xref: /petsc/src/ksp/pc/impls/gamg/geo.c (revision 8fcddce65efd55a8fe3f87d4c08c15577ce4cbef)
1 /*
2  GAMG geometric-algebric multiogrid PC - Mark Adams 2011
3  */
4 
5 #include <../src/ksp/pc/impls/gamg/gamg.h>        /*I "petscpc.h" I*/
6 
7 #if defined(PETSC_HAVE_TRIANGLE)
8 #define REAL PetscReal
9 #include <triangle.h>
10 #endif
11 
12 #include <petscblaslapack.h>
13 
14 /* Private context for the GAMG preconditioner */
15 typedef struct {
16   PetscInt lid;            /* local vertex index */
17   PetscInt degree;         /* vertex degree */
18 } GAMGNode;
19 
20 PETSC_STATIC_INLINE int petsc_geo_mg_compare(const void *a, const void *b)
21 {
22   return (((GAMGNode*)a)->degree - ((GAMGNode*)b)->degree);
23 }
24 
25 /* -------------------------------------------------------------------------- */
26 /*
27    PCSetCoordinates_GEO
28 
29    Input Parameter:
30    .  pc - the preconditioner context
31 */
32 PetscErrorCode PCSetCoordinates_GEO(PC pc, PetscInt ndm, PetscInt a_nloc, PetscReal *coords)
33 {
34   PC_MG          *mg      = (PC_MG*)pc->data;
35   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
36   PetscErrorCode ierr;
37   PetscInt       arrsz,bs,my0,kk,ii,nloc,Iend,aloc;
38   Mat            Amat = pc->pmat;
39 
40   PetscFunctionBegin;
41   PetscValidHeaderSpecific(Amat, MAT_CLASSID, 1);
42   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
43   ierr = MatGetOwnershipRange(Amat, &my0, &Iend);CHKERRQ(ierr);
44   aloc = (Iend-my0);
45   nloc = (Iend-my0)/bs;
46 
47   if (nloc!=a_nloc && aloc!=a_nloc) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Number of local blocks %D must be %D or %D.",a_nloc,nloc,aloc);
48 
49   pc_gamg->data_cell_rows = 1;
50   if (!coords && nloc > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG, "Need coordinates for pc_gamg_type 'geo'.");
51   pc_gamg->data_cell_cols = ndm; /* coordinates */
52 
53   arrsz = nloc*pc_gamg->data_cell_rows*pc_gamg->data_cell_cols;
54 
55   /* create data - syntactic sugar that should be refactored at some point */
56   if (!pc_gamg->data || (pc_gamg->data_sz != arrsz)) {
57     ierr = PetscFree(pc_gamg->data);CHKERRQ(ierr);
58     ierr = PetscMalloc1(arrsz+1, &pc_gamg->data);CHKERRQ(ierr);
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++) {
66         pc_gamg->data[ii*nloc + kk] =  coords[kk*ndm + ii];
67       }
68     }
69   } else { /* assumes the coordinates are blocked */
70     for (kk = 0; kk < nloc; kk++) {
71       for (ii = 0; ii < ndm; ii++) {
72         pc_gamg->data[ii*nloc + kk] =  coords[bs*kk*ndm + ii];
73       }
74     }
75   }
76   if (pc_gamg->data[arrsz] != -99.) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"pc_gamg->data[arrsz %D] %g != -99.",arrsz,pc_gamg->data[arrsz]);
77   pc_gamg->data_sz = arrsz;
78   PetscFunctionReturn(0);
79 }
80 
81 /* -------------------------------------------------------------------------- */
82 /*
83    PCSetData_GEO
84 
85   Input Parameter:
86    . pc -
87 */
88 PetscErrorCode PCSetData_GEO(PC pc, Mat m)
89 {
90   PetscFunctionBegin;
91   SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"GEO MG needs coordinates");
92 }
93 
94 /* -------------------------------------------------------------------------- */
95 /*
96    PCSetFromOptions_GEO
97 
98   Input Parameter:
99    . pc -
100 */
101 PetscErrorCode PCSetFromOptions_GEO(PetscOptionItems *PetscOptionsObject,PC pc)
102 {
103   PetscErrorCode ierr;
104 
105   PetscFunctionBegin;
106   ierr = PetscOptionsHead(PetscOptionsObject,"GAMG-GEO options");CHKERRQ(ierr);
107   {
108     /* -pc_gamg_sa_nsmooths */
109     /* pc_gamg_sa->smooths = 0; */
110     /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
111     /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
112     /*                        "PCGAMGSetNSmooths_AGG", */
113     /*                        pc_gamg_sa->smooths, */
114     /*                        &pc_gamg_sa->smooths, */
115     /*                        &flag);  */
116     /* CHKERRQ(ierr); */
117   }
118   ierr = PetscOptionsTail();CHKERRQ(ierr);
119   PetscFunctionReturn(0);
120 }
121 
122 /* -------------------------------------------------------------------------- */
123 /*
124  triangulateAndFormProl
125 
126    Input Parameter:
127    . selected_2 - list of selected local ID, includes selected ghosts
128    . data_stride -
129    . coords[2*data_stride] - column vector of local coordinates w/ ghosts
130    . nselected_1 - selected IDs that go with base (1) graph includes selected ghosts
131    . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
132    . agg_lists_1 - list of aggregates selected_1 vertices of aggregate unselected vertices
133    . crsGID[selected.size()] - global index for prolongation operator
134    . bs - block size
135   Output Parameter:
136    . a_Prol - prolongation operator
137    . a_worst_best - measure of worst missed fine vertex, 0 is no misses
138 */
139 static PetscErrorCode triangulateAndFormProl(IS selected_2,PetscInt data_stride,PetscReal coords[],PetscInt nselected_1,const PetscInt clid_lid_1[],const PetscCoarsenData *agg_lists_1,
140                                              const PetscInt crsGID[],PetscInt bs,Mat a_Prol,PetscReal *a_worst_best)
141 {
142 #if defined(PETSC_HAVE_TRIANGLE)
143   PetscErrorCode       ierr;
144   PetscInt             jj,tid,tt,idx,nselected_2;
145   struct triangulateio in,mid;
146   const PetscInt       *selected_idx_2;
147   PetscMPIInt          rank;
148   PetscInt             Istart,Iend,nFineLoc,myFine0;
149   int                  kk,nPlotPts,sid;
150   MPI_Comm             comm;
151   PetscReal            tm;
152 
153   PetscFunctionBegin;
154   ierr = PetscObjectGetComm((PetscObject)a_Prol,&comm);CHKERRQ(ierr);
155   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
156   ierr = ISGetSize(selected_2, &nselected_2);CHKERRQ(ierr);
157   if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
158     *a_worst_best = 100.0; /* this will cause a stop, but not globalized (should not happen) */
159   } else *a_worst_best = 0.0;
160   ierr = MPIU_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRQ(ierr);
161   if (tm > 0.0) {
162     *a_worst_best = 100.0;
163     PetscFunctionReturn(0);
164   }
165   ierr     = MatGetOwnershipRange(a_Prol, &Istart, &Iend);CHKERRQ(ierr);
166   nFineLoc = (Iend-Istart)/bs; myFine0 = Istart/bs;
167   nPlotPts = nFineLoc; /* locals */
168   /* traingle */
169   /* Define input points - in*/
170   in.numberofpoints          = nselected_2;
171   in.numberofpointattributes = 0;
172   /* get nselected points */
173   ierr = PetscMalloc1(2*nselected_2, &in.pointlist);CHKERRQ(ierr);
174   ierr = ISGetIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
175 
176   for (kk=0,sid=0; kk<nselected_2; kk++,sid += 2) {
177     PetscInt lid = selected_idx_2[kk];
178     in.pointlist[sid]   = coords[lid];
179     in.pointlist[sid+1] = coords[data_stride + lid];
180     if (lid>=nFineLoc) nPlotPts++;
181   }
182   if (sid != 2*nselected_2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != 2*nselected_2 %D",sid,nselected_2);
183 
184   in.numberofsegments      = 0;
185   in.numberofedges         = 0;
186   in.numberofholes         = 0;
187   in.numberofregions       = 0;
188   in.trianglelist          = 0;
189   in.segmentmarkerlist     = 0;
190   in.pointattributelist    = 0;
191   in.pointmarkerlist       = 0;
192   in.triangleattributelist = 0;
193   in.trianglearealist      = 0;
194   in.segmentlist           = 0;
195   in.holelist              = 0;
196   in.regionlist            = 0;
197   in.edgelist              = 0;
198   in.edgemarkerlist        = 0;
199   in.normlist              = 0;
200 
201   /* triangulate */
202   mid.pointlist = 0;            /* Not needed if -N switch used. */
203   /* Not needed if -N switch used or number of point attributes is zero: */
204   mid.pointattributelist = 0;
205   mid.pointmarkerlist    = 0; /* Not needed if -N or -B switch used. */
206   mid.trianglelist       = 0;    /* Not needed if -E switch used. */
207   /* Not needed if -E switch used or number of triangle attributes is zero: */
208   mid.triangleattributelist = 0;
209   mid.neighborlist          = 0; /* Needed only if -n switch used. */
210   /* Needed only if segments are output (-p or -c) and -P not used: */
211   mid.segmentlist = 0;
212   /* Needed only if segments are output (-p or -c) and -P and -B not used: */
213   mid.segmentmarkerlist = 0;
214   mid.edgelist          = 0;    /* Needed only if -e switch used. */
215   mid.edgemarkerlist    = 0; /* Needed if -e used and -B not used. */
216   mid.numberoftriangles = 0;
217 
218   /* Triangulate the points.  Switches are chosen to read and write a  */
219   /*   PSLG (p), preserve the convex hull (c), number everything from  */
220   /*   zero (z), assign a regional attribute to each element (A), and  */
221   /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
222   /*   neighbor list (n).                                            */
223   if (nselected_2 != 0) { /* inactive processor */
224     char args[] = "npczQ"; /* c is needed ? */
225     triangulate(args, &in, &mid, (struct triangulateio*) NULL);
226     /* output .poly files for 'showme' */
227     if (!PETSC_TRUE) {
228       static int level = 1;
229       FILE       *file; char fname[32];
230 
231       sprintf(fname,"C%d_%d.poly",level,rank); file = fopen(fname, "w");
232       /*First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)>*/
233       fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0);
234       /*Following lines: <vertex #> <x> <y> */
235       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid += 2) {
236         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
237       }
238       /*One line: <# of segments> <# of boundary markers (0 or 1)> */
239       fprintf(file, "%d  %d\n",0,0);
240       /*Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
241       /* One line: <# of holes> */
242       fprintf(file, "%d\n",0);
243       /* Following lines: <hole #> <x> <y> */
244       /* Optional line: <# of regional attributes and/or area constraints> */
245       /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
246       fclose(file);
247 
248       /* elems */
249       sprintf(fname,"C%d_%d.ele",level,rank); file = fopen(fname, "w");
250       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
251       fprintf(file, "%d %d %d\n",mid.numberoftriangles,3,0);
252       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
253       for (kk=0,sid=0; kk<mid.numberoftriangles; kk++,sid += 3) {
254         fprintf(file, "%d %d %d %d\n",kk,mid.trianglelist[sid],mid.trianglelist[sid+1],mid.trianglelist[sid+2]);
255       }
256       fclose(file);
257 
258       sprintf(fname,"C%d_%d.node",level,rank); file = fopen(fname, "w");
259       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
260       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
261       fprintf(file, "%d  %d  %d  %d\n",nPlotPts,2,0,0);
262       /*Following lines: <vertex #> <x> <y> */
263       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid+=2) {
264         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
265       }
266 
267       sid /= 2;
268       for (jj=0; jj<nFineLoc; jj++) {
269         PetscBool sel = PETSC_TRUE;
270         for (kk=0; kk<nselected_2 && sel; kk++) {
271           PetscInt lid = selected_idx_2[kk];
272           if (lid == jj) sel = PETSC_FALSE;
273         }
274         if (sel) fprintf(file, "%d %e %e\n",sid++,coords[jj],coords[data_stride + jj]);
275       }
276       fclose(file);
277       if (sid != nPlotPts) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != nPlotPts %D",sid,nPlotPts);
278       level++;
279     }
280   }
281 #if defined PETSC_GAMG_USE_LOG
282   ierr = PetscLogEventBegin(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
283 #endif
284   { /* form P - setup some maps */
285     PetscInt clid,mm,*nTri,*node_tri;
286 
287     ierr = PetscMalloc2(nselected_2, &node_tri,nselected_2, &nTri);CHKERRQ(ierr);
288 
289     /* need list of triangles on node */
290     for (kk=0; kk<nselected_2; kk++) nTri[kk] = 0;
291     for (tid=0,kk=0; tid<mid.numberoftriangles; tid++) {
292       for (jj=0; jj<3; jj++) {
293         PetscInt cid = mid.trianglelist[kk++];
294         if (nTri[cid] == 0) node_tri[cid] = tid;
295         nTri[cid]++;
296       }
297     }
298 #define EPS 1.e-12
299     /* find points and set prolongation */
300     for (mm = clid = 0; mm < nFineLoc; mm++) {
301       PetscBool ise;
302       ierr = PetscCDEmptyAt(agg_lists_1,mm,&ise);CHKERRQ(ierr);
303       if (!ise) {
304         const PetscInt lid = mm;
305         PetscScalar    AA[3][3];
306         PetscBLASInt   N=3,NRHS=1,LDA=3,IPIV[3],LDB=3,INFO;
307         PetscCDIntNd   *pos;
308 
309         ierr = PetscCDGetHeadPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
310         while (pos) {
311           PetscInt flid;
312           ierr = PetscCDIntNdGetID(pos, &flid);CHKERRQ(ierr);
313           ierr = PetscCDGetNextPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
314 
315           if (flid < nFineLoc) {  /* could be a ghost */
316             PetscInt       bestTID = -1; PetscReal best_alpha = 1.e10;
317             const PetscInt fgid    = flid + myFine0;
318             /* compute shape function for gid */
319             const PetscReal fcoord[3] = {coords[flid],coords[data_stride+flid],1.0};
320             PetscBool       haveit    =PETSC_FALSE; PetscScalar alpha[3]; PetscInt clids[3];
321 
322             /* look for it */
323             for (tid = node_tri[clid], jj=0;
324                  jj < 5 && !haveit && tid != -1;
325                  jj++) {
326               for (tt=0; tt<3; tt++) {
327                 PetscInt cid2 = mid.trianglelist[3*tid + tt];
328                 PetscInt lid2 = selected_idx_2[cid2];
329                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
330                 clids[tt] = cid2; /* store for interp */
331               }
332 
333               for (tt=0; tt<3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];
334 
335               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
336               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
337               {
338                 PetscBool have=PETSC_TRUE;  PetscReal lowest=1.e10;
339                 for (tt = 0, idx = 0; tt < 3; tt++) {
340                   if (PetscRealPart(alpha[tt]) > (1.0+EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
341                   if (PetscRealPart(alpha[tt]) < lowest) {
342                     lowest = PetscRealPart(alpha[tt]);
343                     idx    = tt;
344                   }
345                 }
346                 haveit = have;
347               }
348               tid = mid.neighborlist[3*tid + idx];
349             }
350 
351             if (!haveit) {
352               /* brute force */
353               for (tid=0; tid<mid.numberoftriangles && !haveit; tid++) {
354                 for (tt=0; tt<3; tt++) {
355                   PetscInt cid2 = mid.trianglelist[3*tid + tt];
356                   PetscInt lid2 = selected_idx_2[cid2];
357                   AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
358                   clids[tt] = cid2; /* store for interp */
359                 }
360                 for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
361                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
362                 PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
363                 {
364                   PetscBool have=PETSC_TRUE;  PetscReal worst=0.0, v;
365                   for (tt=0; tt<3 && have; tt++) {
366                     if (PetscRealPart(alpha[tt]) > 1.0+EPS || PetscRealPart(alpha[tt]) < -EPS) have=PETSC_FALSE;
367                     if ((v=PetscAbs(PetscRealPart(alpha[tt])-0.5)) > worst) worst = v;
368                   }
369                   if (worst < best_alpha) {
370                     best_alpha = worst; bestTID = tid;
371                   }
372                   haveit = have;
373                 }
374               }
375             }
376             if (!haveit) {
377               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
378               /* use best one */
379               for (tt=0; tt<3; tt++) {
380                 PetscInt cid2 = mid.trianglelist[3*bestTID + tt];
381                 PetscInt lid2 = selected_idx_2[cid2];
382                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
383                 clids[tt] = cid2; /* store for interp */
384               }
385               for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
386               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
387               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
388             }
389 
390             /* put in row of P */
391             for (idx=0; idx<3; idx++) {
392               PetscScalar shp = alpha[idx];
393               if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
394                 PetscInt cgid = crsGID[clids[idx]];
395                 PetscInt jj   = cgid*bs, ii = fgid*bs; /* need to gloalize */
396                 for (tt=0; tt < bs; tt++, ii++, jj++) {
397                   ierr = MatSetValues(a_Prol,1,&ii,1,&jj,&shp,INSERT_VALUES);CHKERRQ(ierr);
398                 }
399               }
400             }
401           }
402         } /* aggregates iterations */
403         clid++;
404       } /* a coarse agg */
405     } /* for all fine nodes */
406 
407     ierr = ISRestoreIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
408     ierr = MatAssemblyBegin(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
409     ierr = MatAssemblyEnd(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
410 
411     ierr = PetscFree2(node_tri,nTri);CHKERRQ(ierr);
412   }
413 #if defined PETSC_GAMG_USE_LOG
414   ierr = PetscLogEventEnd(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
415 #endif
416   free(mid.trianglelist);
417   free(mid.neighborlist);
418   ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
419   PetscFunctionReturn(0);
420 #else
421   SETERRQ(PetscObjectComm((PetscObject)a_Prol),PETSC_ERR_PLIB,"configure with TRIANGLE to use geometric MG");
422 #endif
423 }
424 /* -------------------------------------------------------------------------- */
425 /*
426    getGIDsOnSquareGraph - square graph, get
427 
428    Input Parameter:
429    . nselected_1 - selected local indices (includes ghosts in input Gmat1)
430    . clid_lid_1 - [nselected_1] lids of selected nodes
431    . Gmat1 - graph that goes with 'selected_1'
432    Output Parameter:
433    . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
434    . a_Gmat_2 - graph that is squared of 'Gmat_1'
435    . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
436 */
437 static PetscErrorCode getGIDsOnSquareGraph(PetscInt nselected_1,const PetscInt clid_lid_1[],const Mat Gmat1,IS *a_selected_2,Mat *a_Gmat_2,PetscInt **a_crsGID)
438 {
439   PetscErrorCode ierr;
440   PetscMPIInt    size;
441   PetscInt       *crsGID, kk,my0,Iend,nloc;
442   MPI_Comm       comm;
443 
444   PetscFunctionBegin;
445   ierr = PetscObjectGetComm((PetscObject)Gmat1,&comm);CHKERRQ(ierr);
446   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
447   ierr = MatGetOwnershipRange(Gmat1,&my0,&Iend);CHKERRQ(ierr); /* AIJ */
448   nloc = Iend - my0; /* this does not change */
449 
450   if (size == 1) { /* not much to do in serial */
451     ierr = PetscMalloc1(nselected_1, &crsGID);CHKERRQ(ierr);
452     for (kk=0; kk<nselected_1; kk++) crsGID[kk] = kk;
453     *a_Gmat_2 = 0;
454     ierr      = ISCreateGeneral(PETSC_COMM_SELF,nselected_1,clid_lid_1,PETSC_COPY_VALUES,a_selected_2);CHKERRQ(ierr);
455   } else {
456     PetscInt    idx,num_fine_ghosts,num_crs_ghost,myCrs0;
457     Mat_MPIAIJ  *mpimat2;
458     Mat         Gmat2;
459     Vec         locState;
460     PetscScalar *cpcol_state;
461 
462     /* scan my coarse zero gid, set 'lid_state' with coarse GID */
463     kk = nselected_1;
464     ierr = MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
465     myCrs0 -= nselected_1;
466 
467     if (a_Gmat_2) { /* output */
468       /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
469       ierr      = MatTransposeMatMult(Gmat1, Gmat1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Gmat2);CHKERRQ(ierr);
470       *a_Gmat_2 = Gmat2; /* output */
471     } else Gmat2 = Gmat1;  /* use local to get crsGIDs at least */
472     /* get coarse grid GIDS for selected (locals and ghosts) */
473     mpimat2 = (Mat_MPIAIJ*)Gmat2->data;
474     ierr    = MatCreateVecs(Gmat2, &locState, 0);CHKERRQ(ierr);
475     ierr    = VecSet(locState, (PetscScalar)(PetscReal)(-1));CHKERRQ(ierr); /* set with UNKNOWN state */
476     for (kk=0; kk<nselected_1; kk++) {
477       PetscInt    fgid = clid_lid_1[kk] + my0;
478       PetscScalar v    = (PetscScalar)(kk+myCrs0);
479       ierr = VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES);CHKERRQ(ierr); /* set with PID */
480     }
481     ierr = VecAssemblyBegin(locState);CHKERRQ(ierr);
482     ierr = VecAssemblyEnd(locState);CHKERRQ(ierr);
483     ierr = VecScatterBegin(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
484     ierr =   VecScatterEnd(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
485     ierr = VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts);CHKERRQ(ierr);
486     ierr = VecGetArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
487     for (kk=0,num_crs_ghost=0; kk<num_fine_ghosts; kk++) {
488       if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
489     }
490     ierr = PetscMalloc1(nselected_1+num_crs_ghost, &crsGID);CHKERRQ(ierr); /* output */
491     {
492       PetscInt *selected_set;
493       ierr = PetscMalloc1(nselected_1+num_crs_ghost, &selected_set);CHKERRQ(ierr);
494       /* do ghost of 'crsGID' */
495       for (kk=0,idx=nselected_1; kk<num_fine_ghosts; kk++) {
496         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
497           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
498           selected_set[idx] = nloc + kk;
499           crsGID[idx++]     = cgid;
500         }
501       }
502       if (idx != (nselected_1+num_crs_ghost)) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"idx %D != (nselected_1 %D + num_crs_ghost %D)",idx,nselected_1,num_crs_ghost);
503       ierr = VecRestoreArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
504       /* do locals in 'crsGID' */
505       ierr = VecGetArray(locState, &cpcol_state);CHKERRQ(ierr);
506       for (kk=0,idx=0; kk<nloc; kk++) {
507         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
508           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
509           selected_set[idx] = kk;
510           crsGID[idx++]     = cgid;
511         }
512       }
513       if (idx != nselected_1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"idx %D != nselected_1 %D",idx,nselected_1);
514       ierr = VecRestoreArray(locState, &cpcol_state);CHKERRQ(ierr);
515 
516       if (a_selected_2 != 0) { /* output */
517         ierr = ISCreateGeneral(PETSC_COMM_SELF,(nselected_1+num_crs_ghost),selected_set,PETSC_OWN_POINTER,a_selected_2);CHKERRQ(ierr);
518       } else {
519         ierr = PetscFree(selected_set);CHKERRQ(ierr);
520       }
521     }
522     ierr = VecDestroy(&locState);CHKERRQ(ierr);
523   }
524   *a_crsGID = crsGID; /* output */
525   PetscFunctionReturn(0);
526 }
527 
528 /* -------------------------------------------------------------------------- */
529 /*
530    PCGAMGGraph_GEO
531 
532   Input Parameter:
533    . pc - this
534    . Amat - matrix on this fine level
535   Output Parameter:
536    . a_Gmat
537 */
538 PetscErrorCode PCGAMGGraph_GEO(PC pc,Mat Amat,Mat *a_Gmat)
539 {
540   PetscErrorCode  ierr;
541   PC_MG           *mg      = (PC_MG*)pc->data;
542   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
543   const PetscReal vfilter  = pc_gamg->threshold[0];
544   MPI_Comm        comm;
545   Mat             Gmat;
546   PetscBool       set,flg,symm;
547 
548   PetscFunctionBegin;
549   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
550   ierr = PetscLogEventBegin(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
551 
552   ierr = MatIsSymmetricKnown(Amat, &set, &flg);CHKERRQ(ierr);
553   symm = (PetscBool)!(set && flg);
554 
555   ierr = PCGAMGCreateGraph(Amat, &Gmat);CHKERRQ(ierr);
556   ierr = PCGAMGFilterGraph(&Gmat, vfilter, symm);CHKERRQ(ierr);
557 
558   *a_Gmat = Gmat;
559   ierr = PetscLogEventEnd(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
560   PetscFunctionReturn(0);
561 }
562 
563 /* -------------------------------------------------------------------------- */
564 /*
565    PCGAMGCoarsen_GEO
566 
567   Input Parameter:
568    . a_pc - this
569    . a_Gmat - graph
570   Output Parameter:
571    . a_llist_parent - linked list from selected indices for data locality only
572 */
573 PetscErrorCode PCGAMGCoarsen_GEO(PC a_pc,Mat *a_Gmat,PetscCoarsenData **a_llist_parent)
574 {
575   PetscErrorCode ierr;
576   PetscInt       Istart,Iend,nloc,kk,Ii,ncols;
577   IS             perm;
578   GAMGNode       *gnodes;
579   PetscInt       *permute;
580   Mat            Gmat  = *a_Gmat;
581   MPI_Comm       comm;
582   MatCoarsen     crs;
583 
584   PetscFunctionBegin;
585   ierr = PetscObjectGetComm((PetscObject)a_pc,&comm);CHKERRQ(ierr);
586   ierr = PetscLogEventBegin(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
587   ierr = MatGetOwnershipRange(Gmat, &Istart, &Iend);CHKERRQ(ierr);
588   nloc = (Iend-Istart);
589 
590   /* create random permutation with sort for geo-mg */
591   ierr = PetscMalloc1(nloc, &gnodes);CHKERRQ(ierr);
592   ierr = PetscMalloc1(nloc, &permute);CHKERRQ(ierr);
593 
594   for (Ii=Istart; Ii<Iend; Ii++) { /* locals only? */
595     ierr = MatGetRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
596     {
597       PetscInt lid = Ii - Istart;
598       gnodes[lid].lid    = lid;
599       gnodes[lid].degree = ncols;
600     }
601     ierr = MatRestoreRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
602   }
603   if (PETSC_TRUE) {
604     PetscRandom  rand;
605     PetscBool    *bIndexSet;
606     PetscReal    rr;
607     PetscInt     iSwapIndex;
608 
609     ierr = PetscRandomCreate(comm,&rand);CHKERRQ(ierr);
610     ierr = PetscCalloc1(nloc, &bIndexSet);CHKERRQ(ierr);
611     for (Ii = 0; Ii < nloc; Ii++) {
612       ierr = PetscRandomGetValueReal(rand,&rr);CHKERRQ(ierr);
613       iSwapIndex = (PetscInt) (rr*nloc);
614       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
615         GAMGNode iTemp = gnodes[iSwapIndex];
616         gnodes[iSwapIndex]    = gnodes[Ii];
617         gnodes[Ii]            = iTemp;
618         bIndexSet[Ii]         = PETSC_TRUE;
619         bIndexSet[iSwapIndex] = PETSC_TRUE;
620       }
621     }
622     ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
623     ierr = PetscFree(bIndexSet);CHKERRQ(ierr);
624   }
625   /* only sort locals */
626   qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
627   /* create IS of permutation */
628   for (kk=0; kk<nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
629   ierr = PetscFree(gnodes);CHKERRQ(ierr);
630   ierr = ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
631 
632   /* get MIS aggs */
633 
634   ierr = MatCoarsenCreate(comm, &crs);CHKERRQ(ierr);
635   ierr = MatCoarsenSetType(crs, MATCOARSENMIS);CHKERRQ(ierr);
636   ierr = MatCoarsenSetGreedyOrdering(crs, perm);CHKERRQ(ierr);
637   ierr = MatCoarsenSetAdjacency(crs, Gmat);CHKERRQ(ierr);
638   ierr = MatCoarsenSetStrictAggs(crs, PETSC_FALSE);CHKERRQ(ierr);
639   ierr = MatCoarsenApply(crs);CHKERRQ(ierr);
640   ierr = MatCoarsenGetData(crs, a_llist_parent);CHKERRQ(ierr);
641   ierr = MatCoarsenDestroy(&crs);CHKERRQ(ierr);
642 
643   ierr = ISDestroy(&perm);CHKERRQ(ierr);
644   ierr = PetscLogEventEnd(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
645   PetscFunctionReturn(0);
646 }
647 
648 /* -------------------------------------------------------------------------- */
649 /*
650  PCGAMGProlongator_GEO
651 
652  Input Parameter:
653  . pc - this
654  . Amat - matrix on this fine level
655  . Graph - used to get ghost data for nodes in
656  . selected_1 - [nselected]
657  . agg_lists - [nselected]
658  Output Parameter:
659  . a_P_out - prolongation operator to the next level
660  */
661 PetscErrorCode PCGAMGProlongator_GEO(PC pc,Mat Amat,Mat Gmat,PetscCoarsenData *agg_lists,Mat *a_P_out)
662 {
663   PC_MG          *mg      = (PC_MG*)pc->data;
664   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
665   const PetscInt dim      = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
666   PetscErrorCode ierr;
667   PetscInt       Istart,Iend,nloc,my0,jj,kk,ncols,nLocalSelected,bs,*clid_flid;
668   Mat            Prol;
669   PetscMPIInt    rank, size;
670   MPI_Comm       comm;
671   IS             selected_2,selected_1;
672   const PetscInt *selected_idx;
673   MatType        mtype;
674 
675   PetscFunctionBegin;
676   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
677   ierr = PetscLogEventBegin(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
678   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
679   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
680   ierr = MatGetOwnershipRange(Amat, &Istart, &Iend);CHKERRQ(ierr);
681   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
682   nloc = (Iend-Istart)/bs; my0 = Istart/bs;
683   if ((Iend-Istart) % bs) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"(Iend %D - Istart %D) % bs %D",Iend,Istart,bs);
684 
685   /* get 'nLocalSelected' */
686   ierr = PetscCDGetMIS(agg_lists, &selected_1);CHKERRQ(ierr);
687   ierr = ISGetSize(selected_1, &jj);CHKERRQ(ierr);
688   ierr = PetscMalloc1(jj, &clid_flid);CHKERRQ(ierr);
689   ierr = ISGetIndices(selected_1, &selected_idx);CHKERRQ(ierr);
690   for (kk=0,nLocalSelected=0; kk<jj; kk++) {
691     PetscInt lid = selected_idx[kk];
692     if (lid<nloc) {
693       ierr = MatGetRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
694       if (ncols>1) clid_flid[nLocalSelected++] = lid; /* fiter out singletons */
695       ierr = MatRestoreRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
696     }
697   }
698   ierr = ISRestoreIndices(selected_1, &selected_idx);CHKERRQ(ierr);
699   ierr = ISDestroy(&selected_1);CHKERRQ(ierr); /* this is selected_1 in serial */
700 
701   /* create prolongator  matrix */
702   ierr = MatGetType(Amat,&mtype);CHKERRQ(ierr);
703   ierr = MatCreate(comm, &Prol);CHKERRQ(ierr);
704   ierr = MatSetSizes(Prol,nloc*bs,nLocalSelected*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
705   ierr = MatSetBlockSizes(Prol, bs, bs);CHKERRQ(ierr);
706   ierr = MatSetType(Prol, mtype);CHKERRQ(ierr);
707   ierr = MatSeqAIJSetPreallocation(Prol,3*data_cols,NULL);CHKERRQ(ierr);
708   ierr = MatMPIAIJSetPreallocation(Prol,3*data_cols,NULL,3*data_cols,NULL);CHKERRQ(ierr);
709 
710   /* can get all points "removed" - but not on geomg */
711   ierr =  MatGetSize(Prol, &kk, &jj);CHKERRQ(ierr);
712   if (!jj) {
713     ierr = PetscInfo(pc,"ERROE: no selected points on coarse grid\n");CHKERRQ(ierr);
714     ierr = PetscFree(clid_flid);CHKERRQ(ierr);
715     ierr = MatDestroy(&Prol);CHKERRQ(ierr);
716     *a_P_out = NULL;  /* out */
717     PetscFunctionReturn(0);
718   }
719 
720   {
721     PetscReal *coords;
722     PetscInt  data_stride;
723     PetscInt  *crsGID = NULL;
724     Mat       Gmat2;
725 
726     if (dim != data_cols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim %D != data_cols %D",dim,data_cols);
727     /* grow ghost data for better coarse grid cover of fine grid */
728 #if defined PETSC_GAMG_USE_LOG
729     ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
730 #endif
731     /* messy method, squares graph and gets some data */
732     ierr = getGIDsOnSquareGraph(nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID);CHKERRQ(ierr);
733     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
734 #if defined PETSC_GAMG_USE_LOG
735     ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
736 #endif
737     /* create global vector of coorindates in 'coords' */
738     if (size > 1) {
739       ierr = PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords);CHKERRQ(ierr);
740     } else {
741       coords      = (PetscReal*)pc_gamg->data;
742       data_stride = pc_gamg->data_sz/pc_gamg->data_cell_cols;
743     }
744     ierr = MatDestroy(&Gmat2);CHKERRQ(ierr);
745 
746     /* triangulate */
747     if (dim == 2) {
748       PetscReal metric,tm;
749 #if defined PETSC_GAMG_USE_LOG
750       ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
751 #endif
752       ierr = triangulateAndFormProl(selected_2, data_stride, coords,nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric);CHKERRQ(ierr);
753 #if defined PETSC_GAMG_USE_LOG
754       ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
755 #endif
756       ierr = PetscFree(crsGID);CHKERRQ(ierr);
757 
758       /* clean up and create coordinates for coarse grid (output) */
759       if (size > 1) ierr = PetscFree(coords);CHKERRQ(ierr);
760 
761       ierr = MPIU_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRQ(ierr);
762       if (tm > 1.) { /* needs to be globalized - should not happen */
763         ierr = PetscInfo1(pc," failed metric for coarse grid %e\n",(double)tm);CHKERRQ(ierr);
764         ierr = MatDestroy(&Prol);CHKERRQ(ierr);
765       } else if (metric > .0) {
766         ierr = PetscInfo1(pc,"worst metric for coarse grid = %e\n",(double)metric);CHKERRQ(ierr);
767       }
768     } else SETERRQ(comm,PETSC_ERR_PLIB,"3D not implemented for 'geo' AMG");
769     { /* create next coords - output */
770       PetscReal *crs_crds;
771       ierr = PetscMalloc1(dim*nLocalSelected, &crs_crds);CHKERRQ(ierr);
772       for (kk=0; kk<nLocalSelected; kk++) { /* grab local select nodes to promote - output */
773         PetscInt lid = clid_flid[kk];
774         for (jj=0; jj<dim; jj++) crs_crds[jj*nLocalSelected + kk] = pc_gamg->data[jj*nloc + lid];
775       }
776 
777       ierr             = PetscFree(pc_gamg->data);CHKERRQ(ierr);
778       pc_gamg->data    = crs_crds; /* out */
779       pc_gamg->data_sz = dim*nLocalSelected;
780     }
781     ierr = ISDestroy(&selected_2);CHKERRQ(ierr);
782   }
783 
784   *a_P_out = Prol;  /* out */
785   ierr     = PetscFree(clid_flid);CHKERRQ(ierr);
786   ierr = PetscLogEventEnd(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
787   PetscFunctionReturn(0);
788 }
789 
790 static PetscErrorCode PCDestroy_GAMG_GEO(PC pc)
791 {
792   PetscErrorCode ierr;
793 
794   PetscFunctionBegin;
795   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
796   PetscFunctionReturn(0);
797 }
798 
799 /* -------------------------------------------------------------------------- */
800 /*
801  PCCreateGAMG_GEO
802 
803   Input Parameter:
804    . pc -
805 */
806 PetscErrorCode  PCCreateGAMG_GEO(PC pc)
807 {
808   PetscErrorCode ierr;
809   PC_MG          *mg      = (PC_MG*)pc->data;
810   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
811 
812   PetscFunctionBegin;
813   pc_gamg->ops->setfromoptions = PCSetFromOptions_GEO;
814   pc_gamg->ops->destroy        = PCDestroy_GAMG_GEO;
815   /* reset does not do anything; setup not virtual */
816 
817   /* set internal function pointers */
818   pc_gamg->ops->graph             = PCGAMGGraph_GEO;
819   pc_gamg->ops->coarsen           = PCGAMGCoarsen_GEO;
820   pc_gamg->ops->prolongator       = PCGAMGProlongator_GEO;
821   pc_gamg->ops->optprolongator    = NULL;
822   pc_gamg->ops->createdefaultdata = PCSetData_GEO;
823 
824   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_GEO);CHKERRQ(ierr);
825   PetscFunctionReturn(0);
826 }
827