Actual source code: geo.c

  1: /*
  2:  GAMG geometric-algebraic multigrid PC - Mark Adams 2011
  3:  */

  5: #include <../src/ksp/pc/impls/gamg/gamg.h>

  7: #if defined(PETSC_HAVE_TRIANGLE)
  8:   #if !defined(ANSI_DECLARATORS)
  9:     #define ANSI_DECLARATORS
 10:   #endif
 11:   #include <triangle.h>
 12: #endif

 14: #include <petscblaslapack.h>

 16: /* Private context for the GAMG preconditioner */
 17: typedef struct {
 18:   PetscInt lid;    /* local vertex index */
 19:   PetscInt degree; /* vertex degree */
 20: } GAMGNode;

 22: static inline int petsc_geo_mg_compare(const void *a, const void *b)
 23: {
 24:   return (int)(((GAMGNode *)a)->degree - ((GAMGNode *)b)->degree);
 25: }

 27: // PetscClangLinter pragma disable: -fdoc-sowing-chars
 28: /*
 29:    PCSetCoordinates_GEO

 31:    Input Parameter:
 32:    .  pc - the preconditioner context
 33: */
 34: static PetscErrorCode PCSetCoordinates_GEO(PC pc, PetscInt ndm, PetscInt a_nloc, PetscReal *coords)
 35: {
 36:   PC_MG   *mg      = (PC_MG *)pc->data;
 37:   PC_GAMG *pc_gamg = (PC_GAMG *)mg->innerctx;
 38:   PetscInt arrsz, bs, my0, kk, ii, nloc, Iend, aloc;
 39:   Mat      Amat = pc->pmat;

 41:   PetscFunctionBegin;
 43:   PetscCall(MatGetBlockSize(Amat, &bs));
 44:   PetscCall(MatGetOwnershipRange(Amat, &my0, &Iend));
 45:   aloc = (Iend - my0);
 46:   nloc = (Iend - my0) / bs;

 48:   PetscCheck(nloc == a_nloc || aloc == a_nloc, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of local blocks %" PetscInt_FMT " must be %" PetscInt_FMT " or %" PetscInt_FMT ".", a_nloc, nloc, aloc);

 50:   pc_gamg->data_cell_rows = 1;
 51:   PetscCheck(coords || (nloc <= 0), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Need coordinates for pc_gamg_type 'geo'.");
 52:   pc_gamg->data_cell_cols = ndm; /* coordinates */

 54:   arrsz = nloc * pc_gamg->data_cell_rows * pc_gamg->data_cell_cols;

 56:   /* create data - syntactic sugar that should be refactored at some point */
 57:   if (!pc_gamg->data || (pc_gamg->data_sz != arrsz)) {
 58:     PetscCall(PetscFree(pc_gamg->data));
 59:     PetscCall(PetscMalloc1(arrsz + 1, &pc_gamg->data));
 60:   }
 61:   for (kk = 0; kk < arrsz; kk++) pc_gamg->data[kk] = -999.;
 62:   pc_gamg->data[arrsz] = -99.;
 63:   /* copy data in - column-oriented */
 64:   if (nloc == a_nloc) {
 65:     for (kk = 0; kk < nloc; kk++) {
 66:       for (ii = 0; ii < ndm; ii++) pc_gamg->data[ii * nloc + kk] = coords[kk * ndm + ii];
 67:     }
 68:   } else { /* assumes the coordinates are blocked */
 69:     for (kk = 0; kk < nloc; kk++) {
 70:       for (ii = 0; ii < ndm; ii++) pc_gamg->data[ii * nloc + kk] = coords[bs * kk * ndm + ii];
 71:     }
 72:   }
 73:   PetscCheck(pc_gamg->data[arrsz] == -99., PETSC_COMM_SELF, PETSC_ERR_PLIB, "pc_gamg->data[arrsz %" PetscInt_FMT "] %g != -99.", arrsz, (double)pc_gamg->data[arrsz]);
 74:   pc_gamg->data_sz = arrsz;
 75:   PetscFunctionReturn(PETSC_SUCCESS);
 76: }

 78: // PetscClangLinter pragma disable: -fdoc-sowing-chars
 79: /*
 80:    PCSetData_GEO

 82:   Input Parameter:
 83:    . pc -
 84: */
 85: static PetscErrorCode PCSetData_GEO(PC pc, Mat m)
 86: {
 87:   PetscFunctionBegin;
 88:   SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "GEO MG needs coordinates");
 89: }

 91: static PetscErrorCode PCSetFromOptions_GEO(PC pc, PetscOptionItems *PetscOptionsObject)
 92: {
 93:   PetscFunctionBegin;
 94:   PetscOptionsHeadBegin(PetscOptionsObject, "GAMG-GEO options");
 95:   {
 96:     /* -pc_gamg_sa_nsmooths */
 97:     /* pc_gamg_sa->smooths = 0; */
 98:     /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
 99:     /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
100:     /*                        "PCGAMGSetNSmooths_AGG", */
101:     /*                        pc_gamg_sa->smooths, */
102:     /*                        &pc_gamg_sa->smooths, */
103:     /*                        &flag);  */
104:   }
105:   PetscOptionsHeadEnd();
106:   PetscFunctionReturn(PETSC_SUCCESS);
107: }

109: // PetscClangLinter pragma disable: -fdoc-sowing-chars
110: /*
111:  triangulateAndFormProl

113:    Input Parameter:
114:    . selected_2 - list of selected local ID, includes selected ghosts
115:    . data_stride -
116:    . coords[2*data_stride] - column vector of local coordinates w/ ghosts
117:    . nselected_1 - selected IDs that go with base (1) graph includes selected ghosts
118:    . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
119:    . agg_lists_1 - list of aggregates selected_1 vertices of aggregate unselected vertices
120:    . crsGID[selected.size()] - global index for prolongation operator
121:    . bs - block size
122:   Output Parameter:
123:    . a_Prol - prolongation operator
124:    . a_worst_best - measure of worst missed fine vertex, 0 is no misses
125: */
126: static PetscErrorCode triangulateAndFormProl(IS selected_2, PetscInt data_stride, PetscReal coords[], PetscInt nselected_1, const PetscInt clid_lid_1[], const PetscCoarsenData *agg_lists_1, const PetscInt crsGID[], PetscInt bs, Mat a_Prol, PetscReal *a_worst_best)
127: {
128: #if defined(PETSC_HAVE_TRIANGLE)
129:   PetscInt             jj, tid, tt, idx, nselected_2;
130:   struct triangulateio in, mid;
131:   const PetscInt      *selected_idx_2;
132:   PetscMPIInt          rank;
133:   PetscInt             Istart, Iend, nFineLoc, myFine0;
134:   int                  kk, nPlotPts, sid;
135:   MPI_Comm             comm;
136:   PetscReal            tm;

138:   PetscFunctionBegin;
139:   PetscCall(PetscObjectGetComm((PetscObject)a_Prol, &comm));
140:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
141:   PetscCall(ISGetSize(selected_2, &nselected_2));
142:   if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
143:     *a_worst_best = 100.0;                    /* this will cause a stop, but not globalized (should not happen) */
144:   } else *a_worst_best = 0.0;
145:   PetscCallMPI(MPIU_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, comm));
146:   if (tm > 0.0) {
147:     *a_worst_best = 100.0;
148:     PetscFunctionReturn(PETSC_SUCCESS);
149:   }
150:   PetscCall(MatGetOwnershipRange(a_Prol, &Istart, &Iend));
151:   nFineLoc = (Iend - Istart) / bs;
152:   myFine0  = Istart / bs;
153:   PetscCall(PetscCIntCast(nFineLoc, &nPlotPts)); /* locals */
154:   /* triangle */
155:   /* Define input points - in */
156:   PetscCall(PetscCIntCast(nselected_2, &in.numberofpoints));
157:   in.numberofpointattributes = 0;
158:   /* get nselected points */
159:   PetscCall(PetscMalloc1(2 * nselected_2, &in.pointlist));
160:   PetscCall(ISGetIndices(selected_2, &selected_idx_2));

162:   for (kk = 0, sid = 0; kk < nselected_2; kk++, sid += 2) {
163:     PetscInt lid          = selected_idx_2[kk];
164:     in.pointlist[sid]     = coords[lid];
165:     in.pointlist[sid + 1] = coords[data_stride + lid];
166:     if (lid >= nFineLoc) nPlotPts++;
167:   }
168:   PetscCheck(sid == 2 * nselected_2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "sid %d != 2*nselected_2 %" PetscInt_FMT, sid, nselected_2);

170:   in.numberofsegments      = 0;
171:   in.numberofedges         = 0;
172:   in.numberofholes         = 0;
173:   in.numberofregions       = 0;
174:   in.trianglelist          = NULL;
175:   in.segmentmarkerlist     = NULL;
176:   in.pointattributelist    = NULL;
177:   in.pointmarkerlist       = NULL;
178:   in.triangleattributelist = NULL;
179:   in.trianglearealist      = NULL;
180:   in.segmentlist           = NULL;
181:   in.holelist              = NULL;
182:   in.regionlist            = NULL;
183:   in.edgelist              = NULL;
184:   in.edgemarkerlist        = NULL;
185:   in.normlist              = NULL;

187:   /* triangulate */
188:   mid.pointlist = NULL; /* Not needed if -N switch used. */
189:   /* Not needed if -N switch used or number of point attributes is zero: */
190:   mid.pointattributelist = NULL;
191:   mid.pointmarkerlist    = NULL; /* Not needed if -N or -B switch used. */
192:   mid.trianglelist       = NULL; /* Not needed if -E switch used. */
193:   /* Not needed if -E switch used or number of triangle attributes is zero: */
194:   mid.triangleattributelist = NULL;
195:   mid.neighborlist          = NULL; /* Needed only if -n switch used. */
196:   /* Needed only if segments are output (-p or -c) and -P not used: */
197:   mid.segmentlist = NULL;
198:   /* Needed only if segments are output (-p or -c) and -P and -B not used: */
199:   mid.segmentmarkerlist = NULL;
200:   mid.edgelist          = NULL; /* Needed only if -e switch used. */
201:   mid.edgemarkerlist    = NULL; /* Needed if -e used and -B not used. */
202:   mid.numberoftriangles = 0;

204:   /* Triangulate the points.  Switches are chosen to read and write a  */
205:   /*   PSLG (p), preserve the convex hull (c), number everything from  */
206:   /*   zero (z), assign a regional attribute to each element (A), and  */
207:   /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
208:   /*   neighbor list (n).                                            */
209:   if (nselected_2 != 0) {  /* inactive processor */
210:     char args[] = "npczQ"; /* c is needed ? */
211:     triangulate(args, &in, &mid, (struct triangulateio *)NULL);
212:     /* output .poly files for 'showme' */
213:     if (!PETSC_TRUE) {
214:       static int level = 1;
215:       FILE      *file;
216:       char       fname[32];

218:       PetscCall(PetscSNPrintf(fname, PETSC_STATIC_ARRAY_LENGTH(fname), "C%d_%d.poly", level, rank));
219:       file = fopen(fname, "w");
220:       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
221:       fprintf(file, "%d  %d  %d  %d\n", in.numberofpoints, 2, 0, 0);
222:       /* Following lines: <vertex #> <x> <y> */
223:       for (kk = 0, sid = 0; kk < in.numberofpoints; kk++, sid += 2) fprintf(file, "%d %e %e\n", kk, in.pointlist[sid], in.pointlist[sid + 1]);
224:       /* One line: <# of segments> <# of boundary markers (0 or 1)> */
225:       fprintf(file, "%d  %d\n", 0, 0);
226:       /* Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
227:       /* One line: <# of holes> */
228:       fprintf(file, "%d\n", 0);
229:       /* Following lines: <hole #> <x> <y> */
230:       /* Optional line: <# of regional attributes and/or area constraints> */
231:       /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
232:       fclose(file);

234:       /* elems */
235:       PetscCall(PetscSNPrintf(fname, PETSC_STATIC_ARRAY_LENGTH(fname), "C%d_%d.ele", level, rank));
236:       file = fopen(fname, "w");
237:       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
238:       fprintf(file, "%d %d %d\n", mid.numberoftriangles, 3, 0);
239:       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
240:       for (kk = 0, sid = 0; kk < mid.numberoftriangles; kk++, sid += 3) fprintf(file, "%d %d %d %d\n", kk, mid.trianglelist[sid], mid.trianglelist[sid + 1], mid.trianglelist[sid + 2]);
241:       fclose(file);

243:       PetscCall(PetscSNPrintf(fname, PETSC_STATIC_ARRAY_LENGTH(fname), "C%d_%d.node", level, rank));
244:       file = fopen(fname, "w");
245:       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
246:       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
247:       fprintf(file, "%d  %d  %d  %d\n", nPlotPts, 2, 0, 0);
248:       /* Following lines: <vertex #> <x> <y> */
249:       for (kk = 0, sid = 0; kk < in.numberofpoints; kk++, sid += 2) fprintf(file, "%d %e %e\n", kk, in.pointlist[sid], in.pointlist[sid + 1]);

251:       sid /= 2;
252:       for (jj = 0; jj < nFineLoc; jj++) {
253:         PetscBool sel = PETSC_TRUE;
254:         for (kk = 0; kk < nselected_2 && sel; kk++) {
255:           PetscInt lid = selected_idx_2[kk];
256:           if (lid == jj) sel = PETSC_FALSE;
257:         }
258:         if (sel) fprintf(file, "%d %e %e\n", sid++, coords[jj], coords[data_stride + jj]);
259:       }
260:       fclose(file);
261:       PetscCheck(sid == nPlotPts, PETSC_COMM_SELF, PETSC_ERR_PLIB, "sid %d != nPlotPts %d", sid, nPlotPts);
262:       level++;
263:     }
264:   }
265:   { /* form P - setup some maps */
266:     PetscInt clid, mm, *nTri, *node_tri;

268:     PetscCall(PetscMalloc2(nselected_2, &node_tri, nselected_2, &nTri));

270:     /* need list of triangles on node */
271:     for (kk = 0; kk < nselected_2; kk++) nTri[kk] = 0;
272:     for (tid = 0, kk = 0; tid < mid.numberoftriangles; tid++) {
273:       for (jj = 0; jj < 3; jj++) {
274:         PetscInt cid = mid.trianglelist[kk++];
275:         if (nTri[cid] == 0) node_tri[cid] = tid;
276:         nTri[cid]++;
277:       }
278:     }
279:   #define EPS 1.e-12
280:     /* find points and set prolongation */
281:     for (mm = clid = 0; mm < nFineLoc; mm++) {
282:       PetscBool ise;
283:       PetscCall(PetscCDIsEmptyAt(agg_lists_1, mm, &ise));
284:       if (!ise) {
285:         const PetscInt lid = mm;
286:         PetscScalar    AA[3][3];
287:         PetscBLASInt   N = 3, NRHS = 1, LDA = 3, IPIV[3], LDB = 3, INFO;
288:         PetscCDIntNd  *pos;

290:         PetscCall(PetscCDGetHeadPos(agg_lists_1, lid, &pos));
291:         while (pos) {
292:           PetscInt flid;
293:           PetscCall(PetscCDIntNdGetID(pos, &flid));
294:           PetscCall(PetscCDGetNextPos(agg_lists_1, lid, &pos));

296:           if (flid < nFineLoc) { /* could be a ghost */
297:             PetscInt       bestTID    = -1;
298:             PetscReal      best_alpha = 1.e10;
299:             const PetscInt fgid       = flid + myFine0;
300:             /* compute shape function for gid */
301:             const PetscReal fcoord[3] = {coords[flid], coords[data_stride + flid], 1.0};
302:             PetscBool       haveit    = PETSC_FALSE;
303:             PetscScalar     alpha[3];
304:             PetscInt        clids[3];

306:             /* look for it */
307:             for (tid = node_tri[clid], jj = 0; jj < 5 && !haveit && tid != -1; jj++) {
308:               for (tt = 0; tt < 3; tt++) {
309:                 PetscInt cid2 = mid.trianglelist[3 * tid + tt];
310:                 PetscInt lid2 = selected_idx_2[cid2];
311:                 AA[tt][0]     = coords[lid2];
312:                 AA[tt][1]     = coords[data_stride + lid2];
313:                 AA[tt][2]     = 1.0;
314:                 clids[tt]     = cid2; /* store for interp */
315:               }

317:               for (tt = 0; tt < 3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];

319:               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
320:               PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
321:               {
322:                 PetscBool have   = PETSC_TRUE;
323:                 PetscReal lowest = 1.e10;
324:                 for (tt = 0, idx = 0; tt < 3; tt++) {
325:                   if (PetscRealPart(alpha[tt]) > (1.0 + EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
326:                   if (PetscRealPart(alpha[tt]) < lowest) {
327:                     lowest = PetscRealPart(alpha[tt]);
328:                     idx    = tt;
329:                   }
330:                 }
331:                 haveit = have;
332:               }
333:               tid = mid.neighborlist[3 * tid + idx];
334:             }

336:             if (!haveit) {
337:               /* brute force */
338:               for (tid = 0; tid < mid.numberoftriangles && !haveit; tid++) {
339:                 for (tt = 0; tt < 3; tt++) {
340:                   PetscInt cid2 = mid.trianglelist[3 * tid + tt];
341:                   PetscInt lid2 = selected_idx_2[cid2];
342:                   AA[tt][0]     = coords[lid2];
343:                   AA[tt][1]     = coords[data_stride + lid2];
344:                   AA[tt][2]     = 1.0;
345:                   clids[tt]     = cid2; /* store for interp */
346:                 }
347:                 for (tt = 0; tt < 3; tt++) alpha[tt] = fcoord[tt];
348:                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
349:                 PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
350:                 {
351:                   PetscBool have  = PETSC_TRUE;
352:                   PetscReal worst = 0.0, v;
353:                   for (tt = 0; tt < 3 && have; tt++) {
354:                     if (PetscRealPart(alpha[tt]) > 1.0 + EPS || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
355:                     if ((v = PetscAbs(PetscRealPart(alpha[tt]) - 0.5)) > worst) worst = v;
356:                   }
357:                   if (worst < best_alpha) {
358:                     best_alpha = worst;
359:                     bestTID    = tid;
360:                   }
361:                   haveit = have;
362:                 }
363:               }
364:             }
365:             if (!haveit) {
366:               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
367:               /* use best one */
368:               for (tt = 0; tt < 3; tt++) {
369:                 PetscInt cid2 = mid.trianglelist[3 * bestTID + tt];
370:                 PetscInt lid2 = selected_idx_2[cid2];
371:                 AA[tt][0]     = coords[lid2];
372:                 AA[tt][1]     = coords[data_stride + lid2];
373:                 AA[tt][2]     = 1.0;
374:                 clids[tt]     = cid2; /* store for interp */
375:               }
376:               for (tt = 0; tt < 3; tt++) alpha[tt] = fcoord[tt];
377:               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
378:               PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
379:             }

381:             /* put in row of P */
382:             for (idx = 0; idx < 3; idx++) {
383:               PetscScalar shp = alpha[idx];
384:               if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
385:                 PetscInt cgid = crsGID[clids[idx]];
386:                 PetscInt jj = cgid * bs, ii = fgid * bs; /* need to gloalize */
387:                 for (tt = 0; tt < bs; tt++, ii++, jj++) PetscCall(MatSetValues(a_Prol, 1, &ii, 1, &jj, &shp, INSERT_VALUES));
388:               }
389:             }
390:           }
391:         } /* aggregates iterations */
392:         clid++;
393:       } /* a coarse agg */
394:     } /* for all fine nodes */

396:     PetscCall(ISRestoreIndices(selected_2, &selected_idx_2));
397:     PetscCall(MatAssemblyBegin(a_Prol, MAT_FINAL_ASSEMBLY));
398:     PetscCall(MatAssemblyEnd(a_Prol, MAT_FINAL_ASSEMBLY));

400:     PetscCall(PetscFree2(node_tri, nTri));
401:   }
402:   free(mid.trianglelist);
403:   free(mid.neighborlist);
404:   free(mid.segmentlist);
405:   free(mid.segmentmarkerlist);
406:   free(mid.pointlist);
407:   free(mid.pointmarkerlist);
408:   PetscCall(PetscFree(in.pointlist));
409:   PetscFunctionReturn(PETSC_SUCCESS);
410: #else
411:   SETERRQ(PetscObjectComm((PetscObject)a_Prol), PETSC_ERR_PLIB, "configure with TRIANGLE to use geometric MG");
412: #endif
413: }

415: // PetscClangLinter pragma disable: -fdoc-sowing-chars
416: /*
417:    getGIDsOnSquareGraph - square graph, get

419:    Input Parameter:
420:    . nselected_1 - selected local indices (includes ghosts in input Gmat1)
421:    . clid_lid_1 - [nselected_1] lids of selected nodes
422:    . Gmat1 - graph that goes with 'selected_1'
423:    Output Parameter:
424:    . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
425:    . a_Gmat_2 - graph that is squared of 'Gmat_1'
426:    . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
427: */
428: static PetscErrorCode getGIDsOnSquareGraph(PC pc, PetscInt nselected_1, const PetscInt clid_lid_1[], const Mat Gmat1, IS *a_selected_2, Mat *a_Gmat_2, PetscInt **a_crsGID)
429: {
430:   PetscMPIInt size;
431:   PetscInt   *crsGID, kk, my0, Iend, nloc;
432:   MPI_Comm    comm;

434:   PetscFunctionBegin;
435:   PetscCall(PetscObjectGetComm((PetscObject)Gmat1, &comm));
436:   PetscCallMPI(MPI_Comm_size(comm, &size));
437:   PetscCall(MatGetOwnershipRange(Gmat1, &my0, &Iend)); /* AIJ */
438:   nloc = Iend - my0;                                   /* this does not change */

440:   if (size == 1) { /* not much to do in serial */
441:     PetscCall(PetscMalloc1(nselected_1, &crsGID));
442:     for (kk = 0; kk < nselected_1; kk++) crsGID[kk] = kk;
443:     *a_Gmat_2 = NULL;
444:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nselected_1, clid_lid_1, PETSC_COPY_VALUES, a_selected_2));
445:   } else {
446:     PetscInt     idx, num_fine_ghosts, num_crs_ghost, myCrs0;
447:     Mat_MPIAIJ  *mpimat2;
448:     Mat          Gmat2;
449:     Vec          locState;
450:     PetscScalar *cpcol_state;

452:     /* scan my coarse zero gid, set 'lid_state' with coarse GID */
453:     kk = nselected_1;
454:     PetscCallMPI(MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPI_SUM, comm));
455:     myCrs0 -= nselected_1;

457:     if (a_Gmat_2) { /* output */
458:       /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
459:       PetscCall(PCGAMGSquareGraph_GAMG(pc, Gmat1, &Gmat2));
460:       *a_Gmat_2 = Gmat2;  /* output */
461:     } else Gmat2 = Gmat1; /* use local to get crsGIDs at least */
462:     /* get coarse grid GIDS for selected (locals and ghosts) */
463:     mpimat2 = (Mat_MPIAIJ *)Gmat2->data;
464:     PetscCall(MatCreateVecs(Gmat2, &locState, NULL));
465:     PetscCall(VecSet(locState, -1)); /* set with UNKNOWN state */
466:     for (kk = 0; kk < nselected_1; kk++) {
467:       PetscInt    fgid = clid_lid_1[kk] + my0;
468:       PetscScalar v    = (PetscScalar)(kk + myCrs0);
469:       PetscCall(VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES)); /* set with PID */
470:     }
471:     PetscCall(VecAssemblyBegin(locState));
472:     PetscCall(VecAssemblyEnd(locState));
473:     PetscCall(VecScatterBegin(mpimat2->Mvctx, locState, mpimat2->lvec, INSERT_VALUES, SCATTER_FORWARD));
474:     PetscCall(VecScatterEnd(mpimat2->Mvctx, locState, mpimat2->lvec, INSERT_VALUES, SCATTER_FORWARD));
475:     PetscCall(VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts));
476:     PetscCall(VecGetArray(mpimat2->lvec, &cpcol_state));
477:     for (kk = 0, num_crs_ghost = 0; kk < num_fine_ghosts; kk++) {
478:       if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
479:     }
480:     PetscCall(PetscMalloc1(nselected_1 + num_crs_ghost, &crsGID)); /* output */
481:     {
482:       PetscInt *selected_set;
483:       PetscCall(PetscMalloc1(nselected_1 + num_crs_ghost, &selected_set));
484:       /* do ghost of 'crsGID' */
485:       for (kk = 0, idx = nselected_1; kk < num_fine_ghosts; kk++) {
486:         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
487:           PetscInt cgid     = (PetscInt)PetscRealPart(cpcol_state[kk]);
488:           selected_set[idx] = nloc + kk;
489:           crsGID[idx++]     = cgid;
490:         }
491:       }
492:       PetscCheck(idx == (nselected_1 + num_crs_ghost), PETSC_COMM_SELF, PETSC_ERR_PLIB, "idx %" PetscInt_FMT " != (nselected_1 %" PetscInt_FMT " + num_crs_ghost %" PetscInt_FMT ")", idx, nselected_1, num_crs_ghost);
493:       PetscCall(VecRestoreArray(mpimat2->lvec, &cpcol_state));
494:       /* do locals in 'crsGID' */
495:       PetscCall(VecGetArray(locState, &cpcol_state));
496:       for (kk = 0, idx = 0; kk < nloc; kk++) {
497:         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
498:           PetscInt cgid     = (PetscInt)PetscRealPart(cpcol_state[kk]);
499:           selected_set[idx] = kk;
500:           crsGID[idx++]     = cgid;
501:         }
502:       }
503:       PetscCheck(idx == nselected_1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "idx %" PetscInt_FMT " != nselected_1 %" PetscInt_FMT, idx, nselected_1);
504:       PetscCall(VecRestoreArray(locState, &cpcol_state));

506:       if (a_selected_2 != NULL) { /* output */
507:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nselected_1 + num_crs_ghost, selected_set, PETSC_OWN_POINTER, a_selected_2));
508:       } else {
509:         PetscCall(PetscFree(selected_set));
510:       }
511:     }
512:     PetscCall(VecDestroy(&locState));
513:   }
514:   *a_crsGID = crsGID; /* output */
515:   PetscFunctionReturn(PETSC_SUCCESS);
516: }

518: static PetscErrorCode PCGAMGCreateGraph_GEO(PC pc, Mat Amat, Mat *a_Gmat)
519: {
520:   PC_MG          *mg      = (PC_MG *)pc->data;
521:   PC_GAMG        *pc_gamg = (PC_GAMG *)mg->innerctx;
522:   const PetscReal vfilter = pc_gamg->threshold[0];

524:   PetscFunctionBegin;
525:   PetscCall(MatCreateGraph(Amat, PETSC_TRUE, PETSC_TRUE, vfilter, 0, NULL, a_Gmat));
526:   PetscFunctionReturn(PETSC_SUCCESS);
527: }

529: static PetscErrorCode PCGAMGCoarsen_GEO(PC a_pc, Mat *a_Gmat, PetscCoarsenData **a_llist_parent)
530: {
531:   PetscInt   Istart, Iend, nloc, kk, Ii, ncols;
532:   IS         perm;
533:   GAMGNode  *gnodes;
534:   PetscInt  *permute;
535:   Mat        Gmat = *a_Gmat;
536:   MPI_Comm   comm;
537:   MatCoarsen crs;

539:   PetscFunctionBegin;
540:   PetscCall(PetscObjectGetComm((PetscObject)a_pc, &comm));

542:   PetscCall(MatGetOwnershipRange(Gmat, &Istart, &Iend));
543:   nloc = (Iend - Istart);

545:   /* create random permutation with sort for geo-mg */
546:   PetscCall(PetscMalloc1(nloc, &gnodes));
547:   PetscCall(PetscMalloc1(nloc, &permute));

549:   for (Ii = Istart; Ii < Iend; Ii++) { /* locals only? */
550:     PetscCall(MatGetRow(Gmat, Ii, &ncols, NULL, NULL));
551:     {
552:       PetscInt lid       = Ii - Istart;
553:       gnodes[lid].lid    = lid;
554:       gnodes[lid].degree = ncols;
555:     }
556:     PetscCall(MatRestoreRow(Gmat, Ii, &ncols, NULL, NULL));
557:   }
558:   if (PETSC_TRUE) {
559:     PetscRandom rand;
560:     PetscBool  *bIndexSet;
561:     PetscReal   rr;
562:     PetscInt    iSwapIndex;

564:     PetscCall(PetscRandomCreate(comm, &rand));
565:     PetscCall(PetscCalloc1(nloc, &bIndexSet));
566:     for (Ii = 0; Ii < nloc; Ii++) {
567:       PetscCall(PetscRandomGetValueReal(rand, &rr));
568:       iSwapIndex = (PetscInt)(rr * nloc);
569:       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
570:         GAMGNode iTemp        = gnodes[iSwapIndex];
571:         gnodes[iSwapIndex]    = gnodes[Ii];
572:         gnodes[Ii]            = iTemp;
573:         bIndexSet[Ii]         = PETSC_TRUE;
574:         bIndexSet[iSwapIndex] = PETSC_TRUE;
575:       }
576:     }
577:     PetscCall(PetscRandomDestroy(&rand));
578:     PetscCall(PetscFree(bIndexSet));
579:   }
580:   /* only sort locals */
581:   if (gnodes) qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
582:   /* create IS of permutation */
583:   for (kk = 0; kk < nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
584:   PetscCall(PetscFree(gnodes));
585:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm));

587:   /* get MIS aggs */

589:   PetscCall(MatCoarsenCreate(comm, &crs));
590:   PetscCall(MatCoarsenSetType(crs, MATCOARSENMIS));
591:   PetscCall(MatCoarsenSetGreedyOrdering(crs, perm));
592:   PetscCall(MatCoarsenSetAdjacency(crs, Gmat));
593:   PetscCall(MatCoarsenSetStrictAggs(crs, PETSC_FALSE));
594:   PetscCall(MatCoarsenApply(crs));
595:   PetscCall(MatCoarsenGetData(crs, a_llist_parent));
596:   PetscCall(MatCoarsenDestroy(&crs));

598:   PetscCall(ISDestroy(&perm));
599:   PetscFunctionReturn(PETSC_SUCCESS);
600: }

602: static PetscErrorCode PCGAMGProlongator_GEO(PC pc, Mat Amat, PetscCoarsenData *agg_lists, Mat *a_P_out)
603: {
604:   PC_MG          *mg      = (PC_MG *)pc->data;
605:   PC_GAMG        *pc_gamg = (PC_GAMG *)mg->innerctx;
606:   const PetscInt  dim = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
607:   PetscInt        Istart, Iend, nloc, my0, jj, kk, ncols, nLocalSelected, bs, *clid_flid;
608:   Mat             Prol, Gmat;
609:   PetscMPIInt     rank, size;
610:   MPI_Comm        comm;
611:   IS              selected_2, selected_1;
612:   const PetscInt *selected_idx;
613:   MatType         mtype;

615:   PetscFunctionBegin;
616:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));

618:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
619:   PetscCallMPI(MPI_Comm_size(comm, &size));
620:   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
621:   PetscCall(MatGetBlockSize(Amat, &bs));
622:   nloc = (Iend - Istart) / bs;
623:   my0  = Istart / bs;
624:   PetscCheck((Iend - Istart) % bs == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "(Iend %" PetscInt_FMT " - Istart %" PetscInt_FMT ") %% bs %" PetscInt_FMT, Iend, Istart, bs);

626:   /* get 'nLocalSelected' */
627:   PetscCall(PetscCDGetMat(agg_lists, &Gmat)); // get auxiliary matrix for ghost edges
628:   PetscCall(PetscCDGetNonemptyIS(agg_lists, &selected_1));
629:   PetscCall(ISGetSize(selected_1, &jj));
630:   PetscCall(PetscMalloc1(jj, &clid_flid));
631:   PetscCall(ISGetIndices(selected_1, &selected_idx));
632:   for (kk = 0, nLocalSelected = 0; kk < jj; kk++) {
633:     PetscInt lid = selected_idx[kk];
634:     if (lid < nloc) {
635:       PetscCall(MatGetRow(Gmat, lid + my0, &ncols, NULL, NULL));
636:       if (ncols > 1) clid_flid[nLocalSelected++] = lid; /* filter out singletons */
637:       PetscCall(MatRestoreRow(Gmat, lid + my0, &ncols, NULL, NULL));
638:     }
639:   }
640:   PetscCall(ISRestoreIndices(selected_1, &selected_idx));
641:   PetscCall(ISDestroy(&selected_1)); /* this is selected_1 in serial */

643:   /* create prolongator  matrix */
644:   PetscCall(MatGetType(Amat, &mtype));
645:   PetscCall(MatCreate(comm, &Prol));
646:   PetscCall(MatSetSizes(Prol, nloc * bs, nLocalSelected * bs, PETSC_DETERMINE, PETSC_DETERMINE));
647:   PetscCall(MatSetBlockSizes(Prol, bs, bs));
648:   PetscCall(MatSetType(Prol, mtype));
649:   PetscCall(MatSeqAIJSetPreallocation(Prol, 3 * data_cols, NULL));
650:   PetscCall(MatMPIAIJSetPreallocation(Prol, 3 * data_cols, NULL, 3 * data_cols, NULL));

652:   /* can get all points "removed" - but not on geomg */
653:   PetscCall(MatGetSize(Prol, &kk, &jj));
654:   if (!jj) {
655:     PetscCall(PetscInfo(pc, "ERROE: no selected points on coarse grid\n"));
656:     PetscCall(PetscFree(clid_flid));
657:     PetscCall(MatDestroy(&Prol));
658:     *a_P_out = NULL; /* out */
659:     PetscFunctionReturn(PETSC_SUCCESS);
660:   }

662:   {
663:     PetscReal *coords;
664:     PetscInt   data_stride;
665:     PetscInt  *crsGID = NULL;
666:     Mat        Gmat2;

668:     PetscCheck(dim == data_cols, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim %" PetscInt_FMT " != data_cols %" PetscInt_FMT, dim, data_cols);
669:     /* grow ghost data for better coarse grid cover of fine grid */
670:     /* messy method, squares graph and gets some data */
671:     PetscCall(getGIDsOnSquareGraph(pc, nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID));
672:     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
673:     /* create global vector of coorindates in 'coords' */
674:     if (size > 1) {
675:       PetscCall(PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords));
676:     } else {
677:       coords      = pc_gamg->data;
678:       data_stride = pc_gamg->data_sz / pc_gamg->data_cell_cols;
679:     }
680:     PetscCall(MatDestroy(&Gmat2));
681:     /* triangulate */
682:     {
683:       PetscReal metric, tm;

685:       PetscCheck(dim == 2, comm, PETSC_ERR_PLIB, "3D not implemented for 'geo' AMG");
686:       PetscCall(triangulateAndFormProl(selected_2, data_stride, coords, nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric));
687:       PetscCall(PetscFree(crsGID));

689:       /* clean up and create coordinates for coarse grid (output) */
690:       if (size > 1) PetscCall(PetscFree(coords));

692:       PetscCallMPI(MPIU_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, comm));
693:       if (tm > 1.) { /* needs to be globalized - should not happen */
694:         PetscCall(PetscInfo(pc, " failed metric for coarse grid %e\n", (double)tm));
695:         PetscCall(MatDestroy(&Prol));
696:       } else if (metric > .0) {
697:         PetscCall(PetscInfo(pc, "worst metric for coarse grid = %e\n", (double)metric));
698:       }
699:     }
700:     { /* create next coords - output */
701:       PetscReal *crs_crds;
702:       PetscCall(PetscMalloc1(dim * nLocalSelected, &crs_crds));
703:       for (kk = 0; kk < nLocalSelected; kk++) { /* grab local select nodes to promote - output */
704:         PetscInt lid = clid_flid[kk];
705:         for (jj = 0; jj < dim; jj++) crs_crds[jj * nLocalSelected + kk] = pc_gamg->data[jj * nloc + lid];
706:       }

708:       PetscCall(PetscFree(pc_gamg->data));
709:       pc_gamg->data    = crs_crds; /* out */
710:       pc_gamg->data_sz = dim * nLocalSelected;
711:     }
712:     PetscCall(ISDestroy(&selected_2));
713:   }

715:   *a_P_out = Prol; /* out */
716:   PetscCall(PetscFree(clid_flid));
717:   PetscFunctionReturn(PETSC_SUCCESS);
718: }

720: static PetscErrorCode PCDestroy_GAMG_GEO(PC pc)
721: {
722:   PetscFunctionBegin;
723:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
724:   PetscFunctionReturn(PETSC_SUCCESS);
725: }

727: PetscErrorCode PCCreateGAMG_GEO(PC pc)
728: {
729:   PC_MG   *mg      = (PC_MG *)pc->data;
730:   PC_GAMG *pc_gamg = (PC_GAMG *)mg->innerctx;

732:   PetscFunctionBegin;
733:   pc_gamg->ops->setfromoptions = PCSetFromOptions_GEO;
734:   pc_gamg->ops->destroy        = PCDestroy_GAMG_GEO;
735:   /* reset does not do anything; setup not virtual */

737:   /* set internal function pointers */
738:   pc_gamg->ops->creategraph       = PCGAMGCreateGraph_GEO;
739:   pc_gamg->ops->coarsen           = PCGAMGCoarsen_GEO;
740:   pc_gamg->ops->prolongator       = PCGAMGProlongator_GEO;
741:   pc_gamg->ops->optprolongator    = NULL;
742:   pc_gamg->ops->createdefaultdata = PCSetData_GEO;

744:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_GEO));
745:   PetscFunctionReturn(PETSC_SUCCESS);
746: }