xref: /petsc/src/ksp/pc/impls/gamg/geo.c (revision 55e7fe800d976e85ed2b5cd8bfdef564daa37bd9)
1 /*
2  GAMG geometric-algebric multiogrid PC - Mark Adams 2011
3  */
4 
5 #include <../src/ksp/pc/impls/gamg/gamg.h>        /*I "petscpc.h" I*/
6 
7 #if defined(PETSC_HAVE_TRIANGLE)
8 #define REAL PetscReal
9 #include <triangle.h>
10 #endif
11 
12 #include <petscblaslapack.h>
13 
14 /* Private context for the GAMG preconditioner */
15 typedef struct {
16   PetscInt lid;            /* local vertex index */
17   PetscInt degree;         /* vertex degree */
18 } GAMGNode;
19 
20 PETSC_STATIC_INLINE int petsc_geo_mg_compare(const void *a, const void *b)
21 {
22   return (((GAMGNode*)a)->degree - ((GAMGNode*)b)->degree);
23 }
24 
25 /* -------------------------------------------------------------------------- */
26 /*
27    PCSetCoordinates_GEO
28 
29    Input Parameter:
30    .  pc - the preconditioner context
31 */
32 PetscErrorCode PCSetCoordinates_GEO(PC pc, PetscInt ndm, PetscInt a_nloc, PetscReal *coords)
33 {
34   PC_MG          *mg      = (PC_MG*)pc->data;
35   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
36   PetscErrorCode ierr;
37   PetscInt       arrsz,bs,my0,kk,ii,nloc,Iend;
38   Mat            Amat = pc->pmat;
39 
40   PetscFunctionBegin;
41   PetscValidHeaderSpecific(Amat, MAT_CLASSID, 1);
42   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
43   ierr = MatGetOwnershipRange(Amat, &my0, &Iend);CHKERRQ(ierr);
44   nloc = (Iend-my0)/bs;
45 
46   if (nloc!=a_nloc) SETERRQ2(PetscObjectComm((PetscObject)Amat),PETSC_ERR_ARG_WRONG, "Stokes not supported nloc = %D %D.",a_nloc,nloc);
47   if ((Iend-my0)%bs!=0) SETERRQ1(PetscObjectComm((PetscObject)Amat),PETSC_ERR_ARG_WRONG, "Bad local size %D.",nloc);
48 
49   pc_gamg->data_cell_rows = 1;
50   if (!coords && nloc > 0) SETERRQ(PetscObjectComm((PetscObject)Amat),PETSC_ERR_ARG_WRONG, "Need coordinates for pc_gamg_type 'geo'.");
51   pc_gamg->data_cell_cols = ndm; /* coordinates */
52 
53   arrsz = nloc*pc_gamg->data_cell_rows*pc_gamg->data_cell_cols;
54 
55   /* create data - syntactic sugar that should be refactored at some point */
56   if (!pc_gamg->data || (pc_gamg->data_sz != arrsz)) {
57     ierr = PetscFree(pc_gamg->data);CHKERRQ(ierr);
58     ierr = PetscMalloc1(arrsz+1, &pc_gamg->data);CHKERRQ(ierr);
59   }
60   for (kk=0; kk<arrsz; kk++) pc_gamg->data[kk] = -999.;
61   pc_gamg->data[arrsz] = -99.;
62   /* copy data in - column oriented */
63   for (kk = 0; kk < nloc; kk++) {
64     for (ii = 0; ii < ndm; ii++) {
65       pc_gamg->data[ii*nloc + kk] =  coords[kk*ndm + ii];
66     }
67   }
68   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]);
69   pc_gamg->data_sz = arrsz;
70   PetscFunctionReturn(0);
71 }
72 
73 /* -------------------------------------------------------------------------- */
74 /*
75    PCSetData_GEO
76 
77   Input Parameter:
78    . pc -
79 */
80 PetscErrorCode PCSetData_GEO(PC pc, Mat m)
81 {
82   PetscFunctionBegin;
83   SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"GEO MG needs coordinates");
84 }
85 
86 /* -------------------------------------------------------------------------- */
87 /*
88    PCSetFromOptions_GEO
89 
90   Input Parameter:
91    . pc -
92 */
93 PetscErrorCode PCSetFromOptions_GEO(PetscOptionItems *PetscOptionsObject,PC pc)
94 {
95   PetscErrorCode ierr;
96 
97   PetscFunctionBegin;
98   ierr = PetscOptionsHead(PetscOptionsObject,"GAMG-GEO options");CHKERRQ(ierr);
99   {
100     /* -pc_gamg_sa_nsmooths */
101     /* pc_gamg_sa->smooths = 0; */
102     /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
103     /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
104     /*                        "PCGAMGSetNSmooths_AGG", */
105     /*                        pc_gamg_sa->smooths, */
106     /*                        &pc_gamg_sa->smooths, */
107     /*                        &flag);  */
108     /* CHKERRQ(ierr); */
109   }
110   ierr = PetscOptionsTail();CHKERRQ(ierr);
111   PetscFunctionReturn(0);
112 }
113 
114 /* -------------------------------------------------------------------------- */
115 /*
116  triangulateAndFormProl
117 
118    Input Parameter:
119    . selected_2 - list of selected local ID, includes selected ghosts
120    . data_stride -
121    . coords[2*data_stride] - column vector of local coordinates w/ ghosts
122    . nselected_1 - selected IDs that go with base (1) graph includes selected ghosts
123    . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
124    . agg_lists_1 - list of aggregates selected_1 vertices of aggregate unselected vertices
125    . crsGID[selected.size()] - global index for prolongation operator
126    . bs - block size
127   Output Parameter:
128    . a_Prol - prolongation operator
129    . a_worst_best - measure of worst missed fine vertex, 0 is no misses
130 */
131 static PetscErrorCode triangulateAndFormProl(IS selected_2,PetscInt data_stride,PetscReal coords[],PetscInt nselected_1,const PetscInt clid_lid_1[],const PetscCoarsenData *agg_lists_1,
132                                              const PetscInt crsGID[],PetscInt bs,Mat a_Prol,PetscReal *a_worst_best)
133 {
134 #if defined(PETSC_HAVE_TRIANGLE)
135   PetscErrorCode       ierr;
136   PetscInt             jj,tid,tt,idx,nselected_2;
137   struct triangulateio in,mid;
138   const PetscInt       *selected_idx_2;
139   PetscMPIInt          rank;
140   PetscInt             Istart,Iend,nFineLoc,myFine0;
141   int                  kk,nPlotPts,sid;
142   MPI_Comm             comm;
143   PetscReal            tm;
144 
145   PetscFunctionBegin;
146   ierr = PetscObjectGetComm((PetscObject)a_Prol,&comm);CHKERRQ(ierr);
147   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
148   ierr = ISGetSize(selected_2, &nselected_2);CHKERRQ(ierr);
149   if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
150     *a_worst_best = 100.0; /* this will cause a stop, but not globalized (should not happen) */
151   } else *a_worst_best = 0.0;
152   ierr = MPIU_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRQ(ierr);
153   if (tm > 0.0) {
154     *a_worst_best = 100.0;
155     PetscFunctionReturn(0);
156   }
157   ierr     = MatGetOwnershipRange(a_Prol, &Istart, &Iend);CHKERRQ(ierr);
158   nFineLoc = (Iend-Istart)/bs; myFine0 = Istart/bs;
159   nPlotPts = nFineLoc; /* locals */
160   /* traingle */
161   /* Define input points - in*/
162   in.numberofpoints          = nselected_2;
163   in.numberofpointattributes = 0;
164   /* get nselected points */
165   ierr = PetscMalloc1(2*nselected_2, &in.pointlist);CHKERRQ(ierr);
166   ierr = ISGetIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
167 
168   for (kk=0,sid=0; kk<nselected_2; kk++,sid += 2) {
169     PetscInt lid = selected_idx_2[kk];
170     in.pointlist[sid]   = coords[lid];
171     in.pointlist[sid+1] = coords[data_stride + lid];
172     if (lid>=nFineLoc) nPlotPts++;
173   }
174   if (sid != 2*nselected_2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != 2*nselected_2 %D",sid,nselected_2);
175 
176   in.numberofsegments      = 0;
177   in.numberofedges         = 0;
178   in.numberofholes         = 0;
179   in.numberofregions       = 0;
180   in.trianglelist          = 0;
181   in.segmentmarkerlist     = 0;
182   in.pointattributelist    = 0;
183   in.pointmarkerlist       = 0;
184   in.triangleattributelist = 0;
185   in.trianglearealist      = 0;
186   in.segmentlist           = 0;
187   in.holelist              = 0;
188   in.regionlist            = 0;
189   in.edgelist              = 0;
190   in.edgemarkerlist        = 0;
191   in.normlist              = 0;
192 
193   /* triangulate */
194   mid.pointlist = 0;            /* Not needed if -N switch used. */
195   /* Not needed if -N switch used or number of point attributes is zero: */
196   mid.pointattributelist = 0;
197   mid.pointmarkerlist    = 0; /* Not needed if -N or -B switch used. */
198   mid.trianglelist       = 0;    /* Not needed if -E switch used. */
199   /* Not needed if -E switch used or number of triangle attributes is zero: */
200   mid.triangleattributelist = 0;
201   mid.neighborlist          = 0; /* Needed only if -n switch used. */
202   /* Needed only if segments are output (-p or -c) and -P not used: */
203   mid.segmentlist = 0;
204   /* Needed only if segments are output (-p or -c) and -P and -B not used: */
205   mid.segmentmarkerlist = 0;
206   mid.edgelist          = 0;    /* Needed only if -e switch used. */
207   mid.edgemarkerlist    = 0; /* Needed if -e used and -B not used. */
208   mid.numberoftriangles = 0;
209 
210   /* Triangulate the points.  Switches are chosen to read and write a  */
211   /*   PSLG (p), preserve the convex hull (c), number everything from  */
212   /*   zero (z), assign a regional attribute to each element (A), and  */
213   /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
214   /*   neighbor list (n).                                            */
215   if (nselected_2 != 0) { /* inactive processor */
216     char args[] = "npczQ"; /* c is needed ? */
217     triangulate(args, &in, &mid, (struct triangulateio*) NULL);
218     /* output .poly files for 'showme' */
219     if (!PETSC_TRUE) {
220       static int level = 1;
221       FILE       *file; char fname[32];
222 
223       sprintf(fname,"C%d_%d.poly",level,rank); file = fopen(fname, "w");
224       /*First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)>*/
225       fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0);
226       /*Following lines: <vertex #> <x> <y> */
227       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid += 2) {
228         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
229       }
230       /*One line: <# of segments> <# of boundary markers (0 or 1)> */
231       fprintf(file, "%d  %d\n",0,0);
232       /*Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
233       /* One line: <# of holes> */
234       fprintf(file, "%d\n",0);
235       /* Following lines: <hole #> <x> <y> */
236       /* Optional line: <# of regional attributes and/or area constraints> */
237       /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
238       fclose(file);
239 
240       /* elems */
241       sprintf(fname,"C%d_%d.ele",level,rank); file = fopen(fname, "w");
242       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
243       fprintf(file, "%d %d %d\n",mid.numberoftriangles,3,0);
244       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
245       for (kk=0,sid=0; kk<mid.numberoftriangles; kk++,sid += 3) {
246         fprintf(file, "%d %d %d %d\n",kk,mid.trianglelist[sid],mid.trianglelist[sid+1],mid.trianglelist[sid+2]);
247       }
248       fclose(file);
249 
250       sprintf(fname,"C%d_%d.node",level,rank); file = fopen(fname, "w");
251       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
252       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
253       fprintf(file, "%d  %d  %d  %d\n",nPlotPts,2,0,0);
254       /*Following lines: <vertex #> <x> <y> */
255       for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid+=2) {
256         fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
257       }
258 
259       sid /= 2;
260       for (jj=0; jj<nFineLoc; jj++) {
261         PetscBool sel = PETSC_TRUE;
262         for (kk=0; kk<nselected_2 && sel; kk++) {
263           PetscInt lid = selected_idx_2[kk];
264           if (lid == jj) sel = PETSC_FALSE;
265         }
266         if (sel) fprintf(file, "%d %e %e\n",sid++,coords[jj],coords[data_stride + jj]);
267       }
268       fclose(file);
269       if (sid != nPlotPts) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != nPlotPts %D",sid,nPlotPts);
270       level++;
271     }
272   }
273 #if defined PETSC_GAMG_USE_LOG
274   ierr = PetscLogEventBegin(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
275 #endif
276   { /* form P - setup some maps */
277     PetscInt clid,mm,*nTri,*node_tri;
278 
279     ierr = PetscMalloc2(nselected_2, &node_tri,nselected_2, &nTri);CHKERRQ(ierr);
280 
281     /* need list of triangles on node */
282     for (kk=0; kk<nselected_2; kk++) nTri[kk] = 0;
283     for (tid=0,kk=0; tid<mid.numberoftriangles; tid++) {
284       for (jj=0; jj<3; jj++) {
285         PetscInt cid = mid.trianglelist[kk++];
286         if (nTri[cid] == 0) node_tri[cid] = tid;
287         nTri[cid]++;
288       }
289     }
290 #define EPS 1.e-12
291     /* find points and set prolongation */
292     for (mm = clid = 0; mm < nFineLoc; mm++) {
293       PetscBool ise;
294       ierr = PetscCDEmptyAt(agg_lists_1,mm,&ise);CHKERRQ(ierr);
295       if (!ise) {
296         const PetscInt lid = mm;
297         PetscScalar    AA[3][3];
298         PetscBLASInt   N=3,NRHS=1,LDA=3,IPIV[3],LDB=3,INFO;
299         PetscCDIntNd   *pos;
300 
301         ierr = PetscCDGetHeadPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
302         while (pos) {
303           PetscInt flid;
304           ierr = PetscCDIntNdGetID(pos, &flid);CHKERRQ(ierr);
305           ierr = PetscCDGetNextPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
306 
307           if (flid < nFineLoc) {  /* could be a ghost */
308             PetscInt       bestTID = -1; PetscReal best_alpha = 1.e10;
309             const PetscInt fgid    = flid + myFine0;
310             /* compute shape function for gid */
311             const PetscReal fcoord[3] = {coords[flid],coords[data_stride+flid],1.0};
312             PetscBool       haveit    =PETSC_FALSE; PetscScalar alpha[3]; PetscInt clids[3];
313 
314             /* look for it */
315             for (tid = node_tri[clid], jj=0;
316                  jj < 5 && !haveit && tid != -1;
317                  jj++) {
318               for (tt=0; tt<3; tt++) {
319                 PetscInt cid2 = mid.trianglelist[3*tid + tt];
320                 PetscInt lid2 = selected_idx_2[cid2];
321                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
322                 clids[tt] = cid2; /* store for interp */
323               }
324 
325               for (tt=0; tt<3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];
326 
327               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
328               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
329               {
330                 PetscBool have=PETSC_TRUE;  PetscReal lowest=1.e10;
331                 for (tt = 0, idx = 0; tt < 3; tt++) {
332                   if (PetscRealPart(alpha[tt]) > (1.0+EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
333                   if (PetscRealPart(alpha[tt]) < lowest) {
334                     lowest = PetscRealPart(alpha[tt]);
335                     idx    = tt;
336                   }
337                 }
338                 haveit = have;
339               }
340               tid = mid.neighborlist[3*tid + idx];
341             }
342 
343             if (!haveit) {
344               /* brute force */
345               for (tid=0; tid<mid.numberoftriangles && !haveit; tid++) {
346                 for (tt=0; tt<3; tt++) {
347                   PetscInt cid2 = mid.trianglelist[3*tid + tt];
348                   PetscInt lid2 = selected_idx_2[cid2];
349                   AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
350                   clids[tt] = cid2; /* store for interp */
351                 }
352                 for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
353                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
354                 PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
355                 {
356                   PetscBool have=PETSC_TRUE;  PetscReal worst=0.0, v;
357                   for (tt=0; tt<3 && have; tt++) {
358                     if (PetscRealPart(alpha[tt]) > 1.0+EPS || PetscRealPart(alpha[tt]) < -EPS) have=PETSC_FALSE;
359                     if ((v=PetscAbs(PetscRealPart(alpha[tt])-0.5)) > worst) worst = v;
360                   }
361                   if (worst < best_alpha) {
362                     best_alpha = worst; bestTID = tid;
363                   }
364                   haveit = have;
365                 }
366               }
367             }
368             if (!haveit) {
369               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
370               /* use best one */
371               for (tt=0; tt<3; tt++) {
372                 PetscInt cid2 = mid.trianglelist[3*bestTID + tt];
373                 PetscInt lid2 = selected_idx_2[cid2];
374                 AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
375                 clids[tt] = cid2; /* store for interp */
376               }
377               for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
378               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
379               PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
380             }
381 
382             /* put in row of P */
383             for (idx=0; idx<3; idx++) {
384               PetscScalar shp = alpha[idx];
385               if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
386                 PetscInt cgid = crsGID[clids[idx]];
387                 PetscInt jj   = cgid*bs, ii = fgid*bs; /* need to gloalize */
388                 for (tt=0; tt < bs; tt++, ii++, jj++) {
389                   ierr = MatSetValues(a_Prol,1,&ii,1,&jj,&shp,INSERT_VALUES);CHKERRQ(ierr);
390                 }
391               }
392             }
393           }
394         } /* aggregates iterations */
395         clid++;
396       } /* a coarse agg */
397     } /* for all fine nodes */
398 
399     ierr = ISRestoreIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
400     ierr = MatAssemblyBegin(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
401     ierr = MatAssemblyEnd(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
402 
403     ierr = PetscFree2(node_tri,nTri);CHKERRQ(ierr);
404   }
405 #if defined PETSC_GAMG_USE_LOG
406   ierr = PetscLogEventEnd(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
407 #endif
408   free(mid.trianglelist);
409   free(mid.neighborlist);
410   ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
411   PetscFunctionReturn(0);
412 #else
413   SETERRQ(PetscObjectComm((PetscObject)a_Prol),PETSC_ERR_PLIB,"configure with TRIANGLE to use geometric MG");
414 #endif
415 }
416 /* -------------------------------------------------------------------------- */
417 /*
418    getGIDsOnSquareGraph - square graph, get
419 
420    Input Parameter:
421    . nselected_1 - selected local indices (includes ghosts in input Gmat1)
422    . clid_lid_1 - [nselected_1] lids of selected nodes
423    . Gmat1 - graph that goes with 'selected_1'
424    Output Parameter:
425    . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
426    . a_Gmat_2 - graph that is squared of 'Gmat_1'
427    . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
428 */
429 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)
430 {
431   PetscErrorCode ierr;
432   PetscMPIInt    size;
433   PetscInt       *crsGID, kk,my0,Iend,nloc;
434   MPI_Comm       comm;
435 
436   PetscFunctionBegin;
437   ierr = PetscObjectGetComm((PetscObject)Gmat1,&comm);CHKERRQ(ierr);
438   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
439   ierr = MatGetOwnershipRange(Gmat1,&my0,&Iend);CHKERRQ(ierr); /* AIJ */
440   nloc = Iend - my0; /* this does not change */
441 
442   if (size == 1) { /* not much to do in serial */
443     ierr = PetscMalloc1(nselected_1, &crsGID);CHKERRQ(ierr);
444     for (kk=0; kk<nselected_1; kk++) crsGID[kk] = kk;
445     *a_Gmat_2 = 0;
446     ierr      = ISCreateGeneral(PETSC_COMM_SELF,nselected_1,clid_lid_1,PETSC_COPY_VALUES,a_selected_2);CHKERRQ(ierr);
447   } else {
448     PetscInt    idx,num_fine_ghosts,num_crs_ghost,myCrs0;
449     Mat_MPIAIJ  *mpimat2;
450     Mat         Gmat2;
451     Vec         locState;
452     PetscScalar *cpcol_state;
453 
454     /* scan my coarse zero gid, set 'lid_state' with coarse GID */
455     kk = nselected_1;
456     ierr = MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPI_SUM, comm);CHKERRQ(ierr);
457     myCrs0 -= nselected_1;
458 
459     if (a_Gmat_2) { /* output */
460       /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
461       ierr      = MatTransposeMatMult(Gmat1, Gmat1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Gmat2);CHKERRQ(ierr);
462       *a_Gmat_2 = Gmat2; /* output */
463     } else Gmat2 = Gmat1;  /* use local to get crsGIDs at least */
464     /* get coarse grid GIDS for selected (locals and ghosts) */
465     mpimat2 = (Mat_MPIAIJ*)Gmat2->data;
466     ierr    = MatCreateVecs(Gmat2, &locState, 0);CHKERRQ(ierr);
467     ierr    = VecSet(locState, (PetscScalar)(PetscReal)(-1));CHKERRQ(ierr); /* set with UNKNOWN state */
468     for (kk=0; kk<nselected_1; kk++) {
469       PetscInt    fgid = clid_lid_1[kk] + my0;
470       PetscScalar v    = (PetscScalar)(kk+myCrs0);
471       ierr = VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES);CHKERRQ(ierr); /* set with PID */
472     }
473     ierr = VecAssemblyBegin(locState);CHKERRQ(ierr);
474     ierr = VecAssemblyEnd(locState);CHKERRQ(ierr);
475     ierr = VecScatterBegin(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
476     ierr =   VecScatterEnd(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
477     ierr = VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts);CHKERRQ(ierr);
478     ierr = VecGetArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
479     for (kk=0,num_crs_ghost=0; kk<num_fine_ghosts; kk++) {
480       if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
481     }
482     ierr = PetscMalloc1(nselected_1+num_crs_ghost, &crsGID);CHKERRQ(ierr); /* output */
483     {
484       PetscInt *selected_set;
485       ierr = PetscMalloc1(nselected_1+num_crs_ghost, &selected_set);CHKERRQ(ierr);
486       /* do ghost of 'crsGID' */
487       for (kk=0,idx=nselected_1; kk<num_fine_ghosts; kk++) {
488         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
489           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
490           selected_set[idx] = nloc + kk;
491           crsGID[idx++]     = cgid;
492         }
493       }
494       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);
495       ierr = VecRestoreArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
496       /* do locals in 'crsGID' */
497       ierr = VecGetArray(locState, &cpcol_state);CHKERRQ(ierr);
498       for (kk=0,idx=0; kk<nloc; kk++) {
499         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
500           PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
501           selected_set[idx] = kk;
502           crsGID[idx++]     = cgid;
503         }
504       }
505       if (idx != nselected_1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"idx %D != nselected_1 %D",idx,nselected_1);
506       ierr = VecRestoreArray(locState, &cpcol_state);CHKERRQ(ierr);
507 
508       if (a_selected_2 != 0) { /* output */
509         ierr = ISCreateGeneral(PETSC_COMM_SELF,(nselected_1+num_crs_ghost),selected_set,PETSC_OWN_POINTER,a_selected_2);CHKERRQ(ierr);
510       } else {
511         ierr = PetscFree(selected_set);CHKERRQ(ierr);
512       }
513     }
514     ierr = VecDestroy(&locState);CHKERRQ(ierr);
515   }
516   *a_crsGID = crsGID; /* output */
517   PetscFunctionReturn(0);
518 }
519 
520 /* -------------------------------------------------------------------------- */
521 /*
522    PCGAMGGraph_GEO
523 
524   Input Parameter:
525    . pc - this
526    . Amat - matrix on this fine level
527   Output Parameter:
528    . a_Gmat
529 */
530 PetscErrorCode PCGAMGGraph_GEO(PC pc,Mat Amat,Mat *a_Gmat)
531 {
532   PetscErrorCode  ierr;
533   PC_MG           *mg      = (PC_MG*)pc->data;
534   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
535   const PetscReal vfilter  = pc_gamg->threshold[0];
536   MPI_Comm        comm;
537   Mat             Gmat;
538   PetscBool       set,flg,symm;
539 
540   PetscFunctionBegin;
541   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
542   ierr = PetscLogEventBegin(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
543 
544   ierr = MatIsSymmetricKnown(Amat, &set, &flg);CHKERRQ(ierr);
545   symm = (PetscBool)!(set && flg);
546 
547   ierr = PCGAMGCreateGraph(Amat, &Gmat);CHKERRQ(ierr);
548   ierr = PCGAMGFilterGraph(&Gmat, vfilter, symm);CHKERRQ(ierr);
549 
550   *a_Gmat = Gmat;
551   ierr = PetscLogEventEnd(PC_GAMGGraph_GEO,0,0,0,0);CHKERRQ(ierr);
552   PetscFunctionReturn(0);
553 }
554 
555 /* -------------------------------------------------------------------------- */
556 /*
557    PCGAMGCoarsen_GEO
558 
559   Input Parameter:
560    . a_pc - this
561    . a_Gmat - graph
562   Output Parameter:
563    . a_llist_parent - linked list from selected indices for data locality only
564 */
565 PetscErrorCode PCGAMGCoarsen_GEO(PC a_pc,Mat *a_Gmat,PetscCoarsenData **a_llist_parent)
566 {
567   PetscErrorCode ierr;
568   PetscInt       Istart,Iend,nloc,kk,Ii,ncols;
569   IS             perm;
570   GAMGNode       *gnodes;
571   PetscInt       *permute;
572   Mat            Gmat  = *a_Gmat;
573   MPI_Comm       comm;
574   MatCoarsen     crs;
575 
576   PetscFunctionBegin;
577   ierr = PetscObjectGetComm((PetscObject)a_pc,&comm);CHKERRQ(ierr);
578   ierr = PetscLogEventBegin(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
579   ierr = MatGetOwnershipRange(Gmat, &Istart, &Iend);CHKERRQ(ierr);
580   nloc = (Iend-Istart);
581 
582   /* create random permutation with sort for geo-mg */
583   ierr = PetscMalloc1(nloc, &gnodes);CHKERRQ(ierr);
584   ierr = PetscMalloc1(nloc, &permute);CHKERRQ(ierr);
585 
586   for (Ii=Istart; Ii<Iend; Ii++) { /* locals only? */
587     ierr = MatGetRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
588     {
589       PetscInt lid = Ii - Istart;
590       gnodes[lid].lid    = lid;
591       gnodes[lid].degree = ncols;
592     }
593     ierr = MatRestoreRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
594   }
595   if (PETSC_TRUE) {
596     PetscRandom  rand;
597     PetscBool    *bIndexSet;
598     PetscReal    rr;
599     PetscInt     iSwapIndex;
600 
601     ierr = PetscRandomCreate(comm,&rand);CHKERRQ(ierr);
602     ierr = PetscCalloc1(nloc, &bIndexSet);CHKERRQ(ierr);
603     for (Ii = 0; Ii < nloc; Ii++) {
604       ierr = PetscRandomGetValueReal(rand,&rr);CHKERRQ(ierr);
605       iSwapIndex = (PetscInt) (rr*nloc);
606       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
607         GAMGNode iTemp = gnodes[iSwapIndex];
608         gnodes[iSwapIndex]    = gnodes[Ii];
609         gnodes[Ii]            = iTemp;
610         bIndexSet[Ii]         = PETSC_TRUE;
611         bIndexSet[iSwapIndex] = PETSC_TRUE;
612       }
613     }
614     ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
615     ierr = PetscFree(bIndexSet);CHKERRQ(ierr);
616   }
617   /* only sort locals */
618   qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
619   /* create IS of permutation */
620   for (kk=0; kk<nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
621   ierr = PetscFree(gnodes);CHKERRQ(ierr);
622   ierr = ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
623 
624   /* get MIS aggs */
625 
626   ierr = MatCoarsenCreate(comm, &crs);CHKERRQ(ierr);
627   ierr = MatCoarsenSetType(crs, MATCOARSENMIS);CHKERRQ(ierr);
628   ierr = MatCoarsenSetGreedyOrdering(crs, perm);CHKERRQ(ierr);
629   ierr = MatCoarsenSetAdjacency(crs, Gmat);CHKERRQ(ierr);
630   ierr = MatCoarsenSetStrictAggs(crs, PETSC_FALSE);CHKERRQ(ierr);
631   ierr = MatCoarsenApply(crs);CHKERRQ(ierr);
632   ierr = MatCoarsenGetData(crs, a_llist_parent);CHKERRQ(ierr);
633   ierr = MatCoarsenDestroy(&crs);CHKERRQ(ierr);
634 
635   ierr = ISDestroy(&perm);CHKERRQ(ierr);
636   ierr = PetscLogEventEnd(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
637   PetscFunctionReturn(0);
638 }
639 
640 /* -------------------------------------------------------------------------- */
641 /*
642  PCGAMGProlongator_GEO
643 
644  Input Parameter:
645  . pc - this
646  . Amat - matrix on this fine level
647  . Graph - used to get ghost data for nodes in
648  . selected_1 - [nselected]
649  . agg_lists - [nselected]
650  Output Parameter:
651  . a_P_out - prolongation operator to the next level
652  */
653 PetscErrorCode PCGAMGProlongator_GEO(PC pc,Mat Amat,Mat Gmat,PetscCoarsenData *agg_lists,Mat *a_P_out)
654 {
655   PC_MG          *mg      = (PC_MG*)pc->data;
656   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
657   const PetscInt dim      = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
658   PetscErrorCode ierr;
659   PetscInt       Istart,Iend,nloc,my0,jj,kk,ncols,nLocalSelected,bs,*clid_flid;
660   Mat            Prol;
661   PetscMPIInt    rank, size;
662   MPI_Comm       comm;
663   IS             selected_2,selected_1;
664   const PetscInt *selected_idx;
665   MatType        mtype;
666 
667   PetscFunctionBegin;
668   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
669   ierr = PetscLogEventBegin(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
670   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
671   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
672   ierr = MatGetOwnershipRange(Amat, &Istart, &Iend);CHKERRQ(ierr);
673   ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
674   nloc = (Iend-Istart)/bs; my0 = Istart/bs;
675   if ((Iend-Istart) % bs) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"(Iend %D - Istart %D) % bs %D",Iend,Istart,bs);
676 
677   /* get 'nLocalSelected' */
678   ierr = PetscCDGetMIS(agg_lists, &selected_1);CHKERRQ(ierr);
679   ierr = ISGetSize(selected_1, &jj);CHKERRQ(ierr);
680   ierr = PetscMalloc1(jj, &clid_flid);CHKERRQ(ierr);
681   ierr = ISGetIndices(selected_1, &selected_idx);CHKERRQ(ierr);
682   for (kk=0,nLocalSelected=0; kk<jj; kk++) {
683     PetscInt lid = selected_idx[kk];
684     if (lid<nloc) {
685       ierr = MatGetRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
686       if (ncols>1) clid_flid[nLocalSelected++] = lid; /* fiter out singletons */
687       ierr = MatRestoreRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
688     }
689   }
690   ierr = ISRestoreIndices(selected_1, &selected_idx);CHKERRQ(ierr);
691   ierr = ISDestroy(&selected_1);CHKERRQ(ierr); /* this is selected_1 in serial */
692 
693   /* create prolongator  matrix */
694   ierr = MatGetType(Amat,&mtype);CHKERRQ(ierr);
695   ierr = MatCreate(comm, &Prol);CHKERRQ(ierr);
696   ierr = MatSetSizes(Prol,nloc*bs,nLocalSelected*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
697   ierr = MatSetBlockSizes(Prol, bs, bs);CHKERRQ(ierr);
698   ierr = MatSetType(Prol, mtype);CHKERRQ(ierr);
699   ierr = MatSeqAIJSetPreallocation(Prol,3*data_cols,NULL);CHKERRQ(ierr);
700   ierr = MatMPIAIJSetPreallocation(Prol,3*data_cols,NULL,3*data_cols,NULL);CHKERRQ(ierr);
701 
702   /* can get all points "removed" - but not on geomg */
703   ierr =  MatGetSize(Prol, &kk, &jj);CHKERRQ(ierr);
704   if (!jj) {
705     ierr = PetscInfo(pc,"ERROE: no selected points on coarse grid\n");CHKERRQ(ierr);
706     ierr = PetscFree(clid_flid);CHKERRQ(ierr);
707     ierr = MatDestroy(&Prol);CHKERRQ(ierr);
708     *a_P_out = NULL;  /* out */
709     PetscFunctionReturn(0);
710   }
711 
712   {
713     PetscReal *coords;
714     PetscInt  data_stride;
715     PetscInt  *crsGID = NULL;
716     Mat       Gmat2;
717 
718     if (dim != data_cols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim %D != data_cols %D",dim,data_cols);
719     /* grow ghost data for better coarse grid cover of fine grid */
720 #if defined PETSC_GAMG_USE_LOG
721     ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
722 #endif
723     /* messy method, squares graph and gets some data */
724     ierr = getGIDsOnSquareGraph(nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID);CHKERRQ(ierr);
725     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
726 #if defined PETSC_GAMG_USE_LOG
727     ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
728 #endif
729     /* create global vector of coorindates in 'coords' */
730     if (size > 1) {
731       ierr = PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords);CHKERRQ(ierr);
732     } else {
733       coords      = (PetscReal*)pc_gamg->data;
734       data_stride = pc_gamg->data_sz/pc_gamg->data_cell_cols;
735     }
736     ierr = MatDestroy(&Gmat2);CHKERRQ(ierr);
737 
738     /* triangulate */
739     if (dim == 2) {
740       PetscReal metric,tm;
741 #if defined PETSC_GAMG_USE_LOG
742       ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
743 #endif
744       ierr = triangulateAndFormProl(selected_2, data_stride, coords,nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric);CHKERRQ(ierr);
745 #if defined PETSC_GAMG_USE_LOG
746       ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
747 #endif
748       ierr = PetscFree(crsGID);CHKERRQ(ierr);
749 
750       /* clean up and create coordinates for coarse grid (output) */
751       if (size > 1) ierr = PetscFree(coords);CHKERRQ(ierr);
752 
753       ierr = MPIU_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, comm);CHKERRQ(ierr);
754       if (tm > 1.) { /* needs to be globalized - should not happen */
755         ierr = PetscInfo1(pc," failed metric for coarse grid %e\n",(double)tm);CHKERRQ(ierr);
756         ierr = MatDestroy(&Prol);CHKERRQ(ierr);
757       } else if (metric > .0) {
758         ierr = PetscInfo1(pc,"worst metric for coarse grid = %e\n",(double)metric);CHKERRQ(ierr);
759       }
760     } else SETERRQ(comm,PETSC_ERR_PLIB,"3D not implemented for 'geo' AMG");
761     { /* create next coords - output */
762       PetscReal *crs_crds;
763       ierr = PetscMalloc1(dim*nLocalSelected, &crs_crds);CHKERRQ(ierr);
764       for (kk=0; kk<nLocalSelected; kk++) { /* grab local select nodes to promote - output */
765         PetscInt lid = clid_flid[kk];
766         for (jj=0; jj<dim; jj++) crs_crds[jj*nLocalSelected + kk] = pc_gamg->data[jj*nloc + lid];
767       }
768 
769       ierr             = PetscFree(pc_gamg->data);CHKERRQ(ierr);
770       pc_gamg->data    = crs_crds; /* out */
771       pc_gamg->data_sz = dim*nLocalSelected;
772     }
773     ierr = ISDestroy(&selected_2);CHKERRQ(ierr);
774   }
775 
776   *a_P_out = Prol;  /* out */
777   ierr     = PetscFree(clid_flid);CHKERRQ(ierr);
778   ierr = PetscLogEventEnd(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
779   PetscFunctionReturn(0);
780 }
781 
782 static PetscErrorCode PCDestroy_GAMG_GEO(PC pc)
783 {
784   PetscErrorCode ierr;
785 
786   PetscFunctionBegin;
787   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
788   PetscFunctionReturn(0);
789 }
790 
791 /* -------------------------------------------------------------------------- */
792 /*
793  PCCreateGAMG_GEO
794 
795   Input Parameter:
796    . pc -
797 */
798 PetscErrorCode  PCCreateGAMG_GEO(PC pc)
799 {
800   PetscErrorCode ierr;
801   PC_MG          *mg      = (PC_MG*)pc->data;
802   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
803 
804   PetscFunctionBegin;
805   pc_gamg->ops->setfromoptions = PCSetFromOptions_GEO;
806   pc_gamg->ops->destroy        = PCDestroy_GAMG_GEO;
807   /* reset does not do anything; setup not virtual */
808 
809   /* set internal function pointers */
810   pc_gamg->ops->graph             = PCGAMGGraph_GEO;
811   pc_gamg->ops->coarsen           = PCGAMGCoarsen_GEO;
812   pc_gamg->ops->prolongator       = PCGAMGProlongator_GEO;
813   pc_gamg->ops->optprolongator    = NULL;
814   pc_gamg->ops->createdefaultdata = PCSetData_GEO;
815 
816   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_GEO);CHKERRQ(ierr);
817   PetscFunctionReturn(0);
818 }
819