Reference documentation for deal.II version GIT d77e5ebb0a 2023-01-27 22:35:02+00:00
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sparsity_tools.cc
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15 
16 
18 
19 #include <deal.II/lac/exceptions.h>
22 
23 #include <algorithm>
24 #include <functional>
25 #include <memory>
26 #include <set>
27 
28 #ifdef DEAL_II_WITH_MPI
29 # include <deal.II/base/mpi.h>
30 # include <deal.II/base/utilities.h>
31 
34 #endif
35 
36 #ifdef DEAL_II_WITH_METIS
37 extern "C"
38 {
39 # include <metis.h>
40 }
41 #endif
42 
43 #ifdef DEAL_II_TRILINOS_WITH_ZOLTAN
44 # include <zoltan_cpp.h>
45 #endif
46 
47 #include <string>
48 
49 
51 
52 namespace SparsityTools
53 {
54  namespace
55  {
56  void
57  partition_metis(const SparsityPattern & sparsity_pattern,
58  const std::vector<unsigned int> &cell_weights,
59  const unsigned int n_partitions,
60  std::vector<unsigned int> & partition_indices)
61  {
62  // Make sure that METIS is actually
63  // installed and detected
64 #ifndef DEAL_II_WITH_METIS
65  (void)sparsity_pattern;
66  (void)cell_weights;
67  (void)n_partitions;
68  (void)partition_indices;
70 #else
71 
72  // Generate the data structures for METIS. Note that this is particularly
73  // simple, since METIS wants exactly our compressed row storage format.
74  // We only have to set up a few auxiliary arrays and convert from our
75  // unsigned cell weights to signed ones.
76  idx_t n = static_cast<signed int>(sparsity_pattern.n_rows());
77 
78  idx_t ncon = 1; // number of balancing constraints (should be >0)
79 
80  // We can not partition n items into more than n parts. METIS will
81  // generate non-sensical output (everything is owned by a single process)
82  // and complain with a message (but won't return an error code!):
83  // ***Cannot bisect a graph with 0 vertices!
84  // ***You are trying to partition a graph into too many parts!
85  idx_t nparts =
86  std::min(n,
87  static_cast<idx_t>(
88  n_partitions)); // number of subdomains to create
89 
90  // use default options for METIS
91  idx_t options[METIS_NOPTIONS];
92  METIS_SetDefaultOptions(options);
93 
94  // one more nuisance: we have to copy our own data to arrays that store
95  // signed integers :-(
96  std::vector<idx_t> int_rowstart(1);
97  int_rowstart.reserve(sparsity_pattern.n_rows() + 1);
98  std::vector<idx_t> int_colnums;
99  int_colnums.reserve(sparsity_pattern.n_nonzero_elements());
100  for (SparsityPattern::size_type row = 0; row < sparsity_pattern.n_rows();
101  ++row)
102  {
103  for (SparsityPattern::iterator col = sparsity_pattern.begin(row);
104  col < sparsity_pattern.end(row);
105  ++col)
106  int_colnums.push_back(col->column());
107  int_rowstart.push_back(int_colnums.size());
108  }
109 
110  std::vector<idx_t> int_partition_indices(sparsity_pattern.n_rows());
111 
112  // Set up cell weighting option
113  std::vector<idx_t> int_cell_weights;
114  if (cell_weights.size() > 0)
115  {
116  Assert(cell_weights.size() == sparsity_pattern.n_rows(),
117  ExcDimensionMismatch(cell_weights.size(),
118  sparsity_pattern.n_rows()));
119  int_cell_weights.resize(cell_weights.size());
120  std::copy(cell_weights.begin(),
121  cell_weights.end(),
122  int_cell_weights.begin());
123  }
124  // Set a pointer to the optional cell weighting information.
125  // METIS expects a null pointer if there are no weights to be considered.
126  idx_t *const p_int_cell_weights =
127  (cell_weights.size() > 0 ? int_cell_weights.data() : nullptr);
128 
129 
130  // Make use of METIS' error code.
131  int ierr;
132 
133  // Select which type of partitioning to create
134 
135  // Use recursive if the number of partitions is less than or equal to 8
136  idx_t dummy; // output: # of edges cut by the resulting partition
137  if (nparts <= 8)
138  ierr = METIS_PartGraphRecursive(&n,
139  &ncon,
140  int_rowstart.data(),
141  int_colnums.data(),
142  p_int_cell_weights,
143  nullptr,
144  nullptr,
145  &nparts,
146  nullptr,
147  nullptr,
148  options,
149  &dummy,
150  int_partition_indices.data());
151 
152  // Otherwise use kway
153  else
154  ierr = METIS_PartGraphKway(&n,
155  &ncon,
156  int_rowstart.data(),
157  int_colnums.data(),
158  p_int_cell_weights,
159  nullptr,
160  nullptr,
161  &nparts,
162  nullptr,
163  nullptr,
164  options,
165  &dummy,
166  int_partition_indices.data());
167 
168  // If metis returns normally, an error code METIS_OK=1 is returned from
169  // the above functions (see metish.h)
170  AssertThrow(ierr == 1, ExcMETISError(ierr));
171 
172  // now copy back generated indices into the output array
173  std::copy(int_partition_indices.begin(),
174  int_partition_indices.end(),
175  partition_indices.begin());
176 #endif
177  }
178 
179 
180 // Query functions unused if zoltan is not installed
181 #ifdef DEAL_II_TRILINOS_WITH_ZOLTAN
182  // Query functions for partition_zoltan
183  int
184  get_number_of_objects(void *data, int *ierr)
185  {
186  SparsityPattern *graph = reinterpret_cast<SparsityPattern *>(data);
187 
188  *ierr = ZOLTAN_OK;
189 
190  return graph->n_rows();
191  }
192 
193 
194  void
195  get_object_list(void *data,
196  int /*sizeGID*/,
197  int /*sizeLID*/,
198  ZOLTAN_ID_PTR globalID,
199  ZOLTAN_ID_PTR localID,
200  int /*wgt_dim*/,
201  float * /*obj_wgts*/,
202  int *ierr)
203  {
204  SparsityPattern *graph = reinterpret_cast<SparsityPattern *>(data);
205  *ierr = ZOLTAN_OK;
206 
207  Assert(globalID != nullptr, ExcInternalError());
208  Assert(localID != nullptr, ExcInternalError());
209 
210  // set global degrees of freedom
211  auto n_dofs = graph->n_rows();
212 
213  for (unsigned int i = 0; i < n_dofs; ++i)
214  {
215  globalID[i] = i;
216  localID[i] = i; // Same as global ids.
217  }
218  }
219 
220 
221  void
222  get_num_edges_list(void *data,
223  int /*sizeGID*/,
224  int /*sizeLID*/,
225  int num_obj,
226  ZOLTAN_ID_PTR globalID,
227  ZOLTAN_ID_PTR /*localID*/,
228  int *numEdges,
229  int *ierr)
230  {
231  SparsityPattern *graph = reinterpret_cast<SparsityPattern *>(data);
232 
233  *ierr = ZOLTAN_OK;
234 
235  Assert(numEdges != nullptr, ExcInternalError());
236 
237  for (int i = 0; i < num_obj; ++i)
238  {
239  if (graph->exists(i, i)) // Check if diagonal element is present
240  numEdges[i] = graph->row_length(globalID[i]) - 1;
241  else
242  numEdges[i] = graph->row_length(globalID[i]);
243  }
244  }
245 
246 
247 
248  void
249  get_edge_list(void *data,
250  int /*sizeGID*/,
251  int /*sizeLID*/,
252  int num_obj,
253  ZOLTAN_ID_PTR /*globalID*/,
254  ZOLTAN_ID_PTR /*localID*/,
255  int * /*num_edges*/,
256  ZOLTAN_ID_PTR nborGID,
257  int * nborProc,
258  int /*wgt_dim*/,
259  float * /*ewgts*/,
260  int *ierr)
261  {
262  SparsityPattern *graph = reinterpret_cast<SparsityPattern *>(data);
263  *ierr = ZOLTAN_OK;
264 
265  ZOLTAN_ID_PTR nextNborGID = nborGID;
266  int * nextNborProc = nborProc;
267 
268  // Loop through rows corresponding to indices in globalID implicitly
269  for (SparsityPattern::size_type i = 0;
270  i < static_cast<SparsityPattern::size_type>(num_obj);
271  ++i)
272  {
273  // Loop through each column to find neighbours
274  for (SparsityPattern::iterator col = graph->begin(i);
275  col < graph->end(i);
276  ++col)
277  // Ignore diagonal entries. Not needed for partitioning.
278  if (i != col->column())
279  {
280  Assert(nextNborGID != nullptr, ExcInternalError());
281  Assert(nextNborProc != nullptr, ExcInternalError());
282 
283  *nextNborGID++ = col->column();
284  *nextNborProc++ = 0; // All the vertices on processor 0
285  }
286  }
287  }
288 #endif
289 
290 
291  void
292  partition_zoltan(const SparsityPattern & sparsity_pattern,
293  const std::vector<unsigned int> &cell_weights,
294  const unsigned int n_partitions,
295  std::vector<unsigned int> & partition_indices)
296  {
297  // Make sure that ZOLTAN is actually
298  // installed and detected
299 #ifndef DEAL_II_TRILINOS_WITH_ZOLTAN
300  (void)sparsity_pattern;
301  (void)cell_weights;
302  (void)n_partitions;
303  (void)partition_indices;
305 #else
306 
307  Assert(
308  cell_weights.size() == 0,
309  ExcMessage(
310  "The cell weighting functionality for Zoltan has not yet been implemented."));
311  (void)cell_weights;
312 
313  // MPI environment must have been initialized by this point.
314  std::unique_ptr<Zoltan> zz = std::make_unique<Zoltan>(MPI_COMM_SELF);
315 
316  // General parameters
317  // DEBUG_LEVEL call must precede the call to LB_METHOD
318  zz->Set_Param("DEBUG_LEVEL", "0"); // set level of debug info
319  zz->Set_Param(
320  "LB_METHOD",
321  "GRAPH"); // graph based partition method (LB-load balancing)
322  zz->Set_Param("NUM_LOCAL_PARTS",
323  std::to_string(n_partitions)); // set number of partitions
324 
325  // The PHG partitioner is a hypergraph partitioner that Zoltan could use
326  // for graph partitioning.
327  // If number of vertices in hyperedge divided by total vertices in
328  // hypergraph exceeds PHG_EDGE_SIZE_THRESHOLD,
329  // then the hyperedge will be omitted as such (dense) edges will likely
330  // incur high communication costs regardless of the partition.
331  // PHG_EDGE_SIZE_THRESHOLD value is raised to 0.5 from the default
332  // value of 0.25 so that the PHG partitioner doesn't throw warning saying
333  // "PHG_EDGE_SIZE_THRESHOLD is low ..." after removing all dense edges.
334  // For instance, in two dimensions if the triangulation being partitioned
335  // is two quadrilaterals sharing an edge and if PHG_EDGE_SIZE_THRESHOLD
336  // value is set to 0.25, PHG will remove all the edges throwing the
337  // above warning.
338  zz->Set_Param("PHG_EDGE_SIZE_THRESHOLD", "0.5");
339 
340  // Need a non-const object equal to sparsity_pattern
341  SparsityPattern graph;
342  graph.copy_from(sparsity_pattern);
343 
344  // Set query functions
345  zz->Set_Num_Obj_Fn(get_number_of_objects, &graph);
346  zz->Set_Obj_List_Fn(get_object_list, &graph);
347  zz->Set_Num_Edges_Multi_Fn(get_num_edges_list, &graph);
348  zz->Set_Edge_List_Multi_Fn(get_edge_list, &graph);
349 
350  // Variables needed by partition function
351  int changes = 0;
352  int num_gid_entries = 1;
353  int num_lid_entries = 1;
354  int num_import = 0;
355  ZOLTAN_ID_PTR import_global_ids = nullptr;
356  ZOLTAN_ID_PTR import_local_ids = nullptr;
357  int * import_procs = nullptr;
358  int * import_to_part = nullptr;
359  int num_export = 0;
360  ZOLTAN_ID_PTR export_global_ids = nullptr;
361  ZOLTAN_ID_PTR export_local_ids = nullptr;
362  int * export_procs = nullptr;
363  int * export_to_part = nullptr;
364 
365  // call partitioner
366  const int rc = zz->LB_Partition(changes,
367  num_gid_entries,
368  num_lid_entries,
369  num_import,
370  import_global_ids,
371  import_local_ids,
372  import_procs,
373  import_to_part,
374  num_export,
375  export_global_ids,
376  export_local_ids,
377  export_procs,
378  export_to_part);
379  (void)rc;
380 
381  // check for error code in partitioner
382  Assert(rc == ZOLTAN_OK, ExcInternalError());
383 
384  // By default, all indices belong to part 0. After zoltan partition
385  // some are migrated to different part ID, which is stored in
386  // export_to_part array.
387  std::fill(partition_indices.begin(), partition_indices.end(), 0);
388 
389  // copy from export_to_part to partition_indices, whose part_ids != 0.
390  Assert(export_to_part != nullptr, ExcInternalError());
391  for (int i = 0; i < num_export; ++i)
392  partition_indices[export_local_ids[i]] = export_to_part[i];
393 #endif
394  }
395  } // namespace
396 
397 
398  void
399  partition(const SparsityPattern & sparsity_pattern,
400  const unsigned int n_partitions,
401  std::vector<unsigned int> &partition_indices,
402  const Partitioner partitioner)
403  {
404  std::vector<unsigned int> cell_weights;
405 
406  // Call the other more general function
407  partition(sparsity_pattern,
408  cell_weights,
409  n_partitions,
410  partition_indices,
411  partitioner);
412  }
413 
414 
415  void
416  partition(const SparsityPattern & sparsity_pattern,
417  const std::vector<unsigned int> &cell_weights,
418  const unsigned int n_partitions,
419  std::vector<unsigned int> & partition_indices,
420  const Partitioner partitioner)
421  {
422  Assert(sparsity_pattern.n_rows() == sparsity_pattern.n_cols(),
423  ExcNotQuadratic());
424  Assert(sparsity_pattern.is_compressed(),
426 
427  Assert(n_partitions > 0, ExcInvalidNumberOfPartitions(n_partitions));
428  Assert(partition_indices.size() == sparsity_pattern.n_rows(),
429  ExcInvalidArraySize(partition_indices.size(),
430  sparsity_pattern.n_rows()));
431 
432  // check for an easy return
433  if (n_partitions == 1 || (sparsity_pattern.n_rows() == 1))
434  {
435  std::fill_n(partition_indices.begin(), partition_indices.size(), 0U);
436  return;
437  }
438 
439  if (partitioner == Partitioner::metis)
440  partition_metis(sparsity_pattern,
441  cell_weights,
442  n_partitions,
443  partition_indices);
444  else if (partitioner == Partitioner::zoltan)
445  partition_zoltan(sparsity_pattern,
446  cell_weights,
447  n_partitions,
448  partition_indices);
449  else
450  AssertThrow(false, ExcInternalError());
451  }
452 
453 
454  unsigned int
455  color_sparsity_pattern(const SparsityPattern & sparsity_pattern,
456  std::vector<unsigned int> &color_indices)
457  {
458  // Make sure that ZOLTAN is actually
459  // installed and detected
460 #ifndef DEAL_II_TRILINOS_WITH_ZOLTAN
461  (void)sparsity_pattern;
462  (void)color_indices;
464  return 0;
465 #else
466  // coloring algorithm is run in serial by each processor.
467  std::unique_ptr<Zoltan> zz = std::make_unique<Zoltan>(MPI_COMM_SELF);
468 
469  // Coloring parameters
470  // DEBUG_LEVEL must precede all other calls
471  zz->Set_Param("DEBUG_LEVEL", "0"); // level of debug info
472  zz->Set_Param("COLORING_PROBLEM", "DISTANCE-1"); // Standard coloring
473  zz->Set_Param("NUM_GID_ENTRIES", "1"); // 1 entry represents global ID
474  zz->Set_Param("NUM_LID_ENTRIES", "1"); // 1 entry represents local ID
475  zz->Set_Param("OBJ_WEIGHT_DIM", "0"); // object weights not used
476  zz->Set_Param("RECOLORING_NUM_OF_ITERATIONS", "0");
477 
478  // Zoltan::Color function requires a non-const SparsityPattern object
479  SparsityPattern graph;
480  graph.copy_from(sparsity_pattern);
481 
482  // Set query functions required by coloring function
483  zz->Set_Num_Obj_Fn(get_number_of_objects, &graph);
484  zz->Set_Obj_List_Fn(get_object_list, &graph);
485  zz->Set_Num_Edges_Multi_Fn(get_num_edges_list, &graph);
486  zz->Set_Edge_List_Multi_Fn(get_edge_list, &graph);
487 
488  // Variables needed by coloring function
489  int num_gid_entries = 1;
490  const int num_objects = graph.n_rows();
491 
492  // Preallocate input variables. Element type fixed by ZOLTAN.
493  std::vector<ZOLTAN_ID_TYPE> global_ids(num_objects);
494  std::vector<int> color_exp(num_objects);
495 
496  // Set ids for which coloring needs to be done
497  for (int i = 0; i < num_objects; ++i)
498  global_ids[i] = i;
499 
500  // Call ZOLTAN coloring algorithm
501  int rc = zz->Color(num_gid_entries,
502  num_objects,
503  global_ids.data(),
504  color_exp.data());
505 
506  (void)rc;
507  // Check for error code
508  Assert(rc == ZOLTAN_OK, ExcInternalError());
509 
510  // Allocate and assign color indices
511  color_indices.resize(num_objects);
512  Assert(color_exp.size() == color_indices.size(),
513  ExcDimensionMismatch(color_exp.size(), color_indices.size()));
514 
515  std::copy(color_exp.begin(), color_exp.end(), color_indices.begin());
516 
517  unsigned int n_colors =
518  *(std::max_element(color_indices.begin(), color_indices.end()));
519  return n_colors;
520 #endif
521  }
522 
523 
524  namespace internal
525  {
533  const DynamicSparsityPattern & sparsity,
534  const std::vector<DynamicSparsityPattern::size_type> &new_indices)
535  {
536  DynamicSparsityPattern::size_type starting_point =
538  DynamicSparsityPattern::size_type min_coordination = sparsity.n_rows();
539  for (DynamicSparsityPattern::size_type row = 0; row < sparsity.n_rows();
540  ++row)
541  // look over all as-yet unnumbered indices
542  if (new_indices[row] == numbers::invalid_size_type)
543  {
544  if (sparsity.row_length(row) < min_coordination)
545  {
546  min_coordination = sparsity.row_length(row);
547  starting_point = row;
548  }
549  }
550 
551  // now we still have to care for the case that no unnumbered dof has a
552  // coordination number less than sparsity.n_rows(). this rather exotic
553  // case only happens if we only have one cell, as far as I can see,
554  // but there may be others as well.
555  //
556  // if that should be the case, we can chose an arbitrary dof as
557  // starting point, e.g. the first unnumbered one
558  if (starting_point == numbers::invalid_size_type)
559  {
560  for (DynamicSparsityPattern::size_type i = 0; i < new_indices.size();
561  ++i)
562  if (new_indices[i] == numbers::invalid_size_type)
563  {
564  starting_point = i;
565  break;
566  }
567 
568  Assert(starting_point != numbers::invalid_size_type,
569  ExcInternalError());
570  }
571 
572  return starting_point;
573  }
574  } // namespace internal
575 
576 
577 
578  void
580  const DynamicSparsityPattern & sparsity,
581  std::vector<DynamicSparsityPattern::size_type> & new_indices,
582  const std::vector<DynamicSparsityPattern::size_type> &starting_indices)
583  {
584  Assert(sparsity.n_rows() == sparsity.n_cols(),
585  ExcDimensionMismatch(sparsity.n_rows(), sparsity.n_cols()));
586  Assert(sparsity.n_rows() == new_indices.size(),
587  ExcDimensionMismatch(sparsity.n_rows(), new_indices.size()));
588  Assert(starting_indices.size() <= sparsity.n_rows(),
589  ExcMessage(
590  "You can't specify more starting indices than there are rows"));
591  Assert(sparsity.row_index_set().size() == 0 ||
592  sparsity.row_index_set().size() == sparsity.n_rows(),
593  ExcMessage(
594  "Only valid for sparsity patterns which store all rows."));
595  for (const auto starting_index : starting_indices)
596  {
597  (void)starting_index;
598  Assert(starting_index < sparsity.n_rows(),
599  ExcMessage("Invalid starting index: All starting indices need "
600  "to be between zero and the number of rows in the "
601  "sparsity pattern."));
602  }
603 
604  // store the indices of the dofs renumbered in the last round. Default to
605  // starting points
606  std::vector<DynamicSparsityPattern::size_type> last_round_dofs(
607  starting_indices);
608 
609  // initialize the new_indices array with invalid values
610  std::fill(new_indices.begin(),
611  new_indices.end(),
613 
614  // if no starting indices were given: find dof with lowest coordination
615  // number
616  if (last_round_dofs.empty())
617  last_round_dofs.push_back(
618  internal::find_unnumbered_starting_index(sparsity, new_indices));
619 
620  // store next free dof index
621  DynamicSparsityPattern::size_type next_free_number = 0;
622 
623  // enumerate the first round dofs
624  for (const auto &last_round_dof : last_round_dofs)
625  new_indices[last_round_dof] = next_free_number++;
626 
627  // now do as many steps as needed to renumber all dofs
628  while (true)
629  {
630  // store the indices of the dofs to be renumbered in the next round
631  std::vector<DynamicSparsityPattern::size_type> next_round_dofs;
632 
633  // find all neighbors of the dofs numbered in the last round
634  for (const auto dof : last_round_dofs)
635  for (DynamicSparsityPattern::iterator j = sparsity.begin(dof);
636  j < sparsity.end(dof);
637  ++j)
638  next_round_dofs.push_back(j->column());
639 
640  // sort dof numbers
641  std::sort(next_round_dofs.begin(), next_round_dofs.end());
642 
643  // delete multiple entries
644  std::vector<DynamicSparsityPattern::size_type>::iterator end_sorted;
645  end_sorted =
646  std::unique(next_round_dofs.begin(), next_round_dofs.end());
647  next_round_dofs.erase(end_sorted, next_round_dofs.end());
648 
649  // eliminate dofs which are already numbered
650  for (int s = next_round_dofs.size() - 1; s >= 0; --s)
651  if (new_indices[next_round_dofs[s]] != numbers::invalid_size_type)
652  next_round_dofs.erase(next_round_dofs.begin() + s);
653 
654  // check whether there are any new dofs in the list. if there are
655  // none, then we have completely numbered the current component of the
656  // graph. check if there are as yet unnumbered components of the graph
657  // that we would then have to do next
658  if (next_round_dofs.empty())
659  {
660  if (std::find(new_indices.begin(),
661  new_indices.end(),
662  numbers::invalid_size_type) == new_indices.end())
663  // no unnumbered indices, so we can leave now
664  break;
665 
666  // otherwise find a valid starting point for the next component of
667  // the graph and continue with numbering that one. we only do so
668  // if no starting indices were provided by the user (see the
669  // documentation of this function) so produce an error if we got
670  // here and starting indices were given
671  Assert(starting_indices.empty(),
672  ExcMessage("The input graph appears to have more than one "
673  "component, but as stated in the documentation "
674  "we only want to reorder such graphs if no "
675  "starting indices are given. The function was "
676  "called with starting indices, however."))
677 
678  next_round_dofs.push_back(
680  new_indices));
681  }
682 
683 
684 
685  // store for each coordination number the dofs with these coordination
686  // number
687  std::multimap<DynamicSparsityPattern::size_type, int>
688  dofs_by_coordination;
689 
690  // find coordination number for each of these dofs
691  for (const types::global_dof_index next_round_dof : next_round_dofs)
692  {
693  const DynamicSparsityPattern::size_type coordination =
694  sparsity.row_length(next_round_dof);
695 
696  // insert this dof at its coordination number
697  const std::pair<const DynamicSparsityPattern::size_type, int>
698  new_entry(coordination, next_round_dof);
699  dofs_by_coordination.insert(new_entry);
700  }
701 
702  // assign new DoF numbers to the elements of the present front:
703  std::multimap<DynamicSparsityPattern::size_type, int>::iterator i;
704  for (i = dofs_by_coordination.begin(); i != dofs_by_coordination.end();
705  ++i)
706  new_indices[i->second] = next_free_number++;
707 
708  // after that: copy this round's dofs for the next round
709  last_round_dofs = next_round_dofs;
710  }
711 
712  // test for all indices numbered. this mostly tests whether the
713  // front-marching-algorithm (which Cuthill-McKee actually is) has reached
714  // all points.
715  Assert((std::find(new_indices.begin(),
716  new_indices.end(),
717  numbers::invalid_size_type) == new_indices.end()) &&
718  (next_free_number == sparsity.n_rows()),
719  ExcInternalError());
720  }
721 
722 
723 
724  namespace internal
725  {
726  void
728  const DynamicSparsityPattern & connectivity,
729  std::vector<DynamicSparsityPattern::size_type> &renumbering)
730  {
731  AssertDimension(connectivity.n_rows(), connectivity.n_cols());
732  AssertDimension(connectivity.n_rows(), renumbering.size());
733  Assert(connectivity.row_index_set().size() == 0 ||
734  connectivity.row_index_set().size() == connectivity.n_rows(),
735  ExcMessage(
736  "Only valid for sparsity patterns which store all rows."));
737 
738  std::vector<types::global_dof_index> touched_nodes(
739  connectivity.n_rows(), numbers::invalid_dof_index);
740  std::vector<unsigned int> row_lengths(connectivity.n_rows());
741  std::set<types::global_dof_index> current_neighbors;
742  std::vector<std::vector<types::global_dof_index>> groups;
743 
744  // First collect the number of neighbors for each node. We use this
745  // field to find next nodes with the minimum number of non-touched
746  // neighbors in the field n_remaining_neighbors, so we will count down
747  // on this field. We also cache the row lengths because we need this
748  // data frequently and getting it from the sparsity pattern is more
749  // expensive.
750  for (types::global_dof_index row = 0; row < connectivity.n_rows(); ++row)
751  {
752  row_lengths[row] = connectivity.row_length(row);
753  Assert(row_lengths[row] > 0, ExcInternalError());
754  }
755  std::vector<unsigned int> n_remaining_neighbors(row_lengths);
756 
757  // This outer loop is typically traversed only once, unless the global
758  // graph is not connected
759  while (true)
760  {
761  // Find cell with the minimal number of neighbors (typically a
762  // corner node when based on FEM meshes). If no cell is left, we are
763  // done. Together with the outer while loop, this loop can possibly
764  // be of quadratic complexity in the number of disconnected
765  // partitions, i.e. up to connectivity.n_rows() in the worst case,
766  // but that is not the usual use case of this loop and thus not
767  // optimized for.
768  std::pair<types::global_dof_index, types::global_dof_index>
769  min_neighbors(numbers::invalid_dof_index,
771  for (types::global_dof_index i = 0; i < touched_nodes.size(); ++i)
772  if (touched_nodes[i] == numbers::invalid_dof_index)
773  if (row_lengths[i] < min_neighbors.second)
774  {
775  min_neighbors = std::make_pair(i, n_remaining_neighbors[i]);
776  if (n_remaining_neighbors[i] <= 1)
777  break;
778  }
779  if (min_neighbors.first == numbers::invalid_dof_index)
780  break;
781 
782  Assert(min_neighbors.second > 0, ExcInternalError());
783 
784  current_neighbors.clear();
785  current_neighbors.insert(min_neighbors.first);
786  while (!current_neighbors.empty())
787  {
788  // Find node with minimum number of untouched neighbors among the
789  // next set of possible neighbors
790  min_neighbors = std::make_pair(numbers::invalid_dof_index,
792  for (const auto current_neighbor : current_neighbors)
793  {
794  Assert(touched_nodes[current_neighbor] ==
796  ExcInternalError());
797  if (n_remaining_neighbors[current_neighbor] <
798  min_neighbors.second)
799  min_neighbors =
800  std::make_pair(current_neighbor,
801  n_remaining_neighbors[current_neighbor]);
802  }
803 
804  // Among the set of nodes with the minimal number of neighbors,
805  // choose the one with the largest number of touched neighbors,
806  // i.e., the one with the largest row length
807  const types::global_dof_index best_row_length =
808  min_neighbors.second;
809  for (const auto current_neighbor : current_neighbors)
810  if (n_remaining_neighbors[current_neighbor] == best_row_length)
811  if (row_lengths[current_neighbor] > min_neighbors.second)
812  min_neighbors =
813  std::make_pair(current_neighbor,
814  row_lengths[current_neighbor]);
815 
816  // Add the pivot and all direct neighbors of the pivot node not
817  // yet touched to the list of new entries.
818  groups.emplace_back();
819  std::vector<types::global_dof_index> &next_group = groups.back();
820 
821  next_group.push_back(min_neighbors.first);
822  touched_nodes[min_neighbors.first] = groups.size() - 1;
824  connectivity.begin(min_neighbors.first);
825  it != connectivity.end(min_neighbors.first);
826  ++it)
827  if (touched_nodes[it->column()] == numbers::invalid_dof_index)
828  {
829  next_group.push_back(it->column());
830  touched_nodes[it->column()] = groups.size() - 1;
831  }
832 
833  // Add all neighbors of the current list not yet touched to the
834  // set of possible next pivots. The added node is no longer a
835  // valid neighbor (here we assume symmetry of the
836  // connectivity). Delete the entries of the current list from
837  // the set of possible next pivots.
838  for (const auto index : next_group)
839  {
841  connectivity.begin(index);
842  it != connectivity.end(index);
843  ++it)
844  {
845  if (touched_nodes[it->column()] ==
847  current_neighbors.insert(it->column());
848  n_remaining_neighbors[it->column()]--;
849  }
850  current_neighbors.erase(index);
851  }
852  }
853  }
854 
855  // Sanity check: for all nodes, there should not be any neighbors left
856  for (types::global_dof_index row = 0; row < connectivity.n_rows(); ++row)
857  Assert(n_remaining_neighbors[row] == 0, ExcInternalError());
858 
859  // If the number of groups is smaller than the number of nodes, we
860  // continue by recursively calling this method
861  if (groups.size() < connectivity.n_rows())
862  {
863  // Form the connectivity of the groups
864  DynamicSparsityPattern connectivity_next(groups.size(),
865  groups.size());
866  for (types::global_dof_index i = 0; i < groups.size(); ++i)
867  for (types::global_dof_index col = 0; col < groups[i].size(); ++col)
869  connectivity.begin(groups[i][col]);
870  it != connectivity.end(groups[i][col]);
871  ++it)
872  connectivity_next.add(i, touched_nodes[it->column()]);
873 
874  // Recursively call the reordering
875  std::vector<types::global_dof_index> renumbering_next(groups.size());
876  reorder_hierarchical(connectivity_next, renumbering_next);
877 
878  // Renumber the indices group by group according to the incoming
879  // ordering for the groups
880  for (types::global_dof_index i = 0, count = 0; i < groups.size(); ++i)
881  for (types::global_dof_index col = 0;
882  col < groups[renumbering_next[i]].size();
883  ++col, ++count)
884  renumbering[count] = groups[renumbering_next[i]][col];
885  }
886  else
887  {
888  // All groups should have size one and no more recursion is possible,
889  // so use the numbering of the groups
890  for (types::global_dof_index i = 0, count = 0; i < groups.size(); ++i)
891  for (types::global_dof_index col = 0; col < groups[i].size();
892  ++col, ++count)
893  renumbering[count] = groups[i][col];
894  }
895  }
896  } // namespace internal
897 
898  void
900  const DynamicSparsityPattern & connectivity,
901  std::vector<DynamicSparsityPattern::size_type> &renumbering)
902  {
903  // the internal renumbering keeps the numbering the wrong way around (but
904  // we cannot invert the numbering inside that method because it is used
905  // recursively), so invert it here
906  internal::reorder_hierarchical(connectivity, renumbering);
907  renumbering = Utilities::invert_permutation(renumbering);
908  }
909 
910 
911 
912 #ifdef DEAL_II_WITH_MPI
913 
914  void
916  const IndexSet & locally_owned_rows,
917  const MPI_Comm & mpi_comm,
918  const IndexSet & locally_relevant_rows)
919  {
920  using map_vec_t =
921  std::map<unsigned int, std::vector<DynamicSparsityPattern::size_type>>;
922 
923  // 1. limit rows to non owned:
924  IndexSet requested_rows(locally_relevant_rows);
925  requested_rows.subtract_set(locally_owned_rows);
926 
927  std::vector<unsigned int> index_owner =
928  Utilities::MPI::compute_index_owner(locally_owned_rows,
929  requested_rows,
930  mpi_comm);
931 
932  // 2. go through requested_rows, figure out the owner and add the row to
933  // request
934  map_vec_t rows_data;
936  i < requested_rows.n_elements();
937  ++i)
938  {
940  requested_rows.nth_index_in_set(i);
941 
942  rows_data[index_owner[i]].push_back(row);
943  }
944 
945  // 3. get what others ask us to send
946  const auto rows_data_received =
947  Utilities::MPI::some_to_some(mpi_comm, rows_data);
948 
949  // 4. now prepare data to be sent in the same format as in
950  // distribute_sparsity_pattern() below, i.e.
951  // rX,num_rX,cols_rX
952  map_vec_t send_data;
953  for (const auto &data : rows_data_received)
954  {
955  for (const auto &row : data.second)
956  {
957  const auto rlen = dsp.row_length(row);
958 
959  // skip empty lines
960  if (rlen == 0)
961  continue;
962 
963  // save entries
964  send_data[data.first].push_back(row); // row index
965  send_data[data.first].push_back(rlen); // number of entries
966  for (DynamicSparsityPattern::size_type c = 0; c < rlen; ++c)
967  send_data[data.first].push_back(
968  dsp.column_number(row, c)); // columns
969  } // loop over rows
970  } // loop over received data
971 
972  // 5. communicate rows
973  const auto received_data =
974  Utilities::MPI::some_to_some(mpi_comm, send_data);
975 
976  // 6. add result to our sparsity
977  for (const auto &data : received_data)
978  {
979  const auto &recv_buf = data.second;
980  auto ptr = recv_buf.begin();
981  const auto end = recv_buf.end();
982  while (ptr != end)
983  {
984  const auto row = *(ptr++);
985  Assert(ptr != end, ExcInternalError());
986 
987  const auto n_entries = *(ptr++);
988  Assert(n_entries > 0, ExcInternalError());
989  Assert(ptr != end, ExcInternalError());
990 
991  // make sure we clear whatever was previously stored
992  // in these rows. Otherwise we can't guarantee that the
993  // data is consistent across MPI communicator.
994  dsp.clear_row(row);
995 
996  Assert(ptr + (n_entries - 1) != end, ExcInternalError());
997  dsp.add_entries(row, ptr, ptr + n_entries, true);
998  ptr += n_entries;
999  }
1000  Assert(ptr == end, ExcInternalError());
1001  }
1002  }
1003 
1004 
1005 
1006  void
1008  DynamicSparsityPattern & dsp,
1009  const std::vector<DynamicSparsityPattern::size_type> &rows_per_cpu,
1010  const MPI_Comm & mpi_comm,
1011  const IndexSet & myrange)
1012  {
1013  const unsigned int myid = Utilities::MPI::this_mpi_process(mpi_comm);
1014  std::vector<DynamicSparsityPattern::size_type> start_index(
1015  rows_per_cpu.size() + 1);
1016  start_index[0] = 0;
1017  for (DynamicSparsityPattern::size_type i = 0; i < rows_per_cpu.size(); ++i)
1018  start_index[i + 1] = start_index[i] + rows_per_cpu[i];
1019 
1020  IndexSet owned(start_index.back());
1021  owned.add_range(start_index[myid], start_index[myid] + rows_per_cpu[myid]);
1022 
1023  distribute_sparsity_pattern(dsp, owned, mpi_comm, myrange);
1024  }
1025 
1026 
1027 
1028  void
1030  const IndexSet & locally_owned_rows,
1031  const MPI_Comm & mpi_comm,
1032  const IndexSet & locally_relevant_rows)
1033  {
1034  IndexSet requested_rows(locally_relevant_rows);
1035  requested_rows.subtract_set(locally_owned_rows);
1036 
1037  std::vector<unsigned int> index_owner =
1038  Utilities::MPI::compute_index_owner(locally_owned_rows,
1039  requested_rows,
1040  mpi_comm);
1041 
1042  using map_vec_t =
1043  std::map<unsigned int, std::vector<DynamicSparsityPattern::size_type>>;
1044 
1045  map_vec_t send_data;
1046 
1048  i < requested_rows.n_elements();
1049  ++i)
1050  {
1052  requested_rows.nth_index_in_set(i);
1053 
1054  const auto rlen = dsp.row_length(row);
1055 
1056  // skip empty lines
1057  if (rlen == 0)
1058  continue;
1059 
1060  // save entries
1061  send_data[index_owner[i]].push_back(row); // row index
1062  send_data[index_owner[i]].push_back(rlen); // number of entries
1063  for (DynamicSparsityPattern::size_type c = 0; c < rlen; ++c)
1064  {
1065  // columns
1066  const auto column = dsp.column_number(row, c);
1067  send_data[index_owner[i]].push_back(column);
1068  }
1069  }
1070 
1071  const auto receive_data = Utilities::MPI::some_to_some(mpi_comm, send_data);
1072 
1073  // add what we received
1074  for (const auto &data : receive_data)
1075  {
1076  const auto &recv_buf = data.second;
1077  auto ptr = recv_buf.begin();
1078  const auto end = recv_buf.end();
1079  while (ptr != end)
1080  {
1081  const auto row = *(ptr++);
1082  Assert(ptr != end, ExcInternalError());
1083  const auto n_entries = *(ptr++);
1084 
1085  Assert(ptr + (n_entries - 1) != end, ExcInternalError());
1086  dsp.add_entries(row, ptr, ptr + n_entries, true);
1087  ptr += n_entries;
1088  }
1089  Assert(ptr == end, ExcInternalError());
1090  }
1091  }
1092 
1093 
1094 
1095  void
1097  const std::vector<IndexSet> &owned_set_per_cpu,
1098  const MPI_Comm & mpi_comm,
1099  const IndexSet & myrange)
1100  {
1101  const unsigned int myid = Utilities::MPI::this_mpi_process(mpi_comm);
1103  owned_set_per_cpu[myid],
1104  mpi_comm,
1105  myrange);
1106  }
1107 
1108 
1109 
1110  void
1112  const IndexSet & locally_owned_rows,
1113  const MPI_Comm & mpi_comm,
1114  const IndexSet &locally_relevant_rows)
1115  {
1116  using map_vec_t =
1118  std::vector<BlockDynamicSparsityPattern::size_type>>;
1119  map_vec_t send_data;
1120 
1121  IndexSet requested_rows(locally_relevant_rows);
1122  requested_rows.subtract_set(locally_owned_rows);
1123 
1124  std::vector<unsigned int> index_owner =
1125  Utilities::MPI::compute_index_owner(locally_owned_rows,
1126  requested_rows,
1127  mpi_comm);
1128 
1130  i < requested_rows.n_elements();
1131  ++i)
1132  {
1134  requested_rows.nth_index_in_set(i);
1135 
1137 
1138  // skip empty lines
1139  if (rlen == 0)
1140  continue;
1141 
1142  // save entries
1143  std::vector<BlockDynamicSparsityPattern::size_type> &dst =
1144  send_data[index_owner[i]];
1145 
1146  dst.push_back(rlen); // number of entries
1147  dst.push_back(row); // row index
1148  for (BlockDynamicSparsityPattern::size_type c = 0; c < rlen; ++c)
1149  {
1150  // columns
1152  dsp.column_number(row, c);
1153  dst.push_back(column);
1154  }
1155  }
1156 
1157  unsigned int num_receive = 0;
1158  {
1159  std::vector<unsigned int> send_to;
1160  send_to.reserve(send_data.size());
1161  for (const auto &sparsity_line : send_data)
1162  send_to.push_back(sparsity_line.first);
1163 
1164  num_receive =
1166  send_to);
1167  }
1168 
1169  std::vector<MPI_Request> requests(send_data.size());
1170 
1171 
1172  // send data
1173 
1174  static Utilities::MPI::CollectiveMutex mutex;
1175  Utilities::MPI::CollectiveMutex::ScopedLock lock(mutex, mpi_comm);
1176 
1177  const int mpi_tag = Utilities::MPI::internal::Tags::
1179 
1180  {
1181  unsigned int idx = 0;
1182  for (const auto &sparsity_line : send_data)
1183  {
1184  const int ierr = MPI_Isend(sparsity_line.second.data(),
1185  sparsity_line.second.size(),
1187  sparsity_line.first,
1188  mpi_tag,
1189  mpi_comm,
1190  &requests[idx++]);
1191  AssertThrowMPI(ierr);
1192  }
1193  }
1194 
1195  {
1196  // receive
1197  std::vector<BlockDynamicSparsityPattern::size_type> recv_buf;
1198  for (unsigned int index = 0; index < num_receive; ++index)
1199  {
1200  MPI_Status status;
1201  int ierr = MPI_Probe(MPI_ANY_SOURCE, mpi_tag, mpi_comm, &status);
1202  AssertThrowMPI(ierr);
1203 
1204  int len;
1205  ierr = MPI_Get_count(&status, DEAL_II_DOF_INDEX_MPI_TYPE, &len);
1206  AssertThrowMPI(ierr);
1207 
1208  recv_buf.resize(len);
1209  ierr = MPI_Recv(recv_buf.data(),
1210  len,
1212  status.MPI_SOURCE,
1213  status.MPI_TAG,
1214  mpi_comm,
1215  &status);
1216  AssertThrowMPI(ierr);
1217 
1218  std::vector<BlockDynamicSparsityPattern::size_type>::const_iterator
1219  ptr = recv_buf.begin();
1220  std::vector<BlockDynamicSparsityPattern::size_type>::const_iterator
1221  end = recv_buf.end();
1222  while (ptr != end)
1223  {
1225  Assert(ptr != end, ExcInternalError());
1227  for (unsigned int c = 0; c < num; ++c)
1228  {
1229  Assert(ptr != end, ExcInternalError());
1230  dsp.add(row, *ptr);
1231  ++ptr;
1232  }
1233  }
1234  Assert(ptr == end, ExcInternalError());
1235  }
1236  }
1237 
1238  // complete all sends, so that we can safely destroy the buffers.
1239  if (requests.size() > 0)
1240  {
1241  const int ierr =
1242  MPI_Waitall(requests.size(), requests.data(), MPI_STATUSES_IGNORE);
1243  AssertThrowMPI(ierr);
1244  }
1245  }
1246 #endif
1247 } // namespace SparsityTools
1248 
size_type column_number(const size_type row, const unsigned int index) const
unsigned int row_length(const size_type row) const
void add(const size_type i, const size_type j)
void add_entries(const size_type row, ForwardIterator begin, ForwardIterator end, const bool indices_are_unique_and_sorted=false)
types::global_dof_index size_type
const IndexSet & row_index_set() const
size_type row_length(const size_type row) const
size_type column_number(const size_type row, const size_type index) const
void clear_row(const size_type row)
void add(const size_type i, const size_type j)
size_type size() const
Definition: index_set.h:1641
size_type n_elements() const
Definition: index_set.h:1789
void subtract_set(const IndexSet &other)
Definition: index_set.cc:266
void add_range(const size_type begin, const size_type end)
Definition: index_set.h:1677
size_type nth_index_in_set(const size_type local_index) const
Definition: index_set.h:1837
types::global_dof_index size_type
size_type n_rows() const
size_type n_cols() const
bool is_compressed() const
std::size_t n_nonzero_elements() const
bool exists(const size_type i, const size_type j) const
iterator begin() const
void copy_from(const size_type n_rows, const size_type n_cols, const ForwardIterator begin, const ForwardIterator end)
iterator end() const
types::global_dof_index size_type
unsigned int row_length(const size_type row) const
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:461
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:462
static ::ExceptionBase & ExcZOLTANNotInstalled()
static ::ExceptionBase & ExcInvalidNumberOfPartitions(int arg1)
static ::ExceptionBase & ExcInternalError()
static ::ExceptionBase & ExcNotCompressed()
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
#define Assert(cond, exc)
Definition: exceptions.h:1509
#define AssertDimension(dim1, dim2)
Definition: exceptions.h:1703
#define AssertThrowMPI(error_code)
Definition: exceptions.h:1826
static ::ExceptionBase & ExcMETISNotInstalled()
static ::ExceptionBase & ExcInvalidArraySize(int arg1, int arg2)
static ::ExceptionBase & ExcMETISError(int arg1)
static ::ExceptionBase & ExcMessage(std::string arg1)
static ::ExceptionBase & ExcNotQuadratic()
#define AssertThrow(cond, exc)
Definition: exceptions.h:1619
static const char U
std::string to_string(const T &t)
Definition: patterns.h:2394
DynamicSparsityPattern::size_type find_unnumbered_starting_index(const DynamicSparsityPattern &sparsity, const std::vector< DynamicSparsityPattern::size_type > &new_indices)
void reorder_hierarchical(const DynamicSparsityPattern &connectivity, std::vector< DynamicSparsityPattern::size_type > &renumbering)
void gather_sparsity_pattern(DynamicSparsityPattern &dsp, const IndexSet &locally_owned_rows, const MPI_Comm &mpi_comm, const IndexSet &locally_relevant_rows)
unsigned int color_sparsity_pattern(const SparsityPattern &sparsity_pattern, std::vector< unsigned int > &color_indices)
void partition(const SparsityPattern &sparsity_pattern, const unsigned int n_partitions, std::vector< unsigned int > &partition_indices, const Partitioner partitioner=Partitioner::metis)
void reorder_hierarchical(const DynamicSparsityPattern &sparsity, std::vector< DynamicSparsityPattern::size_type > &new_indices)
void reorder_Cuthill_McKee(const DynamicSparsityPattern &sparsity, std::vector< DynamicSparsityPattern::size_type > &new_indices, const std::vector< DynamicSparsityPattern::size_type > &starting_indices=std::vector< DynamicSparsityPattern::size_type >())
void distribute_sparsity_pattern(DynamicSparsityPattern &dsp, const IndexSet &locally_owned_rows, const MPI_Comm &mpi_comm, const IndexSet &locally_relevant_rows)
VectorType::value_type * end(VectorType &V)
@ sparsity_tools_distribute_sparsity_pattern
SparsityTools::sparsity_tools_distribute_sparsity_pattern()
Definition: mpi_tags.h:75
std::map< unsigned int, T > some_to_some(const MPI_Comm &comm, const std::map< unsigned int, T > &objects_to_send)
std::vector< unsigned int > compute_index_owner(const IndexSet &owned_indices, const IndexSet &indices_to_look_up, const MPI_Comm &comm)
Definition: mpi.cc:1034
unsigned int compute_n_point_to_point_communications(const MPI_Comm &mpi_comm, const std::vector< unsigned int > &destinations)
Definition: mpi.cc:425
unsigned int this_mpi_process(const MPI_Comm &mpi_communicator)
Definition: mpi.cc:157
std::vector< Integer > invert_permutation(const std::vector< Integer > &permutation)
Definition: utilities.h:1655
void copy(const T *begin, const T *end, U *dest)
const types::global_dof_index invalid_dof_index
Definition: types.h:226
const types::global_dof_index invalid_size_type
Definition: types.h:215
unsigned int global_dof_index
Definition: types.h:81
#define DEAL_II_DOF_INDEX_MPI_TYPE
Definition: types.h:91