Actual source code: geo.c

  1: /*
  2:  GAMG geometric-algebric multiogrid 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 (((GAMGNode *)a)->degree - ((GAMGNode *)b)->degree);
 25: }

 27: /*
 28:    PCSetCoordinates_GEO

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

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

 47:   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);

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

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

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

 77: /*
 78:    PCSetData_GEO

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

 89: /*
 90:    PCSetFromOptions_GEO

 92:   Input Parameter:
 93:    . pc -
 94: */
 95: PetscErrorCode PCSetFromOptions_GEO(PC pc, PetscOptionItems *PetscOptionsObject)
 96: {
 97:   PetscFunctionBegin;
 98:   PetscOptionsHeadBegin(PetscOptionsObject, "GAMG-GEO options");
 99:   {
100:     /* -pc_gamg_sa_nsmooths */
101:     /* pc_gamg_sa->smooths = 0; */
102:     /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
103:     /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
104:     /*                        "PCGAMGSetNSmooths_AGG", */
105:     /*                        pc_gamg_sa->smooths, */
106:     /*                        &pc_gamg_sa->smooths, */
107:     /*                        &flag);  */
108:   }
109:   PetscOptionsHeadEnd();
110:   PetscFunctionReturn(PETSC_SUCCESS);
111: }

113: /*
114:  triangulateAndFormProl

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

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

165:   for (kk = 0, sid = 0; kk < nselected_2; kk++, sid += 2) {
166:     PetscInt lid          = selected_idx_2[kk];
167:     in.pointlist[sid]     = coords[lid];
168:     in.pointlist[sid + 1] = coords[data_stride + lid];
169:     if (lid >= nFineLoc) nPlotPts++;
170:   }
171:   PetscCheck(sid == 2 * nselected_2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "sid %d != 2*nselected_2 %" PetscInt_FMT, sid, nselected_2);

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

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

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

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

237:       /* elems */
238:       PetscCall(PetscSNPrintf(fname, PETSC_STATIC_ARRAY_LENGTH(fname), "C%d_%d.ele", level, rank));
239:       file = fopen(fname, "w");
240:       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
241:       fprintf(file, "%d %d %d\n", mid.numberoftriangles, 3, 0);
242:       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
243:       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]);
244:       fclose(file);

246:       PetscCall(PetscSNPrintf(fname, PETSC_STATIC_ARRAY_LENGTH(fname), "C%d_%d.node", level, rank));
247:       file = fopen(fname, "w");
248:       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
249:       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
250:       fprintf(file, "%d  %d  %d  %d\n", nPlotPts, 2, 0, 0);
251:       /*Following lines: <vertex #> <x> <y> */
252:       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]);

254:       sid /= 2;
255:       for (jj = 0; jj < nFineLoc; jj++) {
256:         PetscBool sel = PETSC_TRUE;
257:         for (kk = 0; kk < nselected_2 && sel; kk++) {
258:           PetscInt lid = selected_idx_2[kk];
259:           if (lid == jj) sel = PETSC_FALSE;
260:         }
261:         if (sel) fprintf(file, "%d %e %e\n", sid++, coords[jj], coords[data_stride + jj]);
262:       }
263:       fclose(file);
264:       PetscCheck(sid == nPlotPts, PETSC_COMM_SELF, PETSC_ERR_PLIB, "sid %d != nPlotPts %d", sid, nPlotPts);
265:       level++;
266:     }
267:   }
268:   { /* form P - setup some maps */
269:     PetscInt clid, mm, *nTri, *node_tri;

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

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

293:         PetscCall(PetscCDGetHeadPos(agg_lists_1, lid, &pos));
294:         while (pos) {
295:           PetscInt flid;
296:           PetscCall(PetscCDIntNdGetID(pos, &flid));
297:           PetscCall(PetscCDGetNextPos(agg_lists_1, lid, &pos));

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

309:             /* look for it */
310:             for (tid = node_tri[clid], jj = 0; jj < 5 && !haveit && tid != -1; jj++) {
311:               for (tt = 0; tt < 3; tt++) {
312:                 PetscInt cid2 = mid.trianglelist[3 * tid + tt];
313:                 PetscInt lid2 = selected_idx_2[cid2];
314:                 AA[tt][0]     = coords[lid2];
315:                 AA[tt][1]     = coords[data_stride + lid2];
316:                 AA[tt][2]     = 1.0;
317:                 clids[tt]     = cid2; /* store for interp */
318:               }

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

322:               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
323:               PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
324:               {
325:                 PetscBool have   = PETSC_TRUE;
326:                 PetscReal lowest = 1.e10;
327:                 for (tt = 0, idx = 0; tt < 3; tt++) {
328:                   if (PetscRealPart(alpha[tt]) > (1.0 + EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
329:                   if (PetscRealPart(alpha[tt]) < lowest) {
330:                     lowest = PetscRealPart(alpha[tt]);
331:                     idx    = tt;
332:                   }
333:                 }
334:                 haveit = have;
335:               }
336:               tid = mid.neighborlist[3 * tid + idx];
337:             }

339:             if (!haveit) {
340:               /* brute force */
341:               for (tid = 0; tid < mid.numberoftriangles && !haveit; tid++) {
342:                 for (tt = 0; tt < 3; tt++) {
343:                   PetscInt cid2 = mid.trianglelist[3 * tid + tt];
344:                   PetscInt lid2 = selected_idx_2[cid2];
345:                   AA[tt][0]     = coords[lid2];
346:                   AA[tt][1]     = coords[data_stride + lid2];
347:                   AA[tt][2]     = 1.0;
348:                   clids[tt]     = cid2; /* store for interp */
349:                 }
350:                 for (tt = 0; tt < 3; tt++) alpha[tt] = fcoord[tt];
351:                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
352:                 PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
353:                 {
354:                   PetscBool have  = PETSC_TRUE;
355:                   PetscReal worst = 0.0, v;
356:                   for (tt = 0; tt < 3 && have; tt++) {
357:                     if (PetscRealPart(alpha[tt]) > 1.0 + EPS || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
358:                     if ((v = PetscAbs(PetscRealPart(alpha[tt]) - 0.5)) > worst) worst = v;
359:                   }
360:                   if (worst < best_alpha) {
361:                     best_alpha = worst;
362:                     bestTID    = tid;
363:                   }
364:                   haveit = have;
365:                 }
366:               }
367:             }
368:             if (!haveit) {
369:               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
370:               /* use best one */
371:               for (tt = 0; tt < 3; tt++) {
372:                 PetscInt cid2 = mid.trianglelist[3 * bestTID + tt];
373:                 PetscInt lid2 = selected_idx_2[cid2];
374:                 AA[tt][0]     = coords[lid2];
375:                 AA[tt][1]     = coords[data_stride + lid2];
376:                 AA[tt][2]     = 1.0;
377:                 clids[tt]     = cid2; /* store for interp */
378:               }
379:               for (tt = 0; tt < 3; tt++) alpha[tt] = fcoord[tt];
380:               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
381:               PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
382:             }

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

399:     PetscCall(ISRestoreIndices(selected_2, &selected_idx_2));
400:     PetscCall(MatAssemblyBegin(a_Prol, MAT_FINAL_ASSEMBLY));
401:     PetscCall(MatAssemblyEnd(a_Prol, MAT_FINAL_ASSEMBLY));

403:     PetscCall(PetscFree2(node_tri, nTri));
404:   }
405:   free(mid.trianglelist);
406:   free(mid.neighborlist);
407:   free(mid.segmentlist);
408:   free(mid.segmentmarkerlist);
409:   free(mid.pointlist);
410:   free(mid.pointmarkerlist);
411:   PetscCall(PetscFree(in.pointlist));
412:   PetscFunctionReturn(PETSC_SUCCESS);
413: #else
414:   SETERRQ(PetscObjectComm((PetscObject)a_Prol), PETSC_ERR_PLIB, "configure with TRIANGLE to use geometric MG");
415: #endif
416: }

418: /*
419:    getGIDsOnSquareGraph - square graph, get

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

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

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

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

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

508:       if (a_selected_2 != NULL) { /* output */
509:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, (nselected_1 + num_crs_ghost), selected_set, PETSC_OWN_POINTER, a_selected_2));
510:       } else {
511:         PetscCall(PetscFree(selected_set));
512:       }
513:     }
514:     PetscCall(VecDestroy(&locState));
515:   }
516:   *a_crsGID = crsGID; /* output */
517:   PetscFunctionReturn(PETSC_SUCCESS);
518: }

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

526:   PetscFunctionBegin;
527:   PetscCall(MatCreateGraph(Amat, PETSC_TRUE, PETSC_TRUE, vfilter, a_Gmat));
528:   PetscFunctionReturn(PETSC_SUCCESS);
529: }

531: /*
532:    PCGAMGCoarsen_GEO

534:   Input Parameter:
535:    . a_pc - this
536:    . a_Gmat - graph
537:   Output Parameter:
538:    . a_llist_parent - linked list from selected indices for data locality only
539: */
540: PetscErrorCode PCGAMGCoarsen_GEO(PC a_pc, Mat *a_Gmat, PetscCoarsenData **a_llist_parent)
541: {
542:   PetscInt   Istart, Iend, nloc, kk, Ii, ncols;
543:   IS         perm;
544:   GAMGNode  *gnodes;
545:   PetscInt  *permute;
546:   Mat        Gmat = *a_Gmat;
547:   MPI_Comm   comm;
548:   MatCoarsen crs;

550:   PetscFunctionBegin;
551:   PetscCall(PetscObjectGetComm((PetscObject)a_pc, &comm));

553:   PetscCall(MatGetOwnershipRange(Gmat, &Istart, &Iend));
554:   nloc = (Iend - Istart);

556:   /* create random permutation with sort for geo-mg */
557:   PetscCall(PetscMalloc1(nloc, &gnodes));
558:   PetscCall(PetscMalloc1(nloc, &permute));

560:   for (Ii = Istart; Ii < Iend; Ii++) { /* locals only? */
561:     PetscCall(MatGetRow(Gmat, Ii, &ncols, NULL, NULL));
562:     {
563:       PetscInt lid       = Ii - Istart;
564:       gnodes[lid].lid    = lid;
565:       gnodes[lid].degree = ncols;
566:     }
567:     PetscCall(MatRestoreRow(Gmat, Ii, &ncols, NULL, NULL));
568:   }
569:   if (PETSC_TRUE) {
570:     PetscRandom rand;
571:     PetscBool  *bIndexSet;
572:     PetscReal   rr;
573:     PetscInt    iSwapIndex;

575:     PetscCall(PetscRandomCreate(comm, &rand));
576:     PetscCall(PetscCalloc1(nloc, &bIndexSet));
577:     for (Ii = 0; Ii < nloc; Ii++) {
578:       PetscCall(PetscRandomGetValueReal(rand, &rr));
579:       iSwapIndex = (PetscInt)(rr * nloc);
580:       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
581:         GAMGNode iTemp        = gnodes[iSwapIndex];
582:         gnodes[iSwapIndex]    = gnodes[Ii];
583:         gnodes[Ii]            = iTemp;
584:         bIndexSet[Ii]         = PETSC_TRUE;
585:         bIndexSet[iSwapIndex] = PETSC_TRUE;
586:       }
587:     }
588:     PetscCall(PetscRandomDestroy(&rand));
589:     PetscCall(PetscFree(bIndexSet));
590:   }
591:   /* only sort locals */
592:   qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
593:   /* create IS of permutation */
594:   for (kk = 0; kk < nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
595:   PetscCall(PetscFree(gnodes));
596:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm));

598:   /* get MIS aggs */

600:   PetscCall(MatCoarsenCreate(comm, &crs));
601:   PetscCall(MatCoarsenSetType(crs, MATCOARSENMIS));
602:   PetscCall(MatCoarsenSetGreedyOrdering(crs, perm));
603:   PetscCall(MatCoarsenSetAdjacency(crs, Gmat));
604:   PetscCall(MatCoarsenSetStrictAggs(crs, PETSC_FALSE));
605:   PetscCall(MatCoarsenApply(crs));
606:   PetscCall(MatCoarsenGetData(crs, a_llist_parent));
607:   PetscCall(MatCoarsenDestroy(&crs));

609:   PetscCall(ISDestroy(&perm));

611:   PetscFunctionReturn(PETSC_SUCCESS);
612: }

614: /*
615:  PCGAMGProlongator_GEO

617:  Input Parameter:
618:  . pc - this
619:  . Amat - matrix on this fine level
620:  . Graph - used to get ghost data for nodes in
621:  . selected_1 - [nselected]
622:  . agg_lists - [nselected]
623:  Output Parameter:
624:  . a_P_out - prolongation operator to the next level
625:  */
626: PetscErrorCode PCGAMGProlongator_GEO(PC pc, Mat Amat, Mat Gmat, PetscCoarsenData *agg_lists, Mat *a_P_out)
627: {
628:   PC_MG          *mg      = (PC_MG *)pc->data;
629:   PC_GAMG        *pc_gamg = (PC_GAMG *)mg->innerctx;
630:   const PetscInt  dim = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
631:   PetscInt        Istart, Iend, nloc, my0, jj, kk, ncols, nLocalSelected, bs, *clid_flid;
632:   Mat             Prol;
633:   PetscMPIInt     rank, size;
634:   MPI_Comm        comm;
635:   IS              selected_2, selected_1;
636:   const PetscInt *selected_idx;
637:   MatType         mtype;

639:   PetscFunctionBegin;
640:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));

642:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
643:   PetscCallMPI(MPI_Comm_size(comm, &size));
644:   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
645:   PetscCall(MatGetBlockSize(Amat, &bs));
646:   nloc = (Iend - Istart) / bs;
647:   my0  = Istart / bs;
648:   PetscCheck((Iend - Istart) % bs == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "(Iend %" PetscInt_FMT " - Istart %" PetscInt_FMT ") %% bs %" PetscInt_FMT, Iend, Istart, bs);

650:   /* get 'nLocalSelected' */
651:   PetscCall(PetscCDGetMIS(agg_lists, &selected_1));
652:   PetscCall(ISGetSize(selected_1, &jj));
653:   PetscCall(PetscMalloc1(jj, &clid_flid));
654:   PetscCall(ISGetIndices(selected_1, &selected_idx));
655:   for (kk = 0, nLocalSelected = 0; kk < jj; kk++) {
656:     PetscInt lid = selected_idx[kk];
657:     if (lid < nloc) {
658:       PetscCall(MatGetRow(Gmat, lid + my0, &ncols, NULL, NULL));
659:       if (ncols > 1) clid_flid[nLocalSelected++] = lid; /* filter out singletons */
660:       PetscCall(MatRestoreRow(Gmat, lid + my0, &ncols, NULL, NULL));
661:     }
662:   }
663:   PetscCall(ISRestoreIndices(selected_1, &selected_idx));
664:   PetscCall(ISDestroy(&selected_1)); /* this is selected_1 in serial */

666:   /* create prolongator  matrix */
667:   PetscCall(MatGetType(Amat, &mtype));
668:   PetscCall(MatCreate(comm, &Prol));
669:   PetscCall(MatSetSizes(Prol, nloc * bs, nLocalSelected * bs, PETSC_DETERMINE, PETSC_DETERMINE));
670:   PetscCall(MatSetBlockSizes(Prol, bs, bs));
671:   PetscCall(MatSetType(Prol, mtype));
672:   PetscCall(MatSeqAIJSetPreallocation(Prol, 3 * data_cols, NULL));
673:   PetscCall(MatMPIAIJSetPreallocation(Prol, 3 * data_cols, NULL, 3 * data_cols, NULL));

675:   /* can get all points "removed" - but not on geomg */
676:   PetscCall(MatGetSize(Prol, &kk, &jj));
677:   if (!jj) {
678:     PetscCall(PetscInfo(pc, "ERROE: no selected points on coarse grid\n"));
679:     PetscCall(PetscFree(clid_flid));
680:     PetscCall(MatDestroy(&Prol));
681:     *a_P_out = NULL; /* out */
682:     PetscFunctionReturn(PETSC_SUCCESS);
683:   }

685:   {
686:     PetscReal *coords;
687:     PetscInt   data_stride;
688:     PetscInt  *crsGID = NULL;
689:     Mat        Gmat2;

691:     PetscCheck(dim == data_cols, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim %" PetscInt_FMT " != data_cols %" PetscInt_FMT, dim, data_cols);
692:     /* grow ghost data for better coarse grid cover of fine grid */
693:     /* messy method, squares graph and gets some data */
694:     PetscCall(getGIDsOnSquareGraph(pc, nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID));
695:     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
696:     /* create global vector of coorindates in 'coords' */
697:     if (size > 1) {
698:       PetscCall(PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords));
699:     } else {
700:       coords      = (PetscReal *)pc_gamg->data;
701:       data_stride = pc_gamg->data_sz / pc_gamg->data_cell_cols;
702:     }
703:     PetscCall(MatDestroy(&Gmat2));

705:     /* triangulate */
706:     {
707:       PetscReal metric, tm;

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

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

716:       PetscCall(MPIU_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, comm));
717:       if (tm > 1.) { /* needs to be globalized - should not happen */
718:         PetscCall(PetscInfo(pc, " failed metric for coarse grid %e\n", (double)tm));
719:         PetscCall(MatDestroy(&Prol));
720:       } else if (metric > .0) {
721:         PetscCall(PetscInfo(pc, "worst metric for coarse grid = %e\n", (double)metric));
722:       }
723:     }
724:     { /* create next coords - output */
725:       PetscReal *crs_crds;
726:       PetscCall(PetscMalloc1(dim * nLocalSelected, &crs_crds));
727:       for (kk = 0; kk < nLocalSelected; kk++) { /* grab local select nodes to promote - output */
728:         PetscInt lid = clid_flid[kk];
729:         for (jj = 0; jj < dim; jj++) crs_crds[jj * nLocalSelected + kk] = pc_gamg->data[jj * nloc + lid];
730:       }

732:       PetscCall(PetscFree(pc_gamg->data));
733:       pc_gamg->data    = crs_crds; /* out */
734:       pc_gamg->data_sz = dim * nLocalSelected;
735:     }
736:     PetscCall(ISDestroy(&selected_2));
737:   }

739:   *a_P_out = Prol; /* out */
740:   PetscCall(PetscFree(clid_flid));

742:   PetscFunctionReturn(PETSC_SUCCESS);
743: }

745: static PetscErrorCode PCDestroy_GAMG_GEO(PC pc)
746: {
747:   PetscFunctionBegin;
748:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
749:   PetscFunctionReturn(PETSC_SUCCESS);
750: }

752: /*
753:  PCCreateGAMG_GEO

755:   Input Parameter:
756:    . pc -
757: */
758: PetscErrorCode PCCreateGAMG_GEO(PC pc)
759: {
760:   PC_MG   *mg      = (PC_MG *)pc->data;
761:   PC_GAMG *pc_gamg = (PC_GAMG *)mg->innerctx;

763:   PetscFunctionBegin;
764:   pc_gamg->ops->setfromoptions = PCSetFromOptions_GEO;
765:   pc_gamg->ops->destroy        = PCDestroy_GAMG_GEO;
766:   /* reset does not do anything; setup not virtual */

768:   /* set internal function pointers */
769:   pc_gamg->ops->creategraph       = PCGAMGCreateGraph_GEO;
770:   pc_gamg->ops->coarsen           = PCGAMGCoarsen_GEO;
771:   pc_gamg->ops->prolongator       = PCGAMGProlongator_GEO;
772:   pc_gamg->ops->optprolongator    = NULL;
773:   pc_gamg->ops->createdefaultdata = PCSetData_GEO;

775:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_GEO));
776:   PetscFunctionReturn(PETSC_SUCCESS);
777: }