt plen;
8044:       PetscCall(ISGetLocalSize(isarray[j], &plen));
8045:       PetscCall(PetscMPIIntCast(plen, &len));
8046:       psum += len + 1; /* indices + length */
8047:     }
8048:     PetscCall(PetscMalloc1(psum, &send_buffer_idxs_is));
8049:     for (j = 0, psum = 0; j < nis; j++) {
8050:       PetscInt        plen;
8051:       const PetscInt *is_array_idxs;
8052:       PetscCall(ISGetLocalSize(isarray[j], &plen));
8053:       send_buffer_idxs_is[psum] = plen;
8054:       PetscCall(ISGetIndices(isarray[j], &is_array_idxs));
8055:       PetscCall(PetscArraycpy(&send_buffer_idxs_is[psum + 1], is_array_idxs, plen));
8056:       PetscCall(ISRestoreIndices(isarray[j], &is_array_idxs));
8057:       psum += plen + 1; /* indices + length */
8058:     }
8059:     for (i = 0; i < n_sends; i++) ilengths_idxs_is[is_indices[i]] = psum;
8060:     PetscCall(PetscGatherMessageLengths(comm, n_sends, n_recvs, ilengths_idxs_is, &onodes_is, &olengths_idxs_is));
8061:   }
8062:   PetscCall(MatISRestoreLocalMat(mat, &local_mat));

8064:   buf_size_idxs    = 0;
8065:   buf_size_vals    = 0;
8066:   buf_size_idxs_is = 0;
8067:   buf_size_vecs    = 0;
8068:   for (i = 0; i < n_recvs; i++) {
8069:     buf_size_idxs += olengths_idxs[i];
8070:     buf_size_vals += olengths_vals[i];
8071:     if (nis) buf_size_idxs_is += olengths_idxs_is[i];
8072:     if (nvecs) buf_size_vecs += olengths_idxs[i];
8073:   }
8074:   PetscCall(PetscMalloc1(buf_size_idxs, &recv_buffer_idxs));
8075:   PetscCall(PetscMalloc1(buf_size_vals, &recv_buffer_vals));
8076:   PetscCall(PetscMalloc1(buf_size_idxs_is, &recv_buffer_idxs_is));
8077:   PetscCall(PetscMalloc1(buf_size_vecs, &recv_buffer_vecs));

8079:   /* get new tags for clean communications */
8080:   PetscCall(PetscObjectGetNewTag((PetscObject)mat, &tag_idxs));
8081:   PetscCall(PetscObjectGetNewTag((PetscObject)mat, &tag_vals));
8082:   PetscCall(PetscObjectGetNewTag((PetscObject)mat, &tag_idxs_is));
8083:   PetscCall(PetscObjectGetNewTag((PetscObject)mat, &tag_vecs));

8085:   /* allocate for requests */
8086:   PetscCall(PetscMalloc1(n_sends, &send_req_idxs));
8087:   PetscCall(PetscMalloc1(n_sends, &send_req_vals));
8088:   PetscCall(PetscMalloc1(n_sends, &send_req_idxs_is));
8089:   PetscCall(PetscMalloc1(n_sends, &send_req_vecs));
8090:   PetscCall(PetscMalloc1(n_recvs, &recv_req_idxs));
8091:   PetscCall(PetscMalloc1(n_recvs, &recv_req_vals));
8092:   PetscCall(PetscMalloc1(n_recvs, &recv_req_idxs_is));
8093:   PetscCall(PetscMalloc1(n_recvs, &recv_req_vecs));

8095:   /* communications */
8096:   ptr_idxs    = recv_buffer_idxs;
8097:   ptr_vals    = recv_buffer_vals;
8098:   ptr_idxs_is = recv_buffer_idxs_is;
8099:   ptr_vecs    = recv_buffer_vecs;
8100:   for (i = 0; i < n_recvs; i++) {
8101:     PetscCallMPI(MPIU_Irecv(ptr_idxs, olengths_idxs[i], MPIU_INT, onodes[i], tag_idxs, comm, &recv_req_idxs[i]));
8102:     PetscCallMPI(MPIU_Irecv(ptr_vals, olengths_vals[i], MPIU_SCALAR, onodes[i], tag_vals, comm, &recv_req_vals[i]));
8103:     ptr_idxs += olengths_idxs[i];
8104:     ptr_vals += olengths_vals[i];
8105:     if (nis) {
8106:       PetscCallMPI(MPIU_Irecv(ptr_idxs_is, olengths_idxs_is[i], MPIU_INT, onodes_is[i], tag_idxs_is, comm, &recv_req_idxs_is[i]));
8107:       ptr_idxs_is += olengths_idxs_is[i];
8108:     }
8109:     if (nvecs) {
8110:       PetscCallMPI(MPIU_Irecv(ptr_vecs, olengths_idxs[i] - 2, MPIU_SCALAR, onodes[i], tag_vecs, comm, &recv_req_vecs[i]));
8111:       ptr_vecs += olengths_idxs[i] - 2;
8112:     }
8113:   }
8114:   for (i = 0; i < n_sends; i++) {
8115:     PetscCall(PetscMPIIntCast(is_indices[i], &source_dest));
8116:     PetscCallMPI(MPIU_Isend(send_buffer_idxs, ilengths_idxs[source_dest], MPIU_INT, source_dest, tag_idxs, comm, &send_req_idxs[i]));
8117:     PetscCallMPI(MPIU_Isend(send_buffer_vals, ilengths_vals[source_dest], MPIU_SCALAR, source_dest, tag_vals, comm, &send_req_vals[i]));
8118:     if (nis) PetscCallMPI(MPIU_Isend(send_buffer_idxs_is, ilengths_idxs_is[source_dest], MPIU_INT, source_dest, tag_idxs_is, comm, &send_req_idxs_is[i]));
8119:     if (nvecs) {
8120:       PetscCall(VecGetArray(nnsp_vec[0], &send_buffer_vecs));
8121:       PetscCallMPI(MPIU_Isend(send_buffer_vecs, ilengths_idxs[source_dest] - 2, MPIU_SCALAR, source_dest, tag_vecs, comm, &send_req_vecs[i]));
8122:     }
8123:   }
8124:   PetscCall(ISRestoreIndices(is_sends_internal, &is_indices));
8125:   PetscCall(ISDestroy(&is_sends_internal));

8127:   /* assemble new l2g map */
8128:   PetscCallMPI(MPI_Waitall(n_recvs, recv_req_idxs, MPI_STATUSES_IGNORE));
8129:   ptr_idxs       = recv_buffer_idxs;
8130:   new_local_rows = 0;
8131:   for (i = 0; i < n_recvs; i++) {
8132:     new_local_rows += *(ptr_idxs + 1); /* second element is the local size of the l2gmap */
8133:     ptr_idxs += olengths_idxs[i];
8134:   }
8135:   PetscCall(PetscMalloc1(new_local_rows, &l2gmap_indices));
8136:   ptr_idxs       = recv_buffer_idxs;
8137:   new_local_rows = 0;
8138:   for (i = 0; i < n_recvs; i++) {
8139:     PetscCall(PetscArraycpy(&l2gmap_indices[new_local_rows], ptr_idxs + 2, *(ptr_idxs + 1)));
8140:     new_local_rows += *(ptr_idxs + 1); /* second element is the local size of the l2gmap */
8141:     ptr_idxs += olengths_idxs[i];
8142:   }
8143:   PetscCall(PetscSortRemoveDupsInt(&new_local_rows, l2gmap_indices));
8144:   PetscCall(ISLocalToGlobalMappingCreate(comm_n, 1, new_local_rows, l2gmap_indices, PETSC_COPY_VALUES, &l2gmap));
8145:   PetscCall(PetscFree(l2gmap_indices));

8147:   /* infer new local matrix type from received local matrices type */
8148:   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
8149:   /* it also assumes that if the block size is set, than it is the same among all local matrices (see checks at the beginning of the function) */
8150:   if (n_recvs) {
8151:     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
8152:     ptr_idxs                              = recv_buffer_idxs;
8153:     for (i = 0; i < n_recvs; i++) {
8154:       if ((PetscInt)new_local_type_private != *ptr_idxs) {
8155:         new_local_type_private = MATAIJ_PRIVATE;
8156:         break;
8157:       }
8158:       ptr_idxs += olengths_idxs[i];
8159:     }
8160:     switch (new_local_type_private) {
8161:     case MATDENSE_PRIVATE:
8162:       new_local_type = MATSEQAIJ;
8163:       bs             = 1;
8164:       break;
8165:     case MATAIJ_PRIVATE:
8166:       new_local_type = MATSEQAIJ;
8167:       bs             = 1;
8168:       break;
8169:     case MATBAIJ_PRIVATE:
8170:       new_local_type = MATSEQBAIJ;
8171:       break;
8172:     case MATSBAIJ_PRIVATE:
8173:       new_local_type = MATSEQSBAIJ;
8174:       break;
8175:     default:
8176:       SETERRQ(comm, PETSC_ERR_SUP, "Unsupported private type %d in %s", new_local_type_private, PETSC_FUNCTION_NAME);
8177:     }
8178:   } else { /* by default, new_local_type is seqaij */
8179:     new_local_type = MATSEQAIJ;
8180:     bs             = 1;
8181:   }

8183:   /* create MATIS object if needed */
8184:   if (!reuse) {
8185:     PetscCall(MatGetSize(mat, &rows, &cols));
8186:     PetscCall(MatCreateIS(comm_n, bs, PETSC_DECIDE, PETSC_DECIDE, rows, cols, l2gmap, l2gmap, mat_n));
8187:   } else {
8188:     /* it also destroys the local matrices */
8189:     if (*mat_n) {
8190:       PetscCall(MatSetLocalToGlobalMapping(*mat_n, l2gmap, l2gmap));
8191:     } else { /* this is a fake object */
8192:       PetscCall(MatCreateIS(comm_n, bs, PETSC_DECIDE, PETSC_DECIDE, rows, cols, l2gmap, l2gmap, mat_n));
8193:     }
8194:   }
8195:   PetscCall(MatISGetLocalMat(*mat_n, &local_mat));
8196:   PetscCall(MatSetType(local_mat, new_local_type));

8198:   PetscCallMPI(MPI_Waitall(n_recvs, recv_req_vals, MPI_STATUSES_IGNORE));

8200:   /* Global to local map of received indices */
8201:   PetscCall(PetscMalloc1(buf_size_idxs, &recv_buffer_idxs_local)); /* needed for values insertion */
8202:   PetscCall(ISGlobalToLocalMappingApply(l2gmap, IS_GTOLM_MASK, buf_size_idxs, recv_buffer_idxs, &i, recv_buffer_idxs_local));
8203:   PetscCall(ISLocalToGlobalMappingDestroy(&l2gmap));

8205:   /* restore attributes -> type of incoming data and its size */
8206:   buf_size_idxs = 0;
8207:   for (i = 0; i < n_recvs; i++) {
8208:     recv_buffer_idxs_local[buf_size_idxs]     = recv_buffer_idxs[buf_size_idxs];
8209:     recv_buffer_idxs_local[buf_size_idxs + 1] = recv_buffer_idxs[buf_size_idxs + 1];
8210:     buf_size_idxs += olengths_idxs[i];
8211:   }
8212:   PetscCall(PetscFree(recv_buffer_idxs));

8214:   /* set preallocation */
8215:   PetscCall(PetscObjectTypeCompare((PetscObject)local_mat, MATSEQDENSE, &newisdense));
8216:   if (!newisdense) {
8217:     PetscInt *new_local_nnz = NULL;

8219:     ptr_idxs = recv_buffer_idxs_local;
8220:     if (n_recvs) PetscCall(PetscCalloc1(new_local_rows, &new_local_nnz));
8221:     for (i = 0; i < n_recvs; i++) {
8222:       PetscInt j;
8223:       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
8224:         for (j = 0; j < *(ptr_idxs + 1); j++) new_local_nnz[*(ptr_idxs + 2 + j)] += *(ptr_idxs + 1);
8225:       } else {
8226:         /* TODO */
8227:       }
8228:       ptr_idxs += olengths_idxs[i];
8229:     }
8230:     if (new_local_nnz) {
8231:       for (i = 0; i < new_local_rows; i++) new_local_nnz[i] = PetscMin(new_local_nnz[i], new_local_rows);
8232:       PetscCall(MatSeqAIJSetPreallocation(local_mat, 0, new_local_nnz));
8233:       for (i = 0; i < new_local_rows; i++) new_local_nnz[i] /= bs;
8234:       PetscCall(MatSeqBAIJSetPreallocation(local_mat, bs, 0, new_local_nnz));
8235:       for (i = 0; i < new_local_rows; i++) new_local_nnz[i] = PetscMax(new_local_nnz[i] - i, 0);
8236:       PetscCall(MatSeqSBAIJSetPreallocation(local_mat, bs, 0, new_local_nnz));
8237:     } else {
8238:       PetscCall(MatSetUp(local_mat));
8239:     }
8240:     PetscCall(PetscFree(new_local_nnz));
8241:   } else {
8242:     PetscCall(MatSetUp(local_mat));
8243:   }

8245:   /* set values */
8246:   ptr_vals = recv_buffer_vals;
8247:   ptr_idxs = recv_buffer_idxs_local;
8248:   for (i = 0; i < n_recvs; i++) {
8249:     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
8250:       PetscCall(MatSetOption(local_mat, MAT_ROW_ORIENTED, PETSC_FALSE));
8251:       PetscCall(MatSetValues(local_mat, *(ptr_idxs + 1), ptr_idxs + 2, *(ptr_idxs + 1), ptr_idxs + 2, ptr_vals, ADD_VALUES));
8252:       PetscCall(MatAssemblyBegin(local_mat, MAT_FLUSH_ASSEMBLY));
8253:       PetscCall(MatAssemblyEnd(local_mat, MAT_FLUSH_ASSEMBLY));
8254:       PetscCall(MatSetOption(local_mat, MAT_ROW_ORIENTED, PETSC_TRUE));
8255:     } else {
8256:       /* TODO */
8257:     }
8258:     ptr_idxs += olengths_idxs[i];
8259:     ptr_vals += olengths_vals[i];
8260:   }
8261:   PetscCall(MatAssemblyBegin(local_mat, MAT_FINAL_ASSEMBLY));
8262:   PetscCall(MatAssemblyEnd(local_mat, MAT_FINAL_ASSEMBLY));
8263:   PetscCall(MatISRestoreLocalMat(*mat_n, &local_mat));
8264:   PetscCall(MatAssemblyBegin(*mat_n, MAT_FINAL_ASSEMBLY));
8265:   PetscCall(MatAssemblyEnd(*mat_n, MAT_FINAL_ASSEMBLY));
8266:   PetscCall(PetscFree(recv_buffer_vals));

8268: #if 0
8269:   if (!restrict_comm) { /* check */
8270:     Vec       lvec,rvec;
8271:     PetscReal infty_error;

8273:     PetscCall(MatCreateVecs(mat,&rvec,&lvec));
8274:     PetscCall(VecSetRandom(rvec,NULL));
8275:     PetscCall(MatMult(mat,rvec,lvec));
8276:     PetscCall(VecScale(lvec,-1.0));
8277:     PetscCall(MatMultAdd(*mat_n,rvec,lvec,lvec));
8278:     PetscCall(VecNorm(lvec,NORM_INFINITY,&infty_error));
8279:     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error));
8280:     PetscCall(VecDestroy(&rvec));
8281:     PetscCall(VecDestroy(&lvec));
8282:   }
8283: #endif

8285:   /* assemble new additional is (if any) */
8286:   if (nis) {
8287:     PetscInt **temp_idxs, *count_is, j, psum;

8289:     PetscCallMPI(MPI_Waitall(n_recvs, recv_req_idxs_is, MPI_STATUSES_IGNORE));
8290:     PetscCall(PetscCalloc1(nis, &count_is));
8291:     ptr_idxs = recv_buffer_idxs_is;
8292:     psum     = 0;
8293:     for (i = 0; i < n_recvs; i++) {
8294:       for (j = 0; j < nis; j++) {
8295:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
8296:         count_is[j] += plen;         /* increment counting of buffer for j-th IS */
8297:         psum += plen;
8298:         ptr_idxs += plen + 1; /* shift pointer to received data */
8299:       }
8300:     }
8301:     PetscCall(PetscMalloc1(nis, &temp_idxs));
8302:     PetscCall(PetscMalloc1(psum, &temp_idxs[0]));
8303:     for (i = 1; i < nis; i++) temp_idxs[i] = PetscSafePointerPlusOffset(temp_idxs[i - 1], count_is[i - 1]);
8304:     PetscCall(PetscArrayzero(count_is, nis));
8305:     ptr_idxs = recv_buffer_idxs_is;
8306:     for (i = 0; i < n_recvs; i++) {
8307:       for (j = 0; j < nis; j++) {
8308:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
8309:         PetscCall(PetscArraycpy(&temp_idxs[j][count_is[j]], ptr_idxs + 1, plen));
8310:         count_is[j] += plen;  /* increment starting point of buffer for j-th IS */
8311:         ptr_idxs += plen + 1; /* shift pointer to received data */
8312:       }
8313:     }
8314:     for (i = 0; i < nis; i++) {
8315:       PetscCall(ISDestroy(&isarray[i]));
8316:       PetscCall(PetscSortRemoveDupsInt(&count_is[i], temp_idxs[i]));
8317:       PetscCall(ISCreateGeneral(comm_n, count_is[i], temp_idxs[i], PETSC_COPY_VALUES, &isarray[i]));
8318:     }
8319:     PetscCall(PetscFree(count_is));
8320:     PetscCall(PetscFree(temp_idxs[0]));
8321:     PetscCall(PetscFree(temp_idxs));
8322:   }
8323:   /* free workspace */
8324:   PetscCall(PetscFree(recv_buffer_idxs_is));
8325:   PetscCallMPI(MPI_Waitall(n_sends, send_req_idxs, MPI_STATUSES_IGNORE));
8326:   PetscCall(PetscFree(send_buffer_idxs));
8327:   PetscCallMPI(MPI_Waitall(n_sends, send_req_vals, MPI_STATUSES_IGNORE));
8328:   if (isdense) {
8329:     PetscCall(MatISGetLocalMat(mat, &local_mat));
8330:     PetscCall(MatDenseRestoreArrayRead(local_mat, &send_buffer_vals));
8331:     PetscCall(MatISRestoreLocalMat(mat, &local_mat));
8332:   } else {
8333:     /* PetscCall(PetscFree(send_buffer_vals)); */
8334:   }
8335:   if (nis) {
8336:     PetscCallMPI(MPI_Waitall(n_sends, send_req_idxs_is, MPI_STATUSES_IGNORE));
8337:     PetscCall(PetscFree(send_buffer_idxs_is));
8338:   }

8340:   if (nvecs) {
8341:     PetscCallMPI(MPI_Waitall(n_recvs, recv_req_vecs, MPI_STATUSES_IGNORE));
8342:     PetscCallMPI(MPI_Waitall(n_sends, send_req_vecs, MPI_STATUSES_IGNORE));
8343:     PetscCall(VecRestoreArray(nnsp_vec[0], &send_buffer_vecs));
8344:     PetscCall(VecDestroy(&nnsp_vec[0]));
8345:     PetscCall(VecCreate(comm_n, &nnsp_vec[0]));
8346:     PetscCall(VecSetSizes(nnsp_vec[0], new_local_rows, PETSC_DECIDE));
8347:     PetscCall(VecSetType(nnsp_vec[0], VECSTANDARD));
8348:     /* set values */
8349:     ptr_vals = recv_buffer_vecs;
8350:     ptr_idxs = recv_buffer_idxs_local;
8351:     PetscCall(VecGetArray(nnsp_vec[0], &send_buffer_vecs));
8352:     for (i = 0; i < n_recvs; i++) {
8353:       PetscInt j;
8354:       for (j = 0; j < *(ptr_idxs + 1); j++) send_buffer_vecs[*(ptr_idxs + 2 + j)] += *(ptr_vals + j);
8355:       ptr_idxs += olengths_idxs[i];
8356:       ptr_vals += olengths_idxs[i] - 2;
8357:     }
8358:     PetscCall(VecRestoreArray(nnsp_vec[0], &send_buffer_vecs));
8359:     PetscCall(VecAssemblyBegin(nnsp_vec[0]));
8360:     PetscCall(VecAssemblyEnd(nnsp_vec[0]));
8361:   }

8363:   PetscCall(PetscFree(recv_buffer_vecs));
8364:   PetscCall(PetscFree(recv_buffer_idxs_local));
8365:   PetscCall(PetscFree(recv_req_idxs));
8366:   PetscCall(PetscFree(recv_req_vals));
8367:   PetscCall(PetscFree(recv_req_vecs));
8368:   PetscCall(PetscFree(recv_req_idxs_is));
8369:   PetscCall(PetscFree(send_req_idxs));
8370:   PetscCall(PetscFree(send_req_vals));
8371:   PetscCall(PetscFree(send_req_vecs));
8372:   PetscCall(PetscFree(send_req_idxs_is));
8373:   PetscCall(PetscFree(ilengths_vals));
8374:   PetscCall(PetscFree(ilengths_idxs));
8375:   PetscCall(PetscFree(olengths_vals));
8376:   PetscCall(PetscFree(olengths_idxs));
8377:   PetscCall(PetscFree(onodes));
8378:   if (nis) {
8379:     PetscCall(PetscFree(ilengths_idxs_is));
8380:     PetscCall(PetscFree(olengths_idxs_is));
8381:     PetscCall(PetscFree(onodes_is));
8382:   }
8383:   PetscCall(PetscSubcommDestroy(&subcomm));
8384:   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not participate */
8385:     PetscCall(MatDestroy(mat_n));
8386:     for (i = 0; i < nis; i++) PetscCall(ISDestroy(&isarray[i]));
8387:     if (nvecs) { /* need to match VecDestroy nnsp_vec called in the other code path */
8388:       PetscCall(VecDestroy(&nnsp_vec[0]));
8389:     }
8390:     *mat_n = NULL;
8391:   }
8392:   PetscFunctionReturn(PETSC_SUCCESS);
8393: }

8395: /* temporary hack into ksp private data structure */
8396: #include <petsc/private/kspimpl.h>

8398: PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc, Mat coarse_submat)
8399: {
8400:   PC_BDDC               *pcbddc = (PC_BDDC *)pc->data;
8401:   PC_IS                 *pcis   = (PC_IS *)pc->data;
8402:   PCBDDCGraph            graph  = pcbddc->mat_graph;
8403:   Mat                    coarse_mat, coarse_mat_is;
8404:   Mat                    coarsedivudotp = NULL;
8405:   Mat                    coarseG, t_coarse_mat_is;
8406:   MatNullSpace           CoarseNullSpace = NULL;
8407:   ISLocalToGlobalMapping coarse_islg;
8408:   IS                     coarse_is, *isarray, corners;
8409:   PetscInt               i, im_active = -1, active_procs = -1;
8410:   PetscInt               nis, nisdofs, nisneu, nisvert;
8411:   PetscInt               coarse_eqs_per_proc, coarsening_ratio;
8412:   PC                     pc_temp;
8413:   PCType                 coarse_pc_type;
8414:   KSPType                coarse_ksp_type;
8415:   PetscBool              multilevel_requested, multilevel_allowed;
8416:   PetscBool              coarse_reuse, multi_element = graph->multi_element;
8417:   PetscInt               ncoarse, nedcfield;
8418:   PetscBool              compute_vecs = PETSC_FALSE;
8419:   PetscScalar           *array;
8420:   MatReuse               coarse_mat_reuse;
8421:   PetscBool              restr, full_restr, have_void;
8422:   PetscMPIInt            size;

8424:   PetscFunctionBegin;
8425:   PetscCall(PetscLogEventBegin(PC_BDDC_CoarseSetUp[pcbddc->current_level], pc, 0, 0, 0));
8426:   /* Assign global numbering to coarse dofs */
8427:   if (pcbddc->new_primal_space || pcbddc->coarse_size == -1) { /* a new primal space is present or it is the first initialization, so recompute global numbering */
8428:     PetscInt ocoarse_size;
8429:     compute_vecs = PETSC_TRUE;

8431:     pcbddc->new_primal_space = PETSC_TRUE;
8432:     ocoarse_size             = pcbddc->coarse_size;
8433:     PetscCall(PetscFree(pcbddc->global_primal_indices));
8434:     PetscCall(PCBDDCComputePrimalNumbering(pc, &pcbddc->coarse_size, &pcbddc->global_primal_indices));
8435:     /* see if we can avoid some work */
8436:     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
8437:       /* if the coarse size is different or we are using adaptive selection, better to not reuse the coarse matrix */
8438:       if (ocoarse_size != pcbddc->coarse_size || pcbddc->adaptive_selection) {
8439:         PetscCall(KSPReset(pcbddc->coarse_ksp));
8440:         coarse_reuse = PETSC_FALSE;
8441:       } else { /* we can safely reuse already computed coarse matrix */
8442:         coarse_reuse = PETSC_TRUE;
8443:       }
8444:     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
8445:       coarse_reuse = PETSC_FALSE;
8446:     }
8447:     /* reset any subassembling information */
8448:     if (!coarse_reuse || pcbddc->recompute_topography) PetscCall(ISDestroy(&pcbddc->coarse_subassembling));
8449:   } else { /* primal space is unchanged, so we can reuse coarse matrix */
8450:     coarse_reuse = PETSC_TRUE;
8451:   }
8452:   if (coarse_reuse && pcbddc->coarse_ksp) {
8453:     PetscCall(KSPGetOperators(pcbddc->coarse_ksp, &coarse_mat, NULL));
8454:     PetscCall(PetscObjectReference((PetscObject)coarse_mat));
8455:     coarse_mat_reuse = MAT_REUSE_MATRIX;
8456:   } else {
8457:     coarse_mat       = NULL;
8458:     coarse_mat_reuse = MAT_INITIAL_MATRIX;
8459:   }

8461:   /* creates temporary l2gmap and IS for coarse indexes */
8462:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), pcbddc->local_primal_size, pcbddc->global_primal_indices, PETSC_COPY_VALUES, &coarse_is));
8463:   PetscCall(ISLocalToGlobalMappingCreateIS(coarse_is, &coarse_islg));

8465:   /* creates temporary MATIS object for coarse matrix */
8466:   PetscCall(MatCreate(PetscObjectComm((PetscObject)pc), &t_coarse_mat_is));
8467:   PetscCall(MatSetType(t_coarse_mat_is, MATIS));
8468:   PetscCall(MatSetSizes(t_coarse_mat_is, PETSC_DECIDE, PETSC_DECIDE, pcbddc->coarse_size, pcbddc->coarse_size));
8469:   PetscCall(MatISSetAllowRepeated(t_coarse_mat_is, PETSC_TRUE));
8470:   PetscCall(MatSetLocalToGlobalMapping(t_coarse_mat_is, coarse_islg, coarse_islg));
8471:   PetscCall(MatISSetLocalMat(t_coarse_mat_is, coarse_submat));
8472:   PetscCall(MatAssemblyBegin(t_coarse_mat_is, MAT_FINAL_ASSEMBLY));
8473:   PetscCall(MatAssemblyEnd(t_coarse_mat_is, MAT_FINAL_ASSEMBLY));
8474:   PetscCall(MatViewFromOptions(t_coarse_mat_is, (PetscObject)pc, "-pc_bddc_coarse_mat_is_view"));

8476:   /* count "active" (i.e. with positive local size) and "void" processes */
8477:   im_active = !!pcis->n;
8478:   PetscCallMPI(MPIU_Allreduce(&im_active, &active_procs, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)pc)));

8480:   /* determine number of processes partecipating to coarse solver and compute subassembling pattern */
8481:   /* restr : whether we want to exclude senders (which are not receivers) from the subassembling pattern */
8482:   /* full_restr : just use the receivers from the subassembling pattern */
8483:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
8484:   coarse_mat_is        = NULL;
8485:   multilevel_allowed   = PETSC_FALSE;
8486:   multilevel_requested = PETSC_FALSE;
8487:   coarse_eqs_per_proc  = PetscMin(PetscMax(pcbddc->coarse_size, 1), pcbddc->coarse_eqs_per_proc);
8488:   if (coarse_eqs_per_proc < 0 || size == 1) coarse_eqs_per_proc = PetscMax(pcbddc->coarse_size, 1);
8489:   if (pcbddc->current_level < pcbddc->max_levels) multilevel_requested = PETSC_TRUE;
8490:   if (pcbddc->coarse_size <= pcbddc->coarse_eqs_limit) multilevel_requested = PETSC_FALSE;
8491:   coarsening_ratio = multi_element ? 1 : pcbddc->coarsening_ratio;
8492:   if (multilevel_requested) {
8493:     ncoarse    = active_procs / coarsening_ratio;
8494:     restr      = PETSC_FALSE;
8495:     full_restr = PETSC_FALSE;
8496:   } else {
8497:     ncoarse    = pcbddc->coarse_size / coarse_eqs_per_proc + !!(pcbddc->coarse_size % coarse_eqs_per_proc);
8498:     restr      = PETSC_TRUE;
8499:     full_restr = PETSC_TRUE;
8500:   }
8501:   if (!pcbddc->coarse_size || size == 1) multilevel_allowed = multilevel_requested = restr = full_restr = PETSC_FALSE;
8502:   ncoarse = PetscMax(1, ncoarse);
8503:   if (!pcbddc->coarse_subassembling) {
8504:     if (coarsening_ratio > 1) {
8505:       if (multilevel_requested) {
8506:         PetscCall(PCBDDCMatISGetSubassemblingPattern(pc->pmat, &ncoarse, pcbddc->coarse_adj_red, &pcbddc->coarse_subassembling, &have_void));
8507:       } else {
8508:         PetscCall(PCBDDCMatISGetSubassemblingPattern(t_coarse_mat_is, &ncoarse, pcbddc->coarse_adj_red, &pcbddc->coarse_subassembling, &have_void));
8509:       }
8510:     } else {
8511:       PetscMPIInt rank;

8513:       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
8514:       have_void = (active_procs == size) ? PETSC_FALSE : PETSC_TRUE;
8515:       PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), 1, rank, 1, &pcbddc->coarse_subassembling));
8516:     }
8517:   } else { /* if a subassembling pattern exists, then we can reuse the coarse ksp and compute the number of process involved */
8518:     PetscInt psum;
8519:     if (pcbddc->coarse_ksp) psum = 1;
8520:     else psum = 0;
8521:     PetscCallMPI(MPIU_Allreduce(&psum, &ncoarse, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)pc)));
8522:     have_void = ncoarse < size ? PETSC_TRUE : PETSC_FALSE;
8523:   }
8524:   /* determine if we can go multilevel */
8525:   if (multilevel_requested) {
8526:     if (ncoarse > 1) multilevel_allowed = PETSC_TRUE; /* found enough processes */
8527:     else restr = full_restr = PETSC_TRUE;             /* 1 subdomain, use a direct solver */
8528:   }
8529:   if (multilevel_allowed && have_void) restr = PETSC_TRUE;

8531:   /* dump subassembling pattern */
8532:   if (pcbddc->dbg_flag && multilevel_allowed) PetscCall(ISView(pcbddc->coarse_subassembling, pcbddc->dbg_viewer));
8533:   /* compute dofs splitting and neumann boundaries for coarse dofs */
8534:   nedcfield = -1;
8535:   corners   = NULL;
8536:   if (multilevel_allowed && !coarse_reuse && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal || pcbddc->nedclocal || pcbddc->corner_selected)) { /* protects from unneeded computations */
8537:     PetscInt              *tidxs, *tidxs2, nout, tsize, i;
8538:     const PetscInt        *idxs;
8539:     ISLocalToGlobalMapping tmap;

8541:     /* create map between primal indices (in local representative ordering) and local primal numbering */
8542:     PetscCall(ISLocalToGlobalMappingCreate(PETSC_COMM_SELF, 1, pcbddc->local_primal_size, pcbddc->primal_indices_local_idxs, PETSC_COPY_VALUES, &tmap));
8543:     /* allocate space for temporary storage */
8544:     PetscCall(PetscMalloc1(pcbddc->local_primal_size, &tidxs));
8545:     PetscCall(PetscMalloc1(pcbddc->local_primal_size, &tidxs2));
8546:     /* allocate for IS array */
8547:     nisdofs = pcbddc->n_ISForDofsLocal;
8548:     if (pcbddc->nedclocal) {
8549:       if (pcbddc->nedfield > -1) {
8550:         nedcfield = pcbddc->nedfield;
8551:       } else {
8552:         nedcfield = 0;
8553:         PetscCheck(!nisdofs, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "This should not happen (%" PetscInt_FMT ")", nisdofs);
8554:         nisdofs = 1;
8555:       }
8556:     }
8557:     nisneu  = !!pcbddc->NeumannBoundariesLocal;
8558:     nisvert = 0; /* nisvert is not used */
8559:     nis     = nisdofs + nisneu + nisvert;
8560:     PetscCall(PetscMalloc1(nis, &isarray));
8561:     /* dofs splitting */
8562:     for (i = 0; i < nisdofs; i++) {
8563:       /* PetscCall(ISView(pcbddc->ISForDofsLocal[i],0)); */
8564:       if (nedcfield != i) {
8565:         PetscCall(ISGetLocalSize(pcbddc->ISForDofsLocal[i], &tsize));
8566:         PetscCall(ISGetIndices(pcbddc->ISForDofsLocal[i], &idxs));
8567:         PetscCall(ISGlobalToLocalMappingApply(tmap, IS_GTOLM_DROP, tsize, idxs, &nout, tidxs));
8568:         PetscCall(ISRestoreIndices(pcbddc->ISForDofsLocal[i], &idxs));
8569:       } else {
8570:         PetscCall(ISGetLocalSize(pcbddc->nedclocal, &tsize));
8571:         PetscCall(ISGetIndices(pcbddc->nedclocal, &idxs));
8572:         PetscCall(ISGlobalToLocalMappingApply(tmap, IS_GTOLM_DROP, tsize, idxs, &nout, tidxs));
8573:         PetscCheck(tsize == nout, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Failed when mapping coarse nedelec field! %" PetscInt_FMT " != %" PetscInt_FMT, tsize, nout);
8574:         PetscCall(ISRestoreIndices(pcbddc->nedclocal, &idxs));
8575:       }
8576:       PetscCall(ISLocalToGlobalMappingApply(coarse_islg, nout, tidxs, tidxs2));
8577:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nout, tidxs2, PETSC_COPY_VALUES, &isarray[i]));
8578:       /* PetscCall(ISView(isarray[i],0)); */
8579:     }
8580:     /* neumann boundaries */
8581:     if (pcbddc->NeumannBoundariesLocal) {
8582:       /* PetscCall(ISView(pcbddc->NeumannBoundariesLocal,0)); */
8583:       PetscCall(ISGetLocalSize(pcbddc->NeumannBoundariesLocal, &tsize));
8584:       PetscCall(ISGetIndices(pcbddc->NeumannBoundariesLocal, &idxs));
8585:       PetscCall(ISGlobalToLocalMappingApply(tmap, IS_GTOLM_DROP, tsize, idxs, &nout, tidxs));
8586:       PetscCall(ISRestoreIndices(pcbddc->NeumannBoundariesLocal, &idxs));
8587:       PetscCall(ISLocalToGlobalMappingApply(coarse_islg, nout, tidxs, tidxs2));
8588:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nout, tidxs2, PETSC_COPY_VALUES, &isarray[nisdofs]));
8589:       /* PetscCall(ISView(isarray[nisdofs],0)); */
8590:     }
8591:     /* coordinates */
8592:     if (pcbddc->corner_selected) {
8593:       PetscCall(PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &corners));
8594:       PetscCall(ISGetLocalSize(corners, &tsize));
8595:       PetscCall(ISGetIndices(corners, &idxs));
8596:       PetscCall(ISGlobalToLocalMappingApply(tmap, IS_GTOLM_DROP, tsize, idxs, &nout, tidxs));
8597:       PetscCheck(tsize == nout, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Failed when mapping corners! %" PetscInt_FMT " != %" PetscInt_FMT, tsize, nout);
8598:       PetscCall(ISRestoreIndices(corners, &idxs));
8599:       PetscCall(PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &corners));
8600:       PetscCall(ISLocalToGlobalMappingApply(coarse_islg, nout, tidxs, tidxs2));
8601:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nout, tidxs2, PETSC_COPY_VALUES, &corners));
8602:     }
8603:     PetscCall(PetscFree(tidxs));
8604:     PetscCall(PetscFree(tidxs2));
8605:     PetscCall(ISLocalToGlobalMappingDestroy(&tmap));
8606:   } else {
8607:     nis     = 0;
8608:     nisdofs = 0;
8609:     nisneu  = 0;
8610:     nisvert = 0;
8611:     isarray = NULL;
8612:   }
8613:   /* destroy no longer needed map */
8614:   PetscCall(ISLocalToGlobalMappingDestroy(&coarse_islg));

8616:   /* subassemble */
8617:   if (multilevel_allowed) {
8618:     Vec       vp[1];
8619:     PetscInt  nvecs = 0;
8620:     PetscBool reuse;

8622:     vp[0] = NULL;
8623:     /* XXX HDIV also */
8624:     if (pcbddc->benign_have_null) { /* propagate no-net-flux quadrature to coarser level */
8625:       PetscCall(VecCreate(PetscObjectComm((PetscObject)pc), &vp[0]));
8626:       PetscCall(VecSetSizes(vp[0], pcbddc->local_primal_size, PETSC_DECIDE));
8627:       PetscCall(VecSetType(vp[0], VECSTANDARD));
8628:       nvecs = 1;

8630:       if (pcbddc->divudotp) {
8631:         Mat      B, loc_divudotp;
8632:         Vec      v, p;
8633:         IS       dummy;
8634:         PetscInt np;

8636:         PetscCall(MatISGetLocalMat(pcbddc->divudotp, &loc_divudotp));
8637:         PetscCall(MatGetSize(loc_divudotp, &np, NULL));
8638:         PetscCall(ISCreateStride(PETSC_COMM_SELF, np, 0, 1, &dummy));
8639:         PetscCall(MatCreateSubMatrix(loc_divudotp, dummy, pcis->is_B_local, MAT_INITIAL_MATRIX, &B));
8640:         PetscCall(MatCreateVecs(B, &v, &p));
8641:         PetscCall(VecSet(p, 1.));
8642:         PetscCall(MatMultTranspose(B, p, v));
8643:         PetscCall(VecDestroy(&p));
8644:         PetscCall(MatDestroy(&B));
8645:         PetscCall(VecGetArray(vp[0], &array));
8646:         PetscCall(VecPlaceArray(pcbddc->vec1_P, array));
8647:         PetscCall(MatMultTranspose(pcbddc->coarse_phi_B, v, pcbddc->vec1_P));
8648:         PetscCall(VecResetArray(pcbddc->vec1_P));
8649:         PetscCall(VecRestoreArray(vp[0], &array));
8650:         PetscCall(ISDestroy(&dummy));
8651:         PetscCall(VecDestroy(&v));
8652:       }
8653:     }
8654:     if (coarse_mat) reuse = PETSC_TRUE;
8655:     else reuse = PETSC_FALSE;
8656:     if (multi_element) {
8657:       /* XXX divudotp */
8658:       PetscCall(MatISSetAllowRepeated(t_coarse_mat_is, PETSC_FALSE));
8659:       PetscCall(PetscObjectReference((PetscObject)t_coarse_mat_is));
8660:       coarse_mat_is = t_coarse_mat_is;
8661:     } else {
8662:       PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &reuse, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)pc)));
8663:       if (reuse) {
8664:         PetscCall(PCBDDCMatISSubassemble(t_coarse_mat_is, pcbddc->coarse_subassembling, 0, restr, full_restr, PETSC_TRUE, &coarse_mat, nis, isarray, nvecs, vp));
8665:       } else {
8666:         PetscCall(PCBDDCMatISSubassemble(t_coarse_mat_is, pcbddc->coarse_subassembling, 0, restr, full_restr, PETSC_FALSE, &coarse_mat_is, nis, isarray, nvecs, vp));
8667:       }
8668:       if (vp[0]) { /* vp[0] could have been placed on a different set of processes */
8669:         PetscScalar       *arraym;
8670:         const PetscScalar *arrayv;
8671:         PetscInt           nl;
8672:         PetscCall(VecGetLocalSize(vp[0], &nl));
8673:         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 1, nl, NULL, &coarsedivudotp));
8674:         PetscCall(MatDenseGetArray(coarsedivudotp, &arraym));
8675:         PetscCall(VecGetArrayRead(vp[0], &arrayv));
8676:         PetscCall(PetscArraycpy(arraym, arrayv, nl));
8677:         PetscCall(VecRestoreArrayRead(vp[0], &arrayv));
8678:         PetscCall(MatDenseRestoreArray(coarsedivudotp, &arraym));
8679:         PetscCall(VecDestroy(&vp[0]));
8680:       } else {
8681:         PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, 0, 0, 1, NULL, &coarsedivudotp));
8682:       }
8683:     }
8684:   } else {
8685:     if (ncoarse != size) PetscCall(PCBDDCMatISSubassemble(t_coarse_mat_is, pcbddc->coarse_subassembling, 0, restr, full_restr, PETSC_FALSE, &coarse_mat_is, 0, NULL, 0, NULL));
8686:     else {
8687:       PetscCall(PetscObjectReference((PetscObject)t_coarse_mat_is));
8688:       coarse_mat_is = t_coarse_mat_is;
8689:     }
8690:   }
8691:   if (coarse_mat_is || coarse_mat) {
8692:     if (!multilevel_allowed) {
8693:       PetscCall(MatConvert(coarse_mat_is, MATAIJ, coarse_mat_reuse, &coarse_mat));
8694:     } else {
8695:       /* if this matrix is present, it means we are not reusing the coarse matrix */
8696:       if (coarse_mat_is) {
8697:         PetscCheck(!coarse_mat, PetscObjectComm((PetscObject)coarse_mat_is), PETSC_ERR_PLIB, "This should not happen");
8698:         PetscCall(PetscObjectReference((PetscObject)coarse_mat_is));
8699:         coarse_mat = coarse_mat_is;
8700:       }
8701:     }
8702:   }
8703:   PetscCall(MatDestroy(&t_coarse_mat_is));
8704:   PetscCall(MatDestroy(&coarse_mat_is));

8706:   /* create local to global scatters for coarse problem */
8707:   if (compute_vecs) {
8708:     PetscInt lrows;
8709:     PetscCall(VecDestroy(&pcbddc->coarse_vec));
8710:     if (coarse_mat) {
8711:       PetscCall(MatGetLocalSize(coarse_mat, &lrows, NULL));
8712:     } else {
8713:       lrows = 0;
8714:     }
8715:     PetscCall(VecCreate(PetscObjectComm((PetscObject)pc), &pcbddc->coarse_vec));
8716:     PetscCall(VecSetSizes(pcbddc->coarse_vec, lrows, PETSC_DECIDE));
8717:     PetscCall(VecSetType(pcbddc->coarse_vec, coarse_mat ? coarse_mat->defaultvectype : VECSTANDARD));
8718:     PetscCall(VecScatterDestroy(&pcbddc->coarse_loc_to_glob));
8719:     PetscCall(VecScatterCreate(pcbddc->vec1_P, NULL, pcbddc->coarse_vec, coarse_is, &pcbddc->coarse_loc_to_glob));
8720:   }
8721:   PetscCall(ISDestroy(&coarse_is));

8723:   /* set defaults for coarse KSP and PC */
8724:   if (multilevel_allowed) {
8725:     coarse_ksp_type = KSPRICHARDSON;
8726:     coarse_pc_type  = PCBDDC;
8727:   } else {
8728:     coarse_ksp_type = KSPPREONLY;
8729:     coarse_pc_type  = PCREDUNDANT;
8730:   }

8732:   /* print some info if requested */
8733:   if (pcbddc->dbg_flag) {
8734:     if (!multilevel_allowed) {
8735:       PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "--------------------------------------------------\n"));
8736:       if (multilevel_requested) {
8737:         PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "Not enough active processes on level %" PetscInt_FMT " (active processes %" PetscInt_FMT ", coarsening ratio %" PetscInt_FMT ")\n", pcbddc->current_level, active_procs, coarsening_ratio));
8738:       } else if (pcbddc->max_levels) {
8739:         PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "Maximum number of requested levels reached (%" PetscInt_FMT ")\n", pcbddc->max_levels));
8740:       }
8741:       PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
8742:     }
8743:   }

8745:   /* communicate coarse discrete gradient */
8746:   coarseG = NULL;
8747:   if (pcbddc->nedcG && multilevel_allowed) {
8748:     MPI_Comm ccomm;
8749:     if (coarse_mat) {
8750:       ccomm = PetscObjectComm((PetscObject)coarse_mat);
8751:     } else {
8752:       ccomm = MPI_COMM_NULL;
8753:     }
8754:     PetscCall(MatMPIAIJRestrict(pcbddc->nedcG, ccomm, &coarseG));
8755:   }

8757:   /* create the coarse KSP object only once with defaults */
8758:   if (coarse_mat) {
8759:     PetscBool   isredundant, isbddc, force, valid;
8760:     PetscViewer dbg_viewer = NULL;
8761:     PetscBool   isset, issym, isher, isspd;

8763:     if (pcbddc->dbg_flag) {
8764:       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat));
8765:       PetscCall(PetscViewerASCIIAddTab(dbg_viewer, 2 * pcbddc->current_level));
8766:     }
8767:     if (!pcbddc->coarse_ksp) {
8768:       char   prefix[256], str_level[16];
8769:       size_t len;

8771:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)coarse_mat), &pcbddc->coarse_ksp));
8772:       PetscCall(KSPSetNestLevel(pcbddc->coarse_ksp, pc->kspnestlevel));
8773:       PetscCall(KSPSetErrorIfNotConverged(pcbddc->coarse_ksp, pc->erroriffailure));
8774:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp, (PetscObject)pc, 1));
8775:       PetscCall(KSPSetTolerances(pcbddc->coarse_ksp, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT, 1));
8776:       PetscCall(KSPSetOperators(pcbddc->coarse_ksp, coarse_mat, coarse_mat));
8777:       PetscCall(KSPSetType(pcbddc->coarse_ksp, coarse_ksp_type));
8778:       PetscCall(KSPSetNormType(pcbddc->coarse_ksp, KSP_NORM_NONE));
8779:       PetscCall(KSPGetPC(pcbddc->coarse_ksp, &pc_temp));
8780:       /* TODO is this logic correct? should check for coarse_mat type */
8781:       PetscCall(PCSetType(pc_temp, coarse_pc_type));
8782:       /* prefix */
8783:       PetscCall(PetscStrncpy(prefix, "", sizeof(prefix)));
8784:       PetscCall(PetscStrncpy(str_level, "", sizeof(str_level)));
8785:       if (!pcbddc->current_level) {
8786:         PetscCall(PetscStrncpy(prefix, ((PetscObject)pc)->prefix, sizeof(prefix)));
8787:         PetscCall(PetscStrlcat(prefix, "pc_bddc_coarse_", sizeof(prefix)));
8788:       } else {
8789:         PetscCall(PetscStrlen(((PetscObject)pc)->prefix, &len));
8790:         if (pcbddc->current_level > 1) len -= 3;  /* remove "lX_" with X level number */
8791:         if (pcbddc->current_level > 10) len -= 1; /* remove another char from level number */
8792:         /* Nonstandard use of PetscStrncpy() to copy only a portion of the string */
8793:         PetscCall(PetscStrncpy(prefix, ((PetscObject)pc)->prefix, len + 1));
8794:         PetscCall(PetscSNPrintf(str_level, sizeof(str_level), "l%" PetscInt_FMT "_", pcbddc->current_level));
8795:         PetscCall(PetscStrlcat(prefix, str_level, sizeof(prefix)));
8796:       }
8797:       PetscCall(KSPSetOptionsPrefix(pcbddc->coarse_ksp, prefix));
8798:       /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
8799:       PetscCall(PCBDDCSetLevel(pc_temp, pcbddc->current_level + 1));
8800:       PetscCall(PCBDDCSetCoarseningRatio(pc_temp, pcbddc->coarsening_ratio));
8801:       PetscCall(PCBDDCSetLevels(pc_temp, pcbddc->max_levels));
8802:       /* allow user customization */
8803:       PetscCall(KSPSetFromOptions(pcbddc->coarse_ksp));
8804:       /* get some info after set from options */
8805:       PetscCall(KSPGetPC(pcbddc->coarse_ksp, &pc_temp));
8806:       /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
8807:       force = PETSC_FALSE;
8808:       PetscCall(PetscOptionsGetBool(NULL, ((PetscObject)pc_temp)->prefix, "-pc_type_forced", &force, NULL));
8809:       PetscCall(PetscObjectTypeCompareAny((PetscObject)pc_temp, &valid, PCBDDC, PCNN, PCHPDDM, ""));
8810:       PetscCall(PetscObjectTypeCompare((PetscObject)pc_temp, PCBDDC, &isbddc));
8811:       if (multilevel_allowed && !force && !valid) {
8812:         isbddc = PETSC_TRUE;
8813:         PetscCall(PCSetType(pc_temp, PCBDDC));
8814:         PetscCall(PCBDDCSetLevel(pc_temp, pcbddc->current_level + 1));
8815:         PetscCall(PCBDDCSetCoarseningRatio(pc_temp, pcbddc->coarsening_ratio));
8816:         PetscCall(PCBDDCSetLevels(pc_temp, pcbddc->max_levels));
8817:         if (pc_temp->ops->setfromoptions) { /* need to setfromoptions again, skipping the pc_type */
8818:           PetscObjectOptionsBegin((PetscObject)pc_temp);
8819:           PetscCall((*pc_temp->ops->setfromoptions)(pc_temp, PetscOptionsObject));
8820:           PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)pc_temp, PetscOptionsObject));
8821:           PetscOptionsEnd();
8822:           pc_temp->setfromoptionscalled++;
8823:         }
8824:       }
8825:     }
8826:     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
8827:     PetscCall(KSPGetPC(pcbddc->coarse_ksp, &pc_temp));
8828:     if (nisdofs) {
8829:       PetscCall(PCBDDCSetDofsSplitting(pc_temp, nisdofs, isarray));
8830:       for (i = 0; i < nisdofs; i++) PetscCall(ISDestroy(&isarray[i]));
8831:     }
8832:     if (nisneu) {
8833:       PetscCall(PCBDDCSetNeumannBoundaries(pc_temp, isarray[nisdofs]));
8834:       PetscCall(ISDestroy(&isarray[nisdofs]));
8835:     }
8836:     if (nisvert) {
8837:       PetscCall(PCBDDCSetPrimalVerticesIS(pc_temp, isarray[nis - 1]));
8838:       PetscCall(ISDestroy(&isarray[nis - 1]));
8839:     }
8840:     if (coarseG) PetscCall(PCBDDCSetDiscreteGradient(pc_temp, coarseG, 1, nedcfield, PETSC_FALSE, PETSC_TRUE));

8842:     /* get some info after set from options */
8843:     PetscCall(PetscObjectTypeCompare((PetscObject)pc_temp, PCBDDC, &isbddc));

8845:     /* multilevel can only be requested via -pc_bddc_levels or PCBDDCSetLevels */
8846:     if (isbddc && !multilevel_allowed) PetscCall(PCSetType(pc_temp, coarse_pc_type));
8847:     /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
8848:     force = PETSC_FALSE;
8849:     PetscCall(PetscOptionsGetBool(NULL, ((PetscObject)pc_temp)->prefix, "-pc_type_forced", &force, NULL));
8850:     PetscCall(PetscObjectTypeCompareAny((PetscObject)pc_temp, &valid, PCBDDC, PCNN, PCHPDDM, ""));
8851:     if (multilevel_requested && multilevel_allowed && !valid && !force) PetscCall(PCSetType(pc_temp, PCBDDC));
8852:     PetscCall(PetscObjectTypeCompare((PetscObject)pc_temp, PCREDUNDANT, &isredundant));
8853:     if (isredundant) {
8854:       KSP inner_ksp;
8855:       PC  inner_pc;

8857:       PetscCall(PCRedundantGetKSP(pc_temp, &inner_ksp));
8858:       PetscCall(KSPGetPC(inner_ksp, &inner_pc));
8859:     }

8861:     /* parameters which miss an API */
8862:     PetscCall(PetscObjectTypeCompare((PetscObject)pc_temp, PCBDDC, &isbddc));
8863:     if (isbddc) {
8864:       PC_BDDC *pcbddc_coarse = (PC_BDDC *)pc_temp->data;

8866:       pcbddc_coarse->detect_disconnected = PETSC_TRUE;
8867:       pcbddc_coarse->coarse_eqs_per_proc = pcbddc->coarse_eqs_per_proc;
8868:       pcbddc_coarse->coarse_eqs_limit    = pcbddc->coarse_eqs_limit;
8869:       pcbddc_coarse->benign_saddle_point = pcbddc->benign_have_null;
8870:       if (pcbddc_coarse->benign_saddle_point) {
8871:         Mat                    coarsedivudotp_is;
8872:         ISLocalToGlobalMapping l2gmap, rl2g, cl2g;
8873:         IS                     row, col;
8874:         const PetscInt        *gidxs;
8875:         PetscInt               n, st, M, N;

8877:         PetscCall(MatGetSize(coarsedivudotp, &n, NULL));
8878:         PetscCallMPI(MPI_Scan(&n, &st, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)coarse_mat)));
8879:         st = st - n;
8880:         PetscCall(ISCreateStride(PetscObjectComm((PetscObject)coarse_mat), 1, st, 1, &row));
8881:         PetscCall(MatISGetLocalToGlobalMapping(coarse_mat, &l2gmap, NULL));
8882:         PetscCall(ISLocalToGlobalMappingGetSize(l2gmap, &n));
8883:         PetscCall(ISLocalToGlobalMappingGetIndices(l2gmap, &gidxs));
8884:         PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)coarse_mat), n, gidxs, PETSC_COPY_VALUES, &col));
8885:         PetscCall(ISLocalToGlobalMappingRestoreIndices(l2gmap, &gidxs));
8886:         PetscCall(ISLocalToGlobalMappingCreateIS(row, &rl2g));
8887:         PetscCall(ISLocalToGlobalMappingCreateIS(col, &cl2g));
8888:         PetscCall(ISGetSize(row, &M));
8889:         PetscCall(MatGetSize(coarse_mat, &N, NULL));
8890:         PetscCall(ISDestroy(&row));
8891:         PetscCall(ISDestroy(&col));
8892:         PetscCall(MatCreate(PetscObjectComm((PetscObject)coarse_mat), &coarsedivudotp_is));
8893:         PetscCall(MatSetType(coarsedivudotp_is, MATIS));
8894:         PetscCall(MatSetSizes(coarsedivudotp_is, PETSC_DECIDE, PETSC_DECIDE, M, N));
8895:         PetscCall(MatSetLocalToGlobalMapping(coarsedivudotp_is, rl2g, cl2g));
8896:         PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
8897:         PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));
8898:         PetscCall(MatISSetLocalMat(coarsedivudotp_is, coarsedivudotp));
8899:         PetscCall(MatDestroy(&coarsedivudotp));
8900:         PetscCall(PCBDDCSetDivergenceMat(pc_temp, coarsedivudotp_is, PETSC_FALSE, NULL));
8901:         PetscCall(MatDestroy(&coarsedivudotp_is));
8902:         pcbddc_coarse->adaptive_userdefined = PETSC_TRUE;
8903:         if (pcbddc->adaptive_threshold[0] == 0.0) pcbddc_coarse->deluxe_zerorows = PETSC_TRUE;
8904:       }
8905:     }

8907:     /* propagate symmetry info of coarse matrix */
8908:     PetscCall(MatSetOption(coarse_mat, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
8909:     PetscCall(MatIsSymmetricKnown(pc->pmat, &isset, &issym));
8910:     if (isset) PetscCall(MatSetOption(coarse_mat, MAT_SYMMETRIC, issym));
8911:     PetscCall(MatIsHermitianKnown(pc->pmat, &isset, &isher));
8912:     if (isset) PetscCall(MatSetOption(coarse_mat, MAT_HERMITIAN, isher));
8913:     PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
8914:     if (isset) PetscCall(MatSetOption(coarse_mat, MAT_SPD, isspd));

8916:     if (pcbddc->benign_saddle_point && !pcbddc->benign_have_null) PetscCall(MatSetOption(coarse_mat, MAT_SPD, PETSC_TRUE));
8917:     /* set operators */
8918:     PetscCall(MatViewFromOptions(coarse_mat, (PetscObject)pc, "-pc_bddc_coarse_mat_view"));
8919:     PetscCall(MatSetOptionsPrefix(coarse_mat, ((PetscObject)pcbddc->coarse_ksp)->prefix));
8920:     PetscCall(KSPSetOperators(pcbddc->coarse_ksp, coarse_mat, coarse_mat));
8921:     if (pcbddc->dbg_flag) PetscCall(PetscViewerASCIISubtractTab(dbg_viewer, 2 * pcbddc->current_level));
8922:   }
8923:   PetscCall(MatDestroy(&coarseG));
8924:   PetscCall(PetscFree(isarray));
8925: #if 0
8926:   {
8927:     PetscViewer viewer;
8928:     char filename[256];
8929:     PetscCall(PetscSNPrintf(filename, PETSC_STATIC_ARRAY_LENGTH(filename), "coarse_mat_level%d.m",pcbddc->current_level));
8930:     PetscCall(PetscViewerASCIIOpen(PetscObjectComm((PetscObject)coarse_mat),filename,&viewer));
8931:     PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
8932:     PetscCall(MatView(coarse_mat,viewer));
8933:     PetscCall(PetscViewerPopFormat(viewer));
8934:     PetscCall(PetscViewerDestroy(&viewer));
8935:   }
8936: #endif

8938:   if (corners) {
8939:     Vec             gv;
8940:     IS              is;
8941:     const PetscInt *idxs;
8942:     PetscInt        i, d, N, n, cdim = pcbddc->mat_graph->cdim;
8943:     PetscScalar    *coords;

8945:     PetscCheck(pcbddc->mat_graph->cloc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing local coordinates");
8946:     PetscCall(VecGetSize(pcbddc->coarse_vec, &N));
8947:     PetscCall(VecGetLocalSize(pcbddc->coarse_vec, &n));
8948:     PetscCall(VecCreate(PetscObjectComm((PetscObject)pcbddc->coarse_vec), &gv));
8949:     PetscCall(VecSetBlockSize(gv, cdim));
8950:     PetscCall(VecSetSizes(gv, n * cdim, N * cdim));
8951:     PetscCall(VecSetType(gv, VECSTANDARD));
8952:     PetscCall(VecSetFromOptions(gv));
8953:     PetscCall(VecSet(gv, PETSC_MAX_REAL)); /* we only propagate coordinates from vertices constraints */

8955:     PetscCall(PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &is));
8956:     PetscCall(ISGetLocalSize(is, &n));
8957:     PetscCall(ISGetIndices(is, &idxs));
8958:     PetscCall(PetscMalloc1(n * cdim, &coords));
8959:     for (i = 0; i < n; i++) {
8960:       for (d = 0; d < cdim; d++) coords[cdim * i + d] = pcbddc->mat_graph->coords[cdim * idxs[i] + d];
8961:     }
8962:     PetscCall(ISRestoreIndices(is, &idxs));
8963:     PetscCall(PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &is));

8965:     PetscCall(ISGetLocalSize(corners, &n));
8966:     PetscCall(ISGetIndices(corners, &idxs));
8967:     PetscCall(VecSetValuesBlocked(gv, n, idxs, coords, INSERT_VALUES));
8968:     PetscCall(ISRestoreIndices(corners, &idxs));
8969:     PetscCall(PetscFree(coords));
8970:     PetscCall(VecAssemblyBegin(gv));
8971:     PetscCall(VecAssemblyEnd(gv));
8972:     PetscCall(VecGetArray(gv, &coords));
8973:     if (pcbddc->coarse_ksp) {
8974:       PC        coarse_pc;
8975:       PetscBool isbddc;

8977:       PetscCall(KSPGetPC(pcbddc->coarse_ksp, &coarse_pc));
8978:       PetscCall(PetscObjectTypeCompare((PetscObject)coarse_pc, PCBDDC, &isbddc));
8979:       if (isbddc) { /* coarse coordinates have PETSC_MAX_REAL, specific for BDDC */
8980:         PetscReal *realcoords;

8982:         PetscCall(VecGetLocalSize(gv, &n));
8983: #if defined(PETSC_USE_COMPLEX)
8984:         PetscCall(PetscMalloc1(n, &realcoords));
8985:         for (i = 0; i < n; i++) realcoords[i] = PetscRealPart(coords[i]);
8986: #else
8987:         realcoords = coords;
8988: #endif
8989:         PetscCall(PCSetCoordinates(coarse_pc, cdim, n / cdim, realcoords));
8990: #if defined(PETSC_USE_COMPLEX)
8991:         PetscCall(PetscFree(realcoords));
8992: #endif
8993:       }
8994:     }
8995:     PetscCall(VecRestoreArray(gv, &coords));
8996:     PetscCall(VecDestroy(&gv));
8997:   }
8998:   PetscCall(ISDestroy(&corners));

9000:   if (pcbddc->coarse_ksp) {
9001:     Vec crhs, csol;

9003:     PetscCall(KSPGetSolution(pcbddc->coarse_ksp, &csol));
9004:     PetscCall(KSPGetRhs(pcbddc->coarse_ksp, &crhs));
9005:     if (!csol) PetscCall(MatCreateVecs(coarse_mat, &pcbddc->coarse_ksp->vec_sol, NULL));
9006:     if (!crhs) PetscCall(MatCreateVecs(coarse_mat, NULL, &pcbddc->coarse_ksp->vec_rhs));
9007:   }
9008:   PetscCall(MatDestroy(&coarsedivudotp));

9010:   /* compute null space for coarse solver if the benign trick has been requested */
9011:   if (pcbddc->benign_null) {
9012:     PetscCall(VecSet(pcbddc->vec1_P, 0.));
9013:     for (i = 0; i < pcbddc->benign_n; i++) PetscCall(VecSetValue(pcbddc->vec1_P, pcbddc->local_primal_size - pcbddc->benign_n + i, 1.0, INSERT_VALUES));
9014:     PetscCall(VecAssemblyBegin(pcbddc->vec1_P));
9015:     PetscCall(VecAssemblyEnd(pcbddc->vec1_P));
9016:     PetscCall(VecScatterBegin(pcbddc->coarse_loc_to_glob, pcbddc->vec1_P, pcbddc->coarse_vec, INSERT_VALUES, SCATTER_FORWARD));
9017:     PetscCall(VecScatterEnd(pcbddc->coarse_loc_to_glob, pcbddc->vec1_P, pcbddc->coarse_vec, INSERT_VALUES, SCATTER_FORWARD));
9018:     if (coarse_mat) {
9019:       Vec          nullv;
9020:       PetscScalar *array, *array2;
9021:       PetscInt     nl;

9023:       PetscCall(MatCreateVecs(coarse_mat, &nullv, NULL));
9024:       PetscCall(VecGetLocalSize(nullv, &nl));
9025:       PetscCall(VecGetArrayRead(pcbddc->coarse_vec, (const PetscScalar **)&array));
9026:       PetscCall(VecGetArray(nullv, &array2));
9027:       PetscCall(PetscArraycpy(array2, array, nl));
9028:       PetscCall(VecRestoreArray(nullv, &array2));
9029:       PetscCall(VecRestoreArrayRead(pcbddc->coarse_vec, (const PetscScalar **)&array));
9030:       PetscCall(VecNormalize(nullv, NULL));
9031:       PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)coarse_mat), PETSC_FALSE, 1, &nullv, &CoarseNullSpace));
9032:       PetscCall(VecDestroy(&nullv));
9033:     }
9034:   }
9035:   PetscCall(PetscLogEventEnd(PC_BDDC_CoarseSetUp[pcbddc->current_level], pc, 0, 0, 0));

9037:   PetscCall(PetscLogEventBegin(PC_BDDC_CoarseSolver[pcbddc->current_level], pc, 0, 0, 0));
9038:   if (pcbddc->coarse_ksp) {
9039:     PetscBool ispreonly;

9041:     if (CoarseNullSpace) {
9042:       PetscBool isnull;

9044:       PetscCall(MatNullSpaceTest(CoarseNullSpace, coarse_mat, &isnull));
9045:       if (isnull) PetscCall(MatSetNullSpace(coarse_mat, CoarseNullSpace));
9046:       /* TODO: add local nullspaces (if any) */
9047:     }
9048:     /* setup coarse ksp */
9049:     PetscCall(KSPSetUp(pcbddc->coarse_ksp));
9050:     /* Check coarse problem if in debug mode or if solving with an iterative method */
9051:     PetscCall(PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp, KSPPREONLY, &ispreonly));
9052:     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates)) {
9053:       KSP         check_ksp;
9054:       KSPType     check_ksp_type;
9055:       PC          check_pc;
9056:       Vec         check_vec, coarse_vec;
9057:       PetscReal   abs_infty_error, infty_error, lambda_min = 1.0, lambda_max = 1.0;
9058:       PetscInt    its;
9059:       PetscBool   compute_eigs;
9060:       PetscReal  *eigs_r, *eigs_c;
9061:       PetscInt    neigs;
9062:       const char *prefix;

9064:       /* Create ksp object suitable for estimation of extreme eigenvalues */
9065:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp), &check_ksp));
9066:       PetscCall(KSPSetNestLevel(check_ksp, pc->kspnestlevel));
9067:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)check_ksp, (PetscObject)pcbddc->coarse_ksp, 0));
9068:       PetscCall(KSPSetErrorIfNotConverged(pcbddc->coarse_ksp, PETSC_FALSE));
9069:       PetscCall(KSPSetOperators(check_ksp, coarse_mat, coarse_mat));
9070:       PetscCall(KSPSetTolerances(check_ksp, 1.e-12, 1.e-12, PETSC_CURRENT, pcbddc->coarse_size));
9071:       /* prevent from setup unneeded object */
9072:       PetscCall(KSPGetPC(check_ksp, &check_pc));
9073:       PetscCall(PCSetType(check_pc, PCNONE));
9074:       if (ispreonly) {
9075:         check_ksp_type = KSPPREONLY;
9076:         compute_eigs   = PETSC_FALSE;
9077:       } else {
9078:         check_ksp_type = KSPGMRES;
9079:         compute_eigs   = PETSC_TRUE;
9080:       }
9081:       PetscCall(KSPSetType(check_ksp, check_ksp_type));
9082:       PetscCall(KSPSetComputeSingularValues(check_ksp, compute_eigs));
9083:       PetscCall(KSPSetComputeEigenvalues(check_ksp, compute_eigs));
9084:       PetscCall(KSPGMRESSetRestart(check_ksp, pcbddc->coarse_size + 1));
9085:       PetscCall(KSPGetOptionsPrefix(pcbddc->coarse_ksp, &prefix));
9086:       PetscCall(KSPSetOptionsPrefix(check_ksp, prefix));
9087:       PetscCall(KSPAppendOptionsPrefix(check_ksp, "check_"));
9088:       PetscCall(KSPSetFromOptions(check_ksp));
9089:       PetscCall(KSPSetUp(check_ksp));
9090:       PetscCall(KSPGetPC(pcbddc->coarse_ksp, &check_pc));
9091:       PetscCall(KSPSetPC(check_ksp, check_pc));
9092:       /* create random vec */
9093:       PetscCall(MatCreateVecs(coarse_mat, &coarse_vec, &check_vec));
9094:       PetscCall(VecSetRandom(check_vec, NULL));
9095:       PetscCall(MatMult(coarse_mat, check_vec, coarse_vec));
9096:       /* solve coarse problem */
9097:       PetscCall(KSPSolve(check_ksp, coarse_vec, coarse_vec));
9098:       PetscCall(KSPCheckSolve(check_ksp, pc, coarse_vec));
9099:       /* set eigenvalue estimation if preonly has not been requested */
9100:       if (compute_eigs) {
9101:         PetscCall(PetscMalloc1(pcbddc->coarse_size + 1, &eigs_r));
9102:         PetscCall(PetscMalloc1(pcbddc->coarse_size + 1, &eigs_c));
9103:         PetscCall(KSPComputeEigenvalues(check_ksp, pcbddc->coarse_size + 1, eigs_r, eigs_c, &neigs));
9104:         if (neigs) {
9105:           lambda_max = eigs_r[neigs - 1];
9106:           lambda_min = eigs_r[0];
9107:           if (pcbddc->use_coarse_estimates) {
9108:             if (lambda_max >= lambda_min) { /* using PETSC_SMALL since lambda_max == lambda_min is not allowed by KSPChebyshevSetEigenvalues */
9109:               PetscCall(KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp, lambda_max + PETSC_SMALL, lambda_min));
9110:               PetscCall(KSPRichardsonSetScale(pcbddc->coarse_ksp, 2.0 / (lambda_max + lambda_min)));
9111:             }
9112:           }
9113:         }
9114:       }

9116:       /* check coarse problem residual error */
9117:       if (pcbddc->dbg_flag) {
9118:         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
9119:         PetscCall(PetscViewerASCIIAddTab(dbg_viewer, 2 * (pcbddc->current_level + 1)));
9120:         PetscCall(VecAXPY(check_vec, -1.0, coarse_vec));
9121:         PetscCall(VecNorm(check_vec, NORM_INFINITY, &infty_error));
9122:         PetscCall(MatMult(coarse_mat, check_vec, coarse_vec));
9123:         PetscCall(VecNorm(coarse_vec, NORM_INFINITY, &abs_infty_error));
9124:         PetscCall(PetscViewerASCIIPrintf(dbg_viewer, "Coarse problem details (use estimates %d)\n", pcbddc->use_coarse_estimates));
9125:         PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)pcbddc->coarse_ksp, dbg_viewer));
9126:         PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)check_pc, dbg_viewer));
9127:         PetscCall(PetscViewerASCIIPrintf(dbg_viewer, "Coarse problem exact infty_error   : %1.6e\n", (double)infty_error));
9128:         PetscCall(PetscViewerASCIIPrintf(dbg_viewer, "Coarse problem residual infty_error: %1.6e\n", (double)abs_infty_error));
9129:         if (CoarseNullSpace) PetscCall(PetscViewerASCIIPrintf(dbg_viewer, "Coarse problem is singular\n"));
9130:         if (compute_eigs) {
9131:           PetscReal          lambda_max_s, lambda_min_s;
9132:           KSPConvergedReason reason;
9133:           PetscCall(KSPGetType(check_ksp, &check_ksp_type));
9134:           PetscCall(KSPGetIterationNumber(check_ksp, &its));
9135:           PetscCall(KSPGetConvergedReason(check_ksp, &reason));
9136:           PetscCall(KSPComputeExtremeSingularValues(check_ksp, &lambda_max_s, &lambda_min_s));
9137:           PetscCall(PetscViewerASCIIPrintf(dbg_viewer, "Coarse problem eigenvalues (estimated with %" PetscInt_FMT " iterations of %s, conv reason %d): %1.6e %1.6e (%1.6e %1.6e)\n", its, check_ksp_type, reason, (double)lambda_min, (double)lambda_max, (double)lambda_min_s, (double)lambda_max_s));
9138:           for (i = 0; i < neigs; i++) PetscCall(PetscViewerASCIIPrintf(dbg_viewer, "%1.6e %1.6ei\n", (double)eigs_r[i], (double)eigs_c[i]));
9139:         }
9140:         PetscCall(PetscViewerFlush(dbg_viewer));
9141:         PetscCall(PetscViewerASCIISubtractTab(dbg_viewer, 2 * (pcbddc->current_level + 1)));
9142:       }
9143:       PetscCall(VecDestroy(&check_vec));
9144:       PetscCall(VecDestroy(&coarse_vec));
9145:       PetscCall(KSPDestroy(&check_ksp));
9146:       if (compute_eigs) {
9147:         PetscCall(PetscFree(eigs_r));
9148:         PetscCall(PetscFree(eigs_c));
9149:       }
9150:     }
9151:   }
9152:   PetscCall(MatNullSpaceDestroy(&CoarseNullSpace));
9153:   /* print additional info */
9154:   if (pcbddc->dbg_flag) {
9155:     /* waits until all processes reaches this point */
9156:     PetscCall(PetscBarrier((PetscObject)pc));
9157:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "Coarse solver setup completed at level %" PetscInt_FMT "\n", pcbddc->current_level));
9158:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
9159:   }

9161:   /* free memory */
9162:   PetscCall(MatDestroy(&coarse_mat));
9163:   PetscCall(PetscLogEventEnd(PC_BDDC_CoarseSolver[pcbddc->current_level], pc, 0, 0, 0));
9164:   PetscFunctionReturn(PETSC_SUCCESS);
9165: }

9167: PetscErrorCode PCBDDCComputePrimalNumbering(PC pc, PetscInt *coarse_size_n, PetscInt **local_primal_indices_n)
9168: {
9169:   PC_BDDC        *pcbddc = (PC_BDDC *)pc->data;
9170:   PC_IS          *pcis   = (PC_IS *)pc->data;
9171:   IS              subset, subset_mult, subset_n;
9172:   PetscInt        local_size, coarse_size = 0;
9173:   PetscInt       *local_primal_indices = NULL;
9174:   const PetscInt *t_local_primal_indices;

9176:   PetscFunctionBegin;
9177:   /* Compute global number of coarse dofs */
9178:   PetscCheck(!pcbddc->local_primal_size || pcbddc->local_primal_ref_node, PETSC_COMM_SELF, PETSC_ERR_PLIB, "BDDC ConstraintsSetUp should be called first");
9179:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc->pmat), pcbddc->local_primal_size_cc, pcbddc->local_primal_ref_node, PETSC_COPY_VALUES, &subset_n));
9180:   PetscCall(ISLocalToGlobalMappingApplyIS(pcis->mapping, subset_n, &subset));
9181:   PetscCall(ISDestroy(&subset_n));
9182:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc->pmat), pcbddc->local_primal_size_cc, pcbddc->local_primal_ref_mult, PETSC_COPY_VALUES, &subset_mult));
9183:   PetscCall(ISRenumber(subset, subset_mult, &coarse_size, &subset_n));
9184:   PetscCall(ISDestroy(&subset));
9185:   PetscCall(ISDestroy(&subset_mult));
9186:   PetscCall(ISGetLocalSize(subset_n, &local_size));
9187:   PetscCheck(local_size == pcbddc->local_primal_size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of local primal indices computed %" PetscInt_FMT " != %" PetscInt_FMT, local_size, pcbddc->local_primal_size);
9188:   PetscCall(PetscMalloc1(local_size, &local_primal_indices));
9189:   PetscCall(ISGetIndices(subset_n, &t_local_primal_indices));
9190:   PetscCall(PetscArraycpy(local_primal_indices, t_local_primal_indices, local_size));
9191:   PetscCall(ISRestoreIndices(subset_n, &t_local_primal_indices));
9192:   PetscCall(ISDestroy(&subset_n));

9194:   if (pcbddc->dbg_flag) {
9195:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
9196:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "--------------------------------------------------\n"));
9197:     PetscCall(PetscViewerASCIIPrintf(pcbddc->dbg_viewer, "Size of coarse problem is %" PetscInt_FMT "\n", coarse_size));
9198:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
9199:   }

9201:   /* get back data */
9202:   *coarse_size_n          = coarse_size;
9203:   *local_primal_indices_n = local_primal_indices;
9204:   PetscFunctionReturn(PETSC_SUCCESS);
9205: }

9207: PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx, Vec gwork, Vec lwork, IS globalis, IS *localis)
9208: {
9209:   IS           localis_t;
9210:   PetscInt     i, lsize, *idxs, n;
9211:   PetscScalar *vals;

9213:   PetscFunctionBegin;
9214:   /* get indices in local ordering exploiting local to global map */
9215:   PetscCall(ISGetLocalSize(globalis, &lsize));
9216:   PetscCall(PetscMalloc1(lsize, &vals));
9217:   for (i = 0; i < lsize; i++) vals[i] = 1.0;
9218:   PetscCall(ISGetIndices(globalis, (const PetscInt **)&idxs));
9219:   PetscCall(VecSet(gwork, 0.0));
9220:   PetscCall(VecSet(lwork, 0.0));
9221:   if (idxs) { /* multilevel guard */
9222:     PetscCall(VecSetOption(gwork, VEC_IGNORE_NEGATIVE_INDICES, PETSC_TRUE));
9223:     PetscCall(VecSetValues(gwork, lsize, idxs, vals, INSERT_VALUES));
9224:   }
9225:   PetscCall(VecAssemblyBegin(gwork));
9226:   PetscCall(ISRestoreIndices(globalis, (const PetscInt **)&idxs));
9227:   PetscCall(PetscFree(vals));
9228:   PetscCall(VecAssemblyEnd(gwork));
9229:   /* now compute set in local ordering */
9230:   PetscCall(VecScatterBegin(g2l_ctx, gwork, lwork, INSERT_VALUES, SCATTER_FORWARD));
9231:   PetscCall(VecScatterEnd(g2l_ctx, gwork, lwork, INSERT_VALUES, SCATTER_FORWARD));
9232:   PetscCall(VecGetArrayRead(lwork, (const PetscScalar **)&vals));
9233:   PetscCall(VecGetSize(lwork, &n));
9234:   for (i = 0, lsize = 0; i < n; i++) {
9235:     if (PetscRealPart(vals[i]) > 0.5) lsize++;
9236:   }
9237:   PetscCall(PetscMalloc1(lsize, &idxs));
9238:   for (i = 0, lsize = 0; i < n; i++) {
9239:     if (PetscRealPart(vals[i]) > 0.5) idxs[lsize++] = i;
9240:   }
9241:   PetscCall(VecRestoreArrayRead(lwork, (const PetscScalar **)&vals));
9242:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)gwork), lsize, idxs, PETSC_OWN_POINTER, &localis_t));
9243:   *localis = localis_t;
9244:   PetscFunctionReturn(PETSC_SUCCESS);
9245: }

9247: PetscErrorCode PCBDDCComputeFakeChange(PC pc, PetscBool constraints, PCBDDCGraph graph, PCBDDCSubSchurs schurs, Mat *change, IS *change_primal, IS *change_primal_mult, PetscBool *change_with_qr)
9248: {
9249:   PC_IS   *pcis   = (PC_IS *)pc->data;
9250:   PC_BDDC *pcbddc = (PC_BDDC *)pc->data;
9251:   PC_IS   *pcisf;
9252:   PC_BDDC *pcbddcf;
9253:   PC       pcf;

9255:   PetscFunctionBegin;
9256:   PetscCall(PCCreate(PetscObjectComm((PetscObject)pc), &pcf));
9257:   PetscCall(PCSetOperators(pcf, pc->mat, pc->pmat));
9258:   PetscCall(PCSetType(pcf, PCBDDC));

9260:   pcisf   = (PC_IS *)pcf->data;
9261:   pcbddcf = (PC_BDDC *)pcf->data;

9263:   pcisf->is_B_local = pcis->is_B_local;
9264:   pcisf->vec1_N     = pcis->vec1_N;
9265:   pcisf->BtoNmap    = pcis->BtoNmap;
9266:   pcisf->n          = pcis->n;
9267:   pcisf->n_B        = pcis->n_B;

9269:   PetscCall(PetscFree(pcbddcf->mat_graph));
9270:   PetscCall(PetscFree(pcbddcf->sub_schurs));
9271:   pcbddcf->mat_graph             = graph ? graph : pcbddc->mat_graph;
9272:   pcbddcf->sub_schurs            = schurs;
9273:   pcbddcf->adaptive_selection    = schurs ? PETSC_TRUE : PETSC_FALSE;
9274:   pcbddcf->adaptive_threshold[0] = pcbddc->adaptive_threshold[0];
9275:   pcbddcf->adaptive_threshold[1] = pcbddc->adaptive_threshold[1];
9276:   pcbddcf->adaptive_nmin         = pcbddc->adaptive_nmin;
9277:   pcbddcf->adaptive_nmax         = pcbddc->adaptive_nmax;
9278:   pcbddcf->use_faces             = PETSC_TRUE;
9279:   pcbddcf->use_change_of_basis   = (PetscBool)!constraints;
9280:   pcbddcf->use_change_on_faces   = (PetscBool)!constraints;
9281:   pcbddcf->use_qr_single         = (PetscBool)!constraints;
9282:   pcbddcf->fake_change           = PETSC_TRUE;
9283:   pcbddcf->dbg_flag              = pcbddc->dbg_flag;

9285:   PetscCall(PCBDDCAdaptiveSelection(pcf));
9286:   PetscCall(PCBDDCConstraintsSetUp(pcf));

9288:   *change = pcbddcf->ConstraintMatrix;
9289:   if (change_primal) PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc->pmat), pcbddcf->local_primal_size_cc, pcbddcf->local_primal_ref_node, PETSC_COPY_VALUES, change_primal));
9290:   if (change_primal_mult) PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc->pmat), pcbddcf->local_primal_size_cc, pcbddcf->local_primal_ref_mult, PETSC_COPY_VALUES, change_primal_mult));
9291:   if (change_with_qr) *change_with_qr = pcbddcf->use_qr_single;

9293:   if (schurs) pcbddcf->sub_schurs = NULL;
9294:   pcbddcf->ConstraintMatrix = NULL;
9295:   pcbddcf->mat_graph        = NULL;
9296:   pcisf->is_B_local         = NULL;
9297:   pcisf->vec1_N             = NULL;
9298:   pcisf->BtoNmap            = NULL;
9299:   PetscCall(PCDestroy(&pcf));
9300:   PetscFunctionReturn(PETSC_SUCCESS);
9301: }

9303: PetscErrorCode PCBDDCSetUpSubSchurs(PC pc)
9304: {
9305:   PC_IS          *pcis       = (PC_IS *)pc->data;
9306:   PC_BDDC        *pcbddc     = (PC_BDDC *)pc->data;
9307:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
9308:   Mat             S_j;
9309:   PetscInt       *used_xadj, *used_adjncy;
9310:   PetscBool       free_used_adj;

9312:   PetscFunctionBegin;
9313:   PetscCall(PetscLogEventBegin(PC_BDDC_Schurs[pcbddc->current_level], pc, 0, 0, 0));
9314:   /* decide the adjacency to be used for determining internal problems for local schur on subsets */
9315:   free_used_adj = PETSC_FALSE;
9316:   if (pcbddc->sub_schurs_layers == -1) {
9317:     used_xadj   = NULL;
9318:     used_adjncy = NULL;
9319:   } else {
9320:     if (pcbddc->sub_schurs_use_useradj && pcbddc->mat_graph->xadj) {
9321:       used_xadj   = pcbddc->mat_graph->xadj;
9322:       used_adjncy = pcbddc->mat_graph->adjncy;
9323:     } else if (pcbddc->computed_rowadj) {
9324:       used_xadj   = pcbddc->mat_graph->xadj;
9325:       used_adjncy = pcbddc->mat_graph->adjncy;
9326:     } else {
9327:       PetscBool       flg_row = PETSC_FALSE;
9328:       const PetscInt *xadj, *adjncy;
9329:       PetscInt        nvtxs;

9331:       PetscCall(MatGetRowIJ(pcbddc->local_mat, 0, PETSC_TRUE, PETSC_FALSE, &nvtxs, &xadj, &adjncy, &flg_row));
9332:       if (flg_row) {
9333:         PetscCall(PetscMalloc2(nvtxs + 1, &used_xadj, xadj[nvtxs], &used_adjncy));
9334:         PetscCall(PetscArraycpy(used_xadj, xadj, nvtxs + 1));
9335:         PetscCall(PetscArraycpy(used_adjncy, adjncy, xadj[nvtxs]));
9336:         free_used_adj = PETSC_TRUE;
9337:       } else {
9338:         pcbddc->sub_schurs_layers = -1;
9339:         used_xadj                 = NULL;
9340:         used_adjncy               = NULL;
9341:       }
9342:       PetscCall(MatRestoreRowIJ(pcbddc->local_mat, 0, PETSC_TRUE, PETSC_FALSE, &nvtxs, &xadj, &adjncy, &flg_row));
9343:     }
9344:   }

9346:   /* setup sub_schurs data */
9347:   PetscCall(MatCreateSchurComplement(pcis->A_II, pcis->pA_II, pcis->A_IB, pcis->A_BI, pcis->A_BB, &S_j));
9348:   if (!sub_schurs->schur_explicit) {
9349:     /* pcbddc->ksp_D up to date only if not using MatFactor with Schur complement support */
9350:     PetscCall(MatSchurComplementSetKSP(S_j, pcbddc->ksp_D));
9351:     PetscCall(PCBDDCSubSchursSetUp(sub_schurs, NULL, S_j, PETSC_FALSE, used_xadj, used_adjncy, pcbddc->sub_schurs_layers, NULL, pcbddc->adaptive_selection, PETSC_FALSE, PETSC_FALSE, 0, NULL, NULL, NULL, NULL));
9352:   } else {
9353:     Mat       change        = NULL;
9354:     Vec       scaling       = NULL;
9355:     IS        change_primal = NULL, iP;
9356:     PetscInt  benign_n;
9357:     PetscBool reuse_solvers     = (PetscBool)!pcbddc->use_change_of_basis;
9358:     PetscBool need_change       = PETSC_FALSE;
9359:     PetscBool discrete_harmonic = PETSC_FALSE;

9361:     if (!pcbddc->use_vertices && reuse_solvers) {
9362:       PetscInt n_vertices;

9364:       PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_vertices));
9365:       reuse_solvers = (PetscBool)!n_vertices;
9366:     }
9367:     if (!pcbddc->benign_change_explicit) {
9368:       benign_n = pcbddc->benign_n;
9369:     } else {
9370:       benign_n = 0;
9371:     }
9372:     /* sub_schurs->change is a local object; instead, PCBDDCConstraintsSetUp and the quantities used in the test below are logically collective on pc.
9373:        We need a global reduction to avoid possible deadlocks.
9374:        We assume that sub_schurs->change is created once, and then reused for different solves, unless the topography has been recomputed */
9375:     if (pcbddc->adaptive_userdefined || (pcbddc->deluxe_zerorows && !pcbddc->use_change_of_basis)) {
9376:       PetscBool have_loc_change = (PetscBool)(!!sub_schurs->change);
9377:       PetscCallMPI(MPIU_Allreduce(&have_loc_change, &need_change, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)pc)));
9378:       need_change = (PetscBool)(!need_change);
9379:     }
9380:     /* If the user defines additional constraints, we import them here */
9381:     if (need_change) {
9382:       PetscCheck(!pcbddc->sub_schurs_rebuild, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot compute change of basis with a different graph");
9383:       PetscCall(PCBDDCComputeFakeChange(pc, PETSC_FALSE, NULL, NULL, &change, &change_primal, NULL, &sub_schurs->change_with_qr));
9384:     }
9385:     if (!pcbddc->use_deluxe_scaling) scaling = pcis->D;

9387:     PetscCall(PetscObjectQuery((PetscObject)pc, "__KSPFETIDP_iP", (PetscObject *)&iP));
9388:     if (iP) {
9389:       PetscOptionsBegin(PetscObjectComm((PetscObject)iP), sub_schurs->prefix, "BDDC sub_schurs options", "PC");
9390:       PetscCall(PetscOptionsBool("-sub_schurs_discrete_harmonic", NULL, NULL, discrete_harmonic, &discrete_harmonic, NULL));
9391:       PetscOptionsEnd();
9392:     }
9393:     if (discrete_harmonic) {
9394:       Mat A;
9395:       PetscCall(MatDuplicate(pcbddc->local_mat, MAT_COPY_VALUES, &A));
9396:       PetscCall(MatZeroRowsColumnsIS(A, iP, 1.0, NULL, NULL));
9397:       PetscCall(PetscObjectCompose((PetscObject)A, "__KSPFETIDP_iP", (PetscObject)iP));
9398:       PetscCall(PCBDDCSubSchursSetUp(sub_schurs, A, S_j, pcbddc->sub_schurs_exact_schur, used_xadj, used_adjncy, pcbddc->sub_schurs_layers, scaling, pcbddc->adaptive_selection, reuse_solvers, pcbddc->benign_saddle_point, benign_n, pcbddc->benign_p0_lidx,
9399:                                      pcbddc->benign_zerodiag_subs, change, change_primal));
9400:       PetscCall(MatDestroy(&A));
9401:     } else {
9402:       PetscCall(PCBDDCSubSchursSetUp(sub_schurs, pcbddc->local_mat, S_j, pcbddc->sub_schurs_exact_schur, used_xadj, used_adjncy, pcbddc->sub_schurs_layers, scaling, pcbddc->adaptive_selection, reuse_solvers, pcbddc->benign_saddle_point, benign_n,
9403:                                      pcbddc->benign_p0_lidx, pcbddc->benign_zerodiag_subs, change, change_primal));
9404:     }
9405:     PetscCall(MatDestroy(&change));
9406:     PetscCall(ISDestroy(&change_primal));
9407:   }
9408:   PetscCall(MatDestroy(&S_j));

9410:   /* free adjacency */
9411:   if (free_used_adj) PetscCall(PetscFree2(used_xadj, used_adjncy));
9412:   PetscCall(PetscLogEventEnd(PC_BDDC_Schurs[pcbddc->current_level], pc, 0, 0, 0));
9413:   PetscFunctionReturn(PETSC_SUCCESS);
9414: }

9416: PetscErrorCode PCBDDCInitSubSchurs(PC pc)
9417: {
9418:   PC_IS      *pcis   = (PC_IS *)pc->data;
9419:   PC_BDDC    *pcbddc = (PC_BDDC *)pc->data;
9420:   PCBDDCGraph graph;

9422:   PetscFunctionBegin;
9423:   /* attach interface graph for determining subsets */
9424:   if (pcbddc->sub_schurs_rebuild) { /* in case rebuild has been requested, it uses a graph generated only by the neighbouring information */
9425:     IS       verticesIS, verticescomm;
9426:     PetscInt vsize, *idxs;

9428:     PetscCall(PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &verticesIS));
9429:     PetscCall(ISGetSize(verticesIS, &vsize));
9430:     PetscCall(ISGetIndices(verticesIS, (const PetscInt **)&idxs));
9431:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), vsize, idxs, PETSC_COPY_VALUES, &verticescomm));
9432:     PetscCall(ISRestoreIndices(verticesIS, (const PetscInt **)&idxs));
9433:     PetscCall(PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &verticesIS));
9434:     PetscCall(PCBDDCGraphCreate(&graph));
9435:     PetscCall(PCBDDCGraphInit(graph, pcbddc->mat_graph->l2gmap, pcbddc->mat_graph->nvtxs_global, pcbddc->graphmaxcount));
9436:     PetscCall(PCBDDCGraphSetUp(graph, pcbddc->mat_graph->custom_minimal_size, NULL, pcbddc->DirichletBoundariesLocal, 0, NULL, verticescomm));
9437:     PetscCall(ISDestroy(&verticescomm));
9438:     PetscCall(PCBDDCGraphComputeConnectedComponents(graph));
9439:   } else {
9440:     graph = pcbddc->mat_graph;
9441:   }
9442:   /* print some info */
9443:   if (pcbddc->dbg_flag && !pcbddc->sub_schurs_rebuild) {
9444:     IS       vertices;
9445:     PetscInt nv, nedges, nfaces;
9446:     PetscCall(PCBDDCGraphASCIIView(graph, pcbddc->dbg_flag, pcbddc->dbg_viewer));
9447:     PetscCall(PCBDDCGraphGetCandidatesIS(graph, &nfaces, NULL, &nedges, NULL, &vertices));
9448:     PetscCall(ISGetSize(vertices, &nv));
9449:     PetscCall(PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer));
9450:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "--------------------------------------------------------------\n"));
9451:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d got %02" PetscInt_FMT " local candidate vertices (%d)\n", PetscGlobalRank, nv, pcbddc->use_vertices));
9452:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d got %02" PetscInt_FMT " local candidate edges    (%d)\n", PetscGlobalRank, nedges, pcbddc->use_edges));
9453:     PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d got %02" PetscInt_FMT " local candidate faces    (%d)\n", PetscGlobalRank, nfaces, pcbddc->use_faces));
9454:     PetscCall(PetscViewerFlush(pcbddc->dbg_viewer));
9455:     PetscCall(PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer));
9456:     PetscCall(PCBDDCGraphRestoreCandidatesIS(graph, &nfaces, NULL, &nedges, NULL, &vertices));
9457:   }

9459:   /* sub_schurs init */
9460:   if (!pcbddc->sub_schurs) PetscCall(PCBDDCSubSchursCreate(&pcbddc->sub_schurs));
9461:   PetscCall(PCBDDCSubSchursInit(pcbddc->sub_schurs, ((PetscObject)pc)->prefix, pcis->is_I_local, pcis->is_B_local, graph, pcis->BtoNmap, pcbddc->sub_schurs_rebuild, PETSC_FALSE));

9463:   /* free graph struct */
9464:   if (pcbddc->sub_schurs_rebuild) PetscCall(PCBDDCGraphDestroy(&graph));
9465:   PetscFunctionReturn(PETSC_SUCCESS);
9466: }

9468: static PetscErrorCode PCBDDCViewGlobalIS(PC pc, IS is, PetscViewer viewer)
9469: {
9470:   Mat_IS         *matis = (Mat_IS *)pc->pmat->data;
9471:   PetscInt        n     = pc->pmat->rmap->n, ln, ni, st;
9472:   const PetscInt *idxs;
9473:   IS              gis;

9475:   PetscFunctionBegin;
9476:   if (!is) PetscFunctionReturn(PETSC_SUCCESS);
9477:   PetscCall(MatGetOwnershipRange(pc->pmat, &st, NULL));
9478:   PetscCall(MatGetLocalSize(matis->A, NULL, &ln));
9479:   PetscCall(PetscArrayzero(matis->sf_leafdata, ln));
9480:   PetscCall(PetscArrayzero(matis->sf_rootdata, n));
9481:   PetscCall(ISGetLocalSize(is, &ni));
9482:   PetscCall(ISGetIndices(is, &idxs));
9483:   for (PetscInt i = 0; i < ni; i++) {
9484:     if (idxs[i] < 0 || idxs[i] >= ln) continue;
9485:     matis->sf_leafdata[idxs[i]] = 1;
9486:   }
9487:   PetscCall(ISRestoreIndices(is, &idxs));
9488:   PetscCall(PetscSFReduceBegin(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_SUM));
9489:   PetscCall(PetscSFReduceEnd(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_SUM));
9490:   ln = 0;
9491:   for (PetscInt i = 0; i < n; i++) {
9492:     if (matis->sf_rootdata[i]) matis->sf_rootdata[ln++] = i + st;
9493:   }
9494:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), ln, matis->sf_rootdata, PETSC_USE_POINTER, &gis));
9495:   PetscCall(ISView(gis, viewer));
9496:   PetscCall(ISDestroy(&gis));
9497:   PetscFunctionReturn(PETSC_SUCCESS);
9498: }

9500: PetscErrorCode PCBDDCLoadOrViewCustomization(PC pc, PetscBool load, const char *outfile)
9501: {
9502:   PetscInt    header[11];
9503:   PC_BDDC    *pcbddc = (PC_BDDC *)pc->data;
9504:   PetscViewer viewer;
9505:   MPI_Comm    comm = PetscObjectComm((PetscObject)pc);

9507:   PetscFunctionBegin;
9508:   PetscCall(PetscViewerBinaryOpen(comm, outfile ? outfile : "bddc_dump.dat", load ? FILE_MODE_READ : FILE_MODE_WRITE, &viewer));
9509:   if (load) {
9510:     IS  is;
9511:     Mat A;

9513:     PetscCall(PetscViewerBinaryRead(viewer, header, PETSC_STATIC_ARRAY_LENGTH(header), NULL, PETSC_INT));
9514:     PetscCheck(header[0] == 0 || header[0] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9515:     PetscCheck(header[1] == 0 || header[1] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9516:     PetscCheck(header[2] >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9517:     PetscCheck(header[3] == 0 || header[3] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9518:     PetscCheck(header[4] == 0 || header[4] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9519:     PetscCheck(header[5] >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9520:     PetscCheck(header[7] == 0 || header[7] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9521:     PetscCheck(header[8] == 0 || header[8] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9522:     PetscCheck(header[9] == 0 || header[9] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9523:     PetscCheck(header[10] == 0 || header[10] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a BDDC dump next in file");
9524:     if (header[0]) {
9525:       PetscCall(ISCreate(comm, &is));
9526:       PetscCall(ISLoad(is, viewer));
9527:       PetscCall(PCBDDCSetDirichletBoundaries(pc, is));
9528:       PetscCall(ISDestroy(&is));
9529:     }
9530:     if (header[1]) {
9531:       PetscCall(ISCreate(comm, &is));
9532:       PetscCall(ISLoad(is, viewer));
9533:       PetscCall(PCBDDCSetNeumannBoundaries(pc, is));
9534:       PetscCall(ISDestroy(&is));
9535:     }
9536:     if (header[2]) {
9537:       IS *isarray;

9539:       PetscCall(PetscMalloc1(header[2], &isarray));
9540:       for (PetscInt i = 0; i < header[2]; i++) {
9541:         PetscCall(ISCreate(comm, &isarray[i]));
9542:         PetscCall(ISLoad(isarray[i], viewer));
9543:       }
9544:       PetscCall(PCBDDCSetDofsSplitting(pc, header[2], isarray));
9545:       for (PetscInt i = 0; i < header[2]; i++) PetscCall(ISDestroy(&isarray[i]));
9546:       PetscCall(PetscFree(isarray));
9547:     }
9548:     if (header[3]) {
9549:       PetscCall(ISCreate(comm, &is));
9550:       PetscCall(ISLoad(is, viewer));
9551:       PetscCall(PCBDDCSetPrimalVerticesIS(pc, is));
9552:       PetscCall(ISDestroy(&is));
9553:     }
9554:     if (header[4]) {
9555:       PetscCall(MatCreate(comm, &A));
9556:       PetscCall(MatSetType(A, MATAIJ));
9557:       PetscCall(MatLoad(A, viewer));
9558:       PetscCall(PCBDDCSetDiscreteGradient(pc, A, header[5], header[6], (PetscBool)header[7], (PetscBool)header[8]));
9559:       PetscCall(MatDestroy(&A));
9560:     }
9561:     if (header[9]) {
9562:       PetscCall(MatCreate(comm, &A));
9563:       PetscCall(MatSetType(A, MATIS));
9564:       PetscCall(MatLoad(A, viewer));
9565:       PetscCall(PCBDDCSetDivergenceMat(pc, A, (PetscBool)header[10], NULL));
9566:       PetscCall(MatDestroy(&A));
9567:     }
9568:   } else {
9569:     header[0]  = (PetscInt)!!pcbddc->DirichletBoundariesLocal;
9570:     header[1]  = (PetscInt)!!pcbddc->NeumannBoundariesLocal;
9571:     header[2]  = pcbddc->n_ISForDofsLocal;
9572:     header[3]  = (PetscInt)!!pcbddc->user_primal_vertices_local;
9573:     header[4]  = (PetscInt)!!pcbddc->discretegradient;
9574:     header[5]  = pcbddc->nedorder;
9575:     header[6]  = pcbddc->nedfield;
9576:     header[7]  = (PetscInt)pcbddc->nedglobal;
9577:     header[8]  = (PetscInt)pcbddc->conforming;
9578:     header[9]  = (PetscInt)!!pcbddc->divudotp;
9579:     header[10] = (PetscInt)pcbddc->divudotp_trans;
9580:     if (header[4]) header[3] = 0;

9582:     PetscCall(PetscViewerBinaryWrite(viewer, header, PETSC_STATIC_ARRAY_LENGTH(header), PETSC_INT));
9583:     PetscCall(PCBDDCViewGlobalIS(pc, pcbddc->DirichletBoundariesLocal, viewer));
9584:     PetscCall(PCBDDCViewGlobalIS(pc, pcbddc->NeumannBoundariesLocal, viewer));
9585:     for (PetscInt i = 0; i < header[2]; i++) PetscCall(PCBDDCViewGlobalIS(pc, pcbddc->ISForDofsLocal[i], viewer));
9586:     if (header[3]) PetscCall(PCBDDCViewGlobalIS(pc, pcbddc->user_primal_vertices_local, viewer));
9587:     if (header[4]) PetscCall(MatView(pcbddc->discretegradient, viewer));
9588:     if (header[9]) PetscCall(MatView(pcbddc->divudotp, viewer));
9589:   }
9590:   PetscCall(PetscViewerDestroy(&viewer));
9591:   PetscFunctionReturn(PETSC_SUCCESS);
9592: }

9594: #include <../src/mat/impls/aij/mpi/mpiaij.h>
9595: static PetscErrorCode MatMPIAIJRestrict(Mat A, MPI_Comm ccomm, Mat *B)
9596: {
9597:   Mat         At;
9598:   IS          rows;
9599:   PetscInt    rst, ren;
9600:   PetscLayout rmap;

9602:   PetscFunctionBegin;
9603:   rst = ren = 0;
9604:   if (ccomm != MPI_COMM_NULL) {
9605:     PetscCall(PetscLayoutCreate(ccomm, &rmap));
9606:     PetscCall(PetscLayoutSetSize(rmap, A->rmap->N));
9607:     PetscCall(PetscLayoutSetBlockSize(rmap, 1));
9608:     PetscCall(PetscLayoutSetUp(rmap));
9609:     PetscCall(PetscLayoutGetRange(rmap, &rst, &ren));
9610:   }
9611:   PetscCall(ISCreateStride(PetscObjectComm((PetscObject)A), ren - rst, rst, 1, &rows));
9612:   PetscCall(MatCreateSubMatrix(A, rows, NULL, MAT_INITIAL_MATRIX, &At));
9613:   PetscCall(ISDestroy(&rows));

9615:   if (ccomm != MPI_COMM_NULL) {
9616:     Mat_MPIAIJ *a, *b;
9617:     IS          from, to;
9618:     Vec         gvec;
9619:     PetscInt    lsize;

9621:     PetscCall(MatCreate(ccomm, B));
9622:     PetscCall(MatSetSizes(*B, ren - rst, PETSC_DECIDE, PETSC_DECIDE, At->cmap->N));
9623:     PetscCall(MatSetType(*B, MATAIJ));
9624:     PetscCall(PetscLayoutDestroy(&(*B)->rmap));
9625:     PetscCall(PetscLayoutSetUp((*B)->cmap));
9626:     a = (Mat_MPIAIJ *)At->data;
9627:     b = (Mat_MPIAIJ *)(*B)->data;
9628:     PetscCallMPI(MPI_Comm_size(ccomm, &b->size));
9629:     PetscCallMPI(MPI_Comm_rank(ccomm, &b->rank));
9630:     PetscCall(PetscObjectReference((PetscObject)a->A));
9631:     PetscCall(PetscObjectReference((PetscObject)a->B));
9632:     b->A = a->A;
9633:     b->B = a->B;

9635:     b->donotstash   = a->donotstash;
9636:     b->roworiented  = a->roworiented;
9637:     b->rowindices   = NULL;
9638:     b->rowvalues    = NULL;
9639:     b->getrowactive = PETSC_FALSE;

9641:     (*B)->rmap         = rmap;
9642:     (*B)->factortype   = A->factortype;
9643:     (*B)->assembled    = PETSC_TRUE;
9644:     (*B)->insertmode   = NOT_SET_VALUES;
9645:     (*B)->preallocated = PETSC_TRUE;

9647:     if (a->colmap) {
9648: #if defined(PETSC_USE_CTABLE)
9649:       PetscCall(PetscHMapIDuplicate(a->colmap, &b->colmap));
9650: #else
9651:       PetscCall(PetscMalloc1(At->cmap->N, &b->colmap));
9652:       PetscCall(PetscArraycpy(b->colmap, a->colmap, At->cmap->N));
9653: #endif
9654:     } else b->colmap = NULL;
9655:     if (a->garray) {
9656:       PetscInt len;
9657:       len = a->B->cmap->n;
9658:       PetscCall(PetscMalloc1(len + 1, &b->garray));
9659:       if (len) PetscCall(PetscArraycpy(b->garray, a->garray, len));
9660:     } else b->garray = NULL;

9662:     PetscCall(PetscObjectReference((PetscObject)a->lvec));
9663:     b->lvec = a->lvec;

9665:     /* cannot use VecScatterCopy */
9666:     PetscCall(VecGetLocalSize(b->lvec, &lsize));
9667:     PetscCall(ISCreateGeneral(ccomm, lsize, b->garray, PETSC_USE_POINTER, &from));
9668:     PetscCall(ISCreateStride(PETSC_COMM_SELF, lsize, 0, 1, &to));
9669:     PetscCall(MatCreateVecs(*B, &gvec, NULL));
9670:     PetscCall(VecScatterCreate(gvec, from, b->lvec, to, &b->Mvctx));
9671:     PetscCall(ISDestroy(&from));
9672:     PetscCall(ISDestroy(&to));
9673:     PetscCall(VecDestroy(&gvec));
9674:   }
9675:   PetscCall(MatDestroy(&At));
9676:   PetscFunctionReturn(PETSC_SUCCESS);
9677: }

9679: /* same as MatCreateSubMatrix(A, rows, NULL,...) but allows repeated rows */
9680: static PetscErrorCode MatAIJExtractRows(Mat A, IS rows, Mat *sA)
9681: {
9682:   PetscBool isaij;
9683:   MPI_Comm  comm;

9685:   PetscFunctionBegin;
9686:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
9687:   PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)A, &isaij, MATSEQAIJ, MATMPIAIJ, ""));
9688:   PetscCheck(isaij, comm, PETSC_ERR_SUP, "Not implemented");
9689:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQAIJ, &isaij));
9690:   if (isaij) { /* SeqAIJ supports repeated rows */
9691:     PetscCall(MatCreateSubMatrix(A, rows, NULL, MAT_INITIAL_MATRIX, sA));
9692:   } else {
9693:     Mat                A_loc;
9694:     Mat_SeqAIJ        *da;
9695:     PetscSF            sf;
9696:     PetscInt           ni, *di, *dj, m = A->rmap->n, c, *ldata, *rdata;
9697:     PetscScalar       *daa;
9698:     const PetscInt    *idxs;
9699:     const PetscSFNode *iremotes;
9700:     PetscSFNode       *remotes;

9702:     /* SF for incoming rows */
9703:     PetscCall(PetscSFCreate(comm, &sf));
9704:     PetscCall(ISGetLocalSize(rows, &ni));
9705:     PetscCall(ISGetIndices(rows, &idxs));
9706:     PetscCall(PetscSFSetGraphLayout(sf, A->rmap, ni, NULL, PETSC_USE_POINTER, idxs));
9707:     PetscCall(ISRestoreIndices(rows, &idxs));

9709:     PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));
9710:     da = (Mat_SeqAIJ *)A_loc->data;
9711:     PetscCall(PetscMalloc2(2 * ni, &ldata, 2 * m, &rdata));
9712:     for (PetscInt i = 0; i < m; i++) {
9713:       rdata[2 * i + 0] = da->i[i + 1] - da->i[i];
9714:       rdata[2 * i + 1] = da->i[i];
9715:     }
9716:     PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, rdata, ldata, MPI_REPLACE));
9717:     PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, rdata, ldata, MPI_REPLACE));
9718:     PetscCall(PetscMalloc1(ni + 1, &di));
9719:     di[0] = 0;
9720:     for (PetscInt i = 0; i < ni; i++) di[i + 1] = di[i] + ldata[2 * i + 0];
9721:     PetscCall(PetscMalloc1(di[ni], &dj));
9722:     PetscCall(PetscMalloc1(di[ni], &daa));
9723:     PetscCall(PetscMalloc1(di[ni], &remotes));

9725:     PetscCall(PetscSFGetGraph(sf, NULL, NULL, NULL, &iremotes));

9727:     /* SF graph for nonzeros */
9728:     c = 0;
9729:     for (PetscInt i = 0; i < ni; i++) {
9730:       const PetscInt rank  = iremotes[i].rank;
9731:       const PetscInt rsize = ldata[2 * i];
9732:       for (PetscInt j = 0; j < rsize; j++) {
9733:         remotes[c].rank  = rank;
9734:         remotes[c].index = ldata[2 * i + 1] + j;
9735:         c++;
9736:       }
9737:     }
9738:     PetscCheck(c == di[ni], PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of local nonzeros %" PetscInt_FMT " != %" PetscInt_FMT, c, di[ni]);
9739:     PetscCall(PetscSFSetGraph(sf, da->i[m], di[ni], NULL, PETSC_USE_POINTER, remotes, PETSC_USE_POINTER));
9740:     PetscCall(PetscSFBcastBegin(sf, MPIU_INT, da->j, dj, MPI_REPLACE));
9741:     PetscCall(PetscSFBcastEnd(sf, MPIU_INT, da->j, dj, MPI_REPLACE));
9742:     PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, da->a, daa, MPI_REPLACE));
9743:     PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, da->a, daa, MPI_REPLACE));

9745:     PetscCall(MatCreateMPIAIJWithArrays(comm, ni, A->cmap->n, PETSC_DECIDE, A->cmap->N, di, dj, daa, sA));
9746:     PetscCall(MatDestroy(&A_loc));
9747:     PetscCall(PetscSFDestroy(&sf));
9748:     PetscCall(PetscFree(di));
9749:     PetscCall(PetscFree(dj));
9750:     PetscCall(PetscFree(daa));
9751:     PetscCall(PetscFree(remotes));
9752:     PetscCall(PetscFree2(ldata, rdata));
9753:   }
9754:   PetscFunctionReturn(PETSC_SUCCESS);
9755: }