xref: /petsc/src/ksp/pc/impls/gamg/geo.c (revision 2205254efee3a00a594e5e2a3a70f74dcb40bc03)
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 #include <petsc-private/kspimpl.h>
7 
8 #if defined(PETSC_HAVE_TRIANGLE)
9 #define REAL PetscReal
10 #include <triangle.h>
11 #endif
12 
13 #include <assert.h>
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 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 EXTERN_C_BEGIN
35 #undef __FUNCT__
36 #define __FUNCT__ "PCSetCoordinates_GEO"
37 PetscErrorCode PCSetCoordinates_GEO(PC pc, PetscInt ndm, PetscInt a_nloc, PetscReal *coords)
38 {
39   PC_MG          *mg      = (PC_MG*)pc->data;
40   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
41   PetscErrorCode ierr;
42   PetscInt       arrsz,bs,my0,kk,ii,nloc,Iend;
43   Mat            Amat = pc->pmat;
44 
45   PetscFunctionBegin;
46   PetscValidHeaderSpecific(Amat, MAT_CLASSID, 1);
47   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
48 
49   ierr = MatGetOwnershipRange(Amat, &my0, &Iend);CHKERRQ(ierr);
50   nloc = (Iend-my0)/bs;
51 
52   if (nloc!=a_nloc) SETERRQ2(((PetscObject)Amat)->comm,PETSC_ERR_ARG_WRONG, "Stokes not supported nloc = %d %d.",a_nloc,nloc);
53   if ((Iend-my0)%bs!=0) SETERRQ1(((PetscObject)Amat)->comm,PETSC_ERR_ARG_WRONG, "Bad local size %d.",nloc);
54 
55   pc_gamg->data_cell_rows = 1;
56   if (coords==0 && nloc > 0) SETERRQ(((PetscObject)Amat)->comm,PETSC_ERR_ARG_WRONG, "Need coordinates for pc_gamg_type 'geo'.");
57   pc_gamg->data_cell_cols = ndm; /* coordinates */
58 
59   arrsz = nloc*pc_gamg->data_cell_rows*pc_gamg->data_cell_cols;
60 
61   /* create data - syntactic sugar that should be refactored at some point */
62   if (pc_gamg->data==0 || (pc_gamg->data_sz != arrsz)) {
63     ierr = PetscFree(pc_gamg->data);CHKERRQ(ierr);
64     ierr = PetscMalloc((arrsz+1)*sizeof(PetscReal), &pc_gamg->data);CHKERRQ(ierr);
65   }
66   for (kk=0; kk<arrsz; kk++) pc_gamg->data[kk] = -999.;
67   pc_gamg->data[arrsz] = -99.;
68   /* copy data in - column oriented */
69   for (kk = 0; kk < nloc; kk++) {
70     for (ii = 0; ii < ndm; ii++) {
71       pc_gamg->data[ii*nloc + kk] =  coords[kk*ndm + ii];
72     }
73   }
74   assert(pc_gamg->data[arrsz] == -99.);
75 
76   pc_gamg->data_sz = arrsz;
77   PetscFunctionReturn(0);
78 }
79 EXTERN_C_END
80 
81 /* -------------------------------------------------------------------------- */
82 /*
83    PCSetData_GEO
84 
85   Input Parameter:
86    . pc -
87 */
88 #undef __FUNCT__
89 #define __FUNCT__ "PCSetData_GEO"
90 PetscErrorCode PCSetData_GEO(PC pc, Mat m)
91 {
92   PetscFunctionBegin;
93   SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_PLIB,"GEO MG needs coordinates");
94 }
95 
96 /* -------------------------------------------------------------------------- */
97 /*
98    PCSetFromOptions_GEO
99 
100   Input Parameter:
101    . pc -
102 */
103 #undef __FUNCT__
104 #define __FUNCT__ "PCSetFromOptions_GEO"
105 PetscErrorCode PCSetFromOptions_GEO(PC pc)
106 {
107   PetscErrorCode ierr;
108   PC_MG          *mg      = (PC_MG*)pc->data;
109   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
110 
111   PetscFunctionBegin;
112   ierr = PetscOptionsHead("GAMG-GEO options");CHKERRQ(ierr);
113   {
114     /* -pc_gamg_sa_nsmooths */
115     /* pc_gamg_sa->smooths = 0; */
116     /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
117     /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
118     /*                        "PCGAMGSetNSmooths_AGG", */
119     /*                        pc_gamg_sa->smooths, */
120     /*                        &pc_gamg_sa->smooths, */
121     /*                        &flag);  */
122     /* CHKERRQ(ierr); */
123   }
124   ierr = PetscOptionsTail();CHKERRQ(ierr);
125 
126   /* call base class */
127   ierr = PCSetFromOptions_GAMG(pc);CHKERRQ(ierr);
128 
129   if (pc_gamg->verbose) {
130     MPI_Comm wcomm = ((PetscObject)pc)->comm;
131     PetscPrintf(wcomm,"[%d]%s done\n",0,__FUNCT__);
132   }
133   PetscFunctionReturn(0);
134 }
135 
136 /* -------------------------------------------------------------------------- */
137 /*
138  triangulateAndFormProl
139 
140    Input Parameter:
141    . selected_2 - list of selected local ID, includes selected ghosts
142    . data_stride -
143    . coords[2*data_stride] - column vector of local coordinates w/ ghosts
144    . nselected_1 - selected IDs that go with base (1) graph
145    . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
146    . agg_lists_1 - list of aggregates
147    . crsGID[selected.size()] - global index for prolongation operator
148    . bs - block size
149   Output Parameter:
150    . a_Prol - prolongation operator
151    . a_worst_best - measure of worst missed fine vertex, 0 is no misses
152 */
153 #undef __FUNCT__
154 #define __FUNCT__ "triangulateAndFormProl"
155 static PetscErrorCode triangulateAndFormProl(IS  selected_2, /* list of selected local ID, includes selected ghosts */
156                                              const PetscInt data_stride,
157                                              const PetscReal coords[], /* column vector of local coordinates w/ ghosts */
158                                              const PetscInt nselected_1, /* list of selected local ID, includes selected ghosts */
159                                              const PetscInt clid_lid_1[],
160                                              const PetscCoarsenData *agg_lists_1, /* selected_1 vertices of aggregate unselected vertices */
161                                              const PetscInt crsGID[],
162                                              const PetscInt bs,
163                                              Mat a_Prol, /* prolongation operator (output) */
164                                              PetscReal *a_worst_best) /* measure of worst missed fine vertex, 0 is no misses */
165 {
166 #if defined(PETSC_HAVE_TRIANGLE)
167   PetscErrorCode       ierr;
168   PetscInt             jj,tid,tt,idx,nselected_2;
169   struct triangulateio in,mid;
170   const PetscInt       *selected_idx_2;
171   PetscMPIInt          rank,size;
172   PetscInt             Istart,Iend,nFineLoc,myFine0;
173   int                  kk,nPlotPts,sid;
174   MPI_Comm             wcomm = ((PetscObject)a_Prol)->comm;
175   PetscReal            tm;
176 
177   PetscFunctionBegin;
178   ierr = MPI_Comm_rank(wcomm,&rank);CHKERRQ(ierr);
179   ierr = MPI_Comm_size(wcomm,&size);CHKERRQ(ierr);
180   ierr = ISGetSize(selected_2, &nselected_2);CHKERRQ(ierr);
181   if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
182     *a_worst_best = 100.0; /* this will cause a stop, but not globalized (should not happen) */
183   } else *a_worst_best = 0.0;
184   ierr = MPI_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, wcomm);CHKERRQ(ierr);
185   if (tm > 0.0) {
186     *a_worst_best = 100.0;
187     PetscFunctionReturn(0);
188   }
189   ierr     = MatGetOwnershipRange(a_Prol, &Istart, &Iend);CHKERRQ(ierr);
190   nFineLoc = (Iend-Istart)/bs; myFine0 = Istart/bs;
191   nPlotPts = nFineLoc; /* locals */
192   /* traingle */
193   /* Define input points - in*/
194   in.numberofpoints          = nselected_2;
195   in.numberofpointattributes = 0;
196   /* get nselected points */
197   ierr = PetscMalloc(2*(nselected_2)*sizeof(REAL), &in.pointlist);CHKERRQ(ierr);
198   ierr = ISGetIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
199 
200   for (kk=0,sid=0; kk<nselected_2; kk++,sid += 2) {
201     PetscInt lid = selected_idx_2[kk];
202     in.pointlist[sid]   = coords[lid];
203     in.pointlist[sid+1] = coords[data_stride + lid];
204     if (lid>=nFineLoc) nPlotPts++;
205   }
206   assert(sid==2*nselected_2);
207 
208   in.numberofsegments      = 0;
209   in.numberofedges         = 0;
210   in.numberofholes         = 0;
211   in.numberofregions       = 0;
212   in.trianglelist          = 0;
213   in.segmentmarkerlist     = 0;
214   in.pointattributelist    = 0;
215   in.pointmarkerlist       = 0;
216   in.triangleattributelist = 0;
217   in.trianglearealist      = 0;
218   in.segmentlist           = 0;
219   in.holelist              = 0;
220   in.regionlist            = 0;
221   in.edgelist              = 0;
222   in.edgemarkerlist        = 0;
223   in.normlist              = 0;
224 
225   /* triangulate */
226   mid.pointlist = 0;            /* Not needed if -N switch used. */
227   /* Not needed if -N switch used or number of point attributes is zero: */
228   mid.pointattributelist = 0;
229   mid.pointmarkerlist    = 0; /* Not needed if -N or -B switch used. */
230   mid.trianglelist       = 0;    /* Not needed if -E switch used. */
231   /* Not needed if -E switch used or number of triangle attributes is zero: */
232   mid.triangleattributelist = 0;
233   mid.neighborlist          = 0; /* Needed only if -n switch used. */
234   /* Needed only if segments are output (-p or -c) and -P not used: */
235   mid.segmentlist = 0;
236   /* Needed only if segments are output (-p or -c) and -P and -B not used: */
237   mid.segmentmarkerlist = 0;
238   mid.edgelist          = 0;    /* Needed only if -e switch used. */
239   mid.edgemarkerlist    = 0; /* Needed if -e used and -B not used. */
240   mid.numberoftriangles = 0;
241 
242   /* Triangulate the points.  Switches are chosen to read and write a  */
243   /*   PSLG (p), preserve the convex hull (c), number everything from  */
244   /*   zero (z), assign a regional attribute to each element (A), and  */
245   /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
246   /*   neighbor list (n).                                            */
247   if (nselected_2 != 0) { /* inactive processor */
248     char args[] = "npczQ"; /* c is needed ? */
249     triangulate(args, &in, &mid, (struct triangulateio*) NULL);
250     /* output .poly files for 'showme' */
251     if (!PETSC_TRUE) {
252       static int level = 1;
253       FILE       *file; char fname[32];
254 
255       sprintf(fname,"C%d_%d.poly",level,rank); file = fopen(fname, "w");
256       /*First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)>*/
257       fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0);
258       /*Following lines: <vertex #> <x> <y> */
259       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid += 2) {
260         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
261       }
262       /*One line: <# of segments> <# of boundary markers (0 or 1)> */
263       fprintf(file, "%d  %d\n",0,0);
264       /*Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
265       /* One line: <# of holes> */
266       fprintf(file, "%d\n",0);
267       /* Following lines: <hole #> <x> <y> */
268       /* Optional line: <# of regional attributes and/or area constraints> */
269       /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
270       fclose(file);
271 
272       /* elems */
273       sprintf(fname,"C%d_%d.ele",level,rank); file = fopen(fname, "w");
274       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
275       fprintf(file, "%d %d %d\n",mid.numberoftriangles,3,0);
276       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
277       for (kk=0,sid=0; kk<mid.numberoftriangles; kk++,sid += 3) {
278         fprintf(file, "%d %d %d %d\n",kk,mid.trianglelist[sid],mid.trianglelist[sid+1],mid.trianglelist[sid+2]);
279       }
280       fclose(file);
281 
282       sprintf(fname,"C%d_%d.node",level,rank); file = fopen(fname, "w");
283       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
284       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
285       fprintf(file, "%d  %d  %d  %d\n",nPlotPts,2,0,0);
286       /*Following lines: <vertex #> <x> <y> */
287       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid+=2) {
288         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
289       }
290 
291       sid /= 2;
292       for (jj=0; jj<nFineLoc; jj++) {
293         PetscBool sel = PETSC_TRUE;
294         for (kk=0; kk<nselected_2 && sel; kk++) {
295           PetscInt lid = selected_idx_2[kk];
296           if (lid == jj) sel = PETSC_FALSE;
297         }
298         if (sel) fprintf(file, "%d %e %e\n",sid++,coords[jj],coords[data_stride + jj]);
299       }
300       fclose(file);
301       assert(sid==nPlotPts);
302       level++;
303     }
304   }
305 #if defined PETSC_GAMG_USE_LOG
306   ierr = PetscLogEventBegin(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
307 #endif
308   { /* form P - setup some maps */
309     PetscInt clid,mm,*nTri,*node_tri;
310 
311     ierr = PetscMalloc(nselected_2*sizeof(PetscInt), &node_tri);CHKERRQ(ierr);
312     ierr = PetscMalloc(nselected_2*sizeof(PetscInt), &nTri);CHKERRQ(ierr);
313 
314     /* need list of triangles on node */
315     for (kk=0; kk<nselected_2; kk++) nTri[kk] = 0;
316     for (tid=0,kk=0; tid<mid.numberoftriangles; tid++) {
317       for (jj=0; jj<3; jj++) {
318         PetscInt cid = mid.trianglelist[kk++];
319         if (nTri[cid] == 0) node_tri[cid] = tid;
320         nTri[cid]++;
321       }
322     }
323 #define EPS 1.e-12
324     /* find points and set prolongation */
325     for (mm = clid = 0; mm < nFineLoc; mm++) {
326       PetscBool ise;
327       ierr = PetscCDEmptyAt(agg_lists_1,mm,&ise);CHKERRQ(ierr);
328       if (!ise) {
329         const PetscInt lid = mm;
330         /* for (clid_iterator=0;clid_iterator<nselected_1;clid_iterator++) { */
331         /* PetscInt flid = clid_lid_1[clid_iterator]; assert(flid != -1); */
332         PetscScalar  AA[3][3];
333         PetscBLASInt N=3,NRHS=1,LDA=3,IPIV[3],LDB=3,INFO;
334         PetscCDPos   pos;
335         ierr = PetscCDGetHeadPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
336         while (pos) {
337           PetscInt flid;
338           ierr = PetscLLNGetID(pos, &flid);CHKERRQ(ierr);
339           ierr = PetscCDGetNextPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
340 
341           if (flid < nFineLoc) {  /* could be a ghost */
342             PetscInt       bestTID = -1; PetscReal best_alpha = 1.e10;
343             const PetscInt fgid    = flid + myFine0;
344             /* compute shape function for gid */
345             const PetscReal fcoord[3] = {coords[flid],coords[data_stride+flid],1.0};
346             PetscBool       haveit    =PETSC_FALSE; PetscScalar alpha[3]; PetscInt clids[3];
347 
348             /* look for it */
349             for (tid = node_tri[clid], jj=0;
350                  jj < 5 && !haveit && tid != -1;
351                  jj++) {
352               for (tt=0; tt<3; tt++) {
353                 PetscInt cid2 = mid.trianglelist[3*tid + tt];
354                 PetscInt lid2 = selected_idx_2[cid2];
355                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
356                 clids[tt] = cid2; /* store for interp */
357               }
358 
359               for (tt=0; tt<3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];
360 
361               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
362               LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO);
363               {
364                 PetscBool have=PETSC_TRUE;  PetscReal lowest=1.e10;
365                 for (tt = 0, idx = 0; tt < 3; tt++) {
366                   if (PetscRealPart(alpha[tt]) > (1.0+EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
367                   if (PetscRealPart(alpha[tt]) < lowest) {
368                     lowest = PetscRealPart(alpha[tt]);
369                     idx    = tt;
370                   }
371                 }
372                 haveit = have;
373               }
374               tid = mid.neighborlist[3*tid + idx];
375             }
376 
377             if (!haveit) {
378               /* brute force */
379               for (tid=0; tid<mid.numberoftriangles && !haveit; tid++) {
380                 for (tt=0; tt<3; tt++) {
381                   PetscInt cid2 = mid.trianglelist[3*tid + tt];
382                   PetscInt lid2 = selected_idx_2[cid2];
383                   AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
384                   clids[tt] = cid2; /* store for interp */
385                 }
386                 for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
387                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
388                 LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO);
389                 {
390                   PetscBool have=PETSC_TRUE;  PetscReal worst=0.0, v;
391                   for (tt=0; tt<3 && have; tt++) {
392                     if (PetscRealPart(alpha[tt]) > 1.0+EPS || PetscRealPart(alpha[tt]) < -EPS) have=PETSC_FALSE;
393                     if ((v=PetscAbs(PetscRealPart(alpha[tt])-0.5)) > worst) worst = v;
394                   }
395                   if (worst < best_alpha) {
396                     best_alpha = worst; bestTID = tid;
397                   }
398                   haveit = have;
399                 }
400               }
401             }
402             if (!haveit) {
403               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
404               /* use best one */
405               for (tt=0; tt<3; tt++) {
406                 PetscInt cid2 = mid.trianglelist[3*bestTID + tt];
407                 PetscInt lid2 = selected_idx_2[cid2];
408                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
409                 clids[tt] = cid2; /* store for interp */
410               }
411               for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
412               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
413               LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO);
414             }
415 
416             /* put in row of P */
417             for (idx=0; idx<3; idx++) {
418               PetscScalar shp = alpha[idx];
419               if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
420                 PetscInt cgid = crsGID[clids[idx]];
421                 PetscInt jj   = cgid*bs, ii = fgid*bs; /* need to gloalize */
422                 for (tt=0; tt < bs; tt++, ii++, jj++) {
423                   ierr = MatSetValues(a_Prol,1,&ii,1,&jj,&shp,INSERT_VALUES);CHKERRQ(ierr);
424                 }
425               }
426             }
427           }
428         } /* aggregates iterations */
429         clid++;
430       } /* a coarse agg */
431     } /* for all fine nodes */
432 
433     ierr = ISRestoreIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
434     ierr = MatAssemblyBegin(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
435     ierr = MatAssemblyEnd(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
436 
437     ierr = PetscFree(node_tri);CHKERRQ(ierr);
438     ierr = PetscFree(nTri);CHKERRQ(ierr);
439   }
440 #if defined PETSC_GAMG_USE_LOG
441   ierr = PetscLogEventEnd(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
442 #endif
443   free(mid.trianglelist);
444   free(mid.neighborlist);
445   ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
446   PetscFunctionReturn(0);
447 #else
448   SETERRQ(((PetscObject)a_Prol)->comm,PETSC_ERR_PLIB,"configure with TRIANGLE to use geometric MG");
449 #endif
450 }
451 /* -------------------------------------------------------------------------- */
452 /*
453    getGIDsOnSquareGraph - square graph, get
454 
455    Input Parameter:
456    . nselected_1 - selected local indices (includes ghosts in input Gmat1)
457    . clid_lid_1 - [nselected_1] lids of selected nodes
458    . Gmat1 - graph that goes with 'selected_1'
459    Output Parameter:
460    . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
461    . a_Gmat_2 - graph that is squared of 'Gmat_1'
462    . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
463 */
464 #undef __FUNCT__
465 #define __FUNCT__ "getGIDsOnSquareGraph"
466 static PetscErrorCode getGIDsOnSquareGraph(const PetscInt nselected_1,const PetscInt clid_lid_1[],const Mat Gmat1,IS *a_selected_2,Mat *a_Gmat_2,PetscInt **a_crsGID)
467 {
468   PetscErrorCode ierr;
469   PetscMPIInt    rank,size;
470   PetscInt       *crsGID, kk,my0,Iend,nloc;
471   MPI_Comm       wcomm = ((PetscObject)Gmat1)->comm;
472 
473   PetscFunctionBegin;
474   ierr = MPI_Comm_rank(wcomm,&rank);CHKERRQ(ierr);
475   ierr = MPI_Comm_size(wcomm,&size);CHKERRQ(ierr);
476   ierr = MatGetOwnershipRange(Gmat1,&my0,&Iend);CHKERRQ(ierr); /* AIJ */
477   nloc = Iend - my0; /* this does not change */
478 
479   if (size == 1) { /* not much to do in serial */
480     ierr = PetscMalloc(nselected_1*sizeof(PetscInt), &crsGID);CHKERRQ(ierr);
481     for (kk=0; kk<nselected_1; kk++) crsGID[kk] = kk;
482     *a_Gmat_2 = 0;
483     ierr      = ISCreateGeneral(PETSC_COMM_SELF,nselected_1,clid_lid_1,PETSC_COPY_VALUES,a_selected_2);CHKERRQ(ierr);
484   } else {
485     PetscInt    idx,num_fine_ghosts,num_crs_ghost,myCrs0;
486     Mat_MPIAIJ  *mpimat2;
487     Mat         Gmat2;
488     Vec         locState;
489     PetscScalar *cpcol_state;
490 
491     /* scan my coarse zero gid, set 'lid_state' with coarse GID */
492     kk = nselected_1;
493     MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPIU_SUM, wcomm);
494     myCrs0 -= nselected_1;
495 
496     if (a_Gmat_2) { /* output */
497       /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
498       ierr      = MatTransposeMatMult(Gmat1, Gmat1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Gmat2);CHKERRQ(ierr);
499       *a_Gmat_2 = Gmat2; /* output */
500     } else Gmat2 = Gmat1;  /* use local to get crsGIDs at least */
501     /* get coarse grid GIDS for selected (locals and ghosts) */
502     mpimat2 = (Mat_MPIAIJ*)Gmat2->data;
503     ierr    = MatGetVecs(Gmat2, &locState, 0);CHKERRQ(ierr);
504     ierr    = VecSet(locState, (PetscScalar)(PetscReal)(-1));CHKERRQ(ierr); /* set with UNKNOWN state */
505     for (kk=0; kk<nselected_1; kk++) {
506       PetscInt    fgid = clid_lid_1[kk] + my0;
507       PetscScalar v    = (PetscScalar)(kk+myCrs0);
508       ierr = VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES);CHKERRQ(ierr); /* set with PID */
509     }
510     ierr = VecAssemblyBegin(locState);CHKERRQ(ierr);
511     ierr = VecAssemblyEnd(locState);CHKERRQ(ierr);
512     ierr = VecScatterBegin(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
513     ierr =   VecScatterEnd(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
514     ierr = VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts);CHKERRQ(ierr);
515     ierr = VecGetArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
516     for (kk=0,num_crs_ghost=0; kk<num_fine_ghosts; kk++) {
517       if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
518     }
519     ierr = PetscMalloc((nselected_1+num_crs_ghost)*sizeof(PetscInt), &crsGID);CHKERRQ(ierr); /* output */
520     {
521       PetscInt *selected_set;
522       ierr = PetscMalloc((nselected_1+num_crs_ghost)*sizeof(PetscInt), &selected_set);CHKERRQ(ierr);
523       /* do ghost of 'crsGID' */
524       for (kk=0,idx=nselected_1; kk<num_fine_ghosts; kk++) {
525         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
526           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
527           selected_set[idx] = nloc + kk;
528           crsGID[idx++]     = cgid;
529         }
530       }
531       assert(idx==(nselected_1+num_crs_ghost));
532       ierr = VecRestoreArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
533       /* do locals in 'crsGID' */
534       ierr = VecGetArray(locState, &cpcol_state);CHKERRQ(ierr);
535       for (kk=0,idx=0; kk<nloc; kk++) {
536         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
537           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
538           selected_set[idx] = kk;
539           crsGID[idx++]     = cgid;
540         }
541       }
542       assert(idx==nselected_1);
543       ierr = VecRestoreArray(locState, &cpcol_state);CHKERRQ(ierr);
544 
545       if (a_selected_2 != 0) { /* output */
546         ierr = ISCreateGeneral(PETSC_COMM_SELF,(nselected_1+num_crs_ghost),selected_set,PETSC_OWN_POINTER,a_selected_2);CHKERRQ(ierr);
547       } else {
548         ierr = PetscFree(selected_set);CHKERRQ(ierr);
549       }
550     }
551     ierr = VecDestroy(&locState);CHKERRQ(ierr);
552   }
553   *a_crsGID = crsGID; /* output */
554   PetscFunctionReturn(0);
555 }
556 
557 /* -------------------------------------------------------------------------- */
558 /*
559    PCGAMGgraph_GEO
560 
561   Input Parameter:
562    . pc - this
563    . Amat - matrix on this fine level
564   Output Parameter:
565    . a_Gmat
566 */
567 #undef __FUNCT__
568 #define __FUNCT__ "PCGAMGgraph_GEO"
569 PetscErrorCode PCGAMGgraph_GEO(PC pc,const Mat Amat,Mat *a_Gmat)
570 {
571   PetscErrorCode  ierr;
572   PC_MG           *mg      = (PC_MG*)pc->data;
573   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
574   const PetscInt  verbose  = pc_gamg->verbose;
575   const PetscReal vfilter  = pc_gamg->threshold;
576   PetscMPIInt     rank,size;
577   MPI_Comm        wcomm = ((PetscObject)Amat)->comm;
578   Mat             Gmat;
579   PetscBool       set,flg,symm;
580 
581   PetscFunctionBegin;
582 #if defined PETSC_USE_LOG
583   ierr = PetscLogEventBegin(PC_GAMGGgraph_GEO,0,0,0,0);CHKERRQ(ierr);
584 #endif
585   ierr = MPI_Comm_rank(wcomm, &rank);CHKERRQ(ierr);
586   ierr = MPI_Comm_size(wcomm, &size);CHKERRQ(ierr);
587 
588   ierr = MatIsSymmetricKnown(Amat, &set, &flg);CHKERRQ(ierr);
589   symm = (PetscBool)!(set && flg);
590 
591   ierr = PCGAMGCreateGraph(Amat, &Gmat);CHKERRQ(ierr);
592   ierr = PCGAMGFilterGraph(&Gmat, vfilter, symm, verbose);CHKERRQ(ierr);
593 
594   *a_Gmat = Gmat;
595 #if defined PETSC_USE_LOG
596   ierr = PetscLogEventEnd(PC_GAMGGgraph_GEO,0,0,0,0);CHKERRQ(ierr);
597 #endif
598   PetscFunctionReturn(0);
599 }
600 
601 /* -------------------------------------------------------------------------- */
602 /*
603    PCGAMGcoarsen_GEO
604 
605   Input Parameter:
606    . a_pc - this
607    . a_Gmat - graph
608   Output Parameter:
609    . a_llist_parent - linked list from selected indices for data locality only
610 */
611 #undef __FUNCT__
612 #define __FUNCT__ "PCGAMGcoarsen_GEO"
613 PetscErrorCode PCGAMGcoarsen_GEO(PC a_pc,Mat *a_Gmat,PetscCoarsenData **a_llist_parent)
614 {
615   PetscErrorCode ierr;
616   PC_MG          *mg      = (PC_MG*)a_pc->data;
617   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
618   PetscInt       Istart,Iend,nloc,kk,Ii,ncols;
619   PetscMPIInt    rank,size;
620   IS             perm;
621   GAMGNode       *gnodes;
622   PetscInt       *permute;
623   Mat            Gmat  = *a_Gmat;
624   MPI_Comm       wcomm = ((PetscObject)Gmat)->comm;
625   MatCoarsen     crs;
626 
627   PetscFunctionBegin;
628 #if defined PETSC_USE_LOG
629   ierr = PetscLogEventBegin(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
630 #endif
631   ierr = MPI_Comm_rank(wcomm, &rank);CHKERRQ(ierr);
632   ierr = MPI_Comm_size(wcomm, &size);CHKERRQ(ierr);
633   ierr = MatGetOwnershipRange(Gmat, &Istart, &Iend);CHKERRQ(ierr);
634   nloc = (Iend-Istart);
635 
636   /* create random permutation with sort for geo-mg */
637   ierr = PetscMalloc(nloc*sizeof(GAMGNode), &gnodes);CHKERRQ(ierr);
638   ierr = PetscMalloc(nloc*sizeof(PetscInt), &permute);CHKERRQ(ierr);
639 
640   for (Ii=Istart; Ii<Iend; Ii++) { /* locals only? */
641     ierr = MatGetRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
642     {
643       PetscInt lid = Ii - Istart;
644       gnodes[lid].lid    = lid;
645       gnodes[lid].degree = ncols;
646     }
647     ierr = MatRestoreRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
648   }
649   /* randomize */
650   srand(1); /* make deterministic */
651   if (PETSC_TRUE) {
652     PetscBool *bIndexSet;
653     ierr = PetscMalloc(nloc*sizeof(PetscBool), &bIndexSet);CHKERRQ(ierr);
654     for (Ii = 0; Ii < nloc; Ii++) bIndexSet[Ii] = PETSC_FALSE;
655     for (Ii = 0; Ii < nloc; Ii++) {
656       PetscInt iSwapIndex = rand()%nloc;
657       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
658         GAMGNode iTemp = gnodes[iSwapIndex];
659         gnodes[iSwapIndex]    = gnodes[Ii];
660         gnodes[Ii]            = iTemp;
661         bIndexSet[Ii]         = PETSC_TRUE;
662         bIndexSet[iSwapIndex] = PETSC_TRUE;
663       }
664     }
665     ierr = PetscFree(bIndexSet);CHKERRQ(ierr);
666   }
667   /* only sort locals */
668   qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
669   /* create IS of permutation */
670   for (kk=0; kk<nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
671   ierr = ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
672 
673   ierr = PetscFree(gnodes);CHKERRQ(ierr);
674 
675   /* get MIS aggs */
676 
677   ierr = MatCoarsenCreate(wcomm, &crs);CHKERRQ(ierr);
678   ierr = MatCoarsenSetType(crs, MATCOARSENMIS);CHKERRQ(ierr);
679   ierr = MatCoarsenSetGreedyOrdering(crs, perm);CHKERRQ(ierr);
680   ierr = MatCoarsenSetAdjacency(crs, Gmat);CHKERRQ(ierr);
681   ierr = MatCoarsenSetVerbose(crs, pc_gamg->verbose);CHKERRQ(ierr);
682   ierr = MatCoarsenSetStrictAggs(crs, PETSC_FALSE);CHKERRQ(ierr);
683   ierr = MatCoarsenApply(crs);CHKERRQ(ierr);
684   ierr = MatCoarsenGetData(crs, a_llist_parent);CHKERRQ(ierr);
685   ierr = MatCoarsenDestroy(&crs);CHKERRQ(ierr);
686 
687   ierr = ISDestroy(&perm);CHKERRQ(ierr);
688 #if defined PETSC_USE_LOG
689   ierr = PetscLogEventEnd(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
690 #endif
691   PetscFunctionReturn(0);
692 }
693 
694 /* -------------------------------------------------------------------------- */
695 /*
696  PCGAMGProlongator_GEO
697 
698  Input Parameter:
699  . pc - this
700  . Amat - matrix on this fine level
701  . Graph - used to get ghost data for nodes in
702  . selected_1 - [nselected]
703  . agg_lists - [nselected]
704  Output Parameter:
705  . a_P_out - prolongation operator to the next level
706  */
707 #undef __FUNCT__
708 #define __FUNCT__ "PCGAMGProlongator_GEO"
709 PetscErrorCode PCGAMGProlongator_GEO(PC pc,const Mat Amat,const Mat Gmat,PetscCoarsenData *agg_lists,Mat *a_P_out)
710 {
711   PC_MG          *mg      = (PC_MG*)pc->data;
712   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
713   const PetscInt verbose  = pc_gamg->verbose;
714   const PetscInt dim      = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
715   PetscErrorCode ierr;
716   PetscInt       Istart,Iend,nloc,my0,jj,kk,ncols,nLocalSelected,bs,*clid_flid;
717   Mat            Prol;
718   PetscMPIInt    rank, size;
719   MPI_Comm       wcomm = ((PetscObject)Amat)->comm;
720   IS             selected_2,selected_1;
721   const PetscInt *selected_idx;
722 
723   PetscFunctionBegin;
724 #if defined PETSC_USE_LOG
725   ierr = PetscLogEventBegin(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
726 #endif
727   ierr = MPI_Comm_rank(wcomm,&rank);CHKERRQ(ierr);
728   ierr = MPI_Comm_size(wcomm,&size);CHKERRQ(ierr);
729   ierr = MatGetOwnershipRange(Amat, &Istart, &Iend);CHKERRQ(ierr);
730   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
731   nloc = (Iend-Istart)/bs; my0 = Istart/bs; assert((Iend-Istart)%bs==0);
732 
733   /* get 'nLocalSelected' */
734   ierr = PetscCDGetMIS(agg_lists, &selected_1);CHKERRQ(ierr);
735   ierr = ISGetSize(selected_1, &jj);CHKERRQ(ierr);
736   ierr = PetscMalloc(jj*sizeof(PetscInt), &clid_flid);CHKERRQ(ierr);
737   ierr = ISGetIndices(selected_1, &selected_idx);CHKERRQ(ierr);
738   for (kk=0,nLocalSelected=0; kk<jj; kk++) {
739     PetscInt lid = selected_idx[kk];
740     if (lid<nloc) {
741       ierr = MatGetRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
742       if (ncols>1) clid_flid[nLocalSelected++] = lid; /* fiter out singletons */
743       else assert(0); /* filtered in coarsening */
744       ierr = MatRestoreRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
745     }
746   }
747   ierr = ISRestoreIndices(selected_1, &selected_idx);CHKERRQ(ierr);
748   ierr = ISDestroy(&selected_1);CHKERRQ(ierr); /* this is selected_1 in serial */
749 
750   /* create prolongator, create P matrix */
751   ierr = MatCreate(wcomm, &Prol);CHKERRQ(ierr);
752   ierr = MatSetSizes(Prol,nloc*bs,nLocalSelected*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
753   ierr = MatSetBlockSizes(Prol, bs, bs);CHKERRQ(ierr);
754   ierr = MatSetType(Prol, MATAIJ);CHKERRQ(ierr);
755   ierr = MatSeqAIJSetPreallocation(Prol,3*data_cols,PETSC_NULL);CHKERRQ(ierr);
756   ierr = MatMPIAIJSetPreallocation(Prol,3*data_cols,PETSC_NULL,3*data_cols,PETSC_NULL);CHKERRQ(ierr);
757   /* ierr = MatCreateAIJ(wcomm,  */
758   /*                      nloc*bs, nLocalSelected*bs, */
759   /*                      PETSC_DETERMINE, PETSC_DETERMINE, */
760   /*                      3*data_cols, PETSC_NULL,  */
761   /*                      3*data_cols, PETSC_NULL, */
762   /*                      &Prol); */
763   /* CHKERRQ(ierr); */
764 
765   /* can get all points "removed" - but not on geomg */
766   ierr =  MatGetSize(Prol, &kk, &jj);CHKERRQ(ierr);
767   if (jj==0) {
768     if (verbose) PetscPrintf(wcomm,"[%d]%s ERROE: no selected points on coarse grid\n",rank,__FUNCT__);
769     ierr = PetscFree(clid_flid);CHKERRQ(ierr);
770     ierr = MatDestroy(&Prol);CHKERRQ(ierr);
771     *a_P_out = PETSC_NULL;  /* out */
772     PetscFunctionReturn(0);
773   }
774 
775   {
776     PetscReal *coords;
777     PetscInt  data_stride;
778     PetscInt  *crsGID = PETSC_NULL;
779     Mat       Gmat2;
780 
781     assert(dim==data_cols);
782     /* grow ghost data for better coarse grid cover of fine grid */
783 #if defined PETSC_GAMG_USE_LOG
784     ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
785 #endif
786     /* messy method, squares graph and gets some data */
787     ierr = getGIDsOnSquareGraph(nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID);CHKERRQ(ierr);
788     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
789 #if defined PETSC_GAMG_USE_LOG
790     ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
791 #endif
792     /* create global vector of coorindates in 'coords' */
793     if (size > 1) {
794       ierr = PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords);CHKERRQ(ierr);
795     } else {
796       coords      = (PetscReal*)pc_gamg->data;
797       data_stride = pc_gamg->data_sz/pc_gamg->data_cell_cols;
798     }
799     ierr = MatDestroy(&Gmat2);CHKERRQ(ierr);
800 
801     /* triangulate */
802     if (dim == 2) {
803       PetscReal metric,tm;
804 #if defined PETSC_GAMG_USE_LOG
805       ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
806 #endif
807       ierr = triangulateAndFormProl(selected_2, data_stride, coords,nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric);CHKERRQ(ierr);
808 #if defined PETSC_GAMG_USE_LOG
809       ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
810 #endif
811       ierr = PetscFree(crsGID);CHKERRQ(ierr);
812 
813       /* clean up and create coordinates for coarse grid (output) */
814       if (size > 1) ierr = PetscFree(coords);CHKERRQ(ierr);
815 
816       ierr = MPI_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, wcomm);CHKERRQ(ierr);
817       if (tm > 1.) { /* needs to be globalized - should not happen */
818         if (verbose) PetscPrintf(wcomm,"[%d]%s failed metric for coarse grid %e\n",rank,__FUNCT__,tm);
819         ierr = MatDestroy(&Prol);CHKERRQ(ierr);
820         Prol = PETSC_NULL;
821       } else if (metric > .0) {
822         if (verbose) PetscPrintf(wcomm,"[%d]%s worst metric for coarse grid = %e\n",rank,__FUNCT__,metric);
823       }
824     } else SETERRQ(wcomm,PETSC_ERR_PLIB,"3D not implemented for 'geo' AMG");
825     { /* create next coords - output */
826       PetscReal *crs_crds;
827       ierr = PetscMalloc(dim*nLocalSelected*sizeof(PetscReal), &crs_crds);CHKERRQ(ierr);
828       for (kk=0; kk<nLocalSelected; kk++) { /* grab local select nodes to promote - output */
829         PetscInt lid = clid_flid[kk];
830         for (jj=0; jj<dim; jj++) crs_crds[jj*nLocalSelected + kk] = pc_gamg->data[jj*nloc + lid];
831       }
832 
833       ierr             = PetscFree(pc_gamg->data);CHKERRQ(ierr);
834       pc_gamg->data    = crs_crds; /* out */
835       pc_gamg->data_sz = dim*nLocalSelected;
836     }
837     ierr = ISDestroy(&selected_2);CHKERRQ(ierr);
838   }
839 
840   *a_P_out = Prol;  /* out */
841   ierr     = PetscFree(clid_flid);CHKERRQ(ierr);
842 #if defined PETSC_USE_LOG
843   ierr = PetscLogEventEnd(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
844 #endif
845   PetscFunctionReturn(0);
846 }
847 
848 /* -------------------------------------------------------------------------- */
849 /*
850  PCCreateGAMG_GEO
851 
852   Input Parameter:
853    . pc -
854 */
855 #undef __FUNCT__
856 #define __FUNCT__ "PCCreateGAMG_GEO"
857 PetscErrorCode  PCCreateGAMG_GEO(PC pc)
858 {
859   PetscErrorCode ierr;
860   PC_MG          *mg      = (PC_MG*)pc->data;
861   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
862 
863   PetscFunctionBegin;
864   pc->ops->setfromoptions = PCSetFromOptions_GEO;
865   /* pc->ops->destroy        = PCDestroy_GEO; */
866   /* reset does not do anything; setup not virtual */
867 
868   /* set internal function pointers */
869   pc_gamg->graph       = PCGAMGgraph_GEO;
870   pc_gamg->coarsen     = PCGAMGcoarsen_GEO;
871   pc_gamg->prolongator = PCGAMGProlongator_GEO;
872   pc_gamg->optprol     = 0;
873   pc_gamg->formkktprol = 0;
874 
875   pc_gamg->createdefaultdata = PCSetData_GEO;
876 
877   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,
878                                            "PCSetCoordinates_C",
879                                            "PCSetCoordinates_GEO",
880                                            PCSetCoordinates_GEO);CHKERRQ(ierr);
881   PetscFunctionReturn(0);
882 }
883