xref: /petsc/src/mat/graphops/coarsen/impls/hem/hem.c (revision e0b7e82fd3cf27fce84cc3e37e8d70a5c36a2d4e)
1 #include <petsc/private/matimpl.h> /*I "petscmat.h" I*/
2 #include <../src/mat/impls/aij/seq/aij.h>
3 #include <../src/mat/impls/aij/mpi/mpiaij.h>
4 #include <petscdm.h>
5 
6 /* linked list methods
7  *
8  *  PetscCDCreate
9  */
10 PetscErrorCode PetscCDCreate(PetscInt a_size, PetscCoarsenData **a_out)
11 {
12   PetscCoarsenData *ail;
13 
14   PetscFunctionBegin;
15   /* allocate pool, partially */
16   PetscCall(PetscNew(&ail));
17   *a_out               = ail;
18   ail->pool_list.next  = NULL;
19   ail->pool_list.array = NULL;
20   ail->chk_sz          = 0;
21   /* allocate array */
22   ail->size = a_size;
23   PetscCall(PetscCalloc1(a_size, &ail->array));
24   ail->extra_nodes = NULL;
25   ail->mat         = NULL;
26   PetscFunctionReturn(PETSC_SUCCESS);
27 }
28 
29 /* PetscCDDestroy
30  */
31 PetscErrorCode PetscCDDestroy(PetscCoarsenData *ail)
32 {
33   PetscCDArrNd *n = &ail->pool_list;
34 
35   PetscFunctionBegin;
36   n = n->next;
37   while (n) {
38     PetscCDArrNd *lstn = n;
39     n                  = n->next;
40     PetscCall(PetscFree(lstn));
41   }
42   if (ail->pool_list.array) PetscCall(PetscFree(ail->pool_list.array));
43   PetscCall(PetscFree(ail->array));
44   if (ail->mat) PetscCall(MatDestroy(&ail->mat));
45   /* delete this (+agg+pool array) */
46   PetscCall(PetscFree(ail));
47   PetscFunctionReturn(PETSC_SUCCESS);
48 }
49 
50 /* PetscCDSetChunkSize
51  */
52 PetscErrorCode PetscCDSetChunkSize(PetscCoarsenData *ail, PetscInt a_sz)
53 {
54   PetscFunctionBegin;
55   ail->chk_sz = a_sz;
56   PetscFunctionReturn(PETSC_SUCCESS);
57 }
58 
59 /*  PetscCDGetNewNode
60  */
61 static PetscErrorCode PetscCDGetNewNode(PetscCoarsenData *ail, PetscCDIntNd **a_out, PetscInt a_id)
62 {
63   PetscFunctionBegin;
64   *a_out = NULL; /* squelch -Wmaybe-uninitialized */
65   if (ail->extra_nodes) {
66     PetscCDIntNd *node = ail->extra_nodes;
67     ail->extra_nodes   = node->next;
68     node->gid          = a_id;
69     node->next         = NULL;
70     *a_out             = node;
71   } else {
72     if (!ail->pool_list.array) {
73       if (!ail->chk_sz) ail->chk_sz = 10; /* use a chuck size of ail->size? */
74       PetscCall(PetscMalloc1(ail->chk_sz, &ail->pool_list.array));
75       ail->new_node       = ail->pool_list.array;
76       ail->new_left       = ail->chk_sz;
77       ail->new_node->next = NULL;
78     } else if (!ail->new_left) {
79       PetscCDArrNd *node;
80       PetscCall(PetscMalloc(ail->chk_sz * sizeof(PetscCDIntNd) + sizeof(PetscCDArrNd), &node));
81       node->array         = (PetscCDIntNd *)(node + 1);
82       node->next          = ail->pool_list.next;
83       ail->pool_list.next = node;
84       ail->new_left       = ail->chk_sz;
85       ail->new_node       = node->array;
86     }
87     ail->new_node->gid  = a_id;
88     ail->new_node->next = NULL;
89     *a_out              = ail->new_node++;
90     ail->new_left--;
91   }
92   PetscFunctionReturn(PETSC_SUCCESS);
93 }
94 
95 /* PetscCDIntNdSetID
96  */
97 PetscErrorCode PetscCDIntNdSetID(PetscCDIntNd *a_this, PetscInt a_id)
98 {
99   PetscFunctionBegin;
100   a_this->gid = a_id;
101   PetscFunctionReturn(PETSC_SUCCESS);
102 }
103 
104 /* PetscCDIntNdGetID
105  */
106 PetscErrorCode PetscCDIntNdGetID(const PetscCDIntNd *a_this, PetscInt *a_gid)
107 {
108   PetscFunctionBegin;
109   *a_gid = a_this->gid;
110   PetscFunctionReturn(PETSC_SUCCESS);
111 }
112 
113 /* PetscCDGetHeadPos
114  */
115 PetscErrorCode PetscCDGetHeadPos(const PetscCoarsenData *ail, PetscInt a_idx, PetscCDIntNd **pos)
116 {
117   PetscFunctionBegin;
118   PetscCheck(a_idx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "a_idx >= ail->size: a_idx=%" PetscInt_FMT ".", a_idx);
119   *pos = ail->array[a_idx];
120   PetscFunctionReturn(PETSC_SUCCESS);
121 }
122 
123 /* PetscCDGetNextPos
124  */
125 PetscErrorCode PetscCDGetNextPos(const PetscCoarsenData *ail, PetscInt l_idx, PetscCDIntNd **pos)
126 {
127   PetscFunctionBegin;
128   PetscCheck(*pos, PETSC_COMM_SELF, PETSC_ERR_PLIB, "NULL input position.");
129   *pos = (*pos)->next;
130   PetscFunctionReturn(PETSC_SUCCESS);
131 }
132 
133 /* PetscCDAppendID
134  */
135 PetscErrorCode PetscCDAppendID(PetscCoarsenData *ail, PetscInt a_idx, PetscInt a_id)
136 {
137   PetscCDIntNd *n, *n2;
138 
139   PetscFunctionBegin;
140   PetscCall(PetscCDGetNewNode(ail, &n, a_id));
141   PetscCheck(a_idx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_idx);
142   if (!(n2 = ail->array[a_idx])) ail->array[a_idx] = n;
143   else {
144     do {
145       if (!n2->next) {
146         n2->next = n;
147         PetscCheck(!n->next, PETSC_COMM_SELF, PETSC_ERR_PLIB, "n should not have a next");
148         break;
149       }
150       n2 = n2->next;
151     } while (n2);
152     PetscCheck(n2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "n2 should be non-null");
153   }
154   PetscFunctionReturn(PETSC_SUCCESS);
155 }
156 
157 /* PetscCDAppendNode
158  */
159 PetscErrorCode PetscCDAppendNode(PetscCoarsenData *ail, PetscInt a_idx, PetscCDIntNd *a_n)
160 {
161   PetscCDIntNd *n2;
162 
163   PetscFunctionBegin;
164   PetscCheck(a_idx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_idx);
165   if (!(n2 = ail->array[a_idx])) ail->array[a_idx] = a_n;
166   else {
167     do {
168       if (!n2->next) {
169         n2->next  = a_n;
170         a_n->next = NULL;
171         break;
172       }
173       n2 = n2->next;
174     } while (n2);
175     PetscCheck(n2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "n2 should be non-null");
176   }
177   PetscFunctionReturn(PETSC_SUCCESS);
178 }
179 
180 /* PetscCDRemoveNextNode: a_last->next, this exposes single linked list structure to API (not used)
181  */
182 PetscErrorCode PetscCDRemoveNextNode(PetscCoarsenData *ail, PetscInt a_idx, PetscCDIntNd *a_last)
183 {
184   PetscCDIntNd *del;
185 
186   PetscFunctionBegin;
187   PetscCheck(a_idx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_idx);
188   PetscCheck(a_last->next, PETSC_COMM_SELF, PETSC_ERR_PLIB, "a_last should have a next");
189   del          = a_last->next;
190   a_last->next = del->next;
191   /* del->next = NULL; -- this still used in a iterator so keep it intact -- need to fix this with a double linked list */
192   /* could reuse n2 but PetscCDAppendNode sometimes uses it */
193   PetscFunctionReturn(PETSC_SUCCESS);
194 }
195 
196 /* PetscCDPrint
197  */
198 PetscErrorCode PetscCDPrint(const PetscCoarsenData *ail, PetscInt my0, MPI_Comm comm)
199 {
200   PetscCDIntNd *n, *n2;
201   PetscInt      ii;
202 
203   PetscFunctionBegin;
204   for (ii = 0; ii < ail->size; ii++) {
205     n2 = n = ail->array[ii];
206     if (n) PetscCall(PetscSynchronizedPrintf(comm, "list %" PetscInt_FMT ":", ii + my0));
207     while (n) {
208       PetscCall(PetscSynchronizedPrintf(comm, " %" PetscInt_FMT, n->gid));
209       n = n->next;
210     }
211     if (n2) PetscCall(PetscSynchronizedPrintf(comm, "\n"));
212   }
213   PetscCall(PetscSynchronizedFlush(comm, PETSC_STDOUT));
214   PetscFunctionReturn(PETSC_SUCCESS);
215 }
216 
217 /* PetscCDMoveAppend - take list in a_srcidx and appends to destidx
218  */
219 PetscErrorCode PetscCDMoveAppend(PetscCoarsenData *ail, PetscInt a_destidx, PetscInt a_srcidx)
220 {
221   PetscCDIntNd *n;
222 
223   PetscFunctionBegin;
224   PetscCheck(a_srcidx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_srcidx);
225   PetscCheck(a_destidx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_destidx);
226   PetscCheck(a_destidx != a_srcidx, PETSC_COMM_SELF, PETSC_ERR_PLIB, "a_destidx==a_srcidx %" PetscInt_FMT ".", a_destidx);
227   n = ail->array[a_destidx];
228   if (!n) ail->array[a_destidx] = ail->array[a_srcidx];
229   else {
230     do {
231       if (!n->next) {
232         n->next = ail->array[a_srcidx]; // append
233         break;
234       }
235       n = n->next;
236     } while (1);
237   }
238   ail->array[a_srcidx] = NULL; // empty
239   PetscFunctionReturn(PETSC_SUCCESS);
240 }
241 
242 /* PetscCDRemoveAllAt - empty one list and move data to cache
243  */
244 PetscErrorCode PetscCDRemoveAllAt(PetscCoarsenData *ail, PetscInt a_idx)
245 {
246   PetscCDIntNd *rem, *n1;
247 
248   PetscFunctionBegin;
249   PetscCheck(a_idx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_idx);
250   rem               = ail->array[a_idx];
251   ail->array[a_idx] = NULL;
252   if (!(n1 = ail->extra_nodes)) ail->extra_nodes = rem;
253   else {
254     while (n1->next) n1 = n1->next;
255     n1->next = rem;
256   }
257   PetscFunctionReturn(PETSC_SUCCESS);
258 }
259 
260 /* PetscCDCountAt
261  */
262 PetscErrorCode PetscCDCountAt(const PetscCoarsenData *ail, PetscInt a_idx, PetscInt *a_sz)
263 {
264   PetscCDIntNd *n1;
265   PetscInt      sz = 0;
266 
267   PetscFunctionBegin;
268   PetscCheck(a_idx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_idx);
269   n1 = ail->array[a_idx];
270   while (n1) {
271     n1 = n1->next;
272     sz++;
273   }
274   *a_sz = sz;
275   PetscFunctionReturn(PETSC_SUCCESS);
276 }
277 
278 /* PetscCDSize
279  */
280 PetscErrorCode PetscCDCount(const PetscCoarsenData *ail, PetscInt *a_sz)
281 {
282   PetscInt sz = 0;
283 
284   PetscFunctionBegin;
285   for (int ii = 0; ii < ail->size; ii++) {
286     PetscCDIntNd *n1 = ail->array[ii];
287     while (n1) {
288       n1 = n1->next;
289       sz++;
290     }
291   }
292   *a_sz = sz;
293   PetscFunctionReturn(PETSC_SUCCESS);
294 }
295 
296 /* PetscCDIsEmptyAt - Is the list empty? (not used)
297  */
298 PetscErrorCode PetscCDIsEmptyAt(const PetscCoarsenData *ail, PetscInt a_idx, PetscBool *a_e)
299 {
300   PetscFunctionBegin;
301   PetscCheck(a_idx < ail->size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Index %" PetscInt_FMT " out of range.", a_idx);
302   *a_e = (PetscBool)(ail->array[a_idx] == NULL);
303   PetscFunctionReturn(PETSC_SUCCESS);
304 }
305 
306 /* PetscCDGetNonemptyIS - used for C-F methods
307  */
308 PetscErrorCode PetscCDGetNonemptyIS(PetscCoarsenData *ail, IS *a_mis)
309 {
310   PetscCDIntNd *n;
311   PetscInt      ii, kk;
312   PetscInt     *permute;
313 
314   PetscFunctionBegin;
315   for (ii = kk = 0; ii < ail->size; ii++) {
316     n = ail->array[ii];
317     if (n) kk++;
318   }
319   PetscCall(PetscMalloc1(kk, &permute));
320   for (ii = kk = 0; ii < ail->size; ii++) {
321     n = ail->array[ii];
322     if (n) permute[kk++] = ii;
323   }
324   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, kk, permute, PETSC_OWN_POINTER, a_mis));
325   PetscFunctionReturn(PETSC_SUCCESS);
326 }
327 
328 /* PetscCDGetMat
329  */
330 PetscErrorCode PetscCDGetMat(PetscCoarsenData *ail, Mat *a_mat)
331 {
332   PetscFunctionBegin;
333   *a_mat = ail->mat;
334   PetscFunctionReturn(PETSC_SUCCESS);
335 }
336 
337 /* PetscCDSetMat
338  */
339 PetscErrorCode PetscCDSetMat(PetscCoarsenData *ail, Mat a_mat)
340 {
341   PetscFunctionBegin;
342   if (ail->mat) {
343     PetscCall(MatDestroy(&ail->mat)); //should not happen
344   }
345   ail->mat = a_mat;
346   PetscFunctionReturn(PETSC_SUCCESS);
347 }
348 
349 /* PetscCDClearMat
350  */
351 PetscErrorCode PetscCDClearMat(PetscCoarsenData *ail)
352 {
353   PetscFunctionBegin;
354   ail->mat = NULL;
355   PetscFunctionReturn(PETSC_SUCCESS);
356 }
357 
358 /* PetscCDGetASMBlocks - get IS of aggregates for ASM smoothers
359  */
360 PetscErrorCode PetscCDGetASMBlocks(const PetscCoarsenData *ail, const PetscInt a_bs, PetscInt *a_sz, IS **a_local_is)
361 {
362   PetscCDIntNd *n;
363   PetscInt      lsz, ii, kk, *idxs, jj, gid;
364   IS           *is_loc = NULL;
365 
366   PetscFunctionBegin;
367   for (ii = kk = 0; ii < ail->size; ii++) {
368     if (ail->array[ii]) kk++;
369   }
370   *a_sz = kk;
371   PetscCall(PetscMalloc1(kk, &is_loc));
372   for (ii = kk = 0; ii < ail->size; ii++) {
373     for (lsz = 0, n = ail->array[ii]; n; lsz++, n = n->next) /* void */
374       ;
375     if (lsz) {
376       PetscCall(PetscMalloc1(a_bs * lsz, &idxs));
377       for (lsz = 0, n = ail->array[ii]; n; n = n->next) {
378         PetscCall(PetscCDIntNdGetID(n, &gid));
379         for (jj = 0; jj < a_bs; lsz++, jj++) idxs[lsz] = a_bs * gid + jj;
380       }
381       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, lsz, idxs, PETSC_OWN_POINTER, &is_loc[kk++]));
382     }
383   }
384   PetscCheck(*a_sz == kk, PETSC_COMM_SELF, PETSC_ERR_PLIB, "*a_sz %" PetscInt_FMT " != kk %" PetscInt_FMT, *a_sz, kk);
385   *a_local_is = is_loc; /* out */
386   PetscFunctionReturn(PETSC_SUCCESS);
387 }
388 
389 /* edge for priority queue */
390 typedef struct edge_tag {
391   PetscReal weight;
392   PetscInt  lid0, gid1, ghost1_idx;
393 } Edge;
394 
395 #define MY_MEPS (PETSC_MACHINE_EPSILON * 100)
396 static int gamg_hem_compare(const void *a, const void *b)
397 {
398   PetscReal va = ((Edge *)a)->weight, vb = ((Edge *)b)->weight;
399   return (va <= vb - MY_MEPS) ? 1 : (va > vb + MY_MEPS) ? -1 : 0; /* 0 for equal */
400 }
401 
402 /*
403   MatCoarsenApply_HEM_private - parallel heavy edge matching
404 
405   Input Parameter:
406    . a_Gmat - global matrix of the graph
407    . n_iter - number of matching iterations
408    . threshold - threshold for filtering graphs
409 
410   Output Parameter:
411    . a_locals_llist - array of list of local nodes rooted at local node
412 */
413 static PetscErrorCode MatCoarsenApply_HEM_private(Mat a_Gmat, const PetscInt n_iter, const PetscReal threshold, PetscCoarsenData **a_locals_llist)
414 {
415 #define REQ_BF_SIZE 100
416   PetscBool         isMPI;
417   MPI_Comm          comm;
418   PetscInt          ix, *ii, *aj, Iend, my0, ncomm_procs, bc_agg = -1, *rbuff = NULL, rbuff_sz = 0;
419   PetscMPIInt       rank, size, comm_procs[REQ_BF_SIZE], *lid_max_pe;
420   const PetscInt    nloc = a_Gmat->rmap->n, request_size = PetscCeilReal((PetscReal)sizeof(MPI_Request) / (PetscReal)sizeof(PetscInt));
421   PetscInt         *lid_cprowID;
422   PetscBool        *lid_matched;
423   Mat_SeqAIJ       *matA, *matB = NULL;
424   Mat_MPIAIJ       *mpimat     = NULL;
425   PetscScalar       one        = 1.;
426   PetscCoarsenData *agg_llists = NULL, *ghost_deleted_list = NULL, *bc_list = NULL;
427   Mat               cMat, tMat, P;
428   MatScalar        *ap;
429   IS                info_is;
430 
431   PetscFunctionBegin;
432   PetscCall(PetscObjectGetComm((PetscObject)a_Gmat, &comm));
433   PetscCallMPI(MPI_Comm_rank(comm, &rank));
434   PetscCallMPI(MPI_Comm_size(comm, &size));
435   PetscCall(MatGetOwnershipRange(a_Gmat, &my0, &Iend));
436   PetscCall(ISCreate(comm, &info_is));
437   PetscCall(PetscInfo(info_is, "Start %" PetscInt_FMT " iterations of HEM.\n", n_iter));
438 
439   PetscCall(PetscMalloc1(nloc, &lid_matched));
440   PetscCall(PetscMalloc1(nloc, &lid_cprowID));
441   PetscCall(PetscMalloc1(nloc, &lid_max_pe));
442 
443   PetscCall(PetscCDCreate(nloc, &agg_llists));
444   PetscCall(PetscCDSetChunkSize(agg_llists, nloc + 1));
445   *a_locals_llist = agg_llists;
446   /* add self to all lists */
447   for (int kk = 0; kk < nloc; kk++) PetscCall(PetscCDAppendID(agg_llists, kk, my0 + kk));
448   /* make a copy of the graph, this gets destroyed in iterates */
449   PetscCall(MatDuplicate(a_Gmat, MAT_COPY_VALUES, &cMat));
450   PetscCall(MatConvert(cMat, MATAIJ, MAT_INPLACE_MATRIX, &cMat));
451   isMPI = (PetscBool)(size > 1);
452   if (isMPI) {
453     /* list of deleted ghosts, should compress this */
454     PetscCall(PetscCDCreate(size, &ghost_deleted_list));
455     PetscCall(PetscCDSetChunkSize(ghost_deleted_list, 100));
456   }
457   for (int iter = 0; iter < n_iter; iter++) {
458     const PetscScalar *lghost_max_ew, *lid_max_ew;
459     PetscBool         *lghost_matched;
460     PetscMPIInt       *lghost_pe, *lghost_max_pe;
461     Vec                locMaxEdge, ghostMaxEdge, ghostMaxPE, locMaxPE;
462     PetscInt          *lghost_gid, nEdges, nEdges0, num_ghosts = 0;
463     Edge              *Edges;
464     const int          n_sub_its = 1000; // in case of a bug, stop at some point
465     /* get submatrices of cMat */
466     for (int kk = 0; kk < nloc; kk++) lid_cprowID[kk] = -1;
467     if (isMPI) {
468       mpimat = (Mat_MPIAIJ *)cMat->data;
469       matA   = (Mat_SeqAIJ *)mpimat->A->data;
470       matB   = (Mat_SeqAIJ *)mpimat->B->data;
471       if (!matB->compressedrow.use) {
472         /* force construction of compressed row data structure since code below requires it */
473         PetscCall(MatCheckCompressedRow(mpimat->B, matB->nonzerorowcnt, &matB->compressedrow, matB->i, mpimat->B->rmap->n, -1.0));
474       }
475       /* set index into compressed row 'lid_cprowID' */
476       for (ix = 0; ix < matB->compressedrow.nrows; ix++) {
477         PetscInt *ridx = matB->compressedrow.rindex, lid = ridx[ix];
478         if (ridx[ix] >= 0) lid_cprowID[lid] = ix;
479       }
480     } else {
481       matA = (Mat_SeqAIJ *)cMat->data;
482     }
483     /* set matched flags: true for empty list */
484     for (int kk = 0; kk < nloc; kk++) {
485       PetscCall(PetscCDCountAt(agg_llists, kk, &ix));
486       if (ix > 0) lid_matched[kk] = PETSC_FALSE;
487       else lid_matched[kk] = PETSC_TRUE; // call deleted gids as matched
488     }
489     /* max edge and pe vecs */
490     PetscCall(MatCreateVecs(cMat, &locMaxEdge, NULL));
491     PetscCall(MatCreateVecs(cMat, &locMaxPE, NULL));
492     /* get 'lghost_pe' & 'lghost_gid' & init. 'lghost_matched' using 'mpimat->lvec' */
493     if (isMPI) {
494       Vec                vec;
495       PetscScalar        vval;
496       const PetscScalar *buf;
497       PetscCall(MatCreateVecs(cMat, &vec, NULL));
498       PetscCall(VecGetLocalSize(mpimat->lvec, &num_ghosts));
499       /* lghost_matched */
500       for (PetscInt kk = 0, gid = my0; kk < nloc; kk++, gid++) {
501         PetscScalar vval = lid_matched[kk] ? 1.0 : 0.0;
502         PetscCall(VecSetValues(vec, 1, &gid, &vval, INSERT_VALUES));
503       }
504       PetscCall(VecAssemblyBegin(vec));
505       PetscCall(VecAssemblyEnd(vec));
506       PetscCall(VecScatterBegin(mpimat->Mvctx, vec, mpimat->lvec, INSERT_VALUES, SCATTER_FORWARD));
507       PetscCall(VecScatterEnd(mpimat->Mvctx, vec, mpimat->lvec, INSERT_VALUES, SCATTER_FORWARD));
508       PetscCall(VecGetArrayRead(mpimat->lvec, &buf)); /* get proc ID in 'buf' */
509       PetscCall(PetscMalloc1(num_ghosts, &lghost_matched));
510       for (int kk = 0; kk < num_ghosts; kk++) {
511         lghost_matched[kk] = (PetscBool)(PetscRealPart(buf[kk]) != 0); // the proc of the ghost for now
512       }
513       PetscCall(VecRestoreArrayRead(mpimat->lvec, &buf));
514       /* lghost_pe */
515       vval = (PetscScalar)(rank);
516       for (PetscInt kk = 0, gid = my0; kk < nloc; kk++, gid++) PetscCall(VecSetValues(vec, 1, &gid, &vval, INSERT_VALUES)); /* set with GID */
517       PetscCall(VecAssemblyBegin(vec));
518       PetscCall(VecAssemblyEnd(vec));
519       PetscCall(VecScatterBegin(mpimat->Mvctx, vec, mpimat->lvec, INSERT_VALUES, SCATTER_FORWARD));
520       PetscCall(VecScatterEnd(mpimat->Mvctx, vec, mpimat->lvec, INSERT_VALUES, SCATTER_FORWARD));
521       PetscCall(VecGetArrayRead(mpimat->lvec, &buf)); /* get proc ID in 'buf' */
522       PetscCall(PetscMalloc1(num_ghosts, &lghost_pe));
523       for (int kk = 0; kk < num_ghosts; kk++) lghost_pe[kk] = (PetscMPIInt)PetscRealPart(buf[kk]); // the proc of the ghost for now
524       PetscCall(VecRestoreArrayRead(mpimat->lvec, &buf));
525       /* lghost_gid */
526       for (PetscInt kk = 0, gid = my0; kk < nloc; kk++, gid++) {
527         vval = (PetscScalar)(gid);
528         PetscCall(VecSetValues(vec, 1, &gid, &vval, INSERT_VALUES)); /* set with GID */
529       }
530       PetscCall(VecAssemblyBegin(vec));
531       PetscCall(VecAssemblyEnd(vec));
532       PetscCall(VecScatterBegin(mpimat->Mvctx, vec, mpimat->lvec, INSERT_VALUES, SCATTER_FORWARD));
533       PetscCall(VecScatterEnd(mpimat->Mvctx, vec, mpimat->lvec, INSERT_VALUES, SCATTER_FORWARD));
534       PetscCall(VecDestroy(&vec));
535       PetscCall(VecGetArrayRead(mpimat->lvec, &buf)); /* get proc ID in 'lghost_gid' */
536       PetscCall(PetscMalloc1(num_ghosts, &lghost_gid));
537       for (int kk = 0; kk < num_ghosts; kk++) lghost_gid[kk] = (PetscInt)PetscRealPart(buf[kk]);
538       PetscCall(VecRestoreArrayRead(mpimat->lvec, &buf));
539     }
540     // get 'comm_procs' (could hoist)
541     for (int kk = 0; kk < REQ_BF_SIZE; kk++) comm_procs[kk] = -1;
542     for (ix = 0, ncomm_procs = 0; ix < num_ghosts; ix++) {
543       PetscMPIInt proc = lghost_pe[ix], idx = -1;
544       for (int k = 0; k < ncomm_procs && idx == -1; k++)
545         if (comm_procs[k] == proc) idx = k;
546       if (idx == -1) { comm_procs[ncomm_procs++] = proc; }
547       PetscCheck(ncomm_procs != REQ_BF_SIZE, PETSC_COMM_SELF, PETSC_ERR_SUP, "Receive request array too small: %d", (int)ncomm_procs);
548     }
549     /* count edges, compute initial 'locMaxEdge', 'locMaxPE' */
550     nEdges0 = 0;
551     for (PetscInt kk = 0, gid = my0; kk < nloc; kk++, gid++) {
552       PetscReal   max_e = 0., tt;
553       PetscScalar vval;
554       PetscInt    lid = kk, max_pe = rank, pe, n;
555       ii = matA->i;
556       n  = ii[lid + 1] - ii[lid];
557       aj = PetscSafePointerPlusOffset(matA->j, ii[lid]);
558       ap = PetscSafePointerPlusOffset(matA->a, ii[lid]);
559       for (int jj = 0; jj < n; jj++) {
560         PetscInt lidj = aj[jj];
561         if ((tt = PetscRealPart(ap[jj])) > threshold && lidj != lid) {
562           if (tt > max_e) max_e = tt;
563           if (lidj > lid) nEdges0++;
564         }
565       }
566       if ((ix = lid_cprowID[lid]) != -1) { /* if I have any ghost neighbors */
567         ii = matB->compressedrow.i;
568         n  = ii[ix + 1] - ii[ix];
569         ap = matB->a + ii[ix];
570         aj = matB->j + ii[ix];
571         for (int jj = 0; jj < n; jj++) {
572           if ((tt = PetscRealPart(ap[jj])) > threshold) {
573             if (tt > max_e) max_e = tt;
574             nEdges0++;
575             if ((pe = lghost_pe[aj[jj]]) > max_pe) max_pe = pe;
576           }
577         }
578       }
579       vval = max_e;
580       PetscCall(VecSetValues(locMaxEdge, 1, &gid, &vval, INSERT_VALUES));
581       vval = (PetscScalar)max_pe;
582       PetscCall(VecSetValues(locMaxPE, 1, &gid, &vval, INSERT_VALUES));
583       if (iter == 0 && max_e <= MY_MEPS) { // add BCs to fake aggregate
584         lid_matched[lid] = PETSC_TRUE;
585         if (bc_agg == -1) {
586           bc_agg = lid;
587           PetscCall(PetscCDCreate(1, &bc_list));
588         }
589         PetscCall(PetscCDRemoveAllAt(agg_llists, lid));
590         PetscCall(PetscCDAppendID(bc_list, 0, my0 + lid));
591       }
592     }
593     PetscCall(VecAssemblyBegin(locMaxEdge));
594     PetscCall(VecAssemblyEnd(locMaxEdge));
595     PetscCall(VecAssemblyBegin(locMaxPE));
596     PetscCall(VecAssemblyEnd(locMaxPE));
597     /* make 'ghostMaxEdge_max_ew', 'lghost_max_pe' */
598     if (mpimat) {
599       const PetscScalar *buf;
600       PetscCall(VecDuplicate(mpimat->lvec, &ghostMaxEdge));
601       PetscCall(VecScatterBegin(mpimat->Mvctx, locMaxEdge, ghostMaxEdge, INSERT_VALUES, SCATTER_FORWARD));
602       PetscCall(VecScatterEnd(mpimat->Mvctx, locMaxEdge, ghostMaxEdge, INSERT_VALUES, SCATTER_FORWARD));
603 
604       PetscCall(VecDuplicate(mpimat->lvec, &ghostMaxPE));
605       PetscCall(VecScatterBegin(mpimat->Mvctx, locMaxPE, ghostMaxPE, INSERT_VALUES, SCATTER_FORWARD));
606       PetscCall(VecScatterEnd(mpimat->Mvctx, locMaxPE, ghostMaxPE, INSERT_VALUES, SCATTER_FORWARD));
607       PetscCall(VecGetArrayRead(ghostMaxPE, &buf));
608       PetscCall(PetscMalloc1(num_ghosts, &lghost_max_pe));
609       for (int kk = 0; kk < num_ghosts; kk++) lghost_max_pe[kk] = (PetscMPIInt)PetscRealPart(buf[kk]); // the MAX proc of the ghost now
610       PetscCall(VecRestoreArrayRead(ghostMaxPE, &buf));
611     }
612     { // make lid_max_pe
613       const PetscScalar *buf;
614       PetscCall(VecGetArrayRead(locMaxPE, &buf));
615       for (int kk = 0; kk < nloc; kk++) lid_max_pe[kk] = (PetscMPIInt)PetscRealPart(buf[kk]); // the MAX proc of the ghost now
616       PetscCall(VecRestoreArrayRead(locMaxPE, &buf));
617     }
618     /* setup sorted list of edges, and make 'Edges' */
619     PetscCall(PetscMalloc1(nEdges0, &Edges));
620     nEdges = 0;
621     for (int kk = 0, n; kk < nloc; kk++) {
622       const PetscInt lid = kk;
623       PetscReal      tt;
624       ii = matA->i;
625       n  = ii[lid + 1] - ii[lid];
626       aj = PetscSafePointerPlusOffset(matA->j, ii[lid]);
627       ap = PetscSafePointerPlusOffset(matA->a, ii[lid]);
628       for (int jj = 0; jj < n; jj++) {
629         PetscInt lidj = aj[jj];
630         if ((tt = PetscRealPart(ap[jj])) > threshold && lidj != lid) {
631           if (lidj > lid) {
632             Edges[nEdges].lid0       = lid;
633             Edges[nEdges].gid1       = lidj + my0;
634             Edges[nEdges].ghost1_idx = -1;
635             Edges[nEdges].weight     = tt;
636             nEdges++;
637           }
638         }
639       }
640       if ((ix = lid_cprowID[lid]) != -1) { /* if I have any ghost neighbor */
641         ii = matB->compressedrow.i;
642         n  = ii[ix + 1] - ii[ix];
643         ap = matB->a + ii[ix];
644         aj = matB->j + ii[ix];
645         for (int jj = 0; jj < n; jj++) {
646           if ((tt = PetscRealPart(ap[jj])) > threshold) {
647             Edges[nEdges].lid0       = lid;
648             Edges[nEdges].gid1       = lghost_gid[aj[jj]];
649             Edges[nEdges].ghost1_idx = aj[jj];
650             Edges[nEdges].weight     = tt;
651             nEdges++;
652           }
653         }
654       }
655     }
656     PetscCheck(nEdges == nEdges0, PETSC_COMM_SELF, PETSC_ERR_SUP, "nEdges != nEdges0: %d %d", (int)nEdges0, (int)nEdges);
657     if (Edges) qsort(Edges, nEdges, sizeof(Edge), gamg_hem_compare);
658 
659     PetscCall(PetscInfo(info_is, "[%d] HEM iteration %d with %d edges\n", rank, iter, (int)nEdges));
660 
661     /* projection matrix */
662     PetscCall(MatCreate(comm, &P));
663     PetscCall(MatSetType(P, MATAIJ));
664     PetscCall(MatSetSizes(P, nloc, nloc, PETSC_DETERMINE, PETSC_DETERMINE));
665     PetscCall(MatMPIAIJSetPreallocation(P, 1, NULL, 1, NULL));
666     PetscCall(MatSeqAIJSetPreallocation(P, 1, NULL));
667     PetscCall(MatSetUp(P));
668     /* process - communicate - process */
669     for (int sub_it = 0, old_num_edge = 0; /* sub_it < n_sub_its */; /* sub_it++ */) {
670       PetscInt    nactive_edges = 0, n_act_n[3], gn_act_n[3];
671       PetscMPIInt tag1, tag2;
672       PetscCall(VecGetArrayRead(locMaxEdge, &lid_max_ew));
673       if (isMPI) {
674         PetscCall(VecGetArrayRead(ghostMaxEdge, &lghost_max_ew));
675         PetscCall(PetscCommGetNewTag(comm, &tag1));
676         PetscCall(PetscCommGetNewTag(comm, &tag2));
677       }
678       for (int kk = 0; kk < nEdges; kk++) {
679         /* HEM */
680         const Edge    *e    = &Edges[kk];
681         const PetscInt lid0 = e->lid0, gid1 = e->gid1, ghost1_idx = e->ghost1_idx, gid0 = lid0 + my0, lid1 = gid1 - my0;
682         PetscBool      isOK = PETSC_TRUE, print = PETSC_FALSE;
683         if (print) PetscCall(PetscSynchronizedPrintf(comm, "\t[%d] edge (%d %d), %d %d %d\n", rank, (int)gid0, (int)gid1, lid_matched[lid0], (ghost1_idx != -1 && lghost_matched[ghost1_idx]), (ghost1_idx == -1 && lid_matched[lid1])));
684         /* skip if either vertex is matched already */
685         if (lid_matched[lid0] || (ghost1_idx != -1 && lghost_matched[ghost1_idx]) || (ghost1_idx == -1 && lid_matched[lid1])) continue;
686 
687         nactive_edges++;
688         PetscCheck(PetscRealPart(lid_max_ew[lid0]) >= e->weight - MY_MEPS, PETSC_COMM_SELF, PETSC_ERR_SUP, "edge weight %e > max %e", (double)e->weight, (double)PetscRealPart(lid_max_ew[lid0]));
689         if (print) PetscCall(PetscSynchronizedPrintf(comm, "\t[%d] active edge (%d %d), diff0 = %10.4e\n", rank, (int)gid0, (int)gid1, (double)(PetscRealPart(lid_max_ew[lid0]) - (double)e->weight)));
690         // smaller edge, lid_max_ew get updated - e0
691         if (PetscRealPart(lid_max_ew[lid0]) > e->weight + MY_MEPS) {
692           if (print)
693             PetscCall(PetscSynchronizedPrintf(comm, "\t\t[%d] 1) e0 SKIPPING small edge %20.14e edge (%d %d), diff = %10.4e to proc %d. max = %20.14e, w = %20.14e\n", rank, (double)e->weight, (int)gid0, (int)gid1, (double)(PetscRealPart(lid_max_ew[lid0]) - e->weight), ghost1_idx != -1 ? (int)lghost_pe[ghost1_idx] : rank, (double)PetscRealPart(lid_max_ew[lid0]),
694                                               (double)e->weight));
695           continue; // we are basically filter edges here
696         }
697         // e1 - local
698         if (ghost1_idx == -1) {
699           if (PetscRealPart(lid_max_ew[lid1]) > e->weight + MY_MEPS) {
700             if (print)
701               PetscCall(PetscSynchronizedPrintf(comm, "\t\t%c[%d] 2) e1 SKIPPING small local edge %20.14e edge (%d %d), diff = %10.4e\n", ghost1_idx != -1 ? '\t' : ' ', rank, (double)e->weight, (int)gid0, (int)gid1, (double)(PetscRealPart(lid_max_ew[lid1]) - e->weight)));
702             continue; // we are basically filter edges here
703           }
704         } else { // e1 - ghost
705           /* see if edge might get matched on other proc */
706           PetscReal g_max_e1 = PetscRealPart(lghost_max_ew[ghost1_idx]);
707           if (print)
708             PetscCall(PetscSynchronizedPrintf(comm, "\t\t\t[%d] CHECK GHOST e1, edge (%d %d), E0 MAX EDGE WEIGHT = %10.4e, EDGE WEIGHT = %10.4e, diff1 = %10.4e, ghost proc %d with max pe %d on e0 and %d on e1\n", rank, (int)gid0, (int)gid1, (double)PetscRealPart(lid_max_ew[lid0]),
709                                               (double)e->weight, (double)(PetscRealPart(lghost_max_ew[ghost1_idx]) - e->weight), (int)lghost_pe[ghost1_idx], lid_max_pe[lid0], lghost_max_pe[ghost1_idx]));
710           if (g_max_e1 > e->weight + MY_MEPS) {
711             /* PetscCall(PetscSynchronizedPrintf(comm,"\t\t\t\t[%d] 3) ghost e1 SKIPPING small edge (%d %d), diff = %10.4e from proc %d with max pe %d. max = %20.14e, w = %20.14e\n", rank, (int)gid0, (int)gid1, g_max_e1 - e->weight, (int)lghost_pe[ghost1_idx], lghost_max_pe[ghost1_idx], g_max_e1, e->weight )); */
712             continue;
713           } else if (g_max_e1 >= e->weight - MY_MEPS && lghost_pe[ghost1_idx] > rank) { // is 'lghost_max_pe[ghost1_idx] > rank' needed?
714             /* check for max_ea == to this edge and larger processor that will deal with this */
715             if (print)
716               PetscCall(PetscSynchronizedPrintf(comm, "\t\t\t[%d] ghost e1 SKIPPING EQUAL (%d %d), diff = %10.4e from larger proc %d with max pe %d. max = %20.14e, w = %20.14e\n", rank, (int)gid0, (int)gid1,
717                                                 (double)(PetscRealPart(lid_max_ew[lid0]) - (double)e->weight), (int)lghost_pe[ghost1_idx], (int)lghost_max_pe[ghost1_idx], (double)g_max_e1, (double)e->weight));
718             isOK = PETSC_FALSE; // this guy could delete me
719             continue;
720           } else {
721             /* PetscCall(PetscSynchronizedPrintf(comm,"\t[%d] Edge (%d %d) passes gid0 tests, diff = %10.4e from proc %d with max pe %d. max = %20.14e, w = %20.14e\n", rank, (int)gid0, (int)gid1, g_max_e1 - e->weight, (int)lghost_pe[ghost1_idx], lghost_max_pe[ghost1_idx], g_max_e1, e->weight )); */
722           }
723         }
724         /* check ghost for v0 */
725         if (isOK) {
726           PetscReal max_e, ew;
727           if ((ix = lid_cprowID[lid0]) != -1) { /* if I have any ghost neighbors */
728             int n;
729             ii = matB->compressedrow.i;
730             n  = ii[ix + 1] - ii[ix];
731             ap = matB->a + ii[ix];
732             aj = matB->j + ii[ix];
733             for (int jj = 0; jj < n && isOK; jj++) {
734               PetscInt lidj = aj[jj];
735               if (lghost_matched[lidj]) continue;
736               ew = PetscRealPart(ap[jj]);
737               if (ew <= threshold) continue;
738               max_e = PetscRealPart(lghost_max_ew[lidj]);
739               /* check for max_e == to this edge and larger processor that will deal with this */
740               if (ew >= PetscRealPart(lid_max_ew[lid0]) - MY_MEPS && lghost_max_pe[lidj] > rank) isOK = PETSC_FALSE;
741               PetscCheck(ew <= max_e + MY_MEPS, PETSC_COMM_SELF, PETSC_ERR_SUP, "edge weight %e > max %e. ncols = %d, gid0 = %d, gid1 = %d", (double)PetscRealPart(ew), (double)PetscRealPart(max_e), (int)n, (int)(lid0 + my0), (int)lghost_gid[lidj]);
742               if (print)
743                 PetscCall(PetscSynchronizedPrintf(comm, "\t\t\t\t[%d] e0: looked at ghost adj (%d %d), diff = %10.4e, ghost on proc %d (max %d). isOK = %d, %d %d %d; ew = %e, lid0 max ew = %e, diff = %e, eps = %e\n", rank, (int)gid0, (int)lghost_gid[lidj], (double)(max_e - ew), lghost_pe[lidj], lghost_max_pe[lidj], isOK, (double)(ew) >= (double)(max_e - MY_MEPS), ew >= PetscRealPart(lid_max_ew[lid0]) - MY_MEPS, lghost_pe[lidj] > rank, (double)ew, (double)PetscRealPart(lid_max_ew[lid0]), (double)(ew - PetscRealPart(lid_max_ew[lid0])), (double)MY_MEPS));
744             }
745             if (!isOK && print) PetscCall(PetscSynchronizedPrintf(comm, "\t\t[%d] skip edge (%d %d) from ghost inspection\n", rank, (int)gid0, (int)gid1));
746           }
747           /* check local v1 */
748           if (ghost1_idx == -1) {
749             if ((ix = lid_cprowID[lid1]) != -1) { /* if I have any ghost neighbors */
750               int n;
751               ii = matB->compressedrow.i;
752               n  = ii[ix + 1] - ii[ix];
753               ap = matB->a + ii[ix];
754               aj = matB->j + ii[ix];
755               for (int jj = 0; jj < n && isOK; jj++) {
756                 PetscInt lidj = aj[jj];
757                 if (lghost_matched[lidj]) continue;
758                 ew = PetscRealPart(ap[jj]);
759                 if (ew <= threshold) continue;
760                 max_e = PetscRealPart(lghost_max_ew[lidj]);
761                 /* check for max_e == to this edge and larger processor that will deal with this */
762                 if (ew >= PetscRealPart(lid_max_ew[lid1]) - MY_MEPS && lghost_max_pe[lidj] > rank) isOK = PETSC_FALSE;
763                 PetscCheck(ew <= max_e + MY_MEPS, PETSC_COMM_SELF, PETSC_ERR_SUP, "edge weight %e > max %e", (double)PetscRealPart(ew), (double)PetscRealPart(max_e));
764                 if (print)
765                   PetscCall(PetscSynchronizedPrintf(comm, "\t\t\t\t\t[%d] e1: looked at ghost adj (%d %d), diff = %10.4e, ghost on proc %d (max %d)\n", rank, (int)gid0, (int)lghost_gid[lidj], (double)(max_e - ew), lghost_pe[lidj], lghost_max_pe[lidj]));
766               }
767             }
768             if (!isOK && print) PetscCall(PetscSynchronizedPrintf(comm, "\t\t[%d] skip edge (%d %d) from ghost inspection\n", rank, (int)gid0, (int)gid1));
769           }
770         }
771         PetscReal e1_max_w = (ghost1_idx == -1 ? PetscRealPart(lid_max_ew[lid0]) : PetscRealPart(lghost_max_ew[ghost1_idx]));
772         if (print)
773           PetscCall(PetscSynchronizedPrintf(comm, "\t[%d] MATCHING (%d %d) e1 max weight = %e, e1 weight diff %e, %s. isOK = %d\n", rank, (int)gid0, (int)gid1, (double)e1_max_w, (double)(e1_max_w - e->weight), ghost1_idx == -1 ? "local" : "ghost", isOK));
774         /* do it */
775         if (isOK) {
776           if (ghost1_idx == -1) {
777             PetscCheck(!lid_matched[lid1], PETSC_COMM_SELF, PETSC_ERR_SUP, "local %d is matched", (int)gid1);
778             lid_matched[lid1] = PETSC_TRUE;                       /* keep track of what we've done this round */
779             PetscCall(PetscCDMoveAppend(agg_llists, lid0, lid1)); // takes lid1's list and appends to lid0's
780           } else {
781             /* add gid1 to list of ghost deleted by me -- I need their children */
782             PetscMPIInt proc = lghost_pe[ghost1_idx];
783             PetscCheck(!lghost_matched[ghost1_idx], PETSC_COMM_SELF, PETSC_ERR_SUP, "ghost %d is matched", (int)lghost_gid[ghost1_idx]);
784             lghost_matched[ghost1_idx] = PETSC_TRUE;
785             PetscCall(PetscCDAppendID(ghost_deleted_list, proc, ghost1_idx)); /* cache to send messages */
786             PetscCall(PetscCDAppendID(ghost_deleted_list, proc, lid0));
787           }
788           lid_matched[lid0] = PETSC_TRUE; /* keep track of what we've done this round */
789           /* set projection */
790           PetscCall(MatSetValues(P, 1, &gid0, 1, &gid0, &one, INSERT_VALUES));
791           PetscCall(MatSetValues(P, 1, &gid1, 1, &gid0, &one, INSERT_VALUES));
792           //PetscCall(PetscPrintf(comm,"\t %d.%d) match active EDGE %d : (%d %d)\n",iter,sub_it, (int)nactive_edges, (int)gid0, (int)gid1));
793         } /* matched */
794       } /* edge loop */
795       PetscCall(PetscSynchronizedFlush(comm, PETSC_STDOUT));
796       if (isMPI) PetscCall(VecRestoreArrayRead(ghostMaxEdge, &lghost_max_ew));
797       PetscCall(VecRestoreArrayRead(locMaxEdge, &lid_max_ew));
798       // count active for test, latter, update deleted ghosts
799       n_act_n[0] = nactive_edges;
800       if (ghost_deleted_list) PetscCall(PetscCDCount(ghost_deleted_list, &n_act_n[2]));
801       else n_act_n[2] = 0;
802       PetscCall(PetscCDCount(agg_llists, &n_act_n[1]));
803       PetscCall(MPIU_Allreduce(n_act_n, gn_act_n, 3, MPIU_INT, MPI_SUM, comm));
804       PetscCall(PetscInfo(info_is, "[%d] %d.%d) nactive edges=%" PetscInt_FMT ", ncomm_procs=%d, nEdges=%d, %" PetscInt_FMT " deleted ghosts, N=%" PetscInt_FMT "\n", rank, iter, sub_it, gn_act_n[0], (int)ncomm_procs, (int)nEdges, gn_act_n[2], gn_act_n[1]));
805       /* deal with deleted ghost */
806       if (isMPI) {
807         PetscCDIntNd *pos;
808         PetscInt     *sbuffs1[REQ_BF_SIZE], ndel;
809         PetscInt     *sbuffs2[REQ_BF_SIZE];
810         MPI_Status    status;
811 
812         /* send deleted ghosts */
813         for (int proc_idx = 0; proc_idx < ncomm_procs; proc_idx++) {
814           const PetscMPIInt proc = comm_procs[proc_idx];
815           PetscInt         *sbuff, *pt, scount;
816           MPI_Request      *request;
817           /* count ghosts */
818           PetscCall(PetscCDCountAt(ghost_deleted_list, proc, &ndel));
819           ndel /= 2; // two entries for each proc
820           scount = 2 + 2 * ndel;
821           PetscCall(PetscMalloc1(scount + request_size, &sbuff));
822           /* save requests */
823           sbuffs1[proc_idx] = sbuff;
824           request           = (MPI_Request *)sbuff;
825           sbuff = pt = (PetscInt *)(sbuff + request_size);
826           /* write [ndel, proc, n*[gid1,gid0] */
827           *pt++ = ndel; // number of deleted to send
828           *pt++ = rank; // proc (not used)
829           PetscCall(PetscCDGetHeadPos(ghost_deleted_list, proc, &pos));
830           while (pos) {
831             PetscInt lid0, ghost_idx, gid1;
832             PetscCall(PetscCDIntNdGetID(pos, &ghost_idx));
833             gid1 = lghost_gid[ghost_idx];
834             PetscCall(PetscCDGetNextPos(ghost_deleted_list, proc, &pos));
835             PetscCall(PetscCDIntNdGetID(pos, &lid0));
836             PetscCall(PetscCDGetNextPos(ghost_deleted_list, proc, &pos));
837             *pt++ = gid1;
838             *pt++ = lid0 + my0; // gid0
839           }
840           PetscCheck(pt - sbuff == scount, PETSC_COMM_SELF, PETSC_ERR_SUP, "sbuff-pt != scount: %d", (int)(pt - sbuff));
841           /* MPI_Isend:  tag1 [ndel, proc, n*[gid1,gid0] ] */
842           PetscCallMPI(MPI_Isend(sbuff, scount, MPIU_INT, proc, tag1, comm, request));
843           PetscCall(PetscCDRemoveAllAt(ghost_deleted_list, proc)); // done with this list
844         }
845         /* receive deleted, send back partial aggregates, clear lists */
846         for (int proc_idx = 0; proc_idx < ncomm_procs; proc_idx++) {
847           PetscCallMPI(MPI_Probe(comm_procs[proc_idx] /* MPI_ANY_SOURCE */, tag1, comm, &status));
848           {
849             PetscInt         *pt, *pt2, *pt3, *sbuff, tmp;
850             MPI_Request      *request;
851             int               rcount, scount, ndel;
852             const PetscMPIInt proc = status.MPI_SOURCE;
853             PetscCallMPI(MPI_Get_count(&status, MPIU_INT, &rcount));
854             if (rcount > rbuff_sz) {
855               if (rbuff) PetscCall(PetscFree(rbuff));
856               PetscCall(PetscMalloc1(rcount, &rbuff));
857               rbuff_sz = rcount;
858             }
859             /* MPI_Recv: tag1 [ndel, proc, ndel*[gid1,gid0] ] */
860             PetscCallMPI(MPI_Recv(rbuff, rcount, MPIU_INT, proc, tag1, comm, &status));
861             /* read and count sends *[lid0, n, n*[gid] ] */
862             pt     = rbuff;
863             scount = 0;
864             ndel   = *pt++; // number of deleted to recv
865             tmp    = *pt++; // proc (not used)
866             while (ndel--) {
867               PetscInt gid1 = *pt++, lid1 = gid1 - my0;
868               int      gh_gid0 = *pt++; // gid on other proc (not used here to count)
869               PetscCheck(lid1 >= 0 && lid1 < nloc, PETSC_COMM_SELF, PETSC_ERR_SUP, "received ghost deleted %d", (int)gid1);
870               PetscCheck(!lid_matched[lid1], PETSC_COMM_SELF, PETSC_ERR_PLIB, "%d) received matched local gid %" PetscInt_FMT ",%d, with ghost (lid) %" PetscInt_FMT " from proc %d", sub_it, gid1, gh_gid0, tmp, proc);
871               lid_matched[lid1] = PETSC_TRUE;                    /* keep track of what we've done this round */
872               PetscCall(PetscCDCountAt(agg_llists, lid1, &tmp)); // n
873               /* PetscCheck(tmp == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "sending %d (!= 1) size aggregate. gid-0 %d, from %d (gid-1 %d)", (int)tmp, (int) gid, proc, gh_gid0); */
874               scount += tmp + 2; // lid0, n, n*[gid]
875             }
876             PetscCheck((pt - rbuff) == rcount, PETSC_COMM_SELF, PETSC_ERR_SUP, "receive buffer size != num read: %d; rcount: %d", (int)(pt - rbuff), rcount);
877             /* send tag2: *[gid0, n, n*[gid] ] */
878             PetscCall(PetscMalloc1(scount + request_size, &sbuff));
879             sbuffs2[proc_idx] = sbuff; /* cache request */
880             request           = (MPI_Request *)sbuff;
881             pt2 = sbuff = sbuff + request_size;
882             // read again: n, proc, n*[gid1,gid0]
883             pt   = rbuff;
884             ndel = *pt++;
885             tmp  = *pt++; // proc (not used)
886             while (ndel--) {
887               PetscInt gid1 = *pt++, lid1 = gid1 - my0, gh_gid0 = *pt++;
888               /* write [gid0, aggSz, aggSz[gid] ] */
889               *pt2++ = gh_gid0;
890               pt3    = pt2++; /* save pointer for later */
891               PetscCall(PetscCDGetHeadPos(agg_llists, lid1, &pos));
892               while (pos) {
893                 PetscInt gid;
894                 PetscCall(PetscCDIntNdGetID(pos, &gid));
895                 PetscCall(PetscCDGetNextPos(agg_llists, lid1, &pos));
896                 *pt2++ = gid;
897               }
898               *pt3 = (pt2 - pt3) - 1;
899               /* clear list */
900               PetscCall(PetscCDRemoveAllAt(agg_llists, lid1));
901             }
902             PetscCheck((pt2 - sbuff) == scount, PETSC_COMM_SELF, PETSC_ERR_SUP, "buffer size != num write: %d %d", (int)(pt2 - sbuff), (int)scount);
903             /* MPI_Isend: requested data tag2 *[lid0, n, n*[gid1] ] */
904             PetscCallMPI(MPI_Isend(sbuff, scount, MPIU_INT, proc, tag2, comm, request));
905           }
906         } // proc_idx
907         /* receive tag2 *[gid0, n, n*[gid] ] */
908         for (int proc_idx = 0; proc_idx < ncomm_procs; proc_idx++) {
909           PetscMPIInt proc;
910           PetscInt   *pt;
911           int         rcount;
912           PetscCallMPI(MPI_Probe(comm_procs[proc_idx] /* MPI_ANY_SOURCE */, tag2, comm, &status));
913           PetscCallMPI(MPI_Get_count(&status, MPIU_INT, &rcount));
914           if (rcount > rbuff_sz) {
915             if (rbuff) PetscCall(PetscFree(rbuff));
916             PetscCall(PetscMalloc1(rcount, &rbuff));
917             rbuff_sz = rcount;
918           }
919           proc = status.MPI_SOURCE;
920           /* MPI_Recv:  tag1 [n, proc, n*[gid1,lid0] ] */
921           PetscCallMPI(MPI_Recv(rbuff, rcount, MPIU_INT, proc, tag2, comm, &status));
922           pt = rbuff;
923           while (pt - rbuff < rcount) {
924             PetscInt gid0 = *pt++, n = *pt++;
925             while (n--) {
926               PetscInt gid1 = *pt++;
927               PetscCall(PetscCDAppendID(agg_llists, gid0 - my0, gid1));
928             }
929           }
930           PetscCheck((pt - rbuff) == rcount, PETSC_COMM_SELF, PETSC_ERR_SUP, "recv buffer size != num read: %d %d", (int)(pt - rbuff), (int)rcount);
931         }
932         /* wait for tag1 isends */
933         for (int proc_idx = 0; proc_idx < ncomm_procs; proc_idx++) {
934           MPI_Request *request;
935           request = (MPI_Request *)sbuffs1[proc_idx];
936           PetscCallMPI(MPI_Wait(request, &status));
937           PetscCall(PetscFree(sbuffs1[proc_idx]));
938         }
939         /* wait for tag2 isends */
940         for (int proc_idx = 0; proc_idx < ncomm_procs; proc_idx++) {
941           MPI_Request *request = (MPI_Request *)sbuffs2[proc_idx];
942           PetscCallMPI(MPI_Wait(request, &status));
943           PetscCall(PetscFree(sbuffs2[proc_idx]));
944         }
945       } /* MPI */
946       /* set 'lghost_matched' - use locMaxEdge, ghostMaxEdge (recomputed next) */
947       if (isMPI) {
948         const PetscScalar *sbuff;
949         for (PetscInt kk = 0, gid = my0; kk < nloc; kk++, gid++) {
950           PetscScalar vval = lid_matched[kk] ? 1.0 : 0.0;
951           PetscCall(VecSetValues(locMaxEdge, 1, &gid, &vval, INSERT_VALUES)); /* set with GID */
952         }
953         PetscCall(VecAssemblyBegin(locMaxEdge));
954         PetscCall(VecAssemblyEnd(locMaxEdge));
955         PetscCall(VecScatterBegin(mpimat->Mvctx, locMaxEdge, ghostMaxEdge, INSERT_VALUES, SCATTER_FORWARD));
956         PetscCall(VecScatterEnd(mpimat->Mvctx, locMaxEdge, ghostMaxEdge, INSERT_VALUES, SCATTER_FORWARD));
957         PetscCall(VecGetArrayRead(ghostMaxEdge, &sbuff));
958         for (int kk = 0; kk < num_ghosts; kk++) { lghost_matched[kk] = (PetscBool)(PetscRealPart(sbuff[kk]) != 0.0); }
959         PetscCall(VecRestoreArrayRead(ghostMaxEdge, &sbuff));
960       }
961       /* compute 'locMaxEdge' inside sub iteration b/c max weight can drop as neighbors are matched */
962       for (PetscInt kk = 0, gid = my0; kk < nloc; kk++, gid++) {
963         PetscReal      max_e = 0., tt;
964         PetscScalar    vval;
965         const PetscInt lid    = kk;
966         int            max_pe = rank, pe, n;
967         ii                    = matA->i;
968         n                     = ii[lid + 1] - ii[lid];
969         aj                    = PetscSafePointerPlusOffset(matA->j, ii[lid]);
970         ap                    = PetscSafePointerPlusOffset(matA->a, ii[lid]);
971         for (int jj = 0; jj < n; jj++) {
972           PetscInt lidj = aj[jj];
973           if (lid_matched[lidj]) continue; /* this is new - can change local max */
974           if (lidj != lid && PetscRealPart(ap[jj]) > max_e) max_e = PetscRealPart(ap[jj]);
975         }
976         if (lid_cprowID && (ix = lid_cprowID[lid]) != -1) { /* if I have any ghost neighbors */
977           ii = matB->compressedrow.i;
978           n  = ii[ix + 1] - ii[ix];
979           ap = matB->a + ii[ix];
980           aj = matB->j + ii[ix];
981           for (int jj = 0; jj < n; jj++) {
982             PetscInt lidj = aj[jj];
983             if (lghost_matched[lidj]) continue;
984             if ((tt = PetscRealPart(ap[jj])) > max_e) max_e = tt;
985           }
986         }
987         vval = (PetscScalar)max_e;
988         PetscCall(VecSetValues(locMaxEdge, 1, &gid, &vval, INSERT_VALUES)); /* set with GID */
989         // max PE with max edge
990         if (lid_cprowID && (ix = lid_cprowID[lid]) != -1) { /* if I have any ghost neighbors */
991           ii = matB->compressedrow.i;
992           n  = ii[ix + 1] - ii[ix];
993           ap = matB->a + ii[ix];
994           aj = matB->j + ii[ix];
995           for (int jj = 0; jj < n; jj++) {
996             PetscInt lidj = aj[jj];
997             if (lghost_matched[lidj]) continue;
998             if ((pe = lghost_pe[aj[jj]]) > max_pe && PetscRealPart(ap[jj]) >= max_e - MY_MEPS) { max_pe = pe; }
999           }
1000         }
1001         vval = (PetscScalar)max_pe;
1002         PetscCall(VecSetValues(locMaxPE, 1, &gid, &vval, INSERT_VALUES));
1003       }
1004       PetscCall(VecAssemblyBegin(locMaxEdge));
1005       PetscCall(VecAssemblyEnd(locMaxEdge));
1006       PetscCall(VecAssemblyBegin(locMaxPE));
1007       PetscCall(VecAssemblyEnd(locMaxPE));
1008       /* compute 'lghost_max_ew' and 'lghost_max_pe' to get ready for next iteration*/
1009       if (isMPI) {
1010         const PetscScalar *buf;
1011         PetscCall(VecScatterBegin(mpimat->Mvctx, locMaxEdge, ghostMaxEdge, INSERT_VALUES, SCATTER_FORWARD));
1012         PetscCall(VecScatterEnd(mpimat->Mvctx, locMaxEdge, ghostMaxEdge, INSERT_VALUES, SCATTER_FORWARD));
1013         PetscCall(VecScatterBegin(mpimat->Mvctx, locMaxPE, ghostMaxPE, INSERT_VALUES, SCATTER_FORWARD));
1014         PetscCall(VecScatterEnd(mpimat->Mvctx, locMaxPE, ghostMaxPE, INSERT_VALUES, SCATTER_FORWARD));
1015         PetscCall(VecGetArrayRead(ghostMaxPE, &buf));
1016         for (int kk = 0; kk < num_ghosts; kk++) {
1017           lghost_max_pe[kk] = (PetscMPIInt)PetscRealPart(buf[kk]); // the MAX proc of the ghost now
1018         }
1019         PetscCall(VecRestoreArrayRead(ghostMaxPE, &buf));
1020       }
1021       // if no active edges, stop
1022       if (gn_act_n[0] < 1) break;
1023       // inc and check (self stopping iteration
1024       PetscCheck(old_num_edge != gn_act_n[0], PETSC_COMM_SELF, PETSC_ERR_SUP, "HEM stalled step %d/%d", sub_it + 1, n_sub_its);
1025       sub_it++;
1026       PetscCheck(sub_it < n_sub_its, PETSC_COMM_SELF, PETSC_ERR_SUP, "failed to finish HEM step %d/%d", sub_it + 1, n_sub_its);
1027       old_num_edge = gn_act_n[0];
1028     } /* sub_it loop */
1029     /* clean up iteration */
1030     PetscCall(PetscFree(Edges));
1031     if (mpimat) { // can be hoisted
1032       PetscCall(VecRestoreArrayRead(ghostMaxEdge, &lghost_max_ew));
1033       PetscCall(VecDestroy(&ghostMaxEdge));
1034       PetscCall(VecDestroy(&ghostMaxPE));
1035       PetscCall(PetscFree(lghost_pe));
1036       PetscCall(PetscFree(lghost_gid));
1037       PetscCall(PetscFree(lghost_matched));
1038       PetscCall(PetscFree(lghost_max_pe));
1039     }
1040     PetscCall(VecDestroy(&locMaxEdge));
1041     PetscCall(VecDestroy(&locMaxPE));
1042     /* create next graph */
1043     {
1044       Vec diag;
1045       /* add identity for unmatched vertices so they stay alive */
1046       for (PetscInt kk = 0, gid1, gid = my0; kk < nloc; kk++, gid++) {
1047         if (!lid_matched[kk]) {
1048           const PetscInt lid = kk;
1049           PetscCDIntNd  *pos;
1050           PetscCall(PetscCDGetHeadPos(agg_llists, lid, &pos));
1051           PetscCheck(pos, PETSC_COMM_SELF, PETSC_ERR_PLIB, "empty list in singleton: %d", (int)gid);
1052           PetscCall(PetscCDIntNdGetID(pos, &gid1));
1053           PetscCheck(gid1 == gid, PETSC_COMM_SELF, PETSC_ERR_PLIB, "first in list (%d) in singleton not %d", (int)gid1, (int)gid);
1054           PetscCall(MatSetValues(P, 1, &gid, 1, &gid, &one, INSERT_VALUES));
1055         }
1056       }
1057       PetscCall(MatAssemblyBegin(P, MAT_FINAL_ASSEMBLY));
1058       PetscCall(MatAssemblyEnd(P, MAT_FINAL_ASSEMBLY));
1059 
1060       /* project to make new graph with collapsed edges */
1061       PetscCall(MatPtAP(cMat, P, MAT_INITIAL_MATRIX, 1.0, &tMat));
1062       PetscCall(MatDestroy(&P));
1063       PetscCall(MatDestroy(&cMat));
1064       cMat = tMat;
1065       PetscCall(MatCreateVecs(cMat, &diag, NULL));
1066       PetscCall(MatGetDiagonal(cMat, diag));
1067       PetscCall(VecReciprocal(diag));
1068       PetscCall(VecSqrtAbs(diag));
1069       PetscCall(MatDiagonalScale(cMat, diag, diag));
1070       PetscCall(VecDestroy(&diag));
1071     }
1072   } /* coarsen iterator */
1073 
1074   /* make fake matrix with Mat->B only for smoothed agg QR. Need this if we make an aux graph (ie, PtAP) with k > 1 */
1075   if (size > 1) {
1076     Mat           mat;
1077     PetscCDIntNd *pos;
1078     PetscInt      NN, MM, jj = 0, mxsz = 0;
1079 
1080     for (int kk = 0; kk < nloc; kk++) {
1081       PetscCall(PetscCDCountAt(agg_llists, kk, &jj));
1082       if (jj > mxsz) mxsz = jj;
1083     }
1084     PetscCall(MatGetSize(a_Gmat, &MM, &NN));
1085     if (mxsz > MM - nloc) mxsz = MM - nloc;
1086     /* matrix of ghost adj for square graph */
1087     PetscCall(MatCreateAIJ(comm, nloc, nloc, PETSC_DETERMINE, PETSC_DETERMINE, 0, NULL, mxsz, NULL, &mat));
1088     for (PetscInt lid = 0, gid = my0; lid < nloc; lid++, gid++) {
1089       PetscCall(PetscCDGetHeadPos(agg_llists, lid, &pos));
1090       while (pos) {
1091         PetscInt gid1;
1092         PetscCall(PetscCDIntNdGetID(pos, &gid1));
1093         PetscCall(PetscCDGetNextPos(agg_llists, lid, &pos));
1094         if (gid1 < my0 || gid1 >= my0 + nloc) PetscCall(MatSetValues(mat, 1, &gid, 1, &gid1, &one, ADD_VALUES));
1095       }
1096     }
1097     PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
1098     PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
1099     PetscCall(PetscCDSetMat(agg_llists, mat));
1100     PetscCall(PetscCDDestroy(ghost_deleted_list));
1101     if (rbuff_sz) PetscCall(PetscFree(rbuff)); // always true
1102   }
1103   // move BCs into some node
1104   if (bc_list) {
1105     PetscCDIntNd *pos;
1106     PetscCall(PetscCDGetHeadPos(bc_list, 0, &pos));
1107     while (pos) {
1108       PetscInt gid1;
1109       PetscCall(PetscCDIntNdGetID(pos, &gid1));
1110       PetscCall(PetscCDGetNextPos(bc_list, 0, &pos));
1111       PetscCall(PetscCDAppendID(agg_llists, bc_agg, gid1));
1112     }
1113     PetscCall(PetscCDRemoveAllAt(bc_list, 0));
1114     PetscCall(PetscCDDestroy(bc_list));
1115   }
1116   {
1117     // check sizes -- all vertices must get in graph
1118     PetscInt sz, globalsz, MM;
1119     PetscCall(MatGetSize(a_Gmat, &MM, NULL));
1120     PetscCall(PetscCDCount(agg_llists, &sz));
1121     PetscCall(MPIU_Allreduce(&sz, &globalsz, 1, MPIU_INT, MPI_SUM, comm));
1122     PetscCheck(MM == globalsz, comm, PETSC_ERR_SUP, "lost %d equations ?", (int)(MM - globalsz));
1123   }
1124   // cleanup
1125   PetscCall(MatDestroy(&cMat));
1126   PetscCall(PetscFree(lid_cprowID));
1127   PetscCall(PetscFree(lid_max_pe));
1128   PetscCall(PetscFree(lid_matched));
1129   PetscCall(ISDestroy(&info_is));
1130   PetscFunctionReturn(PETSC_SUCCESS);
1131 }
1132 
1133 /*
1134    HEM coarsen, simple greedy.
1135 */
1136 static PetscErrorCode MatCoarsenApply_HEM(MatCoarsen coarse)
1137 {
1138   Mat mat = coarse->graph;
1139 
1140   PetscFunctionBegin;
1141   PetscCall(MatCoarsenApply_HEM_private(mat, coarse->max_it, coarse->threshold, &coarse->agg_lists));
1142   PetscFunctionReturn(PETSC_SUCCESS);
1143 }
1144 
1145 static PetscErrorCode MatCoarsenView_HEM(MatCoarsen coarse, PetscViewer viewer)
1146 {
1147   PetscMPIInt rank;
1148   PetscBool   iascii;
1149 
1150   PetscFunctionBegin;
1151   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)coarse), &rank));
1152   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1153   if (iascii) {
1154     PetscCDIntNd     *pos, *pos2;
1155     PetscViewerFormat format;
1156 
1157     PetscCall(PetscViewerASCIIPrintf(viewer, "%d matching steps with threshold = %g\n", (int)coarse->max_it, (double)coarse->threshold));
1158     PetscCall(PetscViewerGetFormat(viewer, &format));
1159     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1160       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
1161       for (PetscInt kk = 0; kk < coarse->agg_lists->size; kk++) {
1162         PetscCall(PetscCDGetHeadPos(coarse->agg_lists, kk, &pos));
1163         if ((pos2 = pos)) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "selected local %d: ", (int)kk));
1164         while (pos) {
1165           PetscInt gid1;
1166           PetscCall(PetscCDIntNdGetID(pos, &gid1));
1167           PetscCall(PetscCDGetNextPos(coarse->agg_lists, kk, &pos));
1168           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %d ", (int)gid1));
1169         }
1170         if (pos2) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
1171       }
1172       PetscCall(PetscViewerFlush(viewer));
1173       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
1174     }
1175   }
1176   PetscFunctionReturn(PETSC_SUCCESS);
1177 }
1178 
1179 /*
1180   MatCoarsenCreate_HEM - A coarsener that uses HEM a simple greedy coarsener
1181 */
1182 PETSC_EXTERN PetscErrorCode MatCoarsenCreate_HEM(MatCoarsen coarse)
1183 {
1184   PetscFunctionBegin;
1185   coarse->ops->apply = MatCoarsenApply_HEM;
1186   coarse->ops->view  = MatCoarsenView_HEM;
1187   coarse->max_it     = 4;
1188   PetscFunctionReturn(PETSC_SUCCESS);
1189 }
1190