Reference documentation for deal.II version GIT d6cf33b98c 2023-09-22 19:50:02+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.empty(),
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  // store the indices of the dofs to be renumbered in the next round
628  std::vector<DynamicSparsityPattern::size_type> next_round_dofs;
629 
630  // store for each coordination number the dofs with these coordination
631  // number
632  std::vector<std::pair<unsigned int, DynamicSparsityPattern::size_type>>
633  dofs_by_coordination;
634 
635  // now do as many steps as needed to renumber all dofs
636  while (true)
637  {
638  next_round_dofs.clear();
639 
640  // find all neighbors of the dofs numbered in the last round
641  for (const auto dof : last_round_dofs)
642  {
643  const unsigned int row_length = sparsity.row_length(dof);
644  for (unsigned int i = 0; i < row_length; ++i)
645  {
646  // skip dofs which are already numbered
647  const auto column = sparsity.column_number(dof, i);
648  if (new_indices[column] == numbers::invalid_size_type)
649  {
650  next_round_dofs.push_back(column);
651 
652  // assign a dummy value to 'new_indices' to avoid adding
653  // the same index again; those will get the right number
654  // at the end of the outer 'while' loop
655  new_indices[column] = 0;
656  }
657  }
658  }
659 
660  // check whether there are any new dofs in the list. if there are
661  // none, then we have completely numbered the current component of the
662  // graph. check if there are as yet unnumbered components of the graph
663  // that we would then have to do next
664  if (next_round_dofs.empty())
665  {
666  if (std::find(new_indices.begin(),
667  new_indices.end(),
668  numbers::invalid_size_type) == new_indices.end())
669  // no unnumbered indices, so we can leave now
670  break;
671 
672  // otherwise find a valid starting point for the next component of
673  // the graph and continue with numbering that one. we only do so
674  // if no starting indices were provided by the user (see the
675  // documentation of this function) so produce an error if we got
676  // here and starting indices were given
677  Assert(starting_indices.empty(),
678  ExcMessage("The input graph appears to have more than one "
679  "component, but as stated in the documentation "
680  "we only want to reorder such graphs if no "
681  "starting indices are given. The function was "
682  "called with starting indices, however."))
683 
684  next_round_dofs.push_back(
686  new_indices));
687  }
688 
689 
690  // find coordination number for each of these dofs
691  dofs_by_coordination.clear();
692  for (const types::global_dof_index next_round_dof : next_round_dofs)
693  dofs_by_coordination.emplace_back(sparsity.row_length(next_round_dof),
694  next_round_dof);
695  std::sort(dofs_by_coordination.begin(), dofs_by_coordination.end());
696 
697  // assign new DoF numbers to the elements of the present front:
698  for (const auto &i : dofs_by_coordination)
699  new_indices[i.second] = next_free_number++;
700 
701  // after that: use this round's dofs for the next round
702  last_round_dofs.swap(next_round_dofs);
703  }
704 
705  // test for all indices numbered. this mostly tests whether the
706  // front-marching-algorithm (which Cuthill-McKee actually is) has reached
707  // all points.
708  Assert((std::find(new_indices.begin(),
709  new_indices.end(),
710  numbers::invalid_size_type) == new_indices.end()) &&
711  (next_free_number == sparsity.n_rows()),
712  ExcInternalError());
713  }
714 
715 
716 
717  namespace internal
718  {
719  void
721  const DynamicSparsityPattern &connectivity,
722  std::vector<DynamicSparsityPattern::size_type> &renumbering)
723  {
724  AssertDimension(connectivity.n_rows(), connectivity.n_cols());
725  AssertDimension(connectivity.n_rows(), renumbering.size());
726  Assert(connectivity.row_index_set().size() == 0 ||
727  connectivity.row_index_set().size() == connectivity.n_rows(),
728  ExcMessage(
729  "Only valid for sparsity patterns which store all rows."));
730 
731  std::vector<types::global_dof_index> touched_nodes(
732  connectivity.n_rows(), numbers::invalid_dof_index);
733  std::vector<unsigned int> row_lengths(connectivity.n_rows());
734  std::set<types::global_dof_index> current_neighbors;
735  std::vector<std::vector<types::global_dof_index>> groups;
736 
737  // First collect the number of neighbors for each node. We use this
738  // field to find next nodes with the minimum number of non-touched
739  // neighbors in the field n_remaining_neighbors, so we will count down
740  // on this field. We also cache the row lengths because we need this
741  // data frequently and getting it from the sparsity pattern is more
742  // expensive.
743  for (types::global_dof_index row = 0; row < connectivity.n_rows(); ++row)
744  {
745  row_lengths[row] = connectivity.row_length(row);
746  Assert(row_lengths[row] > 0, ExcInternalError());
747  }
748  std::vector<unsigned int> n_remaining_neighbors(row_lengths);
749 
750  // This outer loop is typically traversed only once, unless the global
751  // graph is not connected
752  while (true)
753  {
754  // Find cell with the minimal number of neighbors (typically a
755  // corner node when based on FEM meshes). If no cell is left, we are
756  // done. Together with the outer while loop, this loop can possibly
757  // be of quadratic complexity in the number of disconnected
758  // partitions, i.e. up to connectivity.n_rows() in the worst case,
759  // but that is not the usual use case of this loop and thus not
760  // optimized for.
761  std::pair<types::global_dof_index, types::global_dof_index>
762  min_neighbors(numbers::invalid_dof_index,
764  for (types::global_dof_index i = 0; i < touched_nodes.size(); ++i)
765  if (touched_nodes[i] == numbers::invalid_dof_index)
766  if (row_lengths[i] < min_neighbors.second)
767  {
768  min_neighbors = std::make_pair(i, n_remaining_neighbors[i]);
769  if (n_remaining_neighbors[i] <= 1)
770  break;
771  }
772  if (min_neighbors.first == numbers::invalid_dof_index)
773  break;
774 
775  Assert(min_neighbors.second > 0, ExcInternalError());
776 
777  current_neighbors.clear();
778  current_neighbors.insert(min_neighbors.first);
779  while (!current_neighbors.empty())
780  {
781  // Find node with minimum number of untouched neighbors among the
782  // next set of possible neighbors
783  min_neighbors = std::make_pair(numbers::invalid_dof_index,
785  for (const auto current_neighbor : current_neighbors)
786  {
787  Assert(touched_nodes[current_neighbor] ==
789  ExcInternalError());
790  if (n_remaining_neighbors[current_neighbor] <
791  min_neighbors.second)
792  min_neighbors =
793  std::make_pair(current_neighbor,
794  n_remaining_neighbors[current_neighbor]);
795  }
796 
797  // Among the set of nodes with the minimal number of neighbors,
798  // choose the one with the largest number of touched neighbors,
799  // i.e., the one with the largest row length
800  const types::global_dof_index best_row_length =
801  min_neighbors.second;
802  for (const auto current_neighbor : current_neighbors)
803  if (n_remaining_neighbors[current_neighbor] == best_row_length)
804  if (row_lengths[current_neighbor] > min_neighbors.second)
805  min_neighbors =
806  std::make_pair(current_neighbor,
807  row_lengths[current_neighbor]);
808 
809  // Add the pivot and all direct neighbors of the pivot node not
810  // yet touched to the list of new entries.
811  groups.emplace_back();
812  std::vector<types::global_dof_index> &next_group = groups.back();
813 
814  next_group.push_back(min_neighbors.first);
815  touched_nodes[min_neighbors.first] = groups.size() - 1;
817  connectivity.begin(min_neighbors.first);
818  it != connectivity.end(min_neighbors.first);
819  ++it)
820  if (touched_nodes[it->column()] == numbers::invalid_dof_index)
821  {
822  next_group.push_back(it->column());
823  touched_nodes[it->column()] = groups.size() - 1;
824  }
825 
826  // Add all neighbors of the current list not yet touched to the
827  // set of possible next pivots. The added node is no longer a
828  // valid neighbor (here we assume symmetry of the
829  // connectivity). Delete the entries of the current list from
830  // the set of possible next pivots.
831  for (const auto index : next_group)
832  {
834  connectivity.begin(index);
835  it != connectivity.end(index);
836  ++it)
837  {
838  if (touched_nodes[it->column()] ==
840  current_neighbors.insert(it->column());
841  n_remaining_neighbors[it->column()]--;
842  }
843  current_neighbors.erase(index);
844  }
845  }
846  }
847 
848  // Sanity check: for all nodes, there should not be any neighbors left
849  for (types::global_dof_index row = 0; row < connectivity.n_rows(); ++row)
850  Assert(n_remaining_neighbors[row] == 0, ExcInternalError());
851 
852  // If the number of groups is smaller than the number of nodes, we
853  // continue by recursively calling this method
854  if (groups.size() < connectivity.n_rows())
855  {
856  // Form the connectivity of the groups
857  DynamicSparsityPattern connectivity_next(groups.size(),
858  groups.size());
859  for (types::global_dof_index i = 0; i < groups.size(); ++i)
860  for (types::global_dof_index col = 0; col < groups[i].size(); ++col)
862  connectivity.begin(groups[i][col]);
863  it != connectivity.end(groups[i][col]);
864  ++it)
865  connectivity_next.add(i, touched_nodes[it->column()]);
866 
867  // Recursively call the reordering
868  std::vector<types::global_dof_index> renumbering_next(groups.size());
869  reorder_hierarchical(connectivity_next, renumbering_next);
870 
871  // Renumber the indices group by group according to the incoming
872  // ordering for the groups
873  for (types::global_dof_index i = 0, count = 0; i < groups.size(); ++i)
874  for (types::global_dof_index col = 0;
875  col < groups[renumbering_next[i]].size();
876  ++col, ++count)
877  renumbering[count] = groups[renumbering_next[i]][col];
878  }
879  else
880  {
881  // All groups should have size one and no more recursion is possible,
882  // so use the numbering of the groups
883  for (types::global_dof_index i = 0, count = 0; i < groups.size(); ++i)
884  for (types::global_dof_index col = 0; col < groups[i].size();
885  ++col, ++count)
886  renumbering[count] = groups[i][col];
887  }
888  }
889  } // namespace internal
890 
891  void
893  const DynamicSparsityPattern &connectivity,
894  std::vector<DynamicSparsityPattern::size_type> &renumbering)
895  {
896  // the internal renumbering keeps the numbering the wrong way around (but
897  // we cannot invert the numbering inside that method because it is used
898  // recursively), so invert it here
899  internal::reorder_hierarchical(connectivity, renumbering);
900  renumbering = Utilities::invert_permutation(renumbering);
901  }
902 
903 
904 
905 #ifdef DEAL_II_WITH_MPI
906 
907  void
909  const IndexSet &locally_owned_rows,
910  const MPI_Comm mpi_comm,
911  const IndexSet &locally_relevant_rows)
912  {
913  using map_vec_t =
914  std::map<unsigned int, std::vector<DynamicSparsityPattern::size_type>>;
915 
916  // 1. limit rows to non owned:
917  IndexSet requested_rows(locally_relevant_rows);
918  requested_rows.subtract_set(locally_owned_rows);
919 
920  std::vector<unsigned int> index_owner =
921  Utilities::MPI::compute_index_owner(locally_owned_rows,
922  requested_rows,
923  mpi_comm);
924 
925  // 2. go through requested_rows, figure out the owner and add the row to
926  // request
927  map_vec_t rows_data;
929  i < requested_rows.n_elements();
930  ++i)
931  {
933  requested_rows.nth_index_in_set(i);
934 
935  rows_data[index_owner[i]].push_back(row);
936  }
937 
938  // 3. get what others ask us to send
939  const auto rows_data_received =
940  Utilities::MPI::some_to_some(mpi_comm, rows_data);
941 
942  // 4. now prepare data to be sent in the same format as in
943  // distribute_sparsity_pattern() below, i.e.
944  // rX,num_rX,cols_rX
945  map_vec_t send_data;
946  for (const auto &data : rows_data_received)
947  {
948  for (const auto &row : data.second)
949  {
950  const auto rlen = dsp.row_length(row);
951 
952  // skip empty lines
953  if (rlen == 0)
954  continue;
955 
956  // save entries
957  send_data[data.first].push_back(row); // row index
958  send_data[data.first].push_back(rlen); // number of entries
959  for (DynamicSparsityPattern::size_type c = 0; c < rlen; ++c)
960  send_data[data.first].push_back(
961  dsp.column_number(row, c)); // columns
962  } // loop over rows
963  } // loop over received data
964 
965  // 5. communicate rows
966  const auto received_data =
967  Utilities::MPI::some_to_some(mpi_comm, send_data);
968 
969  // 6. add result to our sparsity
970  for (const auto &data : received_data)
971  {
972  const auto &recv_buf = data.second;
973  auto ptr = recv_buf.begin();
974  const auto end = recv_buf.end();
975  while (ptr != end)
976  {
977  const auto row = *(ptr++);
978  Assert(ptr != end, ExcInternalError());
979 
980  const auto n_entries = *(ptr++);
981  Assert(n_entries > 0, ExcInternalError());
982  Assert(ptr != end, ExcInternalError());
983 
984  // make sure we clear whatever was previously stored
985  // in these rows. Otherwise we can't guarantee that the
986  // data is consistent across MPI communicator.
987  dsp.clear_row(row);
988 
989  Assert(ptr + (n_entries - 1) != end, ExcInternalError());
990  dsp.add_entries(row, ptr, ptr + n_entries, true);
991  ptr += n_entries;
992  }
993  Assert(ptr == end, ExcInternalError());
994  }
995  }
996 
997 
998 
999  void
1002  const std::vector<DynamicSparsityPattern::size_type> &rows_per_cpu,
1003  const MPI_Comm mpi_comm,
1004  const IndexSet &myrange)
1005  {
1006  const unsigned int myid = Utilities::MPI::this_mpi_process(mpi_comm);
1007  std::vector<DynamicSparsityPattern::size_type> start_index(
1008  rows_per_cpu.size() + 1);
1009  start_index[0] = 0;
1010  for (DynamicSparsityPattern::size_type i = 0; i < rows_per_cpu.size(); ++i)
1011  start_index[i + 1] = start_index[i] + rows_per_cpu[i];
1012 
1013  IndexSet owned(start_index.back());
1014  owned.add_range(start_index[myid], start_index[myid] + rows_per_cpu[myid]);
1015 
1016  distribute_sparsity_pattern(dsp, owned, mpi_comm, myrange);
1017  }
1018 
1019 
1020 
1021  void
1023  const IndexSet &locally_owned_rows,
1024  const MPI_Comm mpi_comm,
1025  const IndexSet &locally_relevant_rows)
1026  {
1027  IndexSet requested_rows(locally_relevant_rows);
1028  requested_rows.subtract_set(locally_owned_rows);
1029 
1030  std::vector<unsigned int> index_owner =
1031  Utilities::MPI::compute_index_owner(locally_owned_rows,
1032  requested_rows,
1033  mpi_comm);
1034 
1035  using map_vec_t =
1036  std::map<unsigned int, std::vector<DynamicSparsityPattern::size_type>>;
1037 
1038  map_vec_t send_data;
1039 
1041  i < requested_rows.n_elements();
1042  ++i)
1043  {
1045  requested_rows.nth_index_in_set(i);
1046 
1047  const auto rlen = dsp.row_length(row);
1048 
1049  // skip empty lines
1050  if (rlen == 0)
1051  continue;
1052 
1053  // save entries
1054  send_data[index_owner[i]].push_back(row); // row index
1055  send_data[index_owner[i]].push_back(rlen); // number of entries
1056  for (DynamicSparsityPattern::size_type c = 0; c < rlen; ++c)
1057  {
1058  // columns
1059  const auto column = dsp.column_number(row, c);
1060  send_data[index_owner[i]].push_back(column);
1061  }
1062  }
1063 
1064  const auto receive_data = Utilities::MPI::some_to_some(mpi_comm, send_data);
1065 
1066  // add what we received
1067  for (const auto &data : receive_data)
1068  {
1069  const auto &recv_buf = data.second;
1070  auto ptr = recv_buf.begin();
1071  const auto end = recv_buf.end();
1072  while (ptr != end)
1073  {
1074  const auto row = *(ptr++);
1075  Assert(ptr != end, ExcInternalError());
1076  const auto n_entries = *(ptr++);
1077 
1078  Assert(ptr + (n_entries - 1) != end, ExcInternalError());
1079  dsp.add_entries(row, ptr, ptr + n_entries, true);
1080  ptr += n_entries;
1081  }
1082  Assert(ptr == end, ExcInternalError());
1083  }
1084  }
1085 
1086 
1087 
1088  void
1090  const std::vector<IndexSet> &owned_set_per_cpu,
1091  const MPI_Comm mpi_comm,
1092  const IndexSet &myrange)
1093  {
1094  const unsigned int myid = Utilities::MPI::this_mpi_process(mpi_comm);
1096  owned_set_per_cpu[myid],
1097  mpi_comm,
1098  myrange);
1099  }
1100 
1101 
1102 
1103  void
1105  const IndexSet &locally_owned_rows,
1106  const MPI_Comm mpi_comm,
1107  const IndexSet &locally_relevant_rows)
1108  {
1109  using map_vec_t =
1111  std::vector<BlockDynamicSparsityPattern::size_type>>;
1112  map_vec_t send_data;
1113 
1114  IndexSet requested_rows(locally_relevant_rows);
1115  requested_rows.subtract_set(locally_owned_rows);
1116 
1117  std::vector<unsigned int> index_owner =
1118  Utilities::MPI::compute_index_owner(locally_owned_rows,
1119  requested_rows,
1120  mpi_comm);
1121 
1123  i < requested_rows.n_elements();
1124  ++i)
1125  {
1127  requested_rows.nth_index_in_set(i);
1128 
1130 
1131  // skip empty lines
1132  if (rlen == 0)
1133  continue;
1134 
1135  // save entries
1136  std::vector<BlockDynamicSparsityPattern::size_type> &dst =
1137  send_data[index_owner[i]];
1138 
1139  dst.push_back(rlen); // number of entries
1140  dst.push_back(row); // row index
1141  for (BlockDynamicSparsityPattern::size_type c = 0; c < rlen; ++c)
1142  {
1143  // columns
1145  dsp.column_number(row, c);
1146  dst.push_back(column);
1147  }
1148  }
1149 
1150  unsigned int num_receive = 0;
1151  {
1152  std::vector<unsigned int> send_to;
1153  send_to.reserve(send_data.size());
1154  for (const auto &sparsity_line : send_data)
1155  send_to.push_back(sparsity_line.first);
1156 
1157  num_receive =
1159  send_to);
1160  }
1161 
1162  std::vector<MPI_Request> requests(send_data.size());
1163 
1164 
1165  // send data
1166 
1167  static Utilities::MPI::CollectiveMutex mutex;
1168  Utilities::MPI::CollectiveMutex::ScopedLock lock(mutex, mpi_comm);
1169 
1170  const int mpi_tag = Utilities::MPI::internal::Tags::
1172 
1173  {
1174  unsigned int idx = 0;
1175  for (const auto &sparsity_line : send_data)
1176  {
1177  const int ierr = MPI_Isend(sparsity_line.second.data(),
1178  sparsity_line.second.size(),
1180  sparsity_line.first,
1181  mpi_tag,
1182  mpi_comm,
1183  &requests[idx++]);
1184  AssertThrowMPI(ierr);
1185  }
1186  }
1187 
1188  {
1189  // receive
1190  std::vector<BlockDynamicSparsityPattern::size_type> recv_buf;
1191  for (unsigned int index = 0; index < num_receive; ++index)
1192  {
1193  MPI_Status status;
1194  int ierr = MPI_Probe(MPI_ANY_SOURCE, mpi_tag, mpi_comm, &status);
1195  AssertThrowMPI(ierr);
1196 
1197  int len;
1198  ierr = MPI_Get_count(&status, DEAL_II_DOF_INDEX_MPI_TYPE, &len);
1199  AssertThrowMPI(ierr);
1200 
1201  recv_buf.resize(len);
1202  ierr = MPI_Recv(recv_buf.data(),
1203  len,
1205  status.MPI_SOURCE,
1206  status.MPI_TAG,
1207  mpi_comm,
1208  &status);
1209  AssertThrowMPI(ierr);
1210 
1211  std::vector<BlockDynamicSparsityPattern::size_type>::const_iterator
1212  ptr = recv_buf.begin();
1213  std::vector<BlockDynamicSparsityPattern::size_type>::const_iterator
1214  end = recv_buf.end();
1215  while (ptr != end)
1216  {
1218  Assert(ptr != end, ExcInternalError());
1220  for (unsigned int c = 0; c < num; ++c)
1221  {
1222  Assert(ptr != end, ExcInternalError());
1223  dsp.add(row, *ptr);
1224  ++ptr;
1225  }
1226  }
1227  Assert(ptr == end, ExcInternalError());
1228  }
1229  }
1230 
1231  // complete all sends, so that we can safely destroy the buffers.
1232  if (requests.size() > 0)
1233  {
1234  const int ierr =
1235  MPI_Waitall(requests.size(), requests.data(), MPI_STATUSES_IGNORE);
1236  AssertThrowMPI(ierr);
1237  }
1238  }
1239 #endif
1240 } // namespace SparsityTools
1241 
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:1696
size_type n_elements() const
Definition: index_set.h:1854
void subtract_set(const IndexSet &other)
Definition: index_set.cc:288
void add_range(const size_type begin, const size_type end)
Definition: index_set.h:1723
size_type nth_index_in_set(const size_type local_index) const
Definition: index_set.h:1902
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:477
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:478
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:1616
#define AssertDimension(dim1, dim2)
Definition: exceptions.h:1789
#define AssertThrowMPI(error_code)
Definition: exceptions.h:1916
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:1705
static const char U
std::string to_string(const T &t)
Definition: patterns.h:2391
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)
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 distribute_sparsity_pattern(DynamicSparsityPattern &dsp, const IndexSet &locally_owned_rows, const MPI_Comm mpi_comm, const IndexSet &locally_relevant_rows)
void gather_sparsity_pattern(DynamicSparsityPattern &dsp, const IndexSet &locally_owned_rows, const MPI_Comm mpi_comm, const IndexSet &locally_relevant_rows)
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 >())
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:1088
unsigned int this_mpi_process(const MPI_Comm mpi_communicator)
Definition: mpi.cc:164
unsigned int compute_n_point_to_point_communications(const MPI_Comm mpi_comm, const std::vector< unsigned int > &destinations)
Definition: mpi.cc:436
std::vector< Integer > invert_permutation(const std::vector< Integer > &permutation)
Definition: utilities.h:1661
void copy(const T *begin, const T *end, U *dest)
const types::global_dof_index invalid_dof_index
Definition: types.h:233
const types::global_dof_index invalid_size_type
Definition: types.h:222
unsigned int global_dof_index
Definition: types.h:82
#define DEAL_II_DOF_INDEX_MPI_TYPE
Definition: types.h:99