xref: /petsc/src/ksp/pc/impls/gamg/geo.c (revision e0f629dd96229b85b8d4fbf4a5ed4f197d232daa)
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 static inline int petsc_geo_mg_compare(const void *a, const void *b) {
23   return (((GAMGNode *)a)->degree - ((GAMGNode *)b)->degree);
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   PC_MG   *mg      = (PC_MG *)pc->data;
34   PC_GAMG *pc_gamg = (PC_GAMG *)mg->innerctx;
35   PetscInt arrsz, bs, my0, kk, ii, nloc, Iend, aloc;
36   Mat      Amat = pc->pmat;
37 
38   PetscFunctionBegin;
39   PetscValidHeaderSpecific(Amat, MAT_CLASSID, 1);
40   PetscCall(MatGetBlockSize(Amat, &bs));
41   PetscCall(MatGetOwnershipRange(Amat, &my0, &Iend));
42   aloc = (Iend - my0);
43   nloc = (Iend - my0) / bs;
44 
45   PetscCheck(nloc == a_nloc || aloc == a_nloc, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of local blocks %" PetscInt_FMT " must be %" PetscInt_FMT " or %" PetscInt_FMT ".", a_nloc, nloc, aloc);
46 
47   pc_gamg->data_cell_rows = 1;
48   PetscCheck(coords || (nloc <= 0), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Need coordinates for pc_gamg_type 'geo'.");
49   pc_gamg->data_cell_cols = ndm; /* coordinates */
50 
51   arrsz = nloc * pc_gamg->data_cell_rows * pc_gamg->data_cell_cols;
52 
53   /* create data - syntactic sugar that should be refactored at some point */
54   if (!pc_gamg->data || (pc_gamg->data_sz != arrsz)) {
55     PetscCall(PetscFree(pc_gamg->data));
56     PetscCall(PetscMalloc1(arrsz + 1, &pc_gamg->data));
57   }
58   for (kk = 0; kk < arrsz; kk++) pc_gamg->data[kk] = -999.;
59   pc_gamg->data[arrsz] = -99.;
60   /* copy data in - column oriented */
61   if (nloc == a_nloc) {
62     for (kk = 0; kk < nloc; kk++) {
63       for (ii = 0; ii < ndm; ii++) pc_gamg->data[ii * nloc + kk] = coords[kk * ndm + ii];
64     }
65   } else { /* assumes the coordinates are blocked */
66     for (kk = 0; kk < nloc; kk++) {
67       for (ii = 0; ii < ndm; ii++) pc_gamg->data[ii * nloc + kk] = coords[bs * kk * ndm + ii];
68     }
69   }
70   PetscCheck(pc_gamg->data[arrsz] == -99., PETSC_COMM_SELF, PETSC_ERR_PLIB, "pc_gamg->data[arrsz %" PetscInt_FMT "] %g != -99.", arrsz, (double)pc_gamg->data[arrsz]);
71   pc_gamg->data_sz = arrsz;
72   PetscFunctionReturn(0);
73 }
74 
75 /*
76    PCSetData_GEO
77 
78   Input Parameter:
79    . pc -
80 */
81 PetscErrorCode PCSetData_GEO(PC pc, Mat m) {
82   PetscFunctionBegin;
83   SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "GEO MG needs coordinates");
84 }
85 
86 /*
87    PCSetFromOptions_GEO
88 
89   Input Parameter:
90    . pc -
91 */
92 PetscErrorCode PCSetFromOptions_GEO(PC pc, PetscOptionItems *PetscOptionsObject) {
93   PetscFunctionBegin;
94   PetscOptionsHeadBegin(PetscOptionsObject, "GAMG-GEO options");
95   {
96     /* -pc_gamg_sa_nsmooths */
97     /* pc_gamg_sa->smooths = 0; */
98     /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
99     /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
100     /*                        "PCGAMGSetNSmooths_AGG", */
101     /*                        pc_gamg_sa->smooths, */
102     /*                        &pc_gamg_sa->smooths, */
103     /*                        &flag);  */
104   }
105   PetscOptionsHeadEnd();
106   PetscFunctionReturn(0);
107 }
108 
109 /*
110  triangulateAndFormProl
111 
112    Input Parameter:
113    . selected_2 - list of selected local ID, includes selected ghosts
114    . data_stride -
115    . coords[2*data_stride] - column vector of local coordinates w/ ghosts
116    . nselected_1 - selected IDs that go with base (1) graph includes selected ghosts
117    . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
118    . agg_lists_1 - list of aggregates selected_1 vertices of aggregate unselected vertices
119    . crsGID[selected.size()] - global index for prolongation operator
120    . bs - block size
121   Output Parameter:
122    . a_Prol - prolongation operator
123    . a_worst_best - measure of worst missed fine vertex, 0 is no misses
124 */
125 static PetscErrorCode triangulateAndFormProl(IS selected_2, PetscInt data_stride, PetscReal coords[], PetscInt nselected_1, const PetscInt clid_lid_1[], const PetscCoarsenData *agg_lists_1, const PetscInt crsGID[], PetscInt bs, Mat a_Prol, PetscReal *a_worst_best) {
126 #if defined(PETSC_HAVE_TRIANGLE)
127   PetscInt             jj, tid, tt, idx, nselected_2;
128   struct triangulateio in, mid;
129   const PetscInt      *selected_idx_2;
130   PetscMPIInt          rank;
131   PetscInt             Istart, Iend, nFineLoc, myFine0;
132   int                  kk, nPlotPts, sid;
133   MPI_Comm             comm;
134   PetscReal            tm;
135 
136   PetscFunctionBegin;
137   PetscCall(PetscObjectGetComm((PetscObject)a_Prol, &comm));
138   PetscCallMPI(MPI_Comm_rank(comm, &rank));
139   PetscCall(ISGetSize(selected_2, &nselected_2));
140   if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
141     *a_worst_best = 100.0;                    /* this will cause a stop, but not globalized (should not happen) */
142   } else *a_worst_best = 0.0;
143   PetscCall(MPIU_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, comm));
144   if (tm > 0.0) {
145     *a_worst_best = 100.0;
146     PetscFunctionReturn(0);
147   }
148   PetscCall(MatGetOwnershipRange(a_Prol, &Istart, &Iend));
149   nFineLoc                   = (Iend - Istart) / bs;
150   myFine0                    = Istart / bs;
151   nPlotPts                   = nFineLoc; /* locals */
152   /* triangle */
153   /* Define input points - in*/
154   in.numberofpoints          = nselected_2;
155   in.numberofpointattributes = 0;
156   /* get nselected points */
157   PetscCall(PetscMalloc1(2 * nselected_2, &in.pointlist));
158   PetscCall(ISGetIndices(selected_2, &selected_idx_2));
159 
160   for (kk = 0, sid = 0; kk < nselected_2; kk++, sid += 2) {
161     PetscInt lid          = selected_idx_2[kk];
162     in.pointlist[sid]     = coords[lid];
163     in.pointlist[sid + 1] = coords[data_stride + lid];
164     if (lid >= nFineLoc) nPlotPts++;
165   }
166   PetscCheck(sid == 2 * nselected_2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "sid %d != 2*nselected_2 %" PetscInt_FMT, sid, nselected_2);
167 
168   in.numberofsegments      = 0;
169   in.numberofedges         = 0;
170   in.numberofholes         = 0;
171   in.numberofregions       = 0;
172   in.trianglelist          = NULL;
173   in.segmentmarkerlist     = NULL;
174   in.pointattributelist    = NULL;
175   in.pointmarkerlist       = NULL;
176   in.triangleattributelist = NULL;
177   in.trianglearealist      = NULL;
178   in.segmentlist           = NULL;
179   in.holelist              = NULL;
180   in.regionlist            = NULL;
181   in.edgelist              = NULL;
182   in.edgemarkerlist        = NULL;
183   in.normlist              = NULL;
184 
185   /* triangulate */
186   mid.pointlist             = NULL; /* Not needed if -N switch used. */
187   /* Not needed if -N switch used or number of point attributes is zero: */
188   mid.pointattributelist    = NULL;
189   mid.pointmarkerlist       = NULL; /* Not needed if -N or -B switch used. */
190   mid.trianglelist          = NULL; /* Not needed if -E switch used. */
191   /* Not needed if -E switch used or number of triangle attributes is zero: */
192   mid.triangleattributelist = NULL;
193   mid.neighborlist          = NULL; /* Needed only if -n switch used. */
194   /* Needed only if segments are output (-p or -c) and -P not used: */
195   mid.segmentlist           = NULL;
196   /* Needed only if segments are output (-p or -c) and -P and -B not used: */
197   mid.segmentmarkerlist     = NULL;
198   mid.edgelist              = NULL; /* Needed only if -e switch used. */
199   mid.edgemarkerlist        = NULL; /* Needed if -e used and -B not used. */
200   mid.numberoftriangles     = 0;
201 
202   /* Triangulate the points.  Switches are chosen to read and write a  */
203   /*   PSLG (p), preserve the convex hull (c), number everything from  */
204   /*   zero (z), assign a regional attribute to each element (A), and  */
205   /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
206   /*   neighbor list (n).                                            */
207   if (nselected_2 != 0) {  /* inactive processor */
208     char args[] = "npczQ"; /* c is needed ? */
209     triangulate(args, &in, &mid, (struct triangulateio *)NULL);
210     /* output .poly files for 'showme' */
211     if (!PETSC_TRUE) {
212       static int level = 1;
213       FILE      *file;
214       char       fname[32];
215 
216       sprintf(fname, "C%d_%d.poly", level, rank);
217       file = fopen(fname, "w");
218       /*First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)>*/
219       fprintf(file, "%d  %d  %d  %d\n", in.numberofpoints, 2, 0, 0);
220       /*Following lines: <vertex #> <x> <y> */
221       for (kk = 0, sid = 0; kk < in.numberofpoints; kk++, sid += 2) fprintf(file, "%d %e %e\n", kk, in.pointlist[sid], in.pointlist[sid + 1]);
222       /*One line: <# of segments> <# of boundary markers (0 or 1)> */
223       fprintf(file, "%d  %d\n", 0, 0);
224       /*Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
225       /* One line: <# of holes> */
226       fprintf(file, "%d\n", 0);
227       /* Following lines: <hole #> <x> <y> */
228       /* Optional line: <# of regional attributes and/or area constraints> */
229       /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
230       fclose(file);
231 
232       /* elems */
233       sprintf(fname, "C%d_%d.ele", level, rank);
234       file = fopen(fname, "w");
235       /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
236       fprintf(file, "%d %d %d\n", mid.numberoftriangles, 3, 0);
237       /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
238       for (kk = 0, sid = 0; kk < mid.numberoftriangles; kk++, sid += 3) fprintf(file, "%d %d %d %d\n", kk, mid.trianglelist[sid], mid.trianglelist[sid + 1], mid.trianglelist[sid + 2]);
239       fclose(file);
240 
241       sprintf(fname, "C%d_%d.node", level, rank);
242       file = fopen(fname, "w");
243       /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
244       /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
245       fprintf(file, "%d  %d  %d  %d\n", nPlotPts, 2, 0, 0);
246       /*Following lines: <vertex #> <x> <y> */
247       for (kk = 0, sid = 0; kk < in.numberofpoints; kk++, sid += 2) fprintf(file, "%d %e %e\n", kk, in.pointlist[sid], in.pointlist[sid + 1]);
248 
249       sid /= 2;
250       for (jj = 0; jj < nFineLoc; jj++) {
251         PetscBool sel = PETSC_TRUE;
252         for (kk = 0; kk < nselected_2 && sel; kk++) {
253           PetscInt lid = selected_idx_2[kk];
254           if (lid == jj) sel = PETSC_FALSE;
255         }
256         if (sel) fprintf(file, "%d %e %e\n", sid++, coords[jj], coords[data_stride + jj]);
257       }
258       fclose(file);
259       PetscCheck(sid == nPlotPts, PETSC_COMM_SELF, PETSC_ERR_PLIB, "sid %d != nPlotPts %d", sid, nPlotPts);
260       level++;
261     }
262   }
263   { /* form P - setup some maps */
264     PetscInt clid, mm, *nTri, *node_tri;
265 
266     PetscCall(PetscMalloc2(nselected_2, &node_tri, nselected_2, &nTri));
267 
268     /* need list of triangles on node */
269     for (kk = 0; kk < nselected_2; kk++) nTri[kk] = 0;
270     for (tid = 0, kk = 0; tid < mid.numberoftriangles; tid++) {
271       for (jj = 0; jj < 3; jj++) {
272         PetscInt cid = mid.trianglelist[kk++];
273         if (nTri[cid] == 0) node_tri[cid] = tid;
274         nTri[cid]++;
275       }
276     }
277 #define EPS 1.e-12
278     /* find points and set prolongation */
279     for (mm = clid = 0; mm < nFineLoc; mm++) {
280       PetscBool ise;
281       PetscCall(PetscCDEmptyAt(agg_lists_1, mm, &ise));
282       if (!ise) {
283         const PetscInt lid = mm;
284         PetscScalar    AA[3][3];
285         PetscBLASInt   N = 3, NRHS = 1, LDA = 3, IPIV[3], LDB = 3, INFO;
286         PetscCDIntNd  *pos;
287 
288         PetscCall(PetscCDGetHeadPos(agg_lists_1, lid, &pos));
289         while (pos) {
290           PetscInt flid;
291           PetscCall(PetscCDIntNdGetID(pos, &flid));
292           PetscCall(PetscCDGetNextPos(agg_lists_1, lid, &pos));
293 
294           if (flid < nFineLoc) { /* could be a ghost */
295             PetscInt        bestTID    = -1;
296             PetscReal       best_alpha = 1.e10;
297             const PetscInt  fgid       = flid + myFine0;
298             /* compute shape function for gid */
299             const PetscReal fcoord[3]  = {coords[flid], coords[data_stride + flid], 1.0};
300             PetscBool       haveit     = PETSC_FALSE;
301             PetscScalar     alpha[3];
302             PetscInt        clids[3];
303 
304             /* look for it */
305             for (tid = node_tri[clid], jj = 0; jj < 5 && !haveit && tid != -1; jj++) {
306               for (tt = 0; tt < 3; tt++) {
307                 PetscInt cid2 = mid.trianglelist[3 * tid + tt];
308                 PetscInt lid2 = selected_idx_2[cid2];
309                 AA[tt][0]     = coords[lid2];
310                 AA[tt][1]     = coords[data_stride + lid2];
311                 AA[tt][2]     = 1.0;
312                 clids[tt]     = cid2; /* store for interp */
313               }
314 
315               for (tt = 0; tt < 3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];
316 
317               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
318               PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
319               {
320                 PetscBool have   = PETSC_TRUE;
321                 PetscReal lowest = 1.e10;
322                 for (tt = 0, idx = 0; tt < 3; tt++) {
323                   if (PetscRealPart(alpha[tt]) > (1.0 + EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
324                   if (PetscRealPart(alpha[tt]) < lowest) {
325                     lowest = PetscRealPart(alpha[tt]);
326                     idx    = tt;
327                   }
328                 }
329                 haveit = have;
330               }
331               tid = mid.neighborlist[3 * tid + idx];
332             }
333 
334             if (!haveit) {
335               /* brute force */
336               for (tid = 0; tid < mid.numberoftriangles && !haveit; tid++) {
337                 for (tt = 0; tt < 3; tt++) {
338                   PetscInt cid2 = mid.trianglelist[3 * tid + tt];
339                   PetscInt lid2 = selected_idx_2[cid2];
340                   AA[tt][0]     = coords[lid2];
341                   AA[tt][1]     = coords[data_stride + lid2];
342                   AA[tt][2]     = 1.0;
343                   clids[tt]     = cid2; /* store for interp */
344                 }
345                 for (tt = 0; tt < 3; tt++) alpha[tt] = fcoord[tt];
346                 /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
347                 PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
348                 {
349                   PetscBool have  = PETSC_TRUE;
350                   PetscReal worst = 0.0, v;
351                   for (tt = 0; tt < 3 && have; tt++) {
352                     if (PetscRealPart(alpha[tt]) > 1.0 + EPS || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
353                     if ((v = PetscAbs(PetscRealPart(alpha[tt]) - 0.5)) > worst) worst = v;
354                   }
355                   if (worst < best_alpha) {
356                     best_alpha = worst;
357                     bestTID    = tid;
358                   }
359                   haveit = have;
360                 }
361               }
362             }
363             if (!haveit) {
364               if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
365               /* use best one */
366               for (tt = 0; tt < 3; tt++) {
367                 PetscInt cid2 = mid.trianglelist[3 * bestTID + tt];
368                 PetscInt lid2 = selected_idx_2[cid2];
369                 AA[tt][0]     = coords[lid2];
370                 AA[tt][1]     = coords[data_stride + lid2];
371                 AA[tt][2]     = 1.0;
372                 clids[tt]     = cid2; /* store for interp */
373               }
374               for (tt = 0; tt < 3; tt++) alpha[tt] = fcoord[tt];
375               /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
376               PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&N, &NRHS, (PetscScalar *)AA, &LDA, IPIV, alpha, &LDB, &INFO));
377             }
378 
379             /* put in row of P */
380             for (idx = 0; idx < 3; idx++) {
381               PetscScalar shp = alpha[idx];
382               if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
383                 PetscInt cgid = crsGID[clids[idx]];
384                 PetscInt jj = cgid * bs, ii = fgid * bs; /* need to gloalize */
385                 for (tt = 0; tt < bs; tt++, ii++, jj++) PetscCall(MatSetValues(a_Prol, 1, &ii, 1, &jj, &shp, INSERT_VALUES));
386               }
387             }
388           }
389         } /* aggregates iterations */
390         clid++;
391       } /* a coarse agg */
392     }   /* for all fine nodes */
393 
394     PetscCall(ISRestoreIndices(selected_2, &selected_idx_2));
395     PetscCall(MatAssemblyBegin(a_Prol, MAT_FINAL_ASSEMBLY));
396     PetscCall(MatAssemblyEnd(a_Prol, MAT_FINAL_ASSEMBLY));
397 
398     PetscCall(PetscFree2(node_tri, nTri));
399   }
400   free(mid.trianglelist);
401   free(mid.neighborlist);
402   free(mid.segmentlist);
403   free(mid.segmentmarkerlist);
404   free(mid.pointlist);
405   free(mid.pointmarkerlist);
406   PetscCall(PetscFree(in.pointlist));
407   PetscFunctionReturn(0);
408 #else
409   SETERRQ(PetscObjectComm((PetscObject)a_Prol), PETSC_ERR_PLIB, "configure with TRIANGLE to use geometric MG");
410 #endif
411 }
412 
413 /*
414    getGIDsOnSquareGraph - square graph, get
415 
416    Input Parameter:
417    . nselected_1 - selected local indices (includes ghosts in input Gmat1)
418    . clid_lid_1 - [nselected_1] lids of selected nodes
419    . Gmat1 - graph that goes with 'selected_1'
420    Output Parameter:
421    . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
422    . a_Gmat_2 - graph that is squared of 'Gmat_1'
423    . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
424 */
425 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) {
426   PetscMPIInt size;
427   PetscInt   *crsGID, kk, my0, Iend, nloc;
428   MPI_Comm    comm;
429 
430   PetscFunctionBegin;
431   PetscCall(PetscObjectGetComm((PetscObject)Gmat1, &comm));
432   PetscCallMPI(MPI_Comm_size(comm, &size));
433   PetscCall(MatGetOwnershipRange(Gmat1, &my0, &Iend)); /* AIJ */
434   nloc = Iend - my0;                                   /* this does not change */
435 
436   if (size == 1) { /* not much to do in serial */
437     PetscCall(PetscMalloc1(nselected_1, &crsGID));
438     for (kk = 0; kk < nselected_1; kk++) crsGID[kk] = kk;
439     *a_Gmat_2 = NULL;
440     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nselected_1, clid_lid_1, PETSC_COPY_VALUES, a_selected_2));
441   } else {
442     PetscInt     idx, num_fine_ghosts, num_crs_ghost, myCrs0;
443     Mat_MPIAIJ  *mpimat2;
444     Mat          Gmat2;
445     Vec          locState;
446     PetscScalar *cpcol_state;
447 
448     /* scan my coarse zero gid, set 'lid_state' with coarse GID */
449     kk = nselected_1;
450     PetscCallMPI(MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPI_SUM, comm));
451     myCrs0 -= nselected_1;
452 
453     if (a_Gmat_2) { /* output */
454       /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
455       PetscCall(PCGAMGSquareGraph_GAMG(pc, Gmat1, &Gmat2));
456       *a_Gmat_2 = Gmat2;  /* output */
457     } else Gmat2 = Gmat1; /* use local to get crsGIDs at least */
458     /* get coarse grid GIDS for selected (locals and ghosts) */
459     mpimat2 = (Mat_MPIAIJ *)Gmat2->data;
460     PetscCall(MatCreateVecs(Gmat2, &locState, NULL));
461     PetscCall(VecSet(locState, (PetscScalar)(PetscReal)(-1))); /* set with UNKNOWN state */
462     for (kk = 0; kk < nselected_1; kk++) {
463       PetscInt    fgid = clid_lid_1[kk] + my0;
464       PetscScalar v    = (PetscScalar)(kk + myCrs0);
465       PetscCall(VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES)); /* set with PID */
466     }
467     PetscCall(VecAssemblyBegin(locState));
468     PetscCall(VecAssemblyEnd(locState));
469     PetscCall(VecScatterBegin(mpimat2->Mvctx, locState, mpimat2->lvec, INSERT_VALUES, SCATTER_FORWARD));
470     PetscCall(VecScatterEnd(mpimat2->Mvctx, locState, mpimat2->lvec, INSERT_VALUES, SCATTER_FORWARD));
471     PetscCall(VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts));
472     PetscCall(VecGetArray(mpimat2->lvec, &cpcol_state));
473     for (kk = 0, num_crs_ghost = 0; kk < num_fine_ghosts; kk++) {
474       if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
475     }
476     PetscCall(PetscMalloc1(nselected_1 + num_crs_ghost, &crsGID)); /* output */
477     {
478       PetscInt *selected_set;
479       PetscCall(PetscMalloc1(nselected_1 + num_crs_ghost, &selected_set));
480       /* do ghost of 'crsGID' */
481       for (kk = 0, idx = nselected_1; kk < num_fine_ghosts; kk++) {
482         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
483           PetscInt cgid     = (PetscInt)PetscRealPart(cpcol_state[kk]);
484           selected_set[idx] = nloc + kk;
485           crsGID[idx++]     = cgid;
486         }
487       }
488       PetscCheck(idx == (nselected_1 + num_crs_ghost), PETSC_COMM_SELF, PETSC_ERR_PLIB, "idx %" PetscInt_FMT " != (nselected_1 %" PetscInt_FMT " + num_crs_ghost %" PetscInt_FMT ")", idx, nselected_1, num_crs_ghost);
489       PetscCall(VecRestoreArray(mpimat2->lvec, &cpcol_state));
490       /* do locals in 'crsGID' */
491       PetscCall(VecGetArray(locState, &cpcol_state));
492       for (kk = 0, idx = 0; kk < nloc; kk++) {
493         if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
494           PetscInt cgid     = (PetscInt)PetscRealPart(cpcol_state[kk]);
495           selected_set[idx] = kk;
496           crsGID[idx++]     = cgid;
497         }
498       }
499       PetscCheck(idx == nselected_1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "idx %" PetscInt_FMT " != nselected_1 %" PetscInt_FMT, idx, nselected_1);
500       PetscCall(VecRestoreArray(locState, &cpcol_state));
501 
502       if (a_selected_2 != NULL) { /* output */
503         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, (nselected_1 + num_crs_ghost), selected_set, PETSC_OWN_POINTER, a_selected_2));
504       } else {
505         PetscCall(PetscFree(selected_set));
506       }
507     }
508     PetscCall(VecDestroy(&locState));
509   }
510   *a_crsGID = crsGID; /* output */
511   PetscFunctionReturn(0);
512 }
513 
514 /*
515    PCGAMGGraph_GEO
516 
517   Input Parameter:
518    . pc - this
519    . Amat - matrix on this fine level
520   Output Parameter:
521    . a_Gmat
522 */
523 PetscErrorCode PCGAMGGraph_GEO(PC pc, Mat Amat, Mat *a_Gmat) {
524   PC_MG          *mg      = (PC_MG *)pc->data;
525   PC_GAMG        *pc_gamg = (PC_GAMG *)mg->innerctx;
526   const PetscReal vfilter = pc_gamg->threshold[0];
527   MPI_Comm        comm;
528   Mat             Gmat, F = NULL;
529   PetscBool       set, flg, symm;
530 
531   PetscFunctionBegin;
532   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
533 
534   PetscCall(MatIsSymmetricKnown(Amat, &set, &flg));
535   symm = (PetscBool) !(set && flg);
536 
537   PetscCall(MatCreateGraph(Amat, symm, PETSC_TRUE, &Gmat));
538   PetscCall(MatFilter(Gmat, vfilter, &F));
539   if (F) {
540     PetscCall(MatDestroy(&Gmat));
541     Gmat = F;
542   }
543   *a_Gmat = Gmat;
544 
545   PetscFunctionReturn(0);
546 }
547 
548 /*
549    PCGAMGCoarsen_GEO
550 
551   Input Parameter:
552    . a_pc - this
553    . a_Gmat - graph
554   Output Parameter:
555    . a_llist_parent - linked list from selected indices for data locality only
556 */
557 PetscErrorCode PCGAMGCoarsen_GEO(PC a_pc, Mat *a_Gmat, PetscCoarsenData **a_llist_parent) {
558   PetscInt   Istart, Iend, nloc, kk, Ii, ncols;
559   IS         perm;
560   GAMGNode  *gnodes;
561   PetscInt  *permute;
562   Mat        Gmat = *a_Gmat;
563   MPI_Comm   comm;
564   MatCoarsen crs;
565 
566   PetscFunctionBegin;
567   PetscCall(PetscObjectGetComm((PetscObject)a_pc, &comm));
568 
569   PetscCall(MatGetOwnershipRange(Gmat, &Istart, &Iend));
570   nloc = (Iend - Istart);
571 
572   /* create random permutation with sort for geo-mg */
573   PetscCall(PetscMalloc1(nloc, &gnodes));
574   PetscCall(PetscMalloc1(nloc, &permute));
575 
576   for (Ii = Istart; Ii < Iend; Ii++) { /* locals only? */
577     PetscCall(MatGetRow(Gmat, Ii, &ncols, NULL, NULL));
578     {
579       PetscInt lid       = Ii - Istart;
580       gnodes[lid].lid    = lid;
581       gnodes[lid].degree = ncols;
582     }
583     PetscCall(MatRestoreRow(Gmat, Ii, &ncols, NULL, NULL));
584   }
585   if (PETSC_TRUE) {
586     PetscRandom rand;
587     PetscBool  *bIndexSet;
588     PetscReal   rr;
589     PetscInt    iSwapIndex;
590 
591     PetscCall(PetscRandomCreate(comm, &rand));
592     PetscCall(PetscCalloc1(nloc, &bIndexSet));
593     for (Ii = 0; Ii < nloc; Ii++) {
594       PetscCall(PetscRandomGetValueReal(rand, &rr));
595       iSwapIndex = (PetscInt)(rr * nloc);
596       if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
597         GAMGNode iTemp        = gnodes[iSwapIndex];
598         gnodes[iSwapIndex]    = gnodes[Ii];
599         gnodes[Ii]            = iTemp;
600         bIndexSet[Ii]         = PETSC_TRUE;
601         bIndexSet[iSwapIndex] = PETSC_TRUE;
602       }
603     }
604     PetscCall(PetscRandomDestroy(&rand));
605     PetscCall(PetscFree(bIndexSet));
606   }
607   /* only sort locals */
608   qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
609   /* create IS of permutation */
610   for (kk = 0; kk < nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
611   PetscCall(PetscFree(gnodes));
612   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm));
613 
614   /* get MIS aggs */
615 
616   PetscCall(MatCoarsenCreate(comm, &crs));
617   PetscCall(MatCoarsenSetType(crs, MATCOARSENMIS));
618   PetscCall(MatCoarsenSetGreedyOrdering(crs, perm));
619   PetscCall(MatCoarsenSetAdjacency(crs, Gmat));
620   PetscCall(MatCoarsenSetStrictAggs(crs, PETSC_FALSE));
621   PetscCall(MatCoarsenApply(crs));
622   PetscCall(MatCoarsenGetData(crs, a_llist_parent));
623   PetscCall(MatCoarsenDestroy(&crs));
624 
625   PetscCall(ISDestroy(&perm));
626 
627   PetscFunctionReturn(0);
628 }
629 
630 /*
631  PCGAMGProlongator_GEO
632 
633  Input Parameter:
634  . pc - this
635  . Amat - matrix on this fine level
636  . Graph - used to get ghost data for nodes in
637  . selected_1 - [nselected]
638  . agg_lists - [nselected]
639  Output Parameter:
640  . a_P_out - prolongation operator to the next level
641  */
642 PetscErrorCode PCGAMGProlongator_GEO(PC pc, Mat Amat, Mat Gmat, PetscCoarsenData *agg_lists, Mat *a_P_out) {
643   PC_MG          *mg      = (PC_MG *)pc->data;
644   PC_GAMG        *pc_gamg = (PC_GAMG *)mg->innerctx;
645   const PetscInt  dim = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
646   PetscInt        Istart, Iend, nloc, my0, jj, kk, ncols, nLocalSelected, bs, *clid_flid;
647   Mat             Prol;
648   PetscMPIInt     rank, size;
649   MPI_Comm        comm;
650   IS              selected_2, selected_1;
651   const PetscInt *selected_idx;
652   MatType         mtype;
653 
654   PetscFunctionBegin;
655   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
656 
657   PetscCallMPI(MPI_Comm_rank(comm, &rank));
658   PetscCallMPI(MPI_Comm_size(comm, &size));
659   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
660   PetscCall(MatGetBlockSize(Amat, &bs));
661   nloc = (Iend - Istart) / bs;
662   my0  = Istart / bs;
663   PetscCheck((Iend - Istart) % bs == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "(Iend %" PetscInt_FMT " - Istart %" PetscInt_FMT ") %% bs %" PetscInt_FMT, Iend, Istart, bs);
664 
665   /* get 'nLocalSelected' */
666   PetscCall(PetscCDGetMIS(agg_lists, &selected_1));
667   PetscCall(ISGetSize(selected_1, &jj));
668   PetscCall(PetscMalloc1(jj, &clid_flid));
669   PetscCall(ISGetIndices(selected_1, &selected_idx));
670   for (kk = 0, nLocalSelected = 0; kk < jj; kk++) {
671     PetscInt lid = selected_idx[kk];
672     if (lid < nloc) {
673       PetscCall(MatGetRow(Gmat, lid + my0, &ncols, NULL, NULL));
674       if (ncols > 1) clid_flid[nLocalSelected++] = lid; /* fiter out singletons */
675       PetscCall(MatRestoreRow(Gmat, lid + my0, &ncols, NULL, NULL));
676     }
677   }
678   PetscCall(ISRestoreIndices(selected_1, &selected_idx));
679   PetscCall(ISDestroy(&selected_1)); /* this is selected_1 in serial */
680 
681   /* create prolongator  matrix */
682   PetscCall(MatGetType(Amat, &mtype));
683   PetscCall(MatCreate(comm, &Prol));
684   PetscCall(MatSetSizes(Prol, nloc * bs, nLocalSelected * bs, PETSC_DETERMINE, PETSC_DETERMINE));
685   PetscCall(MatSetBlockSizes(Prol, bs, bs));
686   PetscCall(MatSetType(Prol, mtype));
687   PetscCall(MatSeqAIJSetPreallocation(Prol, 3 * data_cols, NULL));
688   PetscCall(MatMPIAIJSetPreallocation(Prol, 3 * data_cols, NULL, 3 * data_cols, NULL));
689 
690   /* can get all points "removed" - but not on geomg */
691   PetscCall(MatGetSize(Prol, &kk, &jj));
692   if (!jj) {
693     PetscCall(PetscInfo(pc, "ERROE: no selected points on coarse grid\n"));
694     PetscCall(PetscFree(clid_flid));
695     PetscCall(MatDestroy(&Prol));
696     *a_P_out = NULL; /* out */
697     PetscFunctionReturn(0);
698   }
699 
700   {
701     PetscReal *coords;
702     PetscInt   data_stride;
703     PetscInt  *crsGID = NULL;
704     Mat        Gmat2;
705 
706     PetscCheck(dim == data_cols, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim %" PetscInt_FMT " != data_cols %" PetscInt_FMT, dim, data_cols);
707     /* grow ghost data for better coarse grid cover of fine grid */
708     /* messy method, squares graph and gets some data */
709     PetscCall(getGIDsOnSquareGraph(pc, nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID));
710     /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
711     /* create global vector of coorindates in 'coords' */
712     if (size > 1) {
713       PetscCall(PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords));
714     } else {
715       coords      = (PetscReal *)pc_gamg->data;
716       data_stride = pc_gamg->data_sz / pc_gamg->data_cell_cols;
717     }
718     PetscCall(MatDestroy(&Gmat2));
719 
720     /* triangulate */
721     if (dim == 2) {
722       PetscReal metric, tm;
723       PetscCall(triangulateAndFormProl(selected_2, data_stride, coords, nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric));
724       PetscCall(PetscFree(crsGID));
725 
726       /* clean up and create coordinates for coarse grid (output) */
727       if (size > 1) PetscCall(PetscFree(coords));
728 
729       PetscCall(MPIU_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, comm));
730       if (tm > 1.) { /* needs to be globalized - should not happen */
731         PetscCall(PetscInfo(pc, " failed metric for coarse grid %e\n", (double)tm));
732         PetscCall(MatDestroy(&Prol));
733       } else if (metric > .0) {
734         PetscCall(PetscInfo(pc, "worst metric for coarse grid = %e\n", (double)metric));
735       }
736     } else SETERRQ(comm, PETSC_ERR_PLIB, "3D not implemented for 'geo' AMG");
737     { /* create next coords - output */
738       PetscReal *crs_crds;
739       PetscCall(PetscMalloc1(dim * nLocalSelected, &crs_crds));
740       for (kk = 0; kk < nLocalSelected; kk++) { /* grab local select nodes to promote - output */
741         PetscInt lid = clid_flid[kk];
742         for (jj = 0; jj < dim; jj++) crs_crds[jj * nLocalSelected + kk] = pc_gamg->data[jj * nloc + lid];
743       }
744 
745       PetscCall(PetscFree(pc_gamg->data));
746       pc_gamg->data    = crs_crds; /* out */
747       pc_gamg->data_sz = dim * nLocalSelected;
748     }
749     PetscCall(ISDestroy(&selected_2));
750   }
751 
752   *a_P_out = Prol; /* out */
753   PetscCall(PetscFree(clid_flid));
754 
755   PetscFunctionReturn(0);
756 }
757 
758 static PetscErrorCode PCDestroy_GAMG_GEO(PC pc) {
759   PetscFunctionBegin;
760   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
761   PetscFunctionReturn(0);
762 }
763 
764 /*
765  PCCreateGAMG_GEO
766 
767   Input Parameter:
768    . pc -
769 */
770 PetscErrorCode PCCreateGAMG_GEO(PC pc) {
771   PC_MG   *mg      = (PC_MG *)pc->data;
772   PC_GAMG *pc_gamg = (PC_GAMG *)mg->innerctx;
773 
774   PetscFunctionBegin;
775   pc_gamg->ops->setfromoptions = PCSetFromOptions_GEO;
776   pc_gamg->ops->destroy        = PCDestroy_GAMG_GEO;
777   /* reset does not do anything; setup not virtual */
778 
779   /* set internal function pointers */
780   pc_gamg->ops->graph             = PCGAMGGraph_GEO;
781   pc_gamg->ops->coarsen           = PCGAMGCoarsen_GEO;
782   pc_gamg->ops->prolongator       = PCGAMGProlongator_GEO;
783   pc_gamg->ops->optprolongator    = NULL;
784   pc_gamg->ops->createdefaultdata = PCSetData_GEO;
785 
786   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_GEO));
787   PetscFunctionReturn(0);
788 }
789