xref: /petsc/src/ksp/pc/impls/gamg/geo.c (revision 534a8f05a7a8aff70dd8cfd53d9cd834400a8dbf)
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 #if !defined(ANSI_DECLARATORS)
9 #define ANSI_DECLARATORS
10 #endif
11 #include <triangle.h>
12 #endif
13 
14 #include <petscblaslapack.h>
15 
16 /* Private context for the GAMG preconditioner */
17 typedef struct {
18   PetscInt lid;            /* local vertex index */
19   PetscInt degree;         /* vertex degree */
20 } GAMGNode;
21 
22 PETSC_STATIC_INLINE int petsc_geo_mg_compare(const void *a, const void *b)
23 {
24   return (((GAMGNode*)a)->degree - ((GAMGNode*)b)->degree);
25 }
26 
27 /* -------------------------------------------------------------------------- */
28 /*
29    PCSetCoordinates_GEO
30 
31    Input Parameter:
32    .  pc - the preconditioner context
33 */
34 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   PetscErrorCode ierr;
39   PetscInt       arrsz,bs,my0,kk,ii,nloc,Iend,aloc;
40   Mat            Amat = pc->pmat;
41 
42   PetscFunctionBegin;
43   PetscValidHeaderSpecific(Amat, MAT_CLASSID, 1);
44   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
45   ierr = MatGetOwnershipRange(Amat, &my0, &Iend);CHKERRQ(ierr);
46   aloc = (Iend-my0);
47   nloc = (Iend-my0)/bs;
48 
49   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);
50 
51   pc_gamg->data_cell_rows = 1;
52   if (!coords && nloc > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG, "Need coordinates for pc_gamg_type 'geo'.");
53   pc_gamg->data_cell_cols = ndm; /* coordinates */
54 
55   arrsz = nloc*pc_gamg->data_cell_rows*pc_gamg->data_cell_cols;
56 
57   /* create data - syntactic sugar that should be refactored at some point */
58   if (!pc_gamg->data || (pc_gamg->data_sz != arrsz)) {
59     ierr = PetscFree(pc_gamg->data);CHKERRQ(ierr);
60     ierr = PetscMalloc1(arrsz+1, &pc_gamg->data);CHKERRQ(ierr);
61   }
62   for (kk=0; kk<arrsz; kk++) pc_gamg->data[kk] = -999.;
63   pc_gamg->data[arrsz] = -99.;
64   /* copy data in - column oriented */
65   if (nloc == a_nloc) {
66     for (kk = 0; kk < nloc; kk++) {
67       for (ii = 0; ii < ndm; ii++) {
68         pc_gamg->data[ii*nloc + kk] =  coords[kk*ndm + ii];
69       }
70     }
71   } else { /* assumes the coordinates are blocked */
72     for (kk = 0; kk < nloc; kk++) {
73       for (ii = 0; ii < ndm; ii++) {
74         pc_gamg->data[ii*nloc + kk] =  coords[bs*kk*ndm + ii];
75       }
76     }
77   }
78   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]);
79   pc_gamg->data_sz = arrsz;
80   PetscFunctionReturn(0);
81 }
82 
83 /* -------------------------------------------------------------------------- */
84 /*
85    PCSetData_GEO
86 
87   Input Parameter:
88    . pc -
89 */
90 PetscErrorCode PCSetData_GEO(PC pc, Mat m)
91 {
92   PetscFunctionBegin;
93   SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"GEO MG needs coordinates");
94 }
95 
96 /* -------------------------------------------------------------------------- */
97 /*
98    PCSetFromOptions_GEO
99 
100   Input Parameter:
101    . pc -
102 */
103 PetscErrorCode PCSetFromOptions_GEO(PetscOptionItems *PetscOptionsObject,PC pc)
104 {
105   PetscErrorCode ierr;
106 
107   PetscFunctionBegin;
108   ierr = PetscOptionsHead(PetscOptionsObject,"GAMG-GEO options");CHKERRQ(ierr);
109   {
110     /* -pc_gamg_sa_nsmooths */
111     /* pc_gamg_sa->smooths = 0; */
112     /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
113     /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
114     /*                        "PCGAMGSetNSmooths_AGG", */
115     /*                        pc_gamg_sa->smooths, */
116     /*                        &pc_gamg_sa->smooths, */
117     /*                        &flag);  */
118     /* CHKERRQ(ierr); */
119   }
120   ierr = PetscOptionsTail();CHKERRQ(ierr);
121   PetscFunctionReturn(0);
122 }
123 
124 /* -------------------------------------------------------------------------- */
125 /*
126  triangulateAndFormProl
127 
128    Input Parameter:
129    . selected_2 - list of selected local ID, includes selected ghosts
130    . data_stride -
131    . coords[2*data_stride] - column vector of local coordinates w/ ghosts
132    . nselected_1 - selected IDs that go with base (1) graph includes selected ghosts
133    . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
134    . agg_lists_1 - list of aggregates selected_1 vertices of aggregate unselected vertices
135    . crsGID[selected.size()] - global index for prolongation operator
136    . bs - block size
137   Output Parameter:
138    . a_Prol - prolongation operator
139    . a_worst_best - measure of worst missed fine vertex, 0 is no misses
140 */
141 static PetscErrorCode triangulateAndFormProl(IS selected_2,PetscInt data_stride,PetscReal coords[],PetscInt nselected_1,const PetscInt clid_lid_1[],const PetscCoarsenData *agg_lists_1,
142                                              const PetscInt crsGID[],PetscInt bs,Mat a_Prol,PetscReal *a_worst_best)
143 {
144 #if defined(PETSC_HAVE_TRIANGLE)
145   PetscErrorCode       ierr;
146   PetscInt             jj,tid,tt,idx,nselected_2;
147   struct triangulateio in,mid;
148   const PetscInt       *selected_idx_2;
149   PetscMPIInt          rank;
150   PetscInt             Istart,Iend,nFineLoc,myFine0;
151   int                  kk,nPlotPts,sid;
152   MPI_Comm             comm;
153   PetscReal            tm;
154 
155   PetscFunctionBegin;
156   ierr = PetscObjectGetComm((PetscObject)a_Prol,&comm);CHKERRQ(ierr);
157   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
158   ierr = ISGetSize(selected_2, &nselected_2);CHKERRQ(ierr);
159   if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
160     *a_worst_best = 100.0; /* this will cause a stop, but not globalized (should not happen) */
161   } else *a_worst_best = 0.0;
162   ierr = MPIU_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRQ(ierr);
163   if (tm > 0.0) {
164     *a_worst_best = 100.0;
165     PetscFunctionReturn(0);
166   }
167   ierr     = MatGetOwnershipRange(a_Prol, &Istart, &Iend);CHKERRQ(ierr);
168   nFineLoc = (Iend-Istart)/bs; myFine0 = Istart/bs;
169   nPlotPts = nFineLoc; /* locals */
170   /* traingle */
171   /* Define input points - in*/
172   in.numberofpoints          = nselected_2;
173   in.numberofpointattributes = 0;
174   /* get nselected points */
175   ierr = PetscMalloc1(2*nselected_2, &in.pointlist);CHKERRQ(ierr);
176   ierr = ISGetIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
177 
178   for (kk=0,sid=0; kk<nselected_2; kk++,sid += 2) {
179     PetscInt lid = selected_idx_2[kk];
180     in.pointlist[sid]   = coords[lid];
181     in.pointlist[sid+1] = coords[data_stride + lid];
182     if (lid>=nFineLoc) nPlotPts++;
183   }
184   if (sid != 2*nselected_2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != 2*nselected_2 %D",sid,nselected_2);
185 
186   in.numberofsegments      = 0;
187   in.numberofedges         = 0;
188   in.numberofholes         = 0;
189   in.numberofregions       = 0;
190   in.trianglelist          = 0;
191   in.segmentmarkerlist     = 0;
192   in.pointattributelist    = 0;
193   in.pointmarkerlist       = 0;
194   in.triangleattributelist = 0;
195   in.trianglearealist      = 0;
196   in.segmentlist           = 0;
197   in.holelist              = 0;
198   in.regionlist            = 0;
199   in.edgelist              = 0;
200   in.edgemarkerlist        = 0;
201   in.normlist              = 0;
202 
203   /* triangulate */
204   mid.pointlist = 0;            /* Not needed if -N switch used. */
205   /* Not needed if -N switch used or number of point attributes is zero: */
206   mid.pointattributelist = 0;
207   mid.pointmarkerlist    = 0; /* Not needed if -N or -B switch used. */
208   mid.trianglelist       = 0;    /* Not needed if -E switch used. */
209   /* Not needed if -E switch used or number of triangle attributes is zero: */
210   mid.triangleattributelist = 0;
211   mid.neighborlist          = 0; /* Needed only if -n switch used. */
212   /* Needed only if segments are output (-p or -c) and -P not used: */
213   mid.segmentlist = 0;
214   /* Needed only if segments are output (-p or -c) and -P and -B not used: */
215   mid.segmentmarkerlist = 0;
216   mid.edgelist          = 0;    /* Needed only if -e switch used. */
217   mid.edgemarkerlist    = 0; /* Needed if -e used and -B not used. */
218   mid.numberoftriangles = 0;
219 
220   /* Triangulate the points.  Switches are chosen to read and write a  */
221   /*   PSLG (p), preserve the convex hull (c), number everything from  */
222   /*   zero (z), assign a regional attribute to each element (A), and  */
223   /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
224   /*   neighbor list (n).                                            */
225   if (nselected_2 != 0) { /* inactive processor */
226     char args[] = "npczQ"; /* c is needed ? */
227     triangulate(args, &in, &mid, (struct triangulateio*) NULL);
228     /* output .poly files for 'showme' */
229     if (!PETSC_TRUE) {
230       static int level = 1;
231       FILE       *file; char fname[32];
232 
233       sprintf(fname,"C%d_%d.poly",level,rank); file = fopen(fname, "w");
234       /*First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)>*/
235       fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0);
236       /*Following lines: <vertex #> <x> <y> */
237       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid += 2) {
238         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
239       }
240       /*One line: <# of segments> <# of boundary markers (0 or 1)> */
241       fprintf(file, "%d  %d\n",0,0);
242       /*Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
243       /* One line: <# of holes> */
244       fprintf(file, "%d\n",0);
245       /* Following lines: <hole #> <x> <y> */
246       /* Optional line: <# of regional attributes and/or area constraints> */
247       /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
248       fclose(file);
249 
250       /* elems */
251       sprintf(fname,"C%d_%d.ele",level,rank); file = fopen(fname, "w");
252       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
253       fprintf(file, "%d %d %d\n",mid.numberoftriangles,3,0);
254       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
255       for (kk=0,sid=0; kk<mid.numberoftriangles; kk++,sid += 3) {
256         fprintf(file, "%d %d %d %d\n",kk,mid.trianglelist[sid],mid.trianglelist[sid+1],mid.trianglelist[sid+2]);
257       }
258       fclose(file);
259 
260       sprintf(fname,"C%d_%d.node",level,rank); file = fopen(fname, "w");
261       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
262       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
263       fprintf(file, "%d  %d  %d  %d\n",nPlotPts,2,0,0);
264       /*Following lines: <vertex #> <x> <y> */
265       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid+=2) {
266         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
267       }
268 
269       sid /= 2;
270       for (jj=0; jj<nFineLoc; jj++) {
271         PetscBool sel = PETSC_TRUE;
272         for (kk=0; kk<nselected_2 && sel; kk++) {
273           PetscInt lid = selected_idx_2[kk];
274           if (lid == jj) sel = PETSC_FALSE;
275         }
276         if (sel) fprintf(file, "%d %e %e\n",sid++,coords[jj],coords[data_stride + jj]);
277       }
278       fclose(file);
279       if (sid != nPlotPts) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != nPlotPts %D",sid,nPlotPts);
280       level++;
281     }
282   }
283 #if defined PETSC_GAMG_USE_LOG
284   ierr = PetscLogEventBegin(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
285 #endif
286   { /* form P - setup some maps */
287     PetscInt clid,mm,*nTri,*node_tri;
288 
289     ierr = PetscMalloc2(nselected_2, &node_tri,nselected_2, &nTri);CHKERRQ(ierr);
290 
291     /* need list of triangles on node */
292     for (kk=0; kk<nselected_2; kk++) nTri[kk] = 0;
293     for (tid=0,kk=0; tid<mid.numberoftriangles; tid++) {
294       for (jj=0; jj<3; jj++) {
295         PetscInt cid = mid.trianglelist[kk++];
296         if (nTri[cid] == 0) node_tri[cid] = tid;
297         nTri[cid]++;
298       }
299     }
300 #define EPS 1.e-12
301     /* find points and set prolongation */
302     for (mm = clid = 0; mm < nFineLoc; mm++) {
303       PetscBool ise;
304       ierr = PetscCDEmptyAt(agg_lists_1,mm,&ise);CHKERRQ(ierr);
305       if (!ise) {
306         const PetscInt lid = mm;
307         PetscScalar    AA[3][3];
308         PetscBLASInt   N=3,NRHS=1,LDA=3,IPIV[3],LDB=3,INFO;
309         PetscCDIntNd   *pos;
310 
311         ierr = PetscCDGetHeadPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
312         while (pos) {
313           PetscInt flid;
314           ierr = PetscCDIntNdGetID(pos, &flid);CHKERRQ(ierr);
315           ierr = PetscCDGetNextPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
316 
317           if (flid < nFineLoc) {  /* could be a ghost */
318             PetscInt       bestTID = -1; PetscReal best_alpha = 1.e10;
319             const PetscInt fgid    = flid + myFine0;
320             /* compute shape function for gid */
321             const PetscReal fcoord[3] = {coords[flid],coords[data_stride+flid],1.0};
322             PetscBool       haveit    =PETSC_FALSE; PetscScalar alpha[3]; PetscInt clids[3];
323 
324             /* look for it */
325             for (tid = node_tri[clid], jj=0;
326                  jj < 5 && !haveit && tid != -1;
327                  jj++) {
328               for (tt=0; tt<3; tt++) {
329                 PetscInt cid2 = mid.trianglelist[3*tid + tt];
330                 PetscInt lid2 = selected_idx_2[cid2];
331                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
332                 clids[tt] = cid2; /* store for interp */
333               }
334 
335               for (tt=0; tt<3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];
336 
337               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
338               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
339               {
340                 PetscBool have=PETSC_TRUE;  PetscReal lowest=1.e10;
341                 for (tt = 0, idx = 0; tt < 3; tt++) {
342                   if (PetscRealPart(alpha[tt]) > (1.0+EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
343                   if (PetscRealPart(alpha[tt]) < lowest) {
344                     lowest = PetscRealPart(alpha[tt]);
345                     idx    = tt;
346                   }
347                 }
348                 haveit = have;
349               }
350               tid = mid.neighborlist[3*tid + idx];
351             }
352 
353             if (!haveit) {
354               /* brute force */
355               for (tid=0; tid<mid.numberoftriangles && !haveit; tid++) {
356                 for (tt=0; tt<3; tt++) {
357                   PetscInt cid2 = mid.trianglelist[3*tid + tt];
358                   PetscInt lid2 = selected_idx_2[cid2];
359                   AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
360                   clids[tt] = cid2; /* store for interp */
361                 }
362                 for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
363                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
364                 PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
365                 {
366                   PetscBool have=PETSC_TRUE;  PetscReal worst=0.0, v;
367                   for (tt=0; tt<3 && have; tt++) {
368                     if (PetscRealPart(alpha[tt]) > 1.0+EPS || PetscRealPart(alpha[tt]) < -EPS) have=PETSC_FALSE;
369                     if ((v=PetscAbs(PetscRealPart(alpha[tt])-0.5)) > worst) worst = v;
370                   }
371                   if (worst < best_alpha) {
372                     best_alpha = worst; bestTID = tid;
373                   }
374                   haveit = have;
375                 }
376               }
377             }
378             if (!haveit) {
379               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
380               /* use best one */
381               for (tt=0; tt<3; tt++) {
382                 PetscInt cid2 = mid.trianglelist[3*bestTID + tt];
383                 PetscInt lid2 = selected_idx_2[cid2];
384                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
385                 clids[tt] = cid2; /* store for interp */
386               }
387               for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
388               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
389               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
390             }
391 
392             /* put in row of P */
393             for (idx=0; idx<3; idx++) {
394               PetscScalar shp = alpha[idx];
395               if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
396                 PetscInt cgid = crsGID[clids[idx]];
397                 PetscInt jj   = cgid*bs, ii = fgid*bs; /* need to gloalize */
398                 for (tt=0; tt < bs; tt++, ii++, jj++) {
399                   ierr = MatSetValues(a_Prol,1,&ii,1,&jj,&shp,INSERT_VALUES);CHKERRQ(ierr);
400                 }
401               }
402             }
403           }
404         } /* aggregates iterations */
405         clid++;
406       } /* a coarse agg */
407     } /* for all fine nodes */
408 
409     ierr = ISRestoreIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
410     ierr = MatAssemblyBegin(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
411     ierr = MatAssemblyEnd(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
412 
413     ierr = PetscFree2(node_tri,nTri);CHKERRQ(ierr);
414   }
415 #if defined PETSC_GAMG_USE_LOG
416   ierr = PetscLogEventEnd(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
417 #endif
418   free(mid.trianglelist);
419   free(mid.neighborlist);
420   ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
421   PetscFunctionReturn(0);
422 #else
423   SETERRQ(PetscObjectComm((PetscObject)a_Prol),PETSC_ERR_PLIB,"configure with TRIANGLE to use geometric MG");
424 #endif
425 }
426 /* -------------------------------------------------------------------------- */
427 /*
428    getGIDsOnSquareGraph - square graph, get
429 
430    Input Parameter:
431    . nselected_1 - selected local indices (includes ghosts in input Gmat1)
432    . clid_lid_1 - [nselected_1] lids of selected nodes
433    . Gmat1 - graph that goes with 'selected_1'
434    Output Parameter:
435    . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
436    . a_Gmat_2 - graph that is squared of 'Gmat_1'
437    . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
438 */
439 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)
440 {
441   PetscErrorCode ierr;
442   PetscMPIInt    size;
443   PetscInt       *crsGID, kk,my0,Iend,nloc;
444   MPI_Comm       comm;
445 
446   PetscFunctionBegin;
447   ierr = PetscObjectGetComm((PetscObject)Gmat1,&comm);CHKERRQ(ierr);
448   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
449   ierr = MatGetOwnershipRange(Gmat1,&my0,&Iend);CHKERRQ(ierr); /* AIJ */
450   nloc = Iend - my0; /* this does not change */
451 
452   if (size == 1) { /* not much to do in serial */
453     ierr = PetscMalloc1(nselected_1, &crsGID);CHKERRQ(ierr);
454     for (kk=0; kk<nselected_1; kk++) crsGID[kk] = kk;
455     *a_Gmat_2 = 0;
456     ierr      = ISCreateGeneral(PETSC_COMM_SELF,nselected_1,clid_lid_1,PETSC_COPY_VALUES,a_selected_2);CHKERRQ(ierr);
457   } else {
458     PetscInt    idx,num_fine_ghosts,num_crs_ghost,myCrs0;
459     Mat_MPIAIJ  *mpimat2;
460     Mat         Gmat2;
461     Vec         locState;
462     PetscScalar *cpcol_state;
463 
464     /* scan my coarse zero gid, set 'lid_state' with coarse GID */
465     kk = nselected_1;
466     ierr = MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
467     myCrs0 -= nselected_1;
468 
469     if (a_Gmat_2) { /* output */
470       /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
471       ierr      = MatTransposeMatMult(Gmat1, Gmat1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Gmat2);CHKERRQ(ierr);
472       *a_Gmat_2 = Gmat2; /* output */
473     } else Gmat2 = Gmat1;  /* use local to get crsGIDs at least */
474     /* get coarse grid GIDS for selected (locals and ghosts) */
475     mpimat2 = (Mat_MPIAIJ*)Gmat2->data;
476     ierr    = MatCreateVecs(Gmat2, &locState, 0);CHKERRQ(ierr);
477     ierr    = VecSet(locState, (PetscScalar)(PetscReal)(-1));CHKERRQ(ierr); /* set with UNKNOWN state */
478     for (kk=0; kk<nselected_1; kk++) {
479       PetscInt    fgid = clid_lid_1[kk] + my0;
480       PetscScalar v    = (PetscScalar)(kk+myCrs0);
481       ierr = VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES);CHKERRQ(ierr); /* set with PID */
482     }
483     ierr = VecAssemblyBegin(locState);CHKERRQ(ierr);
484     ierr = VecAssemblyEnd(locState);CHKERRQ(ierr);
485     ierr = VecScatterBegin(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
486     ierr =   VecScatterEnd(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
487     ierr = VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts);CHKERRQ(ierr);
488     ierr = VecGetArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
489     for (kk=0,num_crs_ghost=0; kk<num_fine_ghosts; kk++) {
490       if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
491     }
492     ierr = PetscMalloc1(nselected_1+num_crs_ghost, &crsGID);CHKERRQ(ierr); /* output */
493     {
494       PetscInt *selected_set;
495       ierr = PetscMalloc1(nselected_1+num_crs_ghost, &selected_set);CHKERRQ(ierr);
496       /* do ghost of 'crsGID' */
497       for (kk=0,idx=nselected_1; kk<num_fine_ghosts; kk++) {
498         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
499           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
500           selected_set[idx] = nloc + kk;
501           crsGID[idx++]     = cgid;
502         }
503       }
504       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);
505       ierr = VecRestoreArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
506       /* do locals in 'crsGID' */
507       ierr = VecGetArray(locState, &cpcol_state);CHKERRQ(ierr);
508       for (kk=0,idx=0; kk<nloc; kk++) {
509         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
510           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
511           selected_set[idx] = kk;
512           crsGID[idx++]     = cgid;
513         }
514       }
515       if (idx != nselected_1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"idx %D != nselected_1 %D",idx,nselected_1);
516       ierr = VecRestoreArray(locState, &cpcol_state);CHKERRQ(ierr);
517 
518       if (a_selected_2 != 0) { /* output */
519         ierr = ISCreateGeneral(PETSC_COMM_SELF,(nselected_1+num_crs_ghost),selected_set,PETSC_OWN_POINTER,a_selected_2);CHKERRQ(ierr);
520       } else {
521         ierr = PetscFree(selected_set);CHKERRQ(ierr);
522       }
523     }
524     ierr = VecDestroy(&locState);CHKERRQ(ierr);
525   }
526   *a_crsGID = crsGID; /* output */
527   PetscFunctionReturn(0);
528 }
529 
530 /* -------------------------------------------------------------------------- */
531 /*
532    PCGAMGGraph_GEO
533 
534   Input Parameter:
535    . pc - this
536    . Amat - matrix on this fine level
537   Output Parameter:
538    . a_Gmat
539 */
540 PetscErrorCode PCGAMGGraph_GEO(PC pc,Mat Amat,Mat *a_Gmat)
541 {
542   PetscErrorCode  ierr;
543   PC_MG           *mg      = (PC_MG*)pc->data;
544   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
545   const PetscReal vfilter  = pc_gamg->threshold[0];
546   MPI_Comm        comm;
547   Mat             Gmat;
548   PetscBool       set,flg,symm;
549 
550   PetscFunctionBegin;
551   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
552   ierr = PetscLogEventBegin(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
553 
554   ierr = MatIsSymmetricKnown(Amat, &set, &flg);CHKERRQ(ierr);
555   symm = (PetscBool)!(set && flg);
556 
557   ierr = PCGAMGCreateGraph(Amat, &Gmat);CHKERRQ(ierr);
558   ierr = PCGAMGFilterGraph(&Gmat, vfilter, symm);CHKERRQ(ierr);
559 
560   *a_Gmat = Gmat;
561   ierr = PetscLogEventEnd(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
562   PetscFunctionReturn(0);
563 }
564 
565 /* -------------------------------------------------------------------------- */
566 /*
567    PCGAMGCoarsen_GEO
568 
569   Input Parameter:
570    . a_pc - this
571    . a_Gmat - graph
572   Output Parameter:
573    . a_llist_parent - linked list from selected indices for data locality only
574 */
575 PetscErrorCode PCGAMGCoarsen_GEO(PC a_pc,Mat *a_Gmat,PetscCoarsenData **a_llist_parent)
576 {
577   PetscErrorCode ierr;
578   PetscInt       Istart,Iend,nloc,kk,Ii,ncols;
579   IS             perm;
580   GAMGNode       *gnodes;
581   PetscInt       *permute;
582   Mat            Gmat  = *a_Gmat;
583   MPI_Comm       comm;
584   MatCoarsen     crs;
585 
586   PetscFunctionBegin;
587   ierr = PetscObjectGetComm((PetscObject)a_pc,&comm);CHKERRQ(ierr);
588   ierr = PetscLogEventBegin(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
589   ierr = MatGetOwnershipRange(Gmat, &Istart, &Iend);CHKERRQ(ierr);
590   nloc = (Iend-Istart);
591 
592   /* create random permutation with sort for geo-mg */
593   ierr = PetscMalloc1(nloc, &gnodes);CHKERRQ(ierr);
594   ierr = PetscMalloc1(nloc, &permute);CHKERRQ(ierr);
595 
596   for (Ii=Istart; Ii<Iend; Ii++) { /* locals only? */
597     ierr = MatGetRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
598     {
599       PetscInt lid = Ii - Istart;
600       gnodes[lid].lid    = lid;
601       gnodes[lid].degree = ncols;
602     }
603     ierr = MatRestoreRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
604   }
605   if (PETSC_TRUE) {
606     PetscRandom  rand;
607     PetscBool    *bIndexSet;
608     PetscReal    rr;
609     PetscInt     iSwapIndex;
610 
611     ierr = PetscRandomCreate(comm,&rand);CHKERRQ(ierr);
612     ierr = PetscCalloc1(nloc, &bIndexSet);CHKERRQ(ierr);
613     for (Ii = 0; Ii < nloc; Ii++) {
614       ierr = PetscRandomGetValueReal(rand,&rr);CHKERRQ(ierr);
615       iSwapIndex = (PetscInt) (rr*nloc);
616       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
617         GAMGNode iTemp = gnodes[iSwapIndex];
618         gnodes[iSwapIndex]    = gnodes[Ii];
619         gnodes[Ii]            = iTemp;
620         bIndexSet[Ii]         = PETSC_TRUE;
621         bIndexSet[iSwapIndex] = PETSC_TRUE;
622       }
623     }
624     ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
625     ierr = PetscFree(bIndexSet);CHKERRQ(ierr);
626   }
627   /* only sort locals */
628   qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
629   /* create IS of permutation */
630   for (kk=0; kk<nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
631   ierr = PetscFree(gnodes);CHKERRQ(ierr);
632   ierr = ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
633 
634   /* get MIS aggs */
635 
636   ierr = MatCoarsenCreate(comm, &crs);CHKERRQ(ierr);
637   ierr = MatCoarsenSetType(crs, MATCOARSENMIS);CHKERRQ(ierr);
638   ierr = MatCoarsenSetGreedyOrdering(crs, perm);CHKERRQ(ierr);
639   ierr = MatCoarsenSetAdjacency(crs, Gmat);CHKERRQ(ierr);
640   ierr = MatCoarsenSetStrictAggs(crs, PETSC_FALSE);CHKERRQ(ierr);
641   ierr = MatCoarsenApply(crs);CHKERRQ(ierr);
642   ierr = MatCoarsenGetData(crs, a_llist_parent);CHKERRQ(ierr);
643   ierr = MatCoarsenDestroy(&crs);CHKERRQ(ierr);
644 
645   ierr = ISDestroy(&perm);CHKERRQ(ierr);
646   ierr = PetscLogEventEnd(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
647   PetscFunctionReturn(0);
648 }
649 
650 /* -------------------------------------------------------------------------- */
651 /*
652  PCGAMGProlongator_GEO
653 
654  Input Parameter:
655  . pc - this
656  . Amat - matrix on this fine level
657  . Graph - used to get ghost data for nodes in
658  . selected_1 - [nselected]
659  . agg_lists - [nselected]
660  Output Parameter:
661  . a_P_out - prolongation operator to the next level
662  */
663 PetscErrorCode PCGAMGProlongator_GEO(PC pc,Mat Amat,Mat Gmat,PetscCoarsenData *agg_lists,Mat *a_P_out)
664 {
665   PC_MG          *mg      = (PC_MG*)pc->data;
666   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
667   const PetscInt dim      = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
668   PetscErrorCode ierr;
669   PetscInt       Istart,Iend,nloc,my0,jj,kk,ncols,nLocalSelected,bs,*clid_flid;
670   Mat            Prol;
671   PetscMPIInt    rank, size;
672   MPI_Comm       comm;
673   IS             selected_2,selected_1;
674   const PetscInt *selected_idx;
675   MatType        mtype;
676 
677   PetscFunctionBegin;
678   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
679   ierr = PetscLogEventBegin(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
680   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
681   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
682   ierr = MatGetOwnershipRange(Amat, &Istart, &Iend);CHKERRQ(ierr);
683   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
684   nloc = (Iend-Istart)/bs; my0 = Istart/bs;
685   if ((Iend-Istart) % bs) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"(Iend %D - Istart %D) % bs %D",Iend,Istart,bs);
686 
687   /* get 'nLocalSelected' */
688   ierr = PetscCDGetMIS(agg_lists, &selected_1);CHKERRQ(ierr);
689   ierr = ISGetSize(selected_1, &jj);CHKERRQ(ierr);
690   ierr = PetscMalloc1(jj, &clid_flid);CHKERRQ(ierr);
691   ierr = ISGetIndices(selected_1, &selected_idx);CHKERRQ(ierr);
692   for (kk=0,nLocalSelected=0; kk<jj; kk++) {
693     PetscInt lid = selected_idx[kk];
694     if (lid<nloc) {
695       ierr = MatGetRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
696       if (ncols>1) clid_flid[nLocalSelected++] = lid; /* fiter out singletons */
697       ierr = MatRestoreRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
698     }
699   }
700   ierr = ISRestoreIndices(selected_1, &selected_idx);CHKERRQ(ierr);
701   ierr = ISDestroy(&selected_1);CHKERRQ(ierr); /* this is selected_1 in serial */
702 
703   /* create prolongator  matrix */
704   ierr = MatGetType(Amat,&mtype);CHKERRQ(ierr);
705   ierr = MatCreate(comm, &Prol);CHKERRQ(ierr);
706   ierr = MatSetSizes(Prol,nloc*bs,nLocalSelected*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
707   ierr = MatSetBlockSizes(Prol, bs, bs);CHKERRQ(ierr);
708   ierr = MatSetType(Prol, mtype);CHKERRQ(ierr);
709   ierr = MatSeqAIJSetPreallocation(Prol,3*data_cols,NULL);CHKERRQ(ierr);
710   ierr = MatMPIAIJSetPreallocation(Prol,3*data_cols,NULL,3*data_cols,NULL);CHKERRQ(ierr);
711 
712   /* can get all points "removed" - but not on geomg */
713   ierr =  MatGetSize(Prol, &kk, &jj);CHKERRQ(ierr);
714   if (!jj) {
715     ierr = PetscInfo(pc,"ERROE: no selected points on coarse grid\n");CHKERRQ(ierr);
716     ierr = PetscFree(clid_flid);CHKERRQ(ierr);
717     ierr = MatDestroy(&Prol);CHKERRQ(ierr);
718     *a_P_out = NULL;  /* out */
719     PetscFunctionReturn(0);
720   }
721 
722   {
723     PetscReal *coords;
724     PetscInt  data_stride;
725     PetscInt  *crsGID = NULL;
726     Mat       Gmat2;
727 
728     if (dim != data_cols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim %D != data_cols %D",dim,data_cols);
729     /* grow ghost data for better coarse grid cover of fine grid */
730 #if defined PETSC_GAMG_USE_LOG
731     ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
732 #endif
733     /* messy method, squares graph and gets some data */
734     ierr = getGIDsOnSquareGraph(nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID);CHKERRQ(ierr);
735     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
736 #if defined PETSC_GAMG_USE_LOG
737     ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
738 #endif
739     /* create global vector of coorindates in 'coords' */
740     if (size > 1) {
741       ierr = PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords);CHKERRQ(ierr);
742     } else {
743       coords      = (PetscReal*)pc_gamg->data;
744       data_stride = pc_gamg->data_sz/pc_gamg->data_cell_cols;
745     }
746     ierr = MatDestroy(&Gmat2);CHKERRQ(ierr);
747 
748     /* triangulate */
749     if (dim == 2) {
750       PetscReal metric,tm;
751 #if defined PETSC_GAMG_USE_LOG
752       ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
753 #endif
754       ierr = triangulateAndFormProl(selected_2, data_stride, coords,nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric);CHKERRQ(ierr);
755 #if defined PETSC_GAMG_USE_LOG
756       ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
757 #endif
758       ierr = PetscFree(crsGID);CHKERRQ(ierr);
759 
760       /* clean up and create coordinates for coarse grid (output) */
761       if (size > 1) ierr = PetscFree(coords);CHKERRQ(ierr);
762 
763       ierr = MPIU_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRQ(ierr);
764       if (tm > 1.) { /* needs to be globalized - should not happen */
765         ierr = PetscInfo1(pc," failed metric for coarse grid %e\n",(double)tm);CHKERRQ(ierr);
766         ierr = MatDestroy(&Prol);CHKERRQ(ierr);
767       } else if (metric > .0) {
768         ierr = PetscInfo1(pc,"worst metric for coarse grid = %e\n",(double)metric);CHKERRQ(ierr);
769       }
770     } else SETERRQ(comm,PETSC_ERR_PLIB,"3D not implemented for 'geo' AMG");
771     { /* create next coords - output */
772       PetscReal *crs_crds;
773       ierr = PetscMalloc1(dim*nLocalSelected, &crs_crds);CHKERRQ(ierr);
774       for (kk=0; kk<nLocalSelected; kk++) { /* grab local select nodes to promote - output */
775         PetscInt lid = clid_flid[kk];
776         for (jj=0; jj<dim; jj++) crs_crds[jj*nLocalSelected + kk] = pc_gamg->data[jj*nloc + lid];
777       }
778 
779       ierr             = PetscFree(pc_gamg->data);CHKERRQ(ierr);
780       pc_gamg->data    = crs_crds; /* out */
781       pc_gamg->data_sz = dim*nLocalSelected;
782     }
783     ierr = ISDestroy(&selected_2);CHKERRQ(ierr);
784   }
785 
786   *a_P_out = Prol;  /* out */
787   ierr     = PetscFree(clid_flid);CHKERRQ(ierr);
788   ierr = PetscLogEventEnd(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
789   PetscFunctionReturn(0);
790 }
791 
792 static PetscErrorCode PCDestroy_GAMG_GEO(PC pc)
793 {
794   PetscErrorCode ierr;
795 
796   PetscFunctionBegin;
797   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
798   PetscFunctionReturn(0);
799 }
800 
801 /* -------------------------------------------------------------------------- */
802 /*
803  PCCreateGAMG_GEO
804 
805   Input Parameter:
806    . pc -
807 */
808 PetscErrorCode  PCCreateGAMG_GEO(PC pc)
809 {
810   PetscErrorCode ierr;
811   PC_MG          *mg      = (PC_MG*)pc->data;
812   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
813 
814   PetscFunctionBegin;
815   pc_gamg->ops->setfromoptions = PCSetFromOptions_GEO;
816   pc_gamg->ops->destroy        = PCDestroy_GAMG_GEO;
817   /* reset does not do anything; setup not virtual */
818 
819   /* set internal function pointers */
820   pc_gamg->ops->graph             = PCGAMGGraph_GEO;
821   pc_gamg->ops->coarsen           = PCGAMGCoarsen_GEO;
822   pc_gamg->ops->prolongator       = PCGAMGProlongator_GEO;
823   pc_gamg->ops->optprolongator    = NULL;
824   pc_gamg->ops->createdefaultdata = PCSetData_GEO;
825 
826   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_GEO);CHKERRQ(ierr);
827   PetscFunctionReturn(0);
828 }
829