xref: /petsc/src/ksp/pc/impls/gamg/geo.c (revision ccb4e88a40f0b86eaeca07ff64c64e4de2fae686)
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   }
119   ierr = PetscOptionsTail();CHKERRQ(ierr);
120   PetscFunctionReturn(0);
121 }
122 
123 /* -------------------------------------------------------------------------- */
124 /*
125  triangulateAndFormProl
126 
127    Input Parameter:
128    . selected_2 - list of selected local ID, includes selected ghosts
129    . data_stride -
130    . coords[2*data_stride] - column vector of local coordinates w/ ghosts
131    . nselected_1 - selected IDs that go with base (1) graph includes selected ghosts
132    . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
133    . agg_lists_1 - list of aggregates selected_1 vertices of aggregate unselected vertices
134    . crsGID[selected.size()] - global index for prolongation operator
135    . bs - block size
136   Output Parameter:
137    . a_Prol - prolongation operator
138    . a_worst_best - measure of worst missed fine vertex, 0 is no misses
139 */
140 static PetscErrorCode triangulateAndFormProl(IS selected_2,PetscInt data_stride,PetscReal coords[],PetscInt nselected_1,const PetscInt clid_lid_1[],const PetscCoarsenData *agg_lists_1,
141                                              const PetscInt crsGID[],PetscInt bs,Mat a_Prol,PetscReal *a_worst_best)
142 {
143 #if defined(PETSC_HAVE_TRIANGLE)
144   PetscErrorCode       ierr;
145   PetscInt             jj,tid,tt,idx,nselected_2;
146   struct triangulateio in,mid;
147   const PetscInt       *selected_idx_2;
148   PetscMPIInt          rank;
149   PetscInt             Istart,Iend,nFineLoc,myFine0;
150   int                  kk,nPlotPts,sid;
151   MPI_Comm             comm;
152   PetscReal            tm;
153 
154   PetscFunctionBegin;
155   ierr = PetscObjectGetComm((PetscObject)a_Prol,&comm);CHKERRQ(ierr);
156   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
157   ierr = ISGetSize(selected_2, &nselected_2);CHKERRQ(ierr);
158   if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
159     *a_worst_best = 100.0; /* this will cause a stop, but not globalized (should not happen) */
160   } else *a_worst_best = 0.0;
161   ierr = MPIU_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRMPI(ierr);
162   if (tm > 0.0) {
163     *a_worst_best = 100.0;
164     PetscFunctionReturn(0);
165   }
166   ierr     = MatGetOwnershipRange(a_Prol, &Istart, &Iend);CHKERRQ(ierr);
167   nFineLoc = (Iend-Istart)/bs; myFine0 = Istart/bs;
168   nPlotPts = nFineLoc; /* locals */
169   /* triangle */
170   /* Define input points - in*/
171   in.numberofpoints          = nselected_2;
172   in.numberofpointattributes = 0;
173   /* get nselected points */
174   ierr = PetscMalloc1(2*nselected_2, &in.pointlist);CHKERRQ(ierr);
175   ierr = ISGetIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
176 
177   for (kk=0,sid=0; kk<nselected_2; kk++,sid += 2) {
178     PetscInt lid = selected_idx_2[kk];
179     in.pointlist[sid]   = coords[lid];
180     in.pointlist[sid+1] = coords[data_stride + lid];
181     if (lid>=nFineLoc) nPlotPts++;
182   }
183   if (sid != 2*nselected_2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != 2*nselected_2 %D",sid,nselected_2);
184 
185   in.numberofsegments      = 0;
186   in.numberofedges         = 0;
187   in.numberofholes         = 0;
188   in.numberofregions       = 0;
189   in.trianglelist          = NULL;
190   in.segmentmarkerlist     = NULL;
191   in.pointattributelist    = NULL;
192   in.pointmarkerlist       = NULL;
193   in.triangleattributelist = NULL;
194   in.trianglearealist      = NULL;
195   in.segmentlist           = NULL;
196   in.holelist              = NULL;
197   in.regionlist            = NULL;
198   in.edgelist              = NULL;
199   in.edgemarkerlist        = NULL;
200   in.normlist              = NULL;
201 
202   /* triangulate */
203   mid.pointlist = NULL;          /* Not needed if -N switch used. */
204   /* Not needed if -N switch used or number of point attributes is zero: */
205   mid.pointattributelist = NULL;
206   mid.pointmarkerlist    = NULL; /* Not needed if -N or -B switch used. */
207   mid.trianglelist       = NULL; /* Not needed if -E switch used. */
208   /* Not needed if -E switch used or number of triangle attributes is zero: */
209   mid.triangleattributelist = NULL;
210   mid.neighborlist          = NULL; /* Needed only if -n switch used. */
211   /* Needed only if segments are output (-p or -c) and -P not used: */
212   mid.segmentlist = NULL;
213   /* Needed only if segments are output (-p or -c) and -P and -B not used: */
214   mid.segmentmarkerlist = NULL;
215   mid.edgelist          = NULL; /* Needed only if -e switch used. */
216   mid.edgemarkerlist    = NULL; /* Needed if -e used and -B not used. */
217   mid.numberoftriangles = 0;
218 
219   /* Triangulate the points.  Switches are chosen to read and write a  */
220   /*   PSLG (p), preserve the convex hull (c), number everything from  */
221   /*   zero (z), assign a regional attribute to each element (A), and  */
222   /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
223   /*   neighbor list (n).                                            */
224   if (nselected_2 != 0) { /* inactive processor */
225     char args[] = "npczQ"; /* c is needed ? */
226     triangulate(args, &in, &mid, (struct triangulateio*) NULL);
227     /* output .poly files for 'showme' */
228     if (!PETSC_TRUE) {
229       static int level = 1;
230       FILE       *file; char fname[32];
231 
232       sprintf(fname,"C%d_%d.poly",level,rank); file = fopen(fname, "w");
233       /*First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)>*/
234       fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0);
235       /*Following lines: <vertex #> <x> <y> */
236       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid += 2) {
237         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
238       }
239       /*One line: <# of segments> <# of boundary markers (0 or 1)> */
240       fprintf(file, "%d  %d\n",0,0);
241       /*Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
242       /* One line: <# of holes> */
243       fprintf(file, "%d\n",0);
244       /* Following lines: <hole #> <x> <y> */
245       /* Optional line: <# of regional attributes and/or area constraints> */
246       /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
247       fclose(file);
248 
249       /* elems */
250       sprintf(fname,"C%d_%d.ele",level,rank); file = fopen(fname, "w");
251       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
252       fprintf(file, "%d %d %d\n",mid.numberoftriangles,3,0);
253       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
254       for (kk=0,sid=0; kk<mid.numberoftriangles; kk++,sid += 3) {
255         fprintf(file, "%d %d %d %d\n",kk,mid.trianglelist[sid],mid.trianglelist[sid+1],mid.trianglelist[sid+2]);
256       }
257       fclose(file);
258 
259       sprintf(fname,"C%d_%d.node",level,rank); file = fopen(fname, "w");
260       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
261       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
262       fprintf(file, "%d  %d  %d  %d\n",nPlotPts,2,0,0);
263       /*Following lines: <vertex #> <x> <y> */
264       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid+=2) {
265         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
266       }
267 
268       sid /= 2;
269       for (jj=0; jj<nFineLoc; jj++) {
270         PetscBool sel = PETSC_TRUE;
271         for (kk=0; kk<nselected_2 && sel; kk++) {
272           PetscInt lid = selected_idx_2[kk];
273           if (lid == jj) sel = PETSC_FALSE;
274         }
275         if (sel) fprintf(file, "%d %e %e\n",sid++,coords[jj],coords[data_stride + jj]);
276       }
277       fclose(file);
278       if (sid != nPlotPts) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != nPlotPts %D",sid,nPlotPts);
279       level++;
280     }
281   }
282   ierr = PetscLogEventBegin(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
283   { /* form P - setup some maps */
284     PetscInt clid,mm,*nTri,*node_tri;
285 
286     ierr = PetscMalloc2(nselected_2, &node_tri,nselected_2, &nTri);CHKERRQ(ierr);
287 
288     /* need list of triangles on node */
289     for (kk=0; kk<nselected_2; kk++) nTri[kk] = 0;
290     for (tid=0,kk=0; tid<mid.numberoftriangles; tid++) {
291       for (jj=0; jj<3; jj++) {
292         PetscInt cid = mid.trianglelist[kk++];
293         if (nTri[cid] == 0) node_tri[cid] = tid;
294         nTri[cid]++;
295       }
296     }
297 #define EPS 1.e-12
298     /* find points and set prolongation */
299     for (mm = clid = 0; mm < nFineLoc; mm++) {
300       PetscBool ise;
301       ierr = PetscCDEmptyAt(agg_lists_1,mm,&ise);CHKERRQ(ierr);
302       if (!ise) {
303         const PetscInt lid = mm;
304         PetscScalar    AA[3][3];
305         PetscBLASInt   N=3,NRHS=1,LDA=3,IPIV[3],LDB=3,INFO;
306         PetscCDIntNd   *pos;
307 
308         ierr = PetscCDGetHeadPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
309         while (pos) {
310           PetscInt flid;
311           ierr = PetscCDIntNdGetID(pos, &flid);CHKERRQ(ierr);
312           ierr = PetscCDGetNextPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
313 
314           if (flid < nFineLoc) {  /* could be a ghost */
315             PetscInt       bestTID = -1; PetscReal best_alpha = 1.e10;
316             const PetscInt fgid    = flid + myFine0;
317             /* compute shape function for gid */
318             const PetscReal fcoord[3] = {coords[flid],coords[data_stride+flid],1.0};
319             PetscBool       haveit    =PETSC_FALSE; PetscScalar alpha[3]; PetscInt clids[3];
320 
321             /* look for it */
322             for (tid = node_tri[clid], jj=0;
323                  jj < 5 && !haveit && tid != -1;
324                  jj++) {
325               for (tt=0; tt<3; tt++) {
326                 PetscInt cid2 = mid.trianglelist[3*tid + tt];
327                 PetscInt lid2 = selected_idx_2[cid2];
328                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
329                 clids[tt] = cid2; /* store for interp */
330               }
331 
332               for (tt=0; tt<3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];
333 
334               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
335               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
336               {
337                 PetscBool have=PETSC_TRUE;  PetscReal lowest=1.e10;
338                 for (tt = 0, idx = 0; tt < 3; tt++) {
339                   if (PetscRealPart(alpha[tt]) > (1.0+EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
340                   if (PetscRealPart(alpha[tt]) < lowest) {
341                     lowest = PetscRealPart(alpha[tt]);
342                     idx    = tt;
343                   }
344                 }
345                 haveit = have;
346               }
347               tid = mid.neighborlist[3*tid + idx];
348             }
349 
350             if (!haveit) {
351               /* brute force */
352               for (tid=0; tid<mid.numberoftriangles && !haveit; tid++) {
353                 for (tt=0; tt<3; tt++) {
354                   PetscInt cid2 = mid.trianglelist[3*tid + tt];
355                   PetscInt lid2 = selected_idx_2[cid2];
356                   AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
357                   clids[tt] = cid2; /* store for interp */
358                 }
359                 for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
360                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
361                 PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
362                 {
363                   PetscBool have=PETSC_TRUE;  PetscReal worst=0.0, v;
364                   for (tt=0; tt<3 && have; tt++) {
365                     if (PetscRealPart(alpha[tt]) > 1.0+EPS || PetscRealPart(alpha[tt]) < -EPS) have=PETSC_FALSE;
366                     if ((v=PetscAbs(PetscRealPart(alpha[tt])-0.5)) > worst) worst = v;
367                   }
368                   if (worst < best_alpha) {
369                     best_alpha = worst; bestTID = tid;
370                   }
371                   haveit = have;
372                 }
373               }
374             }
375             if (!haveit) {
376               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
377               /* use best one */
378               for (tt=0; tt<3; tt++) {
379                 PetscInt cid2 = mid.trianglelist[3*bestTID + tt];
380                 PetscInt lid2 = selected_idx_2[cid2];
381                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
382                 clids[tt] = cid2; /* store for interp */
383               }
384               for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
385               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
386               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
387             }
388 
389             /* put in row of P */
390             for (idx=0; idx<3; idx++) {
391               PetscScalar shp = alpha[idx];
392               if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
393                 PetscInt cgid = crsGID[clids[idx]];
394                 PetscInt jj   = cgid*bs, ii = fgid*bs; /* need to gloalize */
395                 for (tt=0; tt < bs; tt++, ii++, jj++) {
396                   ierr = MatSetValues(a_Prol,1,&ii,1,&jj,&shp,INSERT_VALUES);CHKERRQ(ierr);
397                 }
398               }
399             }
400           }
401         } /* aggregates iterations */
402         clid++;
403       } /* a coarse agg */
404     } /* for all fine nodes */
405 
406     ierr = ISRestoreIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
407     ierr = MatAssemblyBegin(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
408     ierr = MatAssemblyEnd(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
409 
410     ierr = PetscFree2(node_tri,nTri);CHKERRQ(ierr);
411   }
412   ierr = PetscLogEventEnd(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
413   free(mid.trianglelist);
414   free(mid.neighborlist);
415   free(mid.segmentlist);
416   free(mid.segmentmarkerlist);
417   free(mid.pointlist);
418   free(mid.pointmarkerlist);
419   ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
420   PetscFunctionReturn(0);
421 #else
422   SETERRQ(PetscObjectComm((PetscObject)a_Prol),PETSC_ERR_PLIB,"configure with TRIANGLE to use geometric MG");
423 #endif
424 }
425 /* -------------------------------------------------------------------------- */
426 /*
427    getGIDsOnSquareGraph - square graph, get
428 
429    Input Parameter:
430    . nselected_1 - selected local indices (includes ghosts in input Gmat1)
431    . clid_lid_1 - [nselected_1] lids of selected nodes
432    . Gmat1 - graph that goes with 'selected_1'
433    Output Parameter:
434    . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
435    . a_Gmat_2 - graph that is squared of 'Gmat_1'
436    . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
437 */
438 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)
439 {
440   PetscErrorCode ierr;
441   PetscMPIInt    size;
442   PetscInt       *crsGID, kk,my0,Iend,nloc;
443   MPI_Comm       comm;
444 
445   PetscFunctionBegin;
446   ierr = PetscObjectGetComm((PetscObject)Gmat1,&comm);CHKERRQ(ierr);
447   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
448   ierr = MatGetOwnershipRange(Gmat1,&my0,&Iend);CHKERRQ(ierr); /* AIJ */
449   nloc = Iend - my0; /* this does not change */
450 
451   if (size == 1) { /* not much to do in serial */
452     ierr = PetscMalloc1(nselected_1, &crsGID);CHKERRQ(ierr);
453     for (kk=0; kk<nselected_1; kk++) crsGID[kk] = kk;
454     *a_Gmat_2 = NULL;
455     ierr      = ISCreateGeneral(PETSC_COMM_SELF,nselected_1,clid_lid_1,PETSC_COPY_VALUES,a_selected_2);CHKERRQ(ierr);
456   } else {
457     PetscInt    idx,num_fine_ghosts,num_crs_ghost,myCrs0;
458     Mat_MPIAIJ  *mpimat2;
459     Mat         Gmat2;
460     Vec         locState;
461     PetscScalar *cpcol_state;
462 
463     /* scan my coarse zero gid, set 'lid_state' with coarse GID */
464     kk = nselected_1;
465     ierr = MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPI_SUM, comm);CHKERRMPI(ierr);
466     myCrs0 -= nselected_1;
467 
468     if (a_Gmat_2) { /* output */
469       /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
470       ierr = PCGAMGSquareGraph_GAMG(pc,Gmat1,&Gmat2);CHKERRQ(ierr);
471       *a_Gmat_2 = Gmat2; /* output */
472     } else Gmat2 = Gmat1;  /* use local to get crsGIDs at least */
473     /* get coarse grid GIDS for selected (locals and ghosts) */
474     mpimat2 = (Mat_MPIAIJ*)Gmat2->data;
475     ierr    = MatCreateVecs(Gmat2, &locState, NULL);CHKERRQ(ierr);
476     ierr    = VecSet(locState, (PetscScalar)(PetscReal)(-1));CHKERRQ(ierr); /* set with UNKNOWN state */
477     for (kk=0; kk<nselected_1; kk++) {
478       PetscInt    fgid = clid_lid_1[kk] + my0;
479       PetscScalar v    = (PetscScalar)(kk+myCrs0);
480       ierr = VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES);CHKERRQ(ierr); /* set with PID */
481     }
482     ierr = VecAssemblyBegin(locState);CHKERRQ(ierr);
483     ierr = VecAssemblyEnd(locState);CHKERRQ(ierr);
484     ierr = VecScatterBegin(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
485     ierr =   VecScatterEnd(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
486     ierr = VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts);CHKERRQ(ierr);
487     ierr = VecGetArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
488     for (kk=0,num_crs_ghost=0; kk<num_fine_ghosts; kk++) {
489       if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
490     }
491     ierr = PetscMalloc1(nselected_1+num_crs_ghost, &crsGID);CHKERRQ(ierr); /* output */
492     {
493       PetscInt *selected_set;
494       ierr = PetscMalloc1(nselected_1+num_crs_ghost, &selected_set);CHKERRQ(ierr);
495       /* do ghost of 'crsGID' */
496       for (kk=0,idx=nselected_1; kk<num_fine_ghosts; kk++) {
497         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
498           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
499           selected_set[idx] = nloc + kk;
500           crsGID[idx++]     = cgid;
501         }
502       }
503       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);
504       ierr = VecRestoreArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
505       /* do locals in 'crsGID' */
506       ierr = VecGetArray(locState, &cpcol_state);CHKERRQ(ierr);
507       for (kk=0,idx=0; kk<nloc; kk++) {
508         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
509           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
510           selected_set[idx] = kk;
511           crsGID[idx++]     = cgid;
512         }
513       }
514       if (idx != nselected_1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"idx %D != nselected_1 %D",idx,nselected_1);
515       ierr = VecRestoreArray(locState, &cpcol_state);CHKERRQ(ierr);
516 
517       if (a_selected_2 != NULL) { /* output */
518         ierr = ISCreateGeneral(PETSC_COMM_SELF,(nselected_1+num_crs_ghost),selected_set,PETSC_OWN_POINTER,a_selected_2);CHKERRQ(ierr);
519       } else {
520         ierr = PetscFree(selected_set);CHKERRQ(ierr);
521       }
522     }
523     ierr = VecDestroy(&locState);CHKERRQ(ierr);
524   }
525   *a_crsGID = crsGID; /* output */
526   PetscFunctionReturn(0);
527 }
528 
529 /* -------------------------------------------------------------------------- */
530 /*
531    PCGAMGGraph_GEO
532 
533   Input Parameter:
534    . pc - this
535    . Amat - matrix on this fine level
536   Output Parameter:
537    . a_Gmat
538 */
539 PetscErrorCode PCGAMGGraph_GEO(PC pc,Mat Amat,Mat *a_Gmat)
540 {
541   PetscErrorCode  ierr;
542   PC_MG           *mg      = (PC_MG*)pc->data;
543   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
544   const PetscReal vfilter  = pc_gamg->threshold[0];
545   MPI_Comm        comm;
546   Mat             Gmat;
547   PetscBool       set,flg,symm;
548 
549   PetscFunctionBegin;
550   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
551   ierr = PetscLogEventBegin(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
552 
553   ierr = MatIsSymmetricKnown(Amat, &set, &flg);CHKERRQ(ierr);
554   symm = (PetscBool)!(set && flg);
555 
556   ierr = PCGAMGCreateGraph(Amat, &Gmat);CHKERRQ(ierr);
557   ierr = PCGAMGFilterGraph(&Gmat, vfilter, symm);CHKERRQ(ierr);
558 
559   *a_Gmat = Gmat;
560   ierr = PetscLogEventEnd(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
561   PetscFunctionReturn(0);
562 }
563 
564 /* -------------------------------------------------------------------------- */
565 /*
566    PCGAMGCoarsen_GEO
567 
568   Input Parameter:
569    . a_pc - this
570    . a_Gmat - graph
571   Output Parameter:
572    . a_llist_parent - linked list from selected indices for data locality only
573 */
574 PetscErrorCode PCGAMGCoarsen_GEO(PC a_pc,Mat *a_Gmat,PetscCoarsenData **a_llist_parent)
575 {
576   PetscErrorCode ierr;
577   PetscInt       Istart,Iend,nloc,kk,Ii,ncols;
578   IS             perm;
579   GAMGNode       *gnodes;
580   PetscInt       *permute;
581   Mat            Gmat  = *a_Gmat;
582   MPI_Comm       comm;
583   MatCoarsen     crs;
584 
585   PetscFunctionBegin;
586   ierr = PetscObjectGetComm((PetscObject)a_pc,&comm);CHKERRQ(ierr);
587   ierr = PetscLogEventBegin(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
588   ierr = MatGetOwnershipRange(Gmat, &Istart, &Iend);CHKERRQ(ierr);
589   nloc = (Iend-Istart);
590 
591   /* create random permutation with sort for geo-mg */
592   ierr = PetscMalloc1(nloc, &gnodes);CHKERRQ(ierr);
593   ierr = PetscMalloc1(nloc, &permute);CHKERRQ(ierr);
594 
595   for (Ii=Istart; Ii<Iend; Ii++) { /* locals only? */
596     ierr = MatGetRow(Gmat,Ii,&ncols,NULL,NULL);CHKERRQ(ierr);
597     {
598       PetscInt lid = Ii - Istart;
599       gnodes[lid].lid    = lid;
600       gnodes[lid].degree = ncols;
601     }
602     ierr = MatRestoreRow(Gmat,Ii,&ncols,NULL,NULL);CHKERRQ(ierr);
603   }
604   if (PETSC_TRUE) {
605     PetscRandom  rand;
606     PetscBool    *bIndexSet;
607     PetscReal    rr;
608     PetscInt     iSwapIndex;
609 
610     ierr = PetscRandomCreate(comm,&rand);CHKERRQ(ierr);
611     ierr = PetscCalloc1(nloc, &bIndexSet);CHKERRQ(ierr);
612     for (Ii = 0; Ii < nloc; Ii++) {
613       ierr = PetscRandomGetValueReal(rand,&rr);CHKERRQ(ierr);
614       iSwapIndex = (PetscInt) (rr*nloc);
615       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
616         GAMGNode iTemp = gnodes[iSwapIndex];
617         gnodes[iSwapIndex]    = gnodes[Ii];
618         gnodes[Ii]            = iTemp;
619         bIndexSet[Ii]         = PETSC_TRUE;
620         bIndexSet[iSwapIndex] = PETSC_TRUE;
621       }
622     }
623     ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
624     ierr = PetscFree(bIndexSet);CHKERRQ(ierr);
625   }
626   /* only sort locals */
627   qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
628   /* create IS of permutation */
629   for (kk=0; kk<nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
630   ierr = PetscFree(gnodes);CHKERRQ(ierr);
631   ierr = ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
632 
633   /* get MIS aggs */
634 
635   ierr = MatCoarsenCreate(comm, &crs);CHKERRQ(ierr);
636   ierr = MatCoarsenSetType(crs, MATCOARSENMIS);CHKERRQ(ierr);
637   ierr = MatCoarsenSetGreedyOrdering(crs, perm);CHKERRQ(ierr);
638   ierr = MatCoarsenSetAdjacency(crs, Gmat);CHKERRQ(ierr);
639   ierr = MatCoarsenSetStrictAggs(crs, PETSC_FALSE);CHKERRQ(ierr);
640   ierr = MatCoarsenApply(crs);CHKERRQ(ierr);
641   ierr = MatCoarsenGetData(crs, a_llist_parent);CHKERRQ(ierr);
642   ierr = MatCoarsenDestroy(&crs);CHKERRQ(ierr);
643 
644   ierr = ISDestroy(&perm);CHKERRQ(ierr);
645   ierr = PetscLogEventEnd(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
646   PetscFunctionReturn(0);
647 }
648 
649 /* -------------------------------------------------------------------------- */
650 /*
651  PCGAMGProlongator_GEO
652 
653  Input Parameter:
654  . pc - this
655  . Amat - matrix on this fine level
656  . Graph - used to get ghost data for nodes in
657  . selected_1 - [nselected]
658  . agg_lists - [nselected]
659  Output Parameter:
660  . a_P_out - prolongation operator to the next level
661  */
662 PetscErrorCode PCGAMGProlongator_GEO(PC pc,Mat Amat,Mat Gmat,PetscCoarsenData *agg_lists,Mat *a_P_out)
663 {
664   PC_MG          *mg      = (PC_MG*)pc->data;
665   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
666   const PetscInt dim      = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
667   PetscErrorCode ierr;
668   PetscInt       Istart,Iend,nloc,my0,jj,kk,ncols,nLocalSelected,bs,*clid_flid;
669   Mat            Prol;
670   PetscMPIInt    rank, size;
671   MPI_Comm       comm;
672   IS             selected_2,selected_1;
673   const PetscInt *selected_idx;
674   MatType        mtype;
675 
676   PetscFunctionBegin;
677   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
678   ierr = PetscLogEventBegin(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
679   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
680   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
681   ierr = MatGetOwnershipRange(Amat, &Istart, &Iend);CHKERRQ(ierr);
682   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
683   nloc = (Iend-Istart)/bs; my0 = Istart/bs;
684   if ((Iend-Istart) % bs) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"(Iend %D - Istart %D) % bs %D",Iend,Istart,bs);
685 
686   /* get 'nLocalSelected' */
687   ierr = PetscCDGetMIS(agg_lists, &selected_1);CHKERRQ(ierr);
688   ierr = ISGetSize(selected_1, &jj);CHKERRQ(ierr);
689   ierr = PetscMalloc1(jj, &clid_flid);CHKERRQ(ierr);
690   ierr = ISGetIndices(selected_1, &selected_idx);CHKERRQ(ierr);
691   for (kk=0,nLocalSelected=0; kk<jj; kk++) {
692     PetscInt lid = selected_idx[kk];
693     if (lid<nloc) {
694       ierr = MatGetRow(Gmat,lid+my0,&ncols,NULL,NULL);CHKERRQ(ierr);
695       if (ncols>1) clid_flid[nLocalSelected++] = lid; /* fiter out singletons */
696       ierr = MatRestoreRow(Gmat,lid+my0,&ncols,NULL,NULL);CHKERRQ(ierr);
697     }
698   }
699   ierr = ISRestoreIndices(selected_1, &selected_idx);CHKERRQ(ierr);
700   ierr = ISDestroy(&selected_1);CHKERRQ(ierr); /* this is selected_1 in serial */
701 
702   /* create prolongator  matrix */
703   ierr = MatGetType(Amat,&mtype);CHKERRQ(ierr);
704   ierr = MatCreate(comm, &Prol);CHKERRQ(ierr);
705   ierr = MatSetSizes(Prol,nloc*bs,nLocalSelected*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
706   ierr = MatSetBlockSizes(Prol, bs, bs);CHKERRQ(ierr);
707   ierr = MatSetType(Prol, mtype);CHKERRQ(ierr);
708   ierr = MatSeqAIJSetPreallocation(Prol,3*data_cols,NULL);CHKERRQ(ierr);
709   ierr = MatMPIAIJSetPreallocation(Prol,3*data_cols,NULL,3*data_cols,NULL);CHKERRQ(ierr);
710 
711   /* can get all points "removed" - but not on geomg */
712   ierr =  MatGetSize(Prol, &kk, &jj);CHKERRQ(ierr);
713   if (!jj) {
714     ierr = PetscInfo(pc,"ERROE: no selected points on coarse grid\n");CHKERRQ(ierr);
715     ierr = PetscFree(clid_flid);CHKERRQ(ierr);
716     ierr = MatDestroy(&Prol);CHKERRQ(ierr);
717     *a_P_out = NULL;  /* out */
718     PetscFunctionReturn(0);
719   }
720 
721   {
722     PetscReal *coords;
723     PetscInt  data_stride;
724     PetscInt  *crsGID = NULL;
725     Mat       Gmat2;
726 
727     if (dim != data_cols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim %D != data_cols %D",dim,data_cols);
728     /* grow ghost data for better coarse grid cover of fine grid */
729     ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
730     /* messy method, squares graph and gets some data */
731     ierr = getGIDsOnSquareGraph(pc, nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID);CHKERRQ(ierr);
732     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
733     ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
734     /* create global vector of coorindates in 'coords' */
735     if (size > 1) {
736       ierr = PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords);CHKERRQ(ierr);
737     } else {
738       coords      = (PetscReal*)pc_gamg->data;
739       data_stride = pc_gamg->data_sz/pc_gamg->data_cell_cols;
740     }
741     ierr = MatDestroy(&Gmat2);CHKERRQ(ierr);
742 
743     /* triangulate */
744     if (dim == 2) {
745       PetscReal metric,tm;
746       ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
747       ierr = triangulateAndFormProl(selected_2, data_stride, coords,nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric);CHKERRQ(ierr);
748       ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
749       ierr = PetscFree(crsGID);CHKERRQ(ierr);
750 
751       /* clean up and create coordinates for coarse grid (output) */
752       if (size > 1) {ierr = PetscFree(coords);CHKERRQ(ierr);}
753 
754       ierr = MPIU_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRMPI(ierr);
755       if (tm > 1.) { /* needs to be globalized - should not happen */
756         ierr = PetscInfo1(pc," failed metric for coarse grid %e\n",(double)tm);CHKERRQ(ierr);
757         ierr = MatDestroy(&Prol);CHKERRQ(ierr);
758       } else if (metric > .0) {
759         ierr = PetscInfo1(pc,"worst metric for coarse grid = %e\n",(double)metric);CHKERRQ(ierr);
760       }
761     } else SETERRQ(comm,PETSC_ERR_PLIB,"3D not implemented for 'geo' AMG");
762     { /* create next coords - output */
763       PetscReal *crs_crds;
764       ierr = PetscMalloc1(dim*nLocalSelected, &crs_crds);CHKERRQ(ierr);
765       for (kk=0; kk<nLocalSelected; kk++) { /* grab local select nodes to promote - output */
766         PetscInt lid = clid_flid[kk];
767         for (jj=0; jj<dim; jj++) crs_crds[jj*nLocalSelected + kk] = pc_gamg->data[jj*nloc + lid];
768       }
769 
770       ierr             = PetscFree(pc_gamg->data);CHKERRQ(ierr);
771       pc_gamg->data    = crs_crds; /* out */
772       pc_gamg->data_sz = dim*nLocalSelected;
773     }
774     ierr = ISDestroy(&selected_2);CHKERRQ(ierr);
775   }
776 
777   *a_P_out = Prol;  /* out */
778   ierr     = PetscFree(clid_flid);CHKERRQ(ierr);
779   ierr = PetscLogEventEnd(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
780   PetscFunctionReturn(0);
781 }
782 
783 static PetscErrorCode PCDestroy_GAMG_GEO(PC pc)
784 {
785   PetscErrorCode ierr;
786 
787   PetscFunctionBegin;
788   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
789   PetscFunctionReturn(0);
790 }
791 
792 /* -------------------------------------------------------------------------- */
793 /*
794  PCCreateGAMG_GEO
795 
796   Input Parameter:
797    . pc -
798 */
799 PetscErrorCode  PCCreateGAMG_GEO(PC pc)
800 {
801   PetscErrorCode ierr;
802   PC_MG          *mg      = (PC_MG*)pc->data;
803   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
804 
805   PetscFunctionBegin;
806   pc_gamg->ops->setfromoptions = PCSetFromOptions_GEO;
807   pc_gamg->ops->destroy        = PCDestroy_GAMG_GEO;
808   /* reset does not do anything; setup not virtual */
809 
810   /* set internal function pointers */
811   pc_gamg->ops->graph             = PCGAMGGraph_GEO;
812   pc_gamg->ops->coarsen           = PCGAMGCoarsen_GEO;
813   pc_gamg->ops->prolongator       = PCGAMGProlongator_GEO;
814   pc_gamg->ops->optprolongator    = NULL;
815   pc_gamg->ops->createdefaultdata = PCSetData_GEO;
816 
817   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_GEO);CHKERRQ(ierr);
818   PetscFunctionReturn(0);
819 }
820