xref: /petsc/src/dm/impls/plex/plexpartition.c (revision 99b539017eea4dad4e6c68f8b55912c159f9b883)
1 #include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 #include <petsc/private/hashseti.h>
3 
4 PetscClassId PETSCPARTITIONER_CLASSID = 0;
5 
6 PetscFunctionList PetscPartitionerList              = NULL;
7 PetscBool         PetscPartitionerRegisterAllCalled = PETSC_FALSE;
8 
9 PetscBool ChacoPartitionercite = PETSC_FALSE;
10 const char ChacoPartitionerCitation[] = "@inproceedings{Chaco95,\n"
11                                "  author    = {Bruce Hendrickson and Robert Leland},\n"
12                                "  title     = {A multilevel algorithm for partitioning graphs},\n"
13                                "  booktitle = {Supercomputing '95: Proceedings of the 1995 ACM/IEEE Conference on Supercomputing (CDROM)},"
14                                "  isbn      = {0-89791-816-9},\n"
15                                "  pages     = {28},\n"
16                                "  doi       = {http://doi.acm.org/10.1145/224170.224228},\n"
17                                "  publisher = {ACM Press},\n"
18                                "  address   = {New York},\n"
19                                "  year      = {1995}\n}\n";
20 
21 PetscBool ParMetisPartitionercite = PETSC_FALSE;
22 const char ParMetisPartitionerCitation[] = "@article{KarypisKumar98,\n"
23                                "  author  = {George Karypis and Vipin Kumar},\n"
24                                "  title   = {A Parallel Algorithm for Multilevel Graph Partitioning and Sparse Matrix Ordering},\n"
25                                "  journal = {Journal of Parallel and Distributed Computing},\n"
26                                "  volume  = {48},\n"
27                                "  pages   = {71--85},\n"
28                                "  year    = {1998}\n}\n";
29 
30 /*@C
31   DMPlexCreatePartitionerGraph - Create a CSR graph of point connections for the partitioner
32 
33   Input Parameters:
34 + dm      - The mesh DM dm
35 - height  - Height of the strata from which to construct the graph
36 
37   Output Parameter:
38 + numVertices     - Number of vertices in the graph
39 . offsets         - Point offsets in the graph
40 . adjacency       - Point connectivity in the graph
41 - globalNumbering - A map from the local cell numbering to the global numbering used in "adjacency".  Negative indicates that the cell is a duplicate from another process.
42 
43   The user can control the definition of adjacency for the mesh using DMSetAdjacency(). They should choose the combination appropriate for the function
44   representation on the mesh.
45 
46   Level: developer
47 
48 .seealso: PetscPartitionerGetType(), PetscPartitionerCreate(), DMSetAdjacency()
49 @*/
50 PetscErrorCode DMPlexCreatePartitionerGraph(DM dm, PetscInt height, PetscInt *numVertices, PetscInt **offsets, PetscInt **adjacency, IS *globalNumbering)
51 {
52   PetscInt       dim, depth, p, pStart, pEnd, a, adjSize, idx, size;
53   PetscInt      *adj = NULL, *vOffsets = NULL, *graph = NULL;
54   IS             cellNumbering;
55   const PetscInt *cellNum;
56   PetscBool      useCone, useClosure;
57   PetscSection   section;
58   PetscSegBuffer adjBuffer;
59   PetscSF        sfPoint;
60   PetscInt       *adjCells = NULL, *remoteCells = NULL;
61   const PetscInt *local;
62   PetscInt       nroots, nleaves, l;
63   PetscMPIInt    rank;
64   PetscErrorCode ierr;
65 
66   PetscFunctionBegin;
67   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
68   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
69   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
70   if (dim != depth) {
71     /* We do not handle the uninterpolated case here */
72     ierr = DMPlexCreateNeighborCSR(dm, height, numVertices, offsets, adjacency);CHKERRQ(ierr);
73     /* DMPlexCreateNeighborCSR does not make a numbering */
74     if (globalNumbering) {ierr = DMPlexCreateCellNumbering_Internal(dm, PETSC_TRUE, globalNumbering);CHKERRQ(ierr);}
75     /* Different behavior for empty graphs */
76     if (!*numVertices) {
77       ierr = PetscMalloc1(1, offsets);CHKERRQ(ierr);
78       (*offsets)[0] = 0;
79     }
80     /* Broken in parallel */
81     if (rank && *numVertices) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Parallel partitioning of uninterpolated meshes not supported");
82     PetscFunctionReturn(0);
83   }
84   ierr = DMPlexGetHeightStratum(dm, height, &pStart, &pEnd);CHKERRQ(ierr);
85   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
86   ierr = PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
87   /* Build adjacency graph via a section/segbuffer */
88   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &section);CHKERRQ(ierr);
89   ierr = PetscSectionSetChart(section, pStart, pEnd);CHKERRQ(ierr);
90   ierr = PetscSegBufferCreate(sizeof(PetscInt),1000,&adjBuffer);CHKERRQ(ierr);
91   /* Always use FVM adjacency to create partitioner graph */
92   ierr = DMGetBasicAdjacency(dm, &useCone, &useClosure);CHKERRQ(ierr);
93   ierr = DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);CHKERRQ(ierr);
94   ierr = DMPlexCreateCellNumbering_Internal(dm, PETSC_TRUE, &cellNumbering);CHKERRQ(ierr);
95   if (globalNumbering) {
96     ierr = PetscObjectReference((PetscObject)cellNumbering);CHKERRQ(ierr);
97     *globalNumbering = cellNumbering;
98   }
99   ierr = ISGetIndices(cellNumbering, &cellNum);CHKERRQ(ierr);
100   /* For all boundary faces (including faces adjacent to a ghost cell), record the local cell in adjCells
101      Broadcast adjCells to remoteCells (to get cells from roots) and Reduce adjCells to remoteCells (to get cells from leaves)
102    */
103   ierr = PetscSFGetGraph(dm->sf, &nroots, &nleaves, &local, NULL);CHKERRQ(ierr);
104   if (nroots >= 0) {
105     PetscInt fStart, fEnd, f;
106 
107     ierr = PetscCalloc2(nroots, &adjCells, nroots, &remoteCells);CHKERRQ(ierr);
108     ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
109     for (l = 0; l < nroots; ++l) adjCells[l] = -3;
110     for (f = fStart; f < fEnd; ++f) {
111       const PetscInt *support;
112       PetscInt        supportSize;
113 
114       ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
115       ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
116       if (supportSize == 1) adjCells[f] = cellNum[support[0]];
117       else if (supportSize == 2) {
118         ierr = PetscFindInt(support[0], nleaves, local, &p);CHKERRQ(ierr);
119         if (p >= 0) adjCells[f] = cellNum[support[1]];
120         ierr = PetscFindInt(support[1], nleaves, local, &p);CHKERRQ(ierr);
121         if (p >= 0) adjCells[f] = cellNum[support[0]];
122       }
123     }
124     for (l = 0; l < nroots; ++l) remoteCells[l] = -1;
125     ierr = PetscSFBcastBegin(dm->sf, MPIU_INT, adjCells, remoteCells);CHKERRQ(ierr);
126     ierr = PetscSFBcastEnd(dm->sf, MPIU_INT, adjCells, remoteCells);CHKERRQ(ierr);
127     ierr = PetscSFReduceBegin(dm->sf, MPIU_INT, adjCells, remoteCells, MPI_MAX);CHKERRQ(ierr);
128     ierr = PetscSFReduceEnd(dm->sf, MPIU_INT, adjCells, remoteCells, MPI_MAX);CHKERRQ(ierr);
129   }
130   /* Combine local and global adjacencies */
131   for (*numVertices = 0, p = pStart; p < pEnd; p++) {
132     const PetscInt *cone;
133     PetscInt        coneSize, c;
134 
135     /* Skip non-owned cells in parallel (ParMetis expects no overlap) */
136     if (nroots > 0) {if (cellNum[p] < 0) continue;}
137     /* Add remote cells */
138     if (remoteCells) {
139       ierr = DMPlexGetCone(dm, p, &cone);CHKERRQ(ierr);
140       ierr = DMPlexGetConeSize(dm, p, &coneSize);CHKERRQ(ierr);
141       for (c = 0; c < coneSize; ++c) {
142         if (remoteCells[cone[c]] != -1) {
143           PetscInt *PETSC_RESTRICT pBuf;
144 
145           ierr = PetscSectionAddDof(section, p, 1);CHKERRQ(ierr);
146           ierr = PetscSegBufferGetInts(adjBuffer, 1, &pBuf);CHKERRQ(ierr);
147           *pBuf = remoteCells[cone[c]];
148         }
149       }
150     }
151     /* Add local cells */
152     adjSize = PETSC_DETERMINE;
153     ierr = DMPlexGetAdjacency(dm, p, &adjSize, &adj);CHKERRQ(ierr);
154     for (a = 0; a < adjSize; ++a) {
155       const PetscInt point = adj[a];
156       if (point != p && pStart <= point && point < pEnd) {
157         PetscInt *PETSC_RESTRICT pBuf;
158         ierr = PetscSectionAddDof(section, p, 1);CHKERRQ(ierr);
159         ierr = PetscSegBufferGetInts(adjBuffer, 1, &pBuf);CHKERRQ(ierr);
160         *pBuf = cellNum[point];
161       }
162     }
163     (*numVertices)++;
164   }
165   ierr = PetscFree2(adjCells, remoteCells);CHKERRQ(ierr);
166   ierr = DMSetBasicAdjacency(dm, useCone, useClosure);CHKERRQ(ierr);
167   /* Derive CSR graph from section/segbuffer */
168   ierr = PetscSectionSetUp(section);CHKERRQ(ierr);
169   ierr = PetscSectionGetStorageSize(section, &size);CHKERRQ(ierr);
170   ierr = PetscMalloc1(*numVertices+1, &vOffsets);CHKERRQ(ierr);
171   for (idx = 0, p = pStart; p < pEnd; p++) {
172     if (nroots > 0) {if (cellNum[p] < 0) continue;}
173     ierr = PetscSectionGetOffset(section, p, &(vOffsets[idx++]));CHKERRQ(ierr);
174   }
175   vOffsets[*numVertices] = size;
176   if (offsets) *offsets = vOffsets;
177   ierr = PetscSegBufferExtractAlloc(adjBuffer, &graph);CHKERRQ(ierr);
178   ierr = ISRestoreIndices(cellNumbering, &cellNum);CHKERRQ(ierr);
179   ierr = ISDestroy(&cellNumbering);CHKERRQ(ierr);
180   if (adjacency) *adjacency = graph;
181   /* Clean up */
182   ierr = PetscSegBufferDestroy(&adjBuffer);CHKERRQ(ierr);
183   ierr = PetscSectionDestroy(&section);CHKERRQ(ierr);
184   ierr = PetscFree(adj);CHKERRQ(ierr);
185   PetscFunctionReturn(0);
186 }
187 
188 /*@C
189   DMPlexCreateNeighborCSR - Create a mesh graph (cell-cell adjacency) in parallel CSR format.
190 
191   Collective
192 
193   Input Arguments:
194 + dm - The DMPlex
195 - cellHeight - The height of mesh points to treat as cells (default should be 0)
196 
197   Output Arguments:
198 + numVertices - The number of local vertices in the graph, or cells in the mesh.
199 . offsets     - The offset to the adjacency list for each cell
200 - adjacency   - The adjacency list for all cells
201 
202   Note: This is suitable for input to a mesh partitioner like ParMetis.
203 
204   Level: advanced
205 
206 .seealso: DMPlexCreate()
207 @*/
208 PetscErrorCode DMPlexCreateNeighborCSR(DM dm, PetscInt cellHeight, PetscInt *numVertices, PetscInt **offsets, PetscInt **adjacency)
209 {
210   const PetscInt maxFaceCases = 30;
211   PetscInt       numFaceCases = 0;
212   PetscInt       numFaceVertices[30]; /* maxFaceCases, C89 sucks sucks sucks */
213   PetscInt      *off, *adj;
214   PetscInt      *neighborCells = NULL;
215   PetscInt       dim, cellDim, depth = 0, faceDepth, cStart, cEnd, c, numCells, cell;
216   PetscErrorCode ierr;
217 
218   PetscFunctionBegin;
219   /* For parallel partitioning, I think you have to communicate supports */
220   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
221   cellDim = dim - cellHeight;
222   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
223   ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
224   if (cEnd - cStart == 0) {
225     if (numVertices) *numVertices = 0;
226     if (offsets)   *offsets   = NULL;
227     if (adjacency) *adjacency = NULL;
228     PetscFunctionReturn(0);
229   }
230   numCells  = cEnd - cStart;
231   faceDepth = depth - cellHeight;
232   if (dim == depth) {
233     PetscInt f, fStart, fEnd;
234 
235     ierr = PetscCalloc1(numCells+1, &off);CHKERRQ(ierr);
236     /* Count neighboring cells */
237     ierr = DMPlexGetHeightStratum(dm, cellHeight+1, &fStart, &fEnd);CHKERRQ(ierr);
238     for (f = fStart; f < fEnd; ++f) {
239       const PetscInt *support;
240       PetscInt        supportSize;
241       ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
242       ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
243       if (supportSize == 2) {
244         PetscInt numChildren;
245 
246         ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
247         if (!numChildren) {
248           ++off[support[0]-cStart+1];
249           ++off[support[1]-cStart+1];
250         }
251       }
252     }
253     /* Prefix sum */
254     for (c = 1; c <= numCells; ++c) off[c] += off[c-1];
255     if (adjacency) {
256       PetscInt *tmp;
257 
258       ierr = PetscMalloc1(off[numCells], &adj);CHKERRQ(ierr);
259       ierr = PetscMalloc1(numCells+1, &tmp);CHKERRQ(ierr);
260       ierr = PetscMemcpy(tmp, off, (numCells+1) * sizeof(PetscInt));CHKERRQ(ierr);
261       /* Get neighboring cells */
262       for (f = fStart; f < fEnd; ++f) {
263         const PetscInt *support;
264         PetscInt        supportSize;
265         ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
266         ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
267         if (supportSize == 2) {
268           PetscInt numChildren;
269 
270           ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
271           if (!numChildren) {
272             adj[tmp[support[0]-cStart]++] = support[1];
273             adj[tmp[support[1]-cStart]++] = support[0];
274           }
275         }
276       }
277 #if defined(PETSC_USE_DEBUG)
278       for (c = 0; c < cEnd-cStart; ++c) if (tmp[c] != off[c+1]) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Offset %d != %d for cell %d", tmp[c], off[c], c+cStart);
279 #endif
280       ierr = PetscFree(tmp);CHKERRQ(ierr);
281     }
282     if (numVertices) *numVertices = numCells;
283     if (offsets)   *offsets   = off;
284     if (adjacency) *adjacency = adj;
285     PetscFunctionReturn(0);
286   }
287   /* Setup face recognition */
288   if (faceDepth == 1) {
289     PetscInt cornersSeen[30] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}; /* Could use PetscBT */
290 
291     for (c = cStart; c < cEnd; ++c) {
292       PetscInt corners;
293 
294       ierr = DMPlexGetConeSize(dm, c, &corners);CHKERRQ(ierr);
295       if (!cornersSeen[corners]) {
296         PetscInt nFV;
297 
298         if (numFaceCases >= maxFaceCases) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Exceeded maximum number of face recognition cases");
299         cornersSeen[corners] = 1;
300 
301         ierr = DMPlexGetNumFaceVertices(dm, cellDim, corners, &nFV);CHKERRQ(ierr);
302 
303         numFaceVertices[numFaceCases++] = nFV;
304       }
305     }
306   }
307   ierr = PetscCalloc1(numCells+1, &off);CHKERRQ(ierr);
308   /* Count neighboring cells */
309   for (cell = cStart; cell < cEnd; ++cell) {
310     PetscInt numNeighbors = PETSC_DETERMINE, n;
311 
312     ierr = DMPlexGetAdjacency_Internal(dm, cell, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &numNeighbors, &neighborCells);CHKERRQ(ierr);
313     /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
314     for (n = 0; n < numNeighbors; ++n) {
315       PetscInt        cellPair[2];
316       PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
317       PetscInt        meetSize = 0;
318       const PetscInt *meet    = NULL;
319 
320       cellPair[0] = cell; cellPair[1] = neighborCells[n];
321       if (cellPair[0] == cellPair[1]) continue;
322       if (!found) {
323         ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
324         if (meetSize) {
325           PetscInt f;
326 
327           for (f = 0; f < numFaceCases; ++f) {
328             if (numFaceVertices[f] == meetSize) {
329               found = PETSC_TRUE;
330               break;
331             }
332           }
333         }
334         ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
335       }
336       if (found) ++off[cell-cStart+1];
337     }
338   }
339   /* Prefix sum */
340   for (cell = 1; cell <= numCells; ++cell) off[cell] += off[cell-1];
341 
342   if (adjacency) {
343     ierr = PetscMalloc1(off[numCells], &adj);CHKERRQ(ierr);
344     /* Get neighboring cells */
345     for (cell = cStart; cell < cEnd; ++cell) {
346       PetscInt numNeighbors = PETSC_DETERMINE, n;
347       PetscInt cellOffset   = 0;
348 
349       ierr = DMPlexGetAdjacency_Internal(dm, cell, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &numNeighbors, &neighborCells);CHKERRQ(ierr);
350       /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
351       for (n = 0; n < numNeighbors; ++n) {
352         PetscInt        cellPair[2];
353         PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
354         PetscInt        meetSize = 0;
355         const PetscInt *meet    = NULL;
356 
357         cellPair[0] = cell; cellPair[1] = neighborCells[n];
358         if (cellPair[0] == cellPair[1]) continue;
359         if (!found) {
360           ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
361           if (meetSize) {
362             PetscInt f;
363 
364             for (f = 0; f < numFaceCases; ++f) {
365               if (numFaceVertices[f] == meetSize) {
366                 found = PETSC_TRUE;
367                 break;
368               }
369             }
370           }
371           ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
372         }
373         if (found) {
374           adj[off[cell-cStart]+cellOffset] = neighborCells[n];
375           ++cellOffset;
376         }
377       }
378     }
379   }
380   ierr = PetscFree(neighborCells);CHKERRQ(ierr);
381   if (numVertices) *numVertices = numCells;
382   if (offsets)   *offsets   = off;
383   if (adjacency) *adjacency = adj;
384   PetscFunctionReturn(0);
385 }
386 
387 /*@C
388   PetscPartitionerRegister - Adds a new PetscPartitioner implementation
389 
390   Not Collective
391 
392   Input Parameters:
393 + name        - The name of a new user-defined creation routine
394 - create_func - The creation routine itself
395 
396   Notes:
397   PetscPartitionerRegister() may be called multiple times to add several user-defined PetscPartitioners
398 
399   Sample usage:
400 .vb
401     PetscPartitionerRegister("my_part", MyPetscPartitionerCreate);
402 .ve
403 
404   Then, your PetscPartitioner type can be chosen with the procedural interface via
405 .vb
406     PetscPartitionerCreate(MPI_Comm, PetscPartitioner *);
407     PetscPartitionerSetType(PetscPartitioner, "my_part");
408 .ve
409    or at runtime via the option
410 .vb
411     -petscpartitioner_type my_part
412 .ve
413 
414   Level: advanced
415 
416 .keywords: PetscPartitioner, register
417 .seealso: PetscPartitionerRegisterAll(), PetscPartitionerRegisterDestroy()
418 
419 @*/
420 PetscErrorCode PetscPartitionerRegister(const char sname[], PetscErrorCode (*function)(PetscPartitioner))
421 {
422   PetscErrorCode ierr;
423 
424   PetscFunctionBegin;
425   ierr = PetscFunctionListAdd(&PetscPartitionerList, sname, function);CHKERRQ(ierr);
426   PetscFunctionReturn(0);
427 }
428 
429 /*@C
430   PetscPartitionerSetType - Builds a particular PetscPartitioner
431 
432   Collective on PetscPartitioner
433 
434   Input Parameters:
435 + part - The PetscPartitioner object
436 - name - The kind of partitioner
437 
438   Options Database Key:
439 . -petscpartitioner_type <type> - Sets the PetscPartitioner type; use -help for a list of available types
440 
441   Level: intermediate
442 
443 .keywords: PetscPartitioner, set, type
444 .seealso: PetscPartitionerGetType(), PetscPartitionerCreate()
445 @*/
446 PetscErrorCode PetscPartitionerSetType(PetscPartitioner part, PetscPartitionerType name)
447 {
448   PetscErrorCode (*r)(PetscPartitioner);
449   PetscBool      match;
450   PetscErrorCode ierr;
451 
452   PetscFunctionBegin;
453   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
454   ierr = PetscObjectTypeCompare((PetscObject) part, name, &match);CHKERRQ(ierr);
455   if (match) PetscFunctionReturn(0);
456 
457   ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);
458   ierr = PetscFunctionListFind(PetscPartitionerList, name, &r);CHKERRQ(ierr);
459   if (!r) SETERRQ1(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscPartitioner type: %s", name);
460 
461   if (part->ops->destroy) {
462     ierr              = (*part->ops->destroy)(part);CHKERRQ(ierr);
463   }
464   ierr = PetscMemzero(part->ops, sizeof(struct _PetscPartitionerOps));CHKERRQ(ierr);
465   ierr = (*r)(part);CHKERRQ(ierr);
466   ierr = PetscObjectChangeTypeName((PetscObject) part, name);CHKERRQ(ierr);
467   PetscFunctionReturn(0);
468 }
469 
470 /*@C
471   PetscPartitionerGetType - Gets the PetscPartitioner type name (as a string) from the object.
472 
473   Not Collective
474 
475   Input Parameter:
476 . part - The PetscPartitioner
477 
478   Output Parameter:
479 . name - The PetscPartitioner type name
480 
481   Level: intermediate
482 
483 .keywords: PetscPartitioner, get, type, name
484 .seealso: PetscPartitionerSetType(), PetscPartitionerCreate()
485 @*/
486 PetscErrorCode PetscPartitionerGetType(PetscPartitioner part, PetscPartitionerType *name)
487 {
488   PetscErrorCode ierr;
489 
490   PetscFunctionBegin;
491   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
492   PetscValidPointer(name, 2);
493   ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);
494   *name = ((PetscObject) part)->type_name;
495   PetscFunctionReturn(0);
496 }
497 
498 /*@C
499   PetscPartitionerView - Views a PetscPartitioner
500 
501   Collective on PetscPartitioner
502 
503   Input Parameter:
504 + part - the PetscPartitioner object to view
505 - v    - the viewer
506 
507   Level: developer
508 
509 .seealso: PetscPartitionerDestroy()
510 @*/
511 PetscErrorCode PetscPartitionerView(PetscPartitioner part, PetscViewer v)
512 {
513   PetscMPIInt    size;
514   PetscBool      isascii;
515   PetscErrorCode ierr;
516 
517   PetscFunctionBegin;
518   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
519   if (!v) {ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) part), &v);CHKERRQ(ierr);}
520   ierr = PetscObjectTypeCompare((PetscObject) v, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
521   if (isascii) {
522     ierr = MPI_Comm_size(PetscObjectComm((PetscObject) part), &size);CHKERRQ(ierr);
523     ierr = PetscViewerASCIIPrintf(v, "Graph Partitioner: %d MPI Process%s\n", size, size > 1 ? "es" : "");CHKERRQ(ierr);
524     ierr = PetscViewerASCIIPrintf(v, "  type: %s\n", part->hdr.type_name);CHKERRQ(ierr);
525     ierr = PetscViewerASCIIPushTab(v);CHKERRQ(ierr);
526     ierr = PetscViewerASCIIPrintf(v, "edge cut: %D\n", part->edgeCut);CHKERRQ(ierr);
527     ierr = PetscViewerASCIIPrintf(v, "balance:  %.2g\n", part->balance);CHKERRQ(ierr);
528     ierr = PetscViewerASCIIPopTab(v);CHKERRQ(ierr);
529   }
530   if (part->ops->view) {ierr = (*part->ops->view)(part, v);CHKERRQ(ierr);}
531   PetscFunctionReturn(0);
532 }
533 
534 static PetscErrorCode PetscPartitionerGetDefaultType(const char *currentType, const char **defaultType)
535 {
536   PetscFunctionBegin;
537   if (!currentType) {
538 #if defined(PETSC_HAVE_CHACO)
539     *defaultType = PETSCPARTITIONERCHACO;
540 #elif defined(PETSC_HAVE_PARMETIS)
541     *defaultType = PETSCPARTITIONERPARMETIS;
542 #elif defined(PETSC_HAVE_PTSCOTCH)
543     *defaultType = PETSCPARTITIONERPTSCOTCH;
544 #else
545     *defaultType = PETSCPARTITIONERSIMPLE;
546 #endif
547   } else {
548     *defaultType = currentType;
549   }
550   PetscFunctionReturn(0);
551 }
552 
553 /*@
554   PetscPartitionerSetFromOptions - sets parameters in a PetscPartitioner from the options database
555 
556   Collective on PetscPartitioner
557 
558   Input Parameter:
559 . part - the PetscPartitioner object to set options for
560 
561   Level: developer
562 
563 .seealso: PetscPartitionerView()
564 @*/
565 PetscErrorCode PetscPartitionerSetFromOptions(PetscPartitioner part)
566 {
567   const char    *defaultType;
568   char           name[256];
569   PetscBool      flg;
570   PetscErrorCode ierr;
571 
572   PetscFunctionBegin;
573   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
574   ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);
575   ierr = PetscPartitionerGetDefaultType(((PetscObject) part)->type_name,&defaultType);CHKERRQ(ierr);
576   ierr = PetscObjectOptionsBegin((PetscObject) part);CHKERRQ(ierr);
577   ierr = PetscOptionsFList("-petscpartitioner_type", "Graph partitioner", "PetscPartitionerSetType", PetscPartitionerList, defaultType, name, sizeof(name), &flg);CHKERRQ(ierr);
578   if (flg) {
579     ierr = PetscPartitionerSetType(part, name);CHKERRQ(ierr);
580   } else if (!((PetscObject) part)->type_name) {
581     ierr = PetscPartitionerSetType(part, defaultType);CHKERRQ(ierr);
582   }
583   if (part->ops->setfromoptions) {
584     ierr = (*part->ops->setfromoptions)(PetscOptionsObject,part);CHKERRQ(ierr);
585   }
586   ierr = PetscOptionsGetViewer(((PetscObject) part)->comm, ((PetscObject) part)->options, ((PetscObject) part)->prefix, "-petscpartitioner_view_graph", &part->viewerGraph, &part->formatGraph, &part->viewGraph);CHKERRQ(ierr);
587   /* process any options handlers added with PetscObjectAddOptionsHandler() */
588   ierr = PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject) part);CHKERRQ(ierr);
589   ierr = PetscOptionsEnd();CHKERRQ(ierr);
590   PetscFunctionReturn(0);
591 }
592 
593 /*@C
594   PetscPartitionerSetUp - Construct data structures for the PetscPartitioner
595 
596   Collective on PetscPartitioner
597 
598   Input Parameter:
599 . part - the PetscPartitioner object to setup
600 
601   Level: developer
602 
603 .seealso: PetscPartitionerView(), PetscPartitionerDestroy()
604 @*/
605 PetscErrorCode PetscPartitionerSetUp(PetscPartitioner part)
606 {
607   PetscErrorCode ierr;
608 
609   PetscFunctionBegin;
610   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
611   if (part->ops->setup) {ierr = (*part->ops->setup)(part);CHKERRQ(ierr);}
612   PetscFunctionReturn(0);
613 }
614 
615 /*@
616   PetscPartitionerDestroy - Destroys a PetscPartitioner object
617 
618   Collective on PetscPartitioner
619 
620   Input Parameter:
621 . part - the PetscPartitioner object to destroy
622 
623   Level: developer
624 
625 .seealso: PetscPartitionerView()
626 @*/
627 PetscErrorCode PetscPartitionerDestroy(PetscPartitioner *part)
628 {
629   PetscErrorCode ierr;
630 
631   PetscFunctionBegin;
632   if (!*part) PetscFunctionReturn(0);
633   PetscValidHeaderSpecific((*part), PETSCPARTITIONER_CLASSID, 1);
634 
635   if (--((PetscObject)(*part))->refct > 0) {*part = 0; PetscFunctionReturn(0);}
636   ((PetscObject) (*part))->refct = 0;
637 
638   ierr = PetscViewerDestroy(&(*part)->viewerGraph);CHKERRQ(ierr);
639   if ((*part)->ops->destroy) {ierr = (*(*part)->ops->destroy)(*part);CHKERRQ(ierr);}
640   ierr = PetscHeaderDestroy(part);CHKERRQ(ierr);
641   PetscFunctionReturn(0);
642 }
643 
644 /*@
645   PetscPartitionerCreate - Creates an empty PetscPartitioner object. The type can then be set with PetscPartitionerSetType().
646 
647   Collective on MPI_Comm
648 
649   Input Parameter:
650 . comm - The communicator for the PetscPartitioner object
651 
652   Output Parameter:
653 . part - The PetscPartitioner object
654 
655   Level: beginner
656 
657 .seealso: PetscPartitionerSetType(), PETSCPARTITIONERCHACO, PETSCPARTITIONERPARMETIS, PETSCPARTITIONERSHELL, PETSCPARTITIONERSIMPLE, PETSCPARTITIONERGATHER
658 @*/
659 PetscErrorCode PetscPartitionerCreate(MPI_Comm comm, PetscPartitioner *part)
660 {
661   PetscPartitioner p;
662   const char       *partitionerType = NULL;
663   PetscErrorCode   ierr;
664 
665   PetscFunctionBegin;
666   PetscValidPointer(part, 2);
667   *part = NULL;
668   ierr = DMInitializePackage();CHKERRQ(ierr);
669 
670   ierr = PetscHeaderCreate(p, PETSCPARTITIONER_CLASSID, "PetscPartitioner", "Graph Partitioner", "PetscPartitioner", comm, PetscPartitionerDestroy, PetscPartitionerView);CHKERRQ(ierr);
671   ierr = PetscPartitionerGetDefaultType(NULL,&partitionerType);CHKERRQ(ierr);
672   ierr = PetscPartitionerSetType(p,partitionerType);CHKERRQ(ierr);
673 
674   p->edgeCut = 0;
675   p->balance = 0.0;
676 
677   *part = p;
678   PetscFunctionReturn(0);
679 }
680 
681 /*@
682   PetscPartitionerPartition - Create a non-overlapping partition of the cells in the mesh
683 
684   Collective on DM
685 
686   Input Parameters:
687 + part    - The PetscPartitioner
688 - dm      - The mesh DM
689 
690   Output Parameters:
691 + partSection     - The PetscSection giving the division of points by partition
692 - partition       - The list of points by partition
693 
694   Options Database:
695 . -petscpartitioner_view_graph - View the graph we are partitioning
696 
697   Note: Instead of cells, points at a given height can be partitioned by calling PetscPartitionerSetPointHeight()
698 
699   Level: developer
700 
701 .seealso DMPlexDistribute(), PetscPartitionerSetPointHeight(), PetscPartitionerCreate()
702 @*/
703 PetscErrorCode PetscPartitionerPartition(PetscPartitioner part, DM dm, PetscSection partSection, IS *partition)
704 {
705   PetscMPIInt    size;
706   PetscErrorCode ierr;
707 
708   PetscFunctionBegin;
709   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
710   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
711   PetscValidHeaderSpecific(partSection, PETSC_SECTION_CLASSID, 4);
712   PetscValidPointer(partition, 5);
713   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) part), &size);CHKERRQ(ierr);
714   if (size == 1) {
715     PetscInt *points;
716     PetscInt  cStart, cEnd, c;
717 
718     ierr = DMPlexGetHeightStratum(dm, part->height, &cStart, &cEnd);CHKERRQ(ierr);
719     ierr = PetscSectionSetChart(partSection, 0, size);CHKERRQ(ierr);
720     ierr = PetscSectionSetDof(partSection, 0, cEnd-cStart);CHKERRQ(ierr);
721     ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
722     ierr = PetscMalloc1(cEnd-cStart, &points);CHKERRQ(ierr);
723     for (c = cStart; c < cEnd; ++c) points[c] = c;
724     ierr = ISCreateGeneral(PetscObjectComm((PetscObject) part), cEnd-cStart, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
725     PetscFunctionReturn(0);
726   }
727   if (part->height == 0) {
728     PetscInt numVertices;
729     PetscInt *start     = NULL;
730     PetscInt *adjacency = NULL;
731     IS       globalNumbering;
732 
733     ierr = DMPlexCreatePartitionerGraph(dm, 0, &numVertices, &start, &adjacency, &globalNumbering);CHKERRQ(ierr);
734     if (part->viewGraph) {
735       PetscViewer viewer = part->viewerGraph;
736       PetscBool   isascii;
737       PetscInt    v, i;
738       PetscMPIInt rank;
739 
740       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) viewer), &rank);CHKERRQ(ierr);
741       ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
742       if (isascii) {
743         ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
744         ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%d]Nv: %D\n", rank, numVertices);CHKERRQ(ierr);
745         for (v = 0; v < numVertices; ++v) {
746           const PetscInt s = start[v];
747           const PetscInt e = start[v+1];
748 
749           ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%d]  ", rank);CHKERRQ(ierr);
750           for (i = s; i < e; ++i) {ierr = PetscViewerASCIISynchronizedPrintf(viewer, "%D ", adjacency[i]);CHKERRQ(ierr);}
751           ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%D-%D)\n", s, e);CHKERRQ(ierr);
752         }
753         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
754         ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
755       }
756     }
757     if (!part->ops->partition) SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_WRONGSTATE, "PetscPartitioner has no type");
758     ierr = (*part->ops->partition)(part, dm, size, numVertices, start, adjacency, partSection, partition);CHKERRQ(ierr);
759     ierr = PetscFree(start);CHKERRQ(ierr);
760     ierr = PetscFree(adjacency);CHKERRQ(ierr);
761     if (globalNumbering) { /* partition is wrt global unique numbering: change this to be wrt local numbering */
762       const PetscInt *globalNum;
763       const PetscInt *partIdx;
764       PetscInt *map, cStart, cEnd;
765       PetscInt *adjusted, i, localSize, offset;
766       IS    newPartition;
767 
768       ierr = ISGetLocalSize(*partition,&localSize);CHKERRQ(ierr);
769       ierr = PetscMalloc1(localSize,&adjusted);CHKERRQ(ierr);
770       ierr = ISGetIndices(globalNumbering,&globalNum);CHKERRQ(ierr);
771       ierr = ISGetIndices(*partition,&partIdx);CHKERRQ(ierr);
772       ierr = PetscMalloc1(localSize,&map);CHKERRQ(ierr);
773       ierr = DMPlexGetHeightStratum(dm, part->height, &cStart, &cEnd);CHKERRQ(ierr);
774       for (i = cStart, offset = 0; i < cEnd; i++) {
775         if (globalNum[i - cStart] >= 0) map[offset++] = i;
776       }
777       for (i = 0; i < localSize; i++) {
778         adjusted[i] = map[partIdx[i]];
779       }
780       ierr = PetscFree(map);CHKERRQ(ierr);
781       ierr = ISRestoreIndices(*partition,&partIdx);CHKERRQ(ierr);
782       ierr = ISRestoreIndices(globalNumbering,&globalNum);CHKERRQ(ierr);
783       ierr = ISCreateGeneral(PETSC_COMM_SELF,localSize,adjusted,PETSC_OWN_POINTER,&newPartition);CHKERRQ(ierr);
784       ierr = ISDestroy(&globalNumbering);CHKERRQ(ierr);
785       ierr = ISDestroy(partition);CHKERRQ(ierr);
786       *partition = newPartition;
787     }
788   } else SETERRQ1(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_OUTOFRANGE, "Invalid height %D for points to partition", part->height);
789   ierr = PetscPartitionerViewFromOptions(part, NULL, "-petscpartitioner_view");CHKERRQ(ierr);
790   PetscFunctionReturn(0);
791 }
792 
793 static PetscErrorCode PetscPartitionerDestroy_Shell(PetscPartitioner part)
794 {
795   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
796   PetscErrorCode          ierr;
797 
798   PetscFunctionBegin;
799   ierr = PetscSectionDestroy(&p->section);CHKERRQ(ierr);
800   ierr = ISDestroy(&p->partition);CHKERRQ(ierr);
801   ierr = PetscFree(p);CHKERRQ(ierr);
802   PetscFunctionReturn(0);
803 }
804 
805 static PetscErrorCode PetscPartitionerView_Shell_Ascii(PetscPartitioner part, PetscViewer viewer)
806 {
807   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
808   PetscErrorCode          ierr;
809 
810   PetscFunctionBegin;
811   if (p->random) {
812     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
813     ierr = PetscViewerASCIIPrintf(viewer, "using random partition\n");CHKERRQ(ierr);
814     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
815   }
816   PetscFunctionReturn(0);
817 }
818 
819 static PetscErrorCode PetscPartitionerView_Shell(PetscPartitioner part, PetscViewer viewer)
820 {
821   PetscBool      iascii;
822   PetscErrorCode ierr;
823 
824   PetscFunctionBegin;
825   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
826   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
827   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
828   if (iascii) {ierr = PetscPartitionerView_Shell_Ascii(part, viewer);CHKERRQ(ierr);}
829   PetscFunctionReturn(0);
830 }
831 
832 static PetscErrorCode PetscPartitionerSetFromOptions_Shell(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
833 {
834   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
835   PetscErrorCode          ierr;
836 
837   PetscFunctionBegin;
838   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner Shell Options");CHKERRQ(ierr);
839   ierr = PetscOptionsBool("-petscpartitioner_shell_random", "Use a random partition", "PetscPartitionerView", PETSC_FALSE, &p->random, NULL);CHKERRQ(ierr);
840   ierr = PetscOptionsTail();CHKERRQ(ierr);
841   PetscFunctionReturn(0);
842 }
843 
844 static PetscErrorCode PetscPartitionerPartition_Shell(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
845 {
846   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
847   PetscInt                np;
848   PetscErrorCode          ierr;
849 
850   PetscFunctionBegin;
851   if (p->random) {
852     PetscRandom r;
853     PetscInt   *sizes, *points, v, p;
854     PetscMPIInt rank;
855 
856     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
857     ierr = PetscRandomCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
858     ierr = PetscRandomSetInterval(r, 0.0, (PetscScalar) nparts);CHKERRQ(ierr);
859     ierr = PetscRandomSetFromOptions(r);CHKERRQ(ierr);
860     ierr = PetscCalloc2(nparts, &sizes, numVertices, &points);CHKERRQ(ierr);
861     for (v = 0; v < numVertices; ++v) {points[v] = v;}
862     for (p = 0; p < nparts; ++p) {sizes[p] = numVertices/nparts + (PetscInt) (p < numVertices % nparts);}
863     for (v = numVertices-1; v > 0; --v) {
864       PetscReal val;
865       PetscInt  w, tmp;
866 
867       ierr = PetscRandomSetInterval(r, 0.0, (PetscScalar) (v+1));CHKERRQ(ierr);
868       ierr = PetscRandomGetValueReal(r, &val);CHKERRQ(ierr);
869       w    = PetscFloorReal(val);
870       tmp       = points[v];
871       points[v] = points[w];
872       points[w] = tmp;
873     }
874     ierr = PetscRandomDestroy(&r);CHKERRQ(ierr);
875     ierr = PetscPartitionerShellSetPartition(part, nparts, sizes, points);CHKERRQ(ierr);
876     ierr = PetscFree2(sizes, points);CHKERRQ(ierr);
877   }
878   if (!p->section) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Shell partitioner information not provided. Please call PetscPartitionerShellSetPartition()");
879   ierr = PetscSectionGetChart(p->section, NULL, &np);CHKERRQ(ierr);
880   if (nparts != np) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of requested partitions %d != configured partitions %d", nparts, np);
881   ierr = ISGetLocalSize(p->partition, &np);CHKERRQ(ierr);
882   if (numVertices != np) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of input vertices %d != configured vertices %d", numVertices, np);
883   ierr = PetscSectionCopy(p->section, partSection);CHKERRQ(ierr);
884   *partition = p->partition;
885   ierr = PetscObjectReference((PetscObject) p->partition);CHKERRQ(ierr);
886   PetscFunctionReturn(0);
887 }
888 
889 static PetscErrorCode PetscPartitionerInitialize_Shell(PetscPartitioner part)
890 {
891   PetscFunctionBegin;
892   part->ops->view           = PetscPartitionerView_Shell;
893   part->ops->setfromoptions = PetscPartitionerSetFromOptions_Shell;
894   part->ops->destroy        = PetscPartitionerDestroy_Shell;
895   part->ops->partition      = PetscPartitionerPartition_Shell;
896   PetscFunctionReturn(0);
897 }
898 
899 /*MC
900   PETSCPARTITIONERSHELL = "shell" - A PetscPartitioner object
901 
902   Level: intermediate
903 
904 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
905 M*/
906 
907 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Shell(PetscPartitioner part)
908 {
909   PetscPartitioner_Shell *p;
910   PetscErrorCode          ierr;
911 
912   PetscFunctionBegin;
913   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
914   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
915   part->data = p;
916 
917   ierr = PetscPartitionerInitialize_Shell(part);CHKERRQ(ierr);
918   p->random = PETSC_FALSE;
919   PetscFunctionReturn(0);
920 }
921 
922 /*@C
923   PetscPartitionerShellSetPartition - Set an artifical partition for a mesh
924 
925   Collective on Part
926 
927   Input Parameters:
928 + part     - The PetscPartitioner
929 . size - The number of partitions
930 . sizes    - array of size size (or NULL) providing the number of points in each partition
931 - points   - array of size sum(sizes) (may be NULL iff sizes is NULL), a permutation of the points that groups those assigned to each partition in order (i.e., partition 0 first, partition 1 next, etc.)
932 
933   Level: developer
934 
935   Notes:
936 
937     It is safe to free the sizes and points arrays after use in this routine.
938 
939 .seealso DMPlexDistribute(), PetscPartitionerCreate()
940 @*/
941 PetscErrorCode PetscPartitionerShellSetPartition(PetscPartitioner part, PetscInt size, const PetscInt sizes[], const PetscInt points[])
942 {
943   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
944   PetscInt                proc, numPoints;
945   PetscErrorCode          ierr;
946 
947   PetscFunctionBegin;
948   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
949   if (sizes)  {PetscValidPointer(sizes, 3);}
950   if (points) {PetscValidPointer(points, 4);}
951   ierr = PetscSectionDestroy(&p->section);CHKERRQ(ierr);
952   ierr = ISDestroy(&p->partition);CHKERRQ(ierr);
953   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) part), &p->section);CHKERRQ(ierr);
954   ierr = PetscSectionSetChart(p->section, 0, size);CHKERRQ(ierr);
955   if (sizes) {
956     for (proc = 0; proc < size; ++proc) {
957       ierr = PetscSectionSetDof(p->section, proc, sizes[proc]);CHKERRQ(ierr);
958     }
959   }
960   ierr = PetscSectionSetUp(p->section);CHKERRQ(ierr);
961   ierr = PetscSectionGetStorageSize(p->section, &numPoints);CHKERRQ(ierr);
962   ierr = ISCreateGeneral(PetscObjectComm((PetscObject) part), numPoints, points, PETSC_COPY_VALUES, &p->partition);CHKERRQ(ierr);
963   PetscFunctionReturn(0);
964 }
965 
966 /*@
967   PetscPartitionerShellSetRandom - Set the flag to use a random partition
968 
969   Collective on Part
970 
971   Input Parameters:
972 + part   - The PetscPartitioner
973 - random - The flag to use a random partition
974 
975   Level: intermediate
976 
977 .seealso PetscPartitionerShellGetRandom(), PetscPartitionerCreate()
978 @*/
979 PetscErrorCode PetscPartitionerShellSetRandom(PetscPartitioner part, PetscBool random)
980 {
981   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
982 
983   PetscFunctionBegin;
984   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
985   p->random = random;
986   PetscFunctionReturn(0);
987 }
988 
989 /*@
990   PetscPartitionerShellGetRandom - get the flag to use a random partition
991 
992   Collective on Part
993 
994   Input Parameter:
995 . part   - The PetscPartitioner
996 
997   Output Parameter
998 . random - The flag to use a random partition
999 
1000   Level: intermediate
1001 
1002 .seealso PetscPartitionerShellSetRandom(), PetscPartitionerCreate()
1003 @*/
1004 PetscErrorCode PetscPartitionerShellGetRandom(PetscPartitioner part, PetscBool *random)
1005 {
1006   PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
1007 
1008   PetscFunctionBegin;
1009   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1010   PetscValidPointer(random, 2);
1011   *random = p->random;
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 static PetscErrorCode PetscPartitionerDestroy_Simple(PetscPartitioner part)
1016 {
1017   PetscPartitioner_Simple *p = (PetscPartitioner_Simple *) part->data;
1018   PetscErrorCode          ierr;
1019 
1020   PetscFunctionBegin;
1021   ierr = PetscFree(p);CHKERRQ(ierr);
1022   PetscFunctionReturn(0);
1023 }
1024 
1025 static PetscErrorCode PetscPartitionerView_Simple_Ascii(PetscPartitioner part, PetscViewer viewer)
1026 {
1027   PetscFunctionBegin;
1028   PetscFunctionReturn(0);
1029 }
1030 
1031 static PetscErrorCode PetscPartitionerView_Simple(PetscPartitioner part, PetscViewer viewer)
1032 {
1033   PetscBool      iascii;
1034   PetscErrorCode ierr;
1035 
1036   PetscFunctionBegin;
1037   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1038   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1039   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1040   if (iascii) {ierr = PetscPartitionerView_Simple_Ascii(part, viewer);CHKERRQ(ierr);}
1041   PetscFunctionReturn(0);
1042 }
1043 
1044 static PetscErrorCode PetscPartitionerPartition_Simple(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1045 {
1046   MPI_Comm       comm;
1047   PetscInt       np;
1048   PetscMPIInt    size;
1049   PetscErrorCode ierr;
1050 
1051   PetscFunctionBegin;
1052   comm = PetscObjectComm((PetscObject)part);
1053   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1054   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1055   ierr = ISCreateStride(PETSC_COMM_SELF, numVertices, 0, 1, partition);CHKERRQ(ierr);
1056   if (size == 1) {
1057     for (np = 0; np < nparts; ++np) {ierr = PetscSectionSetDof(partSection, np, numVertices/nparts + ((numVertices % nparts) > np));CHKERRQ(ierr);}
1058   } else {
1059     PetscMPIInt rank;
1060     PetscInt nvGlobal, *offsets, myFirst, myLast;
1061 
1062     ierr = PetscMalloc1(size+1,&offsets);CHKERRQ(ierr);
1063     offsets[0] = 0;
1064     ierr = MPI_Allgather(&numVertices,1,MPIU_INT,&offsets[1],1,MPIU_INT,comm);CHKERRQ(ierr);
1065     for (np = 2; np <= size; np++) {
1066       offsets[np] += offsets[np-1];
1067     }
1068     nvGlobal = offsets[size];
1069     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1070     myFirst = offsets[rank];
1071     myLast  = offsets[rank + 1] - 1;
1072     ierr = PetscFree(offsets);CHKERRQ(ierr);
1073     if (numVertices) {
1074       PetscInt firstPart = 0, firstLargePart = 0;
1075       PetscInt lastPart = 0, lastLargePart = 0;
1076       PetscInt rem = nvGlobal % nparts;
1077       PetscInt pSmall = nvGlobal/nparts;
1078       PetscInt pBig = nvGlobal/nparts + 1;
1079 
1080 
1081       if (rem) {
1082         firstLargePart = myFirst / pBig;
1083         lastLargePart  = myLast  / pBig;
1084 
1085         if (firstLargePart < rem) {
1086           firstPart = firstLargePart;
1087         } else {
1088           firstPart = rem + (myFirst - (rem * pBig)) / pSmall;
1089         }
1090         if (lastLargePart < rem) {
1091           lastPart = lastLargePart;
1092         } else {
1093           lastPart = rem + (myLast - (rem * pBig)) / pSmall;
1094         }
1095       } else {
1096         firstPart = myFirst / (nvGlobal/nparts);
1097         lastPart  = myLast  / (nvGlobal/nparts);
1098       }
1099 
1100       for (np = firstPart; np <= lastPart; np++) {
1101         PetscInt PartStart =  np    * (nvGlobal/nparts) + PetscMin(nvGlobal % nparts,np);
1102         PetscInt PartEnd   = (np+1) * (nvGlobal/nparts) + PetscMin(nvGlobal % nparts,np+1);
1103 
1104         PartStart = PetscMax(PartStart,myFirst);
1105         PartEnd   = PetscMin(PartEnd,myLast+1);
1106         ierr = PetscSectionSetDof(partSection,np,PartEnd-PartStart);CHKERRQ(ierr);
1107       }
1108     }
1109   }
1110   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1111   PetscFunctionReturn(0);
1112 }
1113 
1114 static PetscErrorCode PetscPartitionerInitialize_Simple(PetscPartitioner part)
1115 {
1116   PetscFunctionBegin;
1117   part->ops->view      = PetscPartitionerView_Simple;
1118   part->ops->destroy   = PetscPartitionerDestroy_Simple;
1119   part->ops->partition = PetscPartitionerPartition_Simple;
1120   PetscFunctionReturn(0);
1121 }
1122 
1123 /*MC
1124   PETSCPARTITIONERSIMPLE = "simple" - A PetscPartitioner object
1125 
1126   Level: intermediate
1127 
1128 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1129 M*/
1130 
1131 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Simple(PetscPartitioner part)
1132 {
1133   PetscPartitioner_Simple *p;
1134   PetscErrorCode           ierr;
1135 
1136   PetscFunctionBegin;
1137   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1138   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1139   part->data = p;
1140 
1141   ierr = PetscPartitionerInitialize_Simple(part);CHKERRQ(ierr);
1142   PetscFunctionReturn(0);
1143 }
1144 
1145 static PetscErrorCode PetscPartitionerDestroy_Gather(PetscPartitioner part)
1146 {
1147   PetscPartitioner_Gather *p = (PetscPartitioner_Gather *) part->data;
1148   PetscErrorCode          ierr;
1149 
1150   PetscFunctionBegin;
1151   ierr = PetscFree(p);CHKERRQ(ierr);
1152   PetscFunctionReturn(0);
1153 }
1154 
1155 static PetscErrorCode PetscPartitionerView_Gather_Ascii(PetscPartitioner part, PetscViewer viewer)
1156 {
1157   PetscFunctionBegin;
1158   PetscFunctionReturn(0);
1159 }
1160 
1161 static PetscErrorCode PetscPartitionerView_Gather(PetscPartitioner part, PetscViewer viewer)
1162 {
1163   PetscBool      iascii;
1164   PetscErrorCode ierr;
1165 
1166   PetscFunctionBegin;
1167   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1168   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1169   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1170   if (iascii) {ierr = PetscPartitionerView_Gather_Ascii(part, viewer);CHKERRQ(ierr);}
1171   PetscFunctionReturn(0);
1172 }
1173 
1174 static PetscErrorCode PetscPartitionerPartition_Gather(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1175 {
1176   PetscInt       np;
1177   PetscErrorCode ierr;
1178 
1179   PetscFunctionBegin;
1180   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1181   ierr = ISCreateStride(PETSC_COMM_SELF, numVertices, 0, 1, partition);CHKERRQ(ierr);
1182   ierr = PetscSectionSetDof(partSection,0,numVertices);CHKERRQ(ierr);
1183   for (np = 1; np < nparts; ++np) {ierr = PetscSectionSetDof(partSection, np, 0);CHKERRQ(ierr);}
1184   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1185   PetscFunctionReturn(0);
1186 }
1187 
1188 static PetscErrorCode PetscPartitionerInitialize_Gather(PetscPartitioner part)
1189 {
1190   PetscFunctionBegin;
1191   part->ops->view      = PetscPartitionerView_Gather;
1192   part->ops->destroy   = PetscPartitionerDestroy_Gather;
1193   part->ops->partition = PetscPartitionerPartition_Gather;
1194   PetscFunctionReturn(0);
1195 }
1196 
1197 /*MC
1198   PETSCPARTITIONERGATHER = "gather" - A PetscPartitioner object
1199 
1200   Level: intermediate
1201 
1202 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1203 M*/
1204 
1205 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Gather(PetscPartitioner part)
1206 {
1207   PetscPartitioner_Gather *p;
1208   PetscErrorCode           ierr;
1209 
1210   PetscFunctionBegin;
1211   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1212   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1213   part->data = p;
1214 
1215   ierr = PetscPartitionerInitialize_Gather(part);CHKERRQ(ierr);
1216   PetscFunctionReturn(0);
1217 }
1218 
1219 
1220 static PetscErrorCode PetscPartitionerDestroy_Chaco(PetscPartitioner part)
1221 {
1222   PetscPartitioner_Chaco *p = (PetscPartitioner_Chaco *) part->data;
1223   PetscErrorCode          ierr;
1224 
1225   PetscFunctionBegin;
1226   ierr = PetscFree(p);CHKERRQ(ierr);
1227   PetscFunctionReturn(0);
1228 }
1229 
1230 static PetscErrorCode PetscPartitionerView_Chaco_Ascii(PetscPartitioner part, PetscViewer viewer)
1231 {
1232   PetscFunctionBegin;
1233   PetscFunctionReturn(0);
1234 }
1235 
1236 static PetscErrorCode PetscPartitionerView_Chaco(PetscPartitioner part, PetscViewer viewer)
1237 {
1238   PetscBool      iascii;
1239   PetscErrorCode ierr;
1240 
1241   PetscFunctionBegin;
1242   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1243   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1244   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1245   if (iascii) {ierr = PetscPartitionerView_Chaco_Ascii(part, viewer);CHKERRQ(ierr);}
1246   PetscFunctionReturn(0);
1247 }
1248 
1249 #if defined(PETSC_HAVE_CHACO)
1250 #if defined(PETSC_HAVE_UNISTD_H)
1251 #include <unistd.h>
1252 #endif
1253 #if defined(PETSC_HAVE_CHACO_INT_ASSIGNMENT)
1254 #include <chaco.h>
1255 #else
1256 /* Older versions of Chaco do not have an include file */
1257 PETSC_EXTERN int interface(int nvtxs, int *start, int *adjacency, int *vwgts,
1258                        float *ewgts, float *x, float *y, float *z, char *outassignname,
1259                        char *outfilename, short *assignment, int architecture, int ndims_tot,
1260                        int mesh_dims[3], double *goal, int global_method, int local_method,
1261                        int rqi_flag, int vmax, int ndims, double eigtol, long seed);
1262 #endif
1263 extern int FREE_GRAPH;
1264 #endif
1265 
1266 static PetscErrorCode PetscPartitionerPartition_Chaco(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1267 {
1268 #if defined(PETSC_HAVE_CHACO)
1269   enum {DEFAULT_METHOD = 1, INERTIAL_METHOD = 3};
1270   MPI_Comm       comm;
1271   int            nvtxs          = numVertices; /* number of vertices in full graph */
1272   int           *vwgts          = NULL;   /* weights for all vertices */
1273   float         *ewgts          = NULL;   /* weights for all edges */
1274   float         *x              = NULL, *y = NULL, *z = NULL; /* coordinates for inertial method */
1275   char          *outassignname  = NULL;   /*  name of assignment output file */
1276   char          *outfilename    = NULL;   /* output file name */
1277   int            architecture   = 1;      /* 0 => hypercube, d => d-dimensional mesh */
1278   int            ndims_tot      = 0;      /* total number of cube dimensions to divide */
1279   int            mesh_dims[3];            /* dimensions of mesh of processors */
1280   double        *goal          = NULL;    /* desired set sizes for each set */
1281   int            global_method = 1;       /* global partitioning algorithm */
1282   int            local_method  = 1;       /* local partitioning algorithm */
1283   int            rqi_flag      = 0;       /* should I use RQI/Symmlq eigensolver? */
1284   int            vmax          = 200;     /* how many vertices to coarsen down to? */
1285   int            ndims         = 1;       /* number of eigenvectors (2^d sets) */
1286   double         eigtol        = 0.001;   /* tolerance on eigenvectors */
1287   long           seed          = 123636512; /* for random graph mutations */
1288 #if defined(PETSC_HAVE_CHACO_INT_ASSIGNMENT)
1289   int           *assignment;              /* Output partition */
1290 #else
1291   short int     *assignment;              /* Output partition */
1292 #endif
1293   int            fd_stdout, fd_pipe[2];
1294   PetscInt      *points;
1295   int            i, v, p;
1296   PetscErrorCode ierr;
1297 
1298   PetscFunctionBegin;
1299   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
1300 #if defined (PETSC_USE_DEBUG)
1301   {
1302     int ival,isum;
1303     PetscBool distributed;
1304 
1305     ival = (numVertices > 0);
1306     ierr = MPI_Allreduce(&ival, &isum, 1, MPI_INT, MPI_SUM, comm);CHKERRQ(ierr);
1307     distributed = (isum > 1) ? PETSC_TRUE : PETSC_FALSE;
1308     if (distributed) SETERRQ(comm, PETSC_ERR_SUP, "Chaco cannot partition a distributed graph");
1309   }
1310 #endif
1311   if (!numVertices) {
1312     ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1313     ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1314     ierr = ISCreateGeneral(comm, 0, NULL, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1315     PetscFunctionReturn(0);
1316   }
1317   FREE_GRAPH = 0;                         /* Do not let Chaco free my memory */
1318   for (i = 0; i < start[numVertices]; ++i) ++adjacency[i];
1319 
1320   if (global_method == INERTIAL_METHOD) {
1321     /* manager.createCellCoordinates(nvtxs, &x, &y, &z); */
1322     SETERRQ(comm, PETSC_ERR_SUP, "Inertial partitioning not yet supported");
1323   }
1324   mesh_dims[0] = nparts;
1325   mesh_dims[1] = 1;
1326   mesh_dims[2] = 1;
1327   ierr = PetscMalloc1(nvtxs, &assignment);CHKERRQ(ierr);
1328   /* Chaco outputs to stdout. We redirect this to a buffer. */
1329   /* TODO: check error codes for UNIX calls */
1330 #if defined(PETSC_HAVE_UNISTD_H)
1331   {
1332     int piperet;
1333     piperet = pipe(fd_pipe);
1334     if (piperet) SETERRQ(comm,PETSC_ERR_SYS,"Could not create pipe");
1335     fd_stdout = dup(1);
1336     close(1);
1337     dup2(fd_pipe[1], 1);
1338   }
1339 #endif
1340   ierr = interface(nvtxs, (int*) start, (int*) adjacency, vwgts, ewgts, x, y, z, outassignname, outfilename,
1341                    assignment, architecture, ndims_tot, mesh_dims, goal, global_method, local_method, rqi_flag,
1342                    vmax, ndims, eigtol, seed);
1343 #if defined(PETSC_HAVE_UNISTD_H)
1344   {
1345     char msgLog[10000];
1346     int  count;
1347 
1348     fflush(stdout);
1349     count = read(fd_pipe[0], msgLog, (10000-1)*sizeof(char));
1350     if (count < 0) count = 0;
1351     msgLog[count] = 0;
1352     close(1);
1353     dup2(fd_stdout, 1);
1354     close(fd_stdout);
1355     close(fd_pipe[0]);
1356     close(fd_pipe[1]);
1357     if (ierr) SETERRQ1(comm, PETSC_ERR_LIB, "Error in Chaco library: %s", msgLog);
1358   }
1359 #else
1360   if (ierr) SETERRQ1(comm, PETSC_ERR_LIB, "Error in Chaco library: %s", "error in stdout");
1361 #endif
1362   /* Convert to PetscSection+IS */
1363   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1364   for (v = 0; v < nvtxs; ++v) {
1365     ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);
1366   }
1367   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1368   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1369   for (p = 0, i = 0; p < nparts; ++p) {
1370     for (v = 0; v < nvtxs; ++v) {
1371       if (assignment[v] == p) points[i++] = v;
1372     }
1373   }
1374   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1375   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1376   if (global_method == INERTIAL_METHOD) {
1377     /* manager.destroyCellCoordinates(nvtxs, &x, &y, &z); */
1378   }
1379   ierr = PetscFree(assignment);CHKERRQ(ierr);
1380   for (i = 0; i < start[numVertices]; ++i) --adjacency[i];
1381   PetscFunctionReturn(0);
1382 #else
1383   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-chaco.");
1384 #endif
1385 }
1386 
1387 static PetscErrorCode PetscPartitionerInitialize_Chaco(PetscPartitioner part)
1388 {
1389   PetscFunctionBegin;
1390   part->ops->view      = PetscPartitionerView_Chaco;
1391   part->ops->destroy   = PetscPartitionerDestroy_Chaco;
1392   part->ops->partition = PetscPartitionerPartition_Chaco;
1393   PetscFunctionReturn(0);
1394 }
1395 
1396 /*MC
1397   PETSCPARTITIONERCHACO = "chaco" - A PetscPartitioner object using the Chaco library
1398 
1399   Level: intermediate
1400 
1401 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1402 M*/
1403 
1404 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Chaco(PetscPartitioner part)
1405 {
1406   PetscPartitioner_Chaco *p;
1407   PetscErrorCode          ierr;
1408 
1409   PetscFunctionBegin;
1410   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1411   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1412   part->data = p;
1413 
1414   ierr = PetscPartitionerInitialize_Chaco(part);CHKERRQ(ierr);
1415   ierr = PetscCitationsRegister(ChacoPartitionerCitation, &ChacoPartitionercite);CHKERRQ(ierr);
1416   PetscFunctionReturn(0);
1417 }
1418 
1419 static const char *ptypes[] = {"kway", "rb"};
1420 
1421 static PetscErrorCode PetscPartitionerDestroy_ParMetis(PetscPartitioner part)
1422 {
1423   PetscPartitioner_ParMetis *p = (PetscPartitioner_ParMetis *) part->data;
1424   PetscErrorCode             ierr;
1425 
1426   PetscFunctionBegin;
1427   ierr = PetscFree(p);CHKERRQ(ierr);
1428   PetscFunctionReturn(0);
1429 }
1430 
1431 static PetscErrorCode PetscPartitionerView_ParMetis_Ascii(PetscPartitioner part, PetscViewer viewer)
1432 {
1433   PetscPartitioner_ParMetis *p = (PetscPartitioner_ParMetis *) part->data;
1434   PetscErrorCode             ierr;
1435 
1436   PetscFunctionBegin;
1437   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1438   ierr = PetscViewerASCIIPrintf(viewer, "ParMetis type: %s\n", ptypes[p->ptype]);CHKERRQ(ierr);
1439   ierr = PetscViewerASCIIPrintf(viewer, "load imbalance ratio %g\n", (double) p->imbalanceRatio);CHKERRQ(ierr);
1440   ierr = PetscViewerASCIIPrintf(viewer, "debug flag %D\n", p->debugFlag);CHKERRQ(ierr);
1441   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1442   PetscFunctionReturn(0);
1443 }
1444 
1445 static PetscErrorCode PetscPartitionerView_ParMetis(PetscPartitioner part, PetscViewer viewer)
1446 {
1447   PetscBool      iascii;
1448   PetscErrorCode ierr;
1449 
1450   PetscFunctionBegin;
1451   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1452   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1453   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1454   if (iascii) {ierr = PetscPartitionerView_ParMetis_Ascii(part, viewer);CHKERRQ(ierr);}
1455   PetscFunctionReturn(0);
1456 }
1457 
1458 static PetscErrorCode PetscPartitionerSetFromOptions_ParMetis(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
1459 {
1460   PetscPartitioner_ParMetis *p = (PetscPartitioner_ParMetis *) part->data;
1461   PetscErrorCode            ierr;
1462 
1463   PetscFunctionBegin;
1464   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner ParMetis Options");CHKERRQ(ierr);
1465   ierr = PetscOptionsEList("-petscpartitioner_parmetis_type", "Partitioning method", "", ptypes, 2, ptypes[p->ptype], &p->ptype, NULL);CHKERRQ(ierr);
1466   ierr = PetscOptionsReal("-petscpartitioner_parmetis_imbalance_ratio", "Load imbalance ratio limit", "", p->imbalanceRatio, &p->imbalanceRatio, NULL);CHKERRQ(ierr);
1467   ierr = PetscOptionsInt("-petscpartitioner_parmetis_debug", "Debugging flag", "", p->debugFlag, &p->debugFlag, NULL);CHKERRQ(ierr);
1468   ierr = PetscOptionsTail();CHKERRQ(ierr);
1469   PetscFunctionReturn(0);
1470 }
1471 
1472 #if defined(PETSC_HAVE_PARMETIS)
1473 #include <parmetis.h>
1474 #endif
1475 
1476 static PetscErrorCode PetscPartitionerPartition_ParMetis(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1477 {
1478 #if defined(PETSC_HAVE_PARMETIS)
1479   PetscPartitioner_ParMetis *pm = (PetscPartitioner_ParMetis *) part->data;
1480   MPI_Comm       comm;
1481   PetscSection   section;
1482   PetscInt       nvtxs       = numVertices; /* The number of vertices in full graph */
1483   PetscInt      *vtxdist;                   /* Distribution of vertices across processes */
1484   PetscInt      *xadj        = start;       /* Start of edge list for each vertex */
1485   PetscInt      *adjncy      = adjacency;   /* Edge lists for all vertices */
1486   PetscInt      *vwgt        = NULL;        /* Vertex weights */
1487   PetscInt      *adjwgt      = NULL;        /* Edge weights */
1488   PetscInt       wgtflag     = 0;           /* Indicates which weights are present */
1489   PetscInt       numflag     = 0;           /* Indicates initial offset (0 or 1) */
1490   PetscInt       ncon        = 1;           /* The number of weights per vertex */
1491   PetscInt       metis_ptype = pm->ptype;   /* kway or recursive bisection */
1492   real_t        *tpwgts;                    /* The fraction of vertex weights assigned to each partition */
1493   real_t        *ubvec;                     /* The balance intolerance for vertex weights */
1494   PetscInt       options[64];               /* Options */
1495   /* Outputs */
1496   PetscInt       v, i, *assignment, *points;
1497   PetscMPIInt    size, rank, p;
1498   PetscErrorCode ierr;
1499 
1500   PetscFunctionBegin;
1501   ierr = PetscObjectGetComm((PetscObject) part, &comm);CHKERRQ(ierr);
1502   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
1503   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1504   /* Calculate vertex distribution */
1505   ierr = PetscMalloc5(size+1,&vtxdist,nparts*ncon,&tpwgts,ncon,&ubvec,nvtxs,&assignment,nvtxs,&vwgt);CHKERRQ(ierr);
1506   vtxdist[0] = 0;
1507   ierr = MPI_Allgather(&nvtxs, 1, MPIU_INT, &vtxdist[1], 1, MPIU_INT, comm);CHKERRQ(ierr);
1508   for (p = 2; p <= size; ++p) {
1509     vtxdist[p] += vtxdist[p-1];
1510   }
1511   /* Calculate partition weights */
1512   for (p = 0; p < nparts; ++p) {
1513     tpwgts[p] = 1.0/nparts;
1514   }
1515   ubvec[0] = pm->imbalanceRatio;
1516   /* Weight cells by dofs on cell by default */
1517   ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1518   if (section) {
1519     PetscInt cStart, cEnd, dof;
1520 
1521     ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1522     for (v = cStart; v < cEnd; ++v) {
1523       ierr = PetscSectionGetDof(section, v, &dof);CHKERRQ(ierr);
1524       /* WARNING: Assumes that meshes with overlap have the overlapped cells at the end of the stratum. */
1525       /* To do this properly, we should use the cell numbering created in DMPlexCreatePartitionerGraph. */
1526       if (v-cStart < numVertices) vwgt[v-cStart] = PetscMax(dof, 1);
1527     }
1528   } else {
1529     for (v = 0; v < nvtxs; ++v) vwgt[v] = 1;
1530   }
1531   wgtflag |= 2; /* have weights on graph vertices */
1532 
1533   if (nparts == 1) {
1534     ierr = PetscMemzero(assignment, nvtxs * sizeof(PetscInt));CHKERRQ(ierr);
1535   } else {
1536     for (p = 0; !vtxdist[p+1] && p < size; ++p);
1537     if (vtxdist[p+1] == vtxdist[size]) {
1538       if (rank == p) {
1539         ierr = METIS_SetDefaultOptions(options); /* initialize all defaults */
1540         if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in METIS_SetDefaultOptions()");
1541         if (metis_ptype == 1) {
1542           PetscStackPush("METIS_PartGraphRecursive");
1543           ierr = METIS_PartGraphRecursive(&nvtxs, &ncon, xadj, adjncy, vwgt, NULL, adjwgt, &nparts, tpwgts, ubvec, options, &part->edgeCut, assignment);
1544           PetscStackPop;
1545           if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in METIS_PartGraphRecursive()");
1546         } else {
1547           /*
1548            It would be nice to activate the two options below, but they would need some actual testing.
1549            - Turning on these options may exercise path of the METIS code that have bugs and may break production runs.
1550            - If CONTIG is set to 1, METIS will exit with error if the graph is disconnected, despite the manual saying the option is ignored in such case.
1551           */
1552           /* options[METIS_OPTION_CONTIG]  = 1; */ /* try to produce partitions that are contiguous */
1553           /* options[METIS_OPTION_MINCONN] = 1; */ /* minimize the maximum degree of the subdomain graph */
1554           PetscStackPush("METIS_PartGraphKway");
1555           ierr = METIS_PartGraphKway(&nvtxs, &ncon, xadj, adjncy, vwgt, NULL, adjwgt, &nparts, tpwgts, ubvec, options, &part->edgeCut, assignment);
1556           PetscStackPop;
1557           if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in METIS_PartGraphKway()");
1558         }
1559       }
1560     } else {
1561       options[0] = 1;
1562       options[1] = pm->debugFlag;
1563       PetscStackPush("ParMETIS_V3_PartKway");
1564       ierr = ParMETIS_V3_PartKway(vtxdist, xadj, adjncy, vwgt, adjwgt, &wgtflag, &numflag, &ncon, &nparts, tpwgts, ubvec, options, &part->edgeCut, assignment, &comm);
1565       PetscStackPop;
1566       if (ierr != METIS_OK) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error %d in ParMETIS_V3_PartKway()", ierr);
1567     }
1568   }
1569   /* Convert to PetscSection+IS */
1570   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1571   for (v = 0; v < nvtxs; ++v) {ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);}
1572   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1573   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1574   for (p = 0, i = 0; p < nparts; ++p) {
1575     for (v = 0; v < nvtxs; ++v) {
1576       if (assignment[v] == p) points[i++] = v;
1577     }
1578   }
1579   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1580   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1581   ierr = PetscFree5(vtxdist,tpwgts,ubvec,assignment,vwgt);CHKERRQ(ierr);
1582   PetscFunctionReturn(0);
1583 #else
1584   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-parmetis.");
1585 #endif
1586 }
1587 
1588 static PetscErrorCode PetscPartitionerInitialize_ParMetis(PetscPartitioner part)
1589 {
1590   PetscFunctionBegin;
1591   part->ops->view           = PetscPartitionerView_ParMetis;
1592   part->ops->setfromoptions = PetscPartitionerSetFromOptions_ParMetis;
1593   part->ops->destroy        = PetscPartitionerDestroy_ParMetis;
1594   part->ops->partition      = PetscPartitionerPartition_ParMetis;
1595   PetscFunctionReturn(0);
1596 }
1597 
1598 /*MC
1599   PETSCPARTITIONERPARMETIS = "parmetis" - A PetscPartitioner object using the ParMetis library
1600 
1601   Level: intermediate
1602 
1603 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1604 M*/
1605 
1606 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_ParMetis(PetscPartitioner part)
1607 {
1608   PetscPartitioner_ParMetis *p;
1609   PetscErrorCode          ierr;
1610 
1611   PetscFunctionBegin;
1612   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1613   ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
1614   part->data = p;
1615 
1616   p->ptype          = 0;
1617   p->imbalanceRatio = 1.05;
1618   p->debugFlag      = 0;
1619 
1620   ierr = PetscPartitionerInitialize_ParMetis(part);CHKERRQ(ierr);
1621   ierr = PetscCitationsRegister(ParMetisPartitionerCitation, &ParMetisPartitionercite);CHKERRQ(ierr);
1622   PetscFunctionReturn(0);
1623 }
1624 
1625 
1626 PetscBool PTScotchPartitionercite = PETSC_FALSE;
1627 const char PTScotchPartitionerCitation[] =
1628   "@article{PTSCOTCH,\n"
1629   "  author  = {C. Chevalier and F. Pellegrini},\n"
1630   "  title   = {{PT-SCOTCH}: a tool for efficient parallel graph ordering},\n"
1631   "  journal = {Parallel Computing},\n"
1632   "  volume  = {34},\n"
1633   "  number  = {6},\n"
1634   "  pages   = {318--331},\n"
1635   "  year    = {2008},\n"
1636   "  doi     = {https://doi.org/10.1016/j.parco.2007.12.001}\n"
1637   "}\n";
1638 
1639 typedef struct {
1640   PetscInt  strategy;
1641   PetscReal imbalance;
1642 } PetscPartitioner_PTScotch;
1643 
1644 static const char *const
1645 PTScotchStrategyList[] = {
1646   "DEFAULT",
1647   "QUALITY",
1648   "SPEED",
1649   "BALANCE",
1650   "SAFETY",
1651   "SCALABILITY",
1652   "RECURSIVE",
1653   "REMAP"
1654 };
1655 
1656 #if defined(PETSC_HAVE_PTSCOTCH)
1657 
1658 EXTERN_C_BEGIN
1659 #include <ptscotch.h>
1660 EXTERN_C_END
1661 
1662 #define CHKERRPTSCOTCH(ierr) do { if (ierr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error calling PT-Scotch library"); } while(0)
1663 
1664 static int PTScotch_Strategy(PetscInt strategy)
1665 {
1666   switch (strategy) {
1667   case  0: return SCOTCH_STRATDEFAULT;
1668   case  1: return SCOTCH_STRATQUALITY;
1669   case  2: return SCOTCH_STRATSPEED;
1670   case  3: return SCOTCH_STRATBALANCE;
1671   case  4: return SCOTCH_STRATSAFETY;
1672   case  5: return SCOTCH_STRATSCALABILITY;
1673   case  6: return SCOTCH_STRATRECURSIVE;
1674   case  7: return SCOTCH_STRATREMAP;
1675   default: return SCOTCH_STRATDEFAULT;
1676   }
1677 }
1678 
1679 
1680 static PetscErrorCode PTScotch_PartGraph_Seq(SCOTCH_Num strategy, double imbalance, SCOTCH_Num n, SCOTCH_Num xadj[], SCOTCH_Num adjncy[],
1681                                              SCOTCH_Num vtxwgt[], SCOTCH_Num adjwgt[], SCOTCH_Num nparts, SCOTCH_Num part[])
1682 {
1683   SCOTCH_Graph   grafdat;
1684   SCOTCH_Strat   stradat;
1685   SCOTCH_Num     vertnbr = n;
1686   SCOTCH_Num     edgenbr = xadj[n];
1687   SCOTCH_Num*    velotab = vtxwgt;
1688   SCOTCH_Num*    edlotab = adjwgt;
1689   SCOTCH_Num     flagval = strategy;
1690   double         kbalval = imbalance;
1691   PetscErrorCode ierr;
1692 
1693   PetscFunctionBegin;
1694   {
1695     PetscBool flg = PETSC_TRUE;
1696     ierr = PetscOptionsGetBool(NULL, NULL, "-petscpartititoner_ptscotch_vertex_weight", &flg, NULL);CHKERRQ(ierr);
1697     if (!flg) velotab = NULL;
1698   }
1699   ierr = SCOTCH_graphInit(&grafdat);CHKERRPTSCOTCH(ierr);
1700   ierr = SCOTCH_graphBuild(&grafdat, 0, vertnbr, xadj, xadj + 1, velotab, NULL, edgenbr, adjncy, edlotab);CHKERRPTSCOTCH(ierr);
1701   ierr = SCOTCH_stratInit(&stradat);CHKERRPTSCOTCH(ierr);
1702   ierr = SCOTCH_stratGraphMapBuild(&stradat, flagval, nparts, kbalval);CHKERRPTSCOTCH(ierr);
1703 #if defined(PETSC_USE_DEBUG)
1704   ierr = SCOTCH_graphCheck(&grafdat);CHKERRPTSCOTCH(ierr);
1705 #endif
1706   ierr = SCOTCH_graphPart(&grafdat, nparts, &stradat, part);CHKERRPTSCOTCH(ierr);
1707   SCOTCH_stratExit(&stradat);
1708   SCOTCH_graphExit(&grafdat);
1709   PetscFunctionReturn(0);
1710 }
1711 
1712 static PetscErrorCode PTScotch_PartGraph_MPI(SCOTCH_Num strategy, double imbalance, SCOTCH_Num vtxdist[], SCOTCH_Num xadj[], SCOTCH_Num adjncy[],
1713                                              SCOTCH_Num vtxwgt[], SCOTCH_Num adjwgt[], SCOTCH_Num nparts, SCOTCH_Num part[], MPI_Comm comm)
1714 {
1715   PetscMPIInt     procglbnbr;
1716   PetscMPIInt     proclocnum;
1717   SCOTCH_Arch     archdat;
1718   SCOTCH_Dgraph   grafdat;
1719   SCOTCH_Dmapping mappdat;
1720   SCOTCH_Strat    stradat;
1721   SCOTCH_Num      vertlocnbr;
1722   SCOTCH_Num      edgelocnbr;
1723   SCOTCH_Num*     veloloctab = vtxwgt;
1724   SCOTCH_Num*     edloloctab = adjwgt;
1725   SCOTCH_Num      flagval = strategy;
1726   double          kbalval = imbalance;
1727   PetscErrorCode  ierr;
1728 
1729   PetscFunctionBegin;
1730   {
1731     PetscBool flg = PETSC_TRUE;
1732     ierr = PetscOptionsGetBool(NULL, NULL, "-petscpartititoner_ptscotch_vertex_weight", &flg, NULL);CHKERRQ(ierr);
1733     if (!flg) veloloctab = NULL;
1734   }
1735   ierr = MPI_Comm_size(comm, &procglbnbr);CHKERRQ(ierr);
1736   ierr = MPI_Comm_rank(comm, &proclocnum);CHKERRQ(ierr);
1737   vertlocnbr = vtxdist[proclocnum + 1] - vtxdist[proclocnum];
1738   edgelocnbr = xadj[vertlocnbr];
1739 
1740   ierr = SCOTCH_dgraphInit(&grafdat, comm);CHKERRPTSCOTCH(ierr);
1741   ierr = SCOTCH_dgraphBuild(&grafdat, 0, vertlocnbr, vertlocnbr, xadj, xadj + 1, veloloctab, NULL, edgelocnbr, edgelocnbr, adjncy, NULL, edloloctab);CHKERRPTSCOTCH(ierr);
1742 #if defined(PETSC_USE_DEBUG)
1743   ierr = SCOTCH_dgraphCheck(&grafdat);CHKERRPTSCOTCH(ierr);
1744 #endif
1745   ierr = SCOTCH_stratInit(&stradat);CHKERRPTSCOTCH(ierr);
1746   ierr = SCOTCH_stratDgraphMapBuild(&stradat, flagval, procglbnbr, nparts, kbalval);CHKERRQ(ierr);
1747   ierr = SCOTCH_archInit(&archdat);CHKERRPTSCOTCH(ierr);
1748   ierr = SCOTCH_archCmplt(&archdat, nparts);CHKERRPTSCOTCH(ierr);
1749   ierr = SCOTCH_dgraphMapInit(&grafdat, &mappdat, &archdat, part);CHKERRPTSCOTCH(ierr);
1750   ierr = SCOTCH_dgraphMapCompute(&grafdat, &mappdat, &stradat);CHKERRPTSCOTCH(ierr);
1751   SCOTCH_dgraphMapExit(&grafdat, &mappdat);
1752   SCOTCH_archExit(&archdat);
1753   SCOTCH_stratExit(&stradat);
1754   SCOTCH_dgraphExit(&grafdat);
1755   PetscFunctionReturn(0);
1756 }
1757 
1758 #endif /* PETSC_HAVE_PTSCOTCH */
1759 
1760 static PetscErrorCode PetscPartitionerDestroy_PTScotch(PetscPartitioner part)
1761 {
1762   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1763   PetscErrorCode             ierr;
1764 
1765   PetscFunctionBegin;
1766   ierr = PetscFree(p);CHKERRQ(ierr);
1767   PetscFunctionReturn(0);
1768 }
1769 
1770 static PetscErrorCode PetscPartitionerView_PTScotch_Ascii(PetscPartitioner part, PetscViewer viewer)
1771 {
1772   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1773   PetscErrorCode            ierr;
1774 
1775   PetscFunctionBegin;
1776   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1777   ierr = PetscViewerASCIIPrintf(viewer, "using partitioning strategy %s\n",PTScotchStrategyList[p->strategy]);CHKERRQ(ierr);
1778   ierr = PetscViewerASCIIPrintf(viewer, "using load imbalance ratio %g\n",(double)p->imbalance);CHKERRQ(ierr);
1779   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1780   PetscFunctionReturn(0);
1781 }
1782 
1783 static PetscErrorCode PetscPartitionerView_PTScotch(PetscPartitioner part, PetscViewer viewer)
1784 {
1785   PetscBool      iascii;
1786   PetscErrorCode ierr;
1787 
1788   PetscFunctionBegin;
1789   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1790   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1791   ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
1792   if (iascii) {ierr = PetscPartitionerView_PTScotch_Ascii(part, viewer);CHKERRQ(ierr);}
1793   PetscFunctionReturn(0);
1794 }
1795 
1796 static PetscErrorCode PetscPartitionerSetFromOptions_PTScotch(PetscOptionItems *PetscOptionsObject, PetscPartitioner part)
1797 {
1798   PetscPartitioner_PTScotch *p = (PetscPartitioner_PTScotch *) part->data;
1799   const char *const         *slist = PTScotchStrategyList;
1800   PetscInt                  nlist = (PetscInt)(sizeof(PTScotchStrategyList)/sizeof(PTScotchStrategyList[0]));
1801   PetscBool                 flag;
1802   PetscErrorCode            ierr;
1803 
1804   PetscFunctionBegin;
1805   ierr = PetscOptionsHead(PetscOptionsObject, "PetscPartitioner PTScotch Options");CHKERRQ(ierr);
1806   ierr = PetscOptionsEList("-petscpartitioner_ptscotch_strategy","Partitioning strategy","",slist,nlist,slist[p->strategy],&p->strategy,&flag);CHKERRQ(ierr);
1807   ierr = PetscOptionsReal("-petscpartitioner_ptscotch_imbalance","Load imbalance ratio","",p->imbalance,&p->imbalance,&flag);CHKERRQ(ierr);
1808   ierr = PetscOptionsTail();CHKERRQ(ierr);
1809   PetscFunctionReturn(0);
1810 }
1811 
1812 static PetscErrorCode PetscPartitionerPartition_PTScotch(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
1813 {
1814 #if defined(PETSC_HAVE_PTSCOTCH)
1815   MPI_Comm       comm       = PetscObjectComm((PetscObject)part);
1816   PetscInt       nvtxs      = numVertices; /* The number of vertices in full graph */
1817   PetscInt      *vtxdist;                  /* Distribution of vertices across processes */
1818   PetscInt      *xadj       = start;       /* Start of edge list for each vertex */
1819   PetscInt      *adjncy     = adjacency;   /* Edge lists for all vertices */
1820   PetscInt      *vwgt       = NULL;        /* Vertex weights */
1821   PetscInt      *adjwgt     = NULL;        /* Edge weights */
1822   PetscInt       v, i, *assignment, *points;
1823   PetscMPIInt    size, rank, p;
1824   PetscErrorCode ierr;
1825 
1826   PetscFunctionBegin;
1827   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
1828   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1829   ierr = PetscMalloc2(size+1,&vtxdist,PetscMax(nvtxs,1),&assignment);CHKERRQ(ierr);
1830 
1831   /* Calculate vertex distribution */
1832   vtxdist[0] = 0;
1833   ierr = MPI_Allgather(&nvtxs, 1, MPIU_INT, &vtxdist[1], 1, MPIU_INT, comm);CHKERRQ(ierr);
1834   for (p = 2; p <= size; ++p) {
1835     vtxdist[p] += vtxdist[p-1];
1836   }
1837 
1838   if (nparts == 1) {
1839     ierr = PetscMemzero(assignment, nvtxs * sizeof(PetscInt));CHKERRQ(ierr);
1840   } else {
1841     PetscSection section;
1842     /* Weight cells by dofs on cell by default */
1843     ierr = PetscMalloc1(PetscMax(nvtxs,1),&vwgt);CHKERRQ(ierr);
1844     ierr = DMGetSection(dm, &section);CHKERRQ(ierr);
1845     if (section) {
1846       PetscInt vStart, vEnd, dof;
1847       ierr = DMPlexGetHeightStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1848       for (v = vStart; v < vEnd; ++v) {
1849         ierr = PetscSectionGetDof(section, v, &dof);CHKERRQ(ierr);
1850         /* WARNING: Assumes that meshes with overlap have the overlapped cells at the end of the stratum. */
1851         /* To do this properly, we should use the cell numbering created in DMPlexCreatePartitionerGraph. */
1852         if (v-vStart < numVertices) vwgt[v-vStart] = PetscMax(dof, 1);
1853       }
1854     } else {
1855       for (v = 0; v < nvtxs; ++v) vwgt[v] = 1;
1856     }
1857     {
1858       PetscPartitioner_PTScotch *pts = (PetscPartitioner_PTScotch *) part->data;
1859       int                       strat = PTScotch_Strategy(pts->strategy);
1860       double                    imbal = (double)pts->imbalance;
1861 
1862       for (p = 0; !vtxdist[p+1] && p < size; ++p);
1863       if (vtxdist[p+1] == vtxdist[size]) {
1864         if (rank == p) {
1865           ierr = PTScotch_PartGraph_Seq(strat, imbal, nvtxs, xadj, adjncy, vwgt, adjwgt, nparts, assignment);CHKERRQ(ierr);
1866         }
1867       } else {
1868         ierr = PTScotch_PartGraph_MPI(strat, imbal, vtxdist, xadj, adjncy, vwgt, adjwgt, nparts, assignment, comm);CHKERRQ(ierr);
1869       }
1870     }
1871     ierr = PetscFree(vwgt);CHKERRQ(ierr);
1872   }
1873 
1874   /* Convert to PetscSection+IS */
1875   ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
1876   for (v = 0; v < nvtxs; ++v) {ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);}
1877   ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
1878   ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
1879   for (p = 0, i = 0; p < nparts; ++p) {
1880     for (v = 0; v < nvtxs; ++v) {
1881       if (assignment[v] == p) points[i++] = v;
1882     }
1883   }
1884   if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
1885   ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
1886 
1887   ierr = PetscFree2(vtxdist,assignment);CHKERRQ(ierr);
1888   PetscFunctionReturn(0);
1889 #else
1890   SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-ptscotch.");
1891 #endif
1892 }
1893 
1894 static PetscErrorCode PetscPartitionerInitialize_PTScotch(PetscPartitioner part)
1895 {
1896   PetscFunctionBegin;
1897   part->ops->view           = PetscPartitionerView_PTScotch;
1898   part->ops->destroy        = PetscPartitionerDestroy_PTScotch;
1899   part->ops->partition      = PetscPartitionerPartition_PTScotch;
1900   part->ops->setfromoptions = PetscPartitionerSetFromOptions_PTScotch;
1901   PetscFunctionReturn(0);
1902 }
1903 
1904 /*MC
1905   PETSCPARTITIONERPTSCOTCH = "ptscotch" - A PetscPartitioner object using the PT-Scotch library
1906 
1907   Level: intermediate
1908 
1909 .seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
1910 M*/
1911 
1912 PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_PTScotch(PetscPartitioner part)
1913 {
1914   PetscPartitioner_PTScotch *p;
1915   PetscErrorCode          ierr;
1916 
1917   PetscFunctionBegin;
1918   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
1919   ierr = PetscNewLog(part, &p);CHKERRQ(ierr);
1920   part->data = p;
1921 
1922   p->strategy  = 0;
1923   p->imbalance = 0.01;
1924 
1925   ierr = PetscPartitionerInitialize_PTScotch(part);CHKERRQ(ierr);
1926   ierr = PetscCitationsRegister(PTScotchPartitionerCitation, &PTScotchPartitionercite);CHKERRQ(ierr);
1927   PetscFunctionReturn(0);
1928 }
1929 
1930 
1931 /*@
1932   DMPlexGetPartitioner - Get the mesh partitioner
1933 
1934   Not collective
1935 
1936   Input Parameter:
1937 . dm - The DM
1938 
1939   Output Parameter:
1940 . part - The PetscPartitioner
1941 
1942   Level: developer
1943 
1944   Note: This gets a borrowed reference, so the user should not destroy this PetscPartitioner.
1945 
1946 .seealso DMPlexDistribute(), DMPlexSetPartitioner(), PetscPartitionerCreate()
1947 @*/
1948 PetscErrorCode DMPlexGetPartitioner(DM dm, PetscPartitioner *part)
1949 {
1950   DM_Plex       *mesh = (DM_Plex *) dm->data;
1951 
1952   PetscFunctionBegin;
1953   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1954   PetscValidPointer(part, 2);
1955   *part = mesh->partitioner;
1956   PetscFunctionReturn(0);
1957 }
1958 
1959 /*@
1960   DMPlexSetPartitioner - Set the mesh partitioner
1961 
1962   logically collective on dm and part
1963 
1964   Input Parameters:
1965 + dm - The DM
1966 - part - The partitioner
1967 
1968   Level: developer
1969 
1970   Note: Any existing PetscPartitioner will be destroyed.
1971 
1972 .seealso DMPlexDistribute(), DMPlexGetPartitioner(), PetscPartitionerCreate()
1973 @*/
1974 PetscErrorCode DMPlexSetPartitioner(DM dm, PetscPartitioner part)
1975 {
1976   DM_Plex       *mesh = (DM_Plex *) dm->data;
1977   PetscErrorCode ierr;
1978 
1979   PetscFunctionBegin;
1980   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1981   PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 2);
1982   ierr = PetscObjectReference((PetscObject)part);CHKERRQ(ierr);
1983   ierr = PetscPartitionerDestroy(&mesh->partitioner);CHKERRQ(ierr);
1984   mesh->partitioner = part;
1985   PetscFunctionReturn(0);
1986 }
1987 
1988 static PetscErrorCode DMPlexAddClosure_Tree(DM dm, PetscHSetI ht, PetscInt point, PetscBool up, PetscBool down)
1989 {
1990   PetscErrorCode ierr;
1991 
1992   PetscFunctionBegin;
1993   if (up) {
1994     PetscInt parent;
1995 
1996     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
1997     if (parent != point) {
1998       PetscInt closureSize, *closure = NULL, i;
1999 
2000       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2001       for (i = 0; i < closureSize; i++) {
2002         PetscInt cpoint = closure[2*i];
2003 
2004         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2005         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
2006       }
2007       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2008     }
2009   }
2010   if (down) {
2011     PetscInt numChildren;
2012     const PetscInt *children;
2013 
2014     ierr = DMPlexGetTreeChildren(dm,point,&numChildren,&children);CHKERRQ(ierr);
2015     if (numChildren) {
2016       PetscInt i;
2017 
2018       for (i = 0; i < numChildren; i++) {
2019         PetscInt cpoint = children[i];
2020 
2021         ierr = PetscHSetIAdd(ht, cpoint);CHKERRQ(ierr);
2022         ierr = DMPlexAddClosure_Tree(dm,ht,cpoint,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
2023       }
2024     }
2025   }
2026   PetscFunctionReturn(0);
2027 }
2028 
2029 PETSC_INTERN PetscErrorCode DMPlexPartitionLabelClosure_Private(DM,DMLabel,PetscInt,PetscInt,const PetscInt[],IS*);
2030 
2031 PetscErrorCode DMPlexPartitionLabelClosure_Private(DM dm, DMLabel label, PetscInt rank, PetscInt numPoints, const PetscInt points[], IS *closureIS)
2032 {
2033   DM_Plex        *mesh = (DM_Plex *)dm->data;
2034   PetscBool      hasTree = (mesh->parentSection || mesh->childSection) ? PETSC_TRUE : PETSC_FALSE;
2035   PetscInt       *closure = NULL, closureSize, nelems, *elems, off = 0, p, c;
2036   PetscHSetI     ht;
2037   PetscErrorCode ierr;
2038 
2039   PetscFunctionBegin;
2040   ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
2041   ierr = PetscHSetIResize(ht, numPoints*16);CHKERRQ(ierr);
2042   for (p = 0; p < numPoints; ++p) {
2043     ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2044     for (c = 0; c < closureSize*2; c += 2) {
2045       ierr = PetscHSetIAdd(ht, closure[c]);CHKERRQ(ierr);
2046       if (hasTree) {ierr = DMPlexAddClosure_Tree(dm, ht, closure[c], PETSC_TRUE, PETSC_TRUE);CHKERRQ(ierr);}
2047     }
2048   }
2049   if (closure) {ierr = DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, NULL, &closure);CHKERRQ(ierr);}
2050   ierr = PetscHSetIGetSize(ht, &nelems);CHKERRQ(ierr);
2051   ierr = PetscMalloc1(nelems, &elems);CHKERRQ(ierr);
2052   ierr = PetscHSetIGetElems(ht, &off, elems);CHKERRQ(ierr);
2053   ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
2054   ierr = PetscSortInt(nelems, elems);CHKERRQ(ierr);
2055   ierr = ISCreateGeneral(PETSC_COMM_SELF, nelems, elems, PETSC_OWN_POINTER, closureIS);CHKERRQ(ierr);
2056   PetscFunctionReturn(0);
2057 }
2058 
2059 /*@
2060   DMPlexPartitionLabelClosure - Add the closure of all points to the partition label
2061 
2062   Input Parameters:
2063 + dm     - The DM
2064 - label  - DMLabel assinging ranks to remote roots
2065 
2066   Level: developer
2067 
2068 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2069 @*/
2070 PetscErrorCode DMPlexPartitionLabelClosure(DM dm, DMLabel label)
2071 {
2072   IS              rankIS,   pointIS, closureIS;
2073   const PetscInt *ranks,   *points;
2074   PetscInt        numRanks, numPoints, r;
2075   PetscErrorCode  ierr;
2076 
2077   PetscFunctionBegin;
2078   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2079   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2080   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2081   for (r = 0; r < numRanks; ++r) {
2082     const PetscInt rank = ranks[r];
2083     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2084     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2085     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2086     ierr = DMPlexPartitionLabelClosure_Private(dm, label, rank, numPoints, points, &closureIS);CHKERRQ(ierr);
2087     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2088     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2089     ierr = DMLabelSetStratumIS(label, rank, closureIS);CHKERRQ(ierr);
2090     ierr = ISDestroy(&closureIS);CHKERRQ(ierr);
2091   }
2092   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2093   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2094   PetscFunctionReturn(0);
2095 }
2096 
2097 /*@
2098   DMPlexPartitionLabelAdjacency - Add one level of adjacent points to the partition label
2099 
2100   Input Parameters:
2101 + dm     - The DM
2102 - label  - DMLabel assinging ranks to remote roots
2103 
2104   Level: developer
2105 
2106 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2107 @*/
2108 PetscErrorCode DMPlexPartitionLabelAdjacency(DM dm, DMLabel label)
2109 {
2110   IS              rankIS,   pointIS;
2111   const PetscInt *ranks,   *points;
2112   PetscInt        numRanks, numPoints, r, p, a, adjSize;
2113   PetscInt       *adj = NULL;
2114   PetscErrorCode  ierr;
2115 
2116   PetscFunctionBegin;
2117   ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
2118   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2119   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2120   for (r = 0; r < numRanks; ++r) {
2121     const PetscInt rank = ranks[r];
2122 
2123     ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
2124     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2125     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2126     for (p = 0; p < numPoints; ++p) {
2127       adjSize = PETSC_DETERMINE;
2128       ierr = DMPlexGetAdjacency(dm, points[p], &adjSize, &adj);CHKERRQ(ierr);
2129       for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(label, adj[a], rank);CHKERRQ(ierr);}
2130     }
2131     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2132     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2133   }
2134   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2135   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2136   ierr = PetscFree(adj);CHKERRQ(ierr);
2137   PetscFunctionReturn(0);
2138 }
2139 
2140 /*@
2141   DMPlexPartitionLabelPropagate - Propagate points in a partition label over the point SF
2142 
2143   Input Parameters:
2144 + dm     - The DM
2145 - label  - DMLabel assinging ranks to remote roots
2146 
2147   Level: developer
2148 
2149   Note: This is required when generating multi-level overlaps to capture
2150   overlap points from non-neighbouring partitions.
2151 
2152 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2153 @*/
2154 PetscErrorCode DMPlexPartitionLabelPropagate(DM dm, DMLabel label)
2155 {
2156   MPI_Comm        comm;
2157   PetscMPIInt     rank;
2158   PetscSF         sfPoint;
2159   DMLabel         lblRoots, lblLeaves;
2160   IS              rankIS, pointIS;
2161   const PetscInt *ranks;
2162   PetscInt        numRanks, r;
2163   PetscErrorCode  ierr;
2164 
2165   PetscFunctionBegin;
2166   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2167   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2168   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2169   /* Pull point contributions from remote leaves into local roots */
2170   ierr = DMLabelGather(label, sfPoint, &lblLeaves);CHKERRQ(ierr);
2171   ierr = DMLabelGetValueIS(lblLeaves, &rankIS);CHKERRQ(ierr);
2172   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2173   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2174   for (r = 0; r < numRanks; ++r) {
2175     const PetscInt remoteRank = ranks[r];
2176     if (remoteRank == rank) continue;
2177     ierr = DMLabelGetStratumIS(lblLeaves, remoteRank, &pointIS);CHKERRQ(ierr);
2178     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2179     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2180   }
2181   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2182   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2183   ierr = DMLabelDestroy(&lblLeaves);CHKERRQ(ierr);
2184   /* Push point contributions from roots into remote leaves */
2185   ierr = DMLabelDistribute(label, sfPoint, &lblRoots);CHKERRQ(ierr);
2186   ierr = DMLabelGetValueIS(lblRoots, &rankIS);CHKERRQ(ierr);
2187   ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
2188   ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
2189   for (r = 0; r < numRanks; ++r) {
2190     const PetscInt remoteRank = ranks[r];
2191     if (remoteRank == rank) continue;
2192     ierr = DMLabelGetStratumIS(lblRoots, remoteRank, &pointIS);CHKERRQ(ierr);
2193     ierr = DMLabelInsertIS(label, pointIS, remoteRank);CHKERRQ(ierr);
2194     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2195   }
2196   ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
2197   ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
2198   ierr = DMLabelDestroy(&lblRoots);CHKERRQ(ierr);
2199   PetscFunctionReturn(0);
2200 }
2201 
2202 /*@
2203   DMPlexPartitionLabelInvert - Create a partition label of remote roots from a local root label
2204 
2205   Input Parameters:
2206 + dm        - The DM
2207 . rootLabel - DMLabel assinging ranks to local roots
2208 . processSF - A star forest mapping into the local index on each remote rank
2209 
2210   Output Parameter:
2211 - leafLabel - DMLabel assinging ranks to remote roots
2212 
2213   Note: The rootLabel defines a send pattern by mapping local points to remote target ranks. The
2214   resulting leafLabel is a receiver mapping of remote roots to their parent rank.
2215 
2216   Level: developer
2217 
2218 .seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
2219 @*/
2220 PetscErrorCode DMPlexPartitionLabelInvert(DM dm, DMLabel rootLabel, PetscSF processSF, DMLabel leafLabel)
2221 {
2222   MPI_Comm           comm;
2223   PetscMPIInt        rank, size, r;
2224   PetscInt           p, n, numNeighbors, numPoints, dof, off, rootSize, l, nleaves, leafSize;
2225   PetscSF            sfPoint;
2226   PetscSection       rootSection;
2227   PetscSFNode       *rootPoints, *leafPoints;
2228   const PetscSFNode *remote;
2229   const PetscInt    *local, *neighbors;
2230   IS                 valueIS;
2231   PetscBool          mpiOverflow = PETSC_FALSE;
2232   PetscErrorCode     ierr;
2233 
2234   PetscFunctionBegin;
2235   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2236   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2237   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
2238   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2239 
2240   /* Convert to (point, rank) and use actual owners */
2241   ierr = PetscSectionCreate(comm, &rootSection);CHKERRQ(ierr);
2242   ierr = PetscSectionSetChart(rootSection, 0, size);CHKERRQ(ierr);
2243   ierr = DMLabelGetValueIS(rootLabel, &valueIS);CHKERRQ(ierr);
2244   ierr = ISGetLocalSize(valueIS, &numNeighbors);CHKERRQ(ierr);
2245   ierr = ISGetIndices(valueIS, &neighbors);CHKERRQ(ierr);
2246   for (n = 0; n < numNeighbors; ++n) {
2247     ierr = DMLabelGetStratumSize(rootLabel, neighbors[n], &numPoints);CHKERRQ(ierr);
2248     ierr = PetscSectionAddDof(rootSection, neighbors[n], numPoints);CHKERRQ(ierr);
2249   }
2250   ierr = PetscSectionSetUp(rootSection);CHKERRQ(ierr);
2251   ierr = PetscSectionGetStorageSize(rootSection, &rootSize);CHKERRQ(ierr);
2252   ierr = PetscMalloc1(rootSize, &rootPoints);CHKERRQ(ierr);
2253   ierr = PetscSFGetGraph(sfPoint, NULL, &nleaves, &local, &remote);CHKERRQ(ierr);
2254   for (n = 0; n < numNeighbors; ++n) {
2255     IS              pointIS;
2256     const PetscInt *points;
2257 
2258     ierr = PetscSectionGetOffset(rootSection, neighbors[n], &off);CHKERRQ(ierr);
2259     ierr = DMLabelGetStratumIS(rootLabel, neighbors[n], &pointIS);CHKERRQ(ierr);
2260     ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
2261     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2262     for (p = 0; p < numPoints; ++p) {
2263       if (local) {ierr = PetscFindInt(points[p], nleaves, local, &l);CHKERRQ(ierr);}
2264       else       {l = -1;}
2265       if (l >= 0) {rootPoints[off+p] = remote[l];}
2266       else        {rootPoints[off+p].index = points[p]; rootPoints[off+p].rank = rank;}
2267     }
2268     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2269     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2270   }
2271 
2272   /* Try to communicate overlap using All-to-All */
2273   if (!processSF) {
2274     PetscInt64  counter = 0;
2275     PetscBool   locOverflow = PETSC_FALSE;
2276     PetscMPIInt *scounts, *sdispls, *rcounts, *rdispls;
2277 
2278     ierr = PetscCalloc4(size, &scounts, size, &sdispls, size, &rcounts, size, &rdispls);CHKERRQ(ierr);
2279     for (n = 0; n < numNeighbors; ++n) {
2280       ierr = PetscSectionGetDof(rootSection, neighbors[n], &dof);CHKERRQ(ierr);
2281       ierr = PetscSectionGetOffset(rootSection, neighbors[n], &off);CHKERRQ(ierr);
2282 #if defined(PETSC_USE_64BIT_INDICES)
2283       if (dof > PETSC_MPI_INT_MAX) {locOverflow = PETSC_TRUE; break;}
2284       if (off > PETSC_MPI_INT_MAX) {locOverflow = PETSC_TRUE; break;}
2285 #endif
2286       scounts[neighbors[n]] = (PetscMPIInt) dof;
2287       sdispls[neighbors[n]] = (PetscMPIInt) off;
2288     }
2289     ierr = MPI_Alltoall(scounts, 1, MPI_INT, rcounts, 1, MPI_INT, comm);CHKERRQ(ierr);
2290     for (r = 0; r < size; ++r) { rdispls[r] = (int)counter; counter += rcounts[r]; }
2291     if (counter > PETSC_MPI_INT_MAX) locOverflow = PETSC_TRUE;
2292     ierr = MPI_Allreduce(&locOverflow, &mpiOverflow, 1, MPIU_BOOL, MPI_LOR, comm);CHKERRQ(ierr);
2293     if (!mpiOverflow) {
2294       leafSize = (PetscInt) counter;
2295       ierr = PetscMalloc1(leafSize, &leafPoints);CHKERRQ(ierr);
2296       ierr = MPI_Alltoallv(rootPoints, scounts, sdispls, MPIU_2INT, leafPoints, rcounts, rdispls, MPIU_2INT, comm);CHKERRQ(ierr);
2297     }
2298     ierr = PetscFree4(scounts, sdispls, rcounts, rdispls);CHKERRQ(ierr);
2299   }
2300 
2301   /* Communicate overlap using process star forest */
2302   if (processSF || mpiOverflow) {
2303     PetscSF      procSF;
2304     PetscSFNode  *remote;
2305     PetscSection leafSection;
2306 
2307     if (processSF) {
2308       ierr = PetscObjectReference((PetscObject)processSF);CHKERRQ(ierr);
2309       procSF = processSF;
2310     } else {
2311       ierr = PetscMalloc1(size, &remote);CHKERRQ(ierr);
2312       for (r = 0; r < size; ++r) { remote[r].rank  = r; remote[r].index = rank; }
2313       ierr = PetscSFCreate(comm, &procSF);CHKERRQ(ierr);
2314       ierr = PetscSFSetGraph(procSF, size, size, NULL, PETSC_OWN_POINTER, remote, PETSC_OWN_POINTER);CHKERRQ(ierr);
2315     }
2316 
2317     ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &leafSection);CHKERRQ(ierr);
2318     ierr = DMPlexDistributeData(dm, processSF, rootSection, MPIU_2INT, rootPoints, leafSection, (void**) &leafPoints);CHKERRQ(ierr);
2319     ierr = PetscSectionGetStorageSize(leafSection, &leafSize);CHKERRQ(ierr);
2320     ierr = PetscSectionDestroy(&leafSection);CHKERRQ(ierr);
2321     ierr = PetscSFDestroy(&procSF);CHKERRQ(ierr);
2322   }
2323 
2324   for (p = 0; p < leafSize; p++) {
2325     ierr = DMLabelSetValue(leafLabel, leafPoints[p].index, leafPoints[p].rank);CHKERRQ(ierr);
2326   }
2327 
2328   ierr = ISRestoreIndices(valueIS, &neighbors);CHKERRQ(ierr);
2329   ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
2330   ierr = PetscSectionDestroy(&rootSection);CHKERRQ(ierr);
2331   ierr = PetscFree(rootPoints);CHKERRQ(ierr);
2332   ierr = PetscFree(leafPoints);CHKERRQ(ierr);
2333   PetscFunctionReturn(0);
2334 }
2335 
2336 /*@
2337   DMPlexPartitionLabelCreateSF - Create a star forest from a label that assigns ranks to points
2338 
2339   Input Parameters:
2340 + dm    - The DM
2341 . label - DMLabel assinging ranks to remote roots
2342 
2343   Output Parameter:
2344 - sf    - The star forest communication context encapsulating the defined mapping
2345 
2346   Note: The incoming label is a receiver mapping of remote points to their parent rank.
2347 
2348   Level: developer
2349 
2350 .seealso: DMPlexDistribute(), DMPlexCreateOverlap
2351 @*/
2352 PetscErrorCode DMPlexPartitionLabelCreateSF(DM dm, DMLabel label, PetscSF *sf)
2353 {
2354   PetscMPIInt     rank, size;
2355   PetscInt        n, numRemote, p, numPoints, pStart, pEnd, idx = 0;
2356   PetscSFNode    *remotePoints;
2357   IS              remoteRootIS;
2358   const PetscInt *remoteRoots;
2359   PetscErrorCode ierr;
2360 
2361   PetscFunctionBegin;
2362   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2363   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2364 
2365   for (numRemote = 0, n = 0; n < size; ++n) {
2366     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2367     numRemote += numPoints;
2368   }
2369   ierr = PetscMalloc1(numRemote, &remotePoints);CHKERRQ(ierr);
2370   /* Put owned points first */
2371   ierr = DMLabelGetStratumSize(label, rank, &numPoints);CHKERRQ(ierr);
2372   if (numPoints > 0) {
2373     ierr = DMLabelGetStratumIS(label, rank, &remoteRootIS);CHKERRQ(ierr);
2374     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2375     for (p = 0; p < numPoints; p++) {
2376       remotePoints[idx].index = remoteRoots[p];
2377       remotePoints[idx].rank = rank;
2378       idx++;
2379     }
2380     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2381     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2382   }
2383   /* Now add remote points */
2384   for (n = 0; n < size; ++n) {
2385     ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
2386     if (numPoints <= 0 || n == rank) continue;
2387     ierr = DMLabelGetStratumIS(label, n, &remoteRootIS);CHKERRQ(ierr);
2388     ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2389     for (p = 0; p < numPoints; p++) {
2390       remotePoints[idx].index = remoteRoots[p];
2391       remotePoints[idx].rank = n;
2392       idx++;
2393     }
2394     ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
2395     ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
2396   }
2397   ierr = PetscSFCreate(PetscObjectComm((PetscObject) dm), sf);CHKERRQ(ierr);
2398   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
2399   ierr = PetscSFSetGraph(*sf, pEnd-pStart, numRemote, NULL, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
2400   PetscFunctionReturn(0);
2401 }
2402