Reference documentation for deal.II version 9.4.0
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
dynamic_sparsity_pattern.cc
Go to the documentation of this file.
1// ---------------------------------------------------------------------
2//
3// Copyright (C) 2008 - 2022 by the deal.II authors
4//
5// This file is part of the deal.II library.
6//
7// The deal.II library is free software; you can use it, redistribute
8// it, and/or modify it under the terms of the GNU Lesser General
9// Public License as published by the Free Software Foundation; either
10// version 2.1 of the License, or (at your option) any later version.
11// The full text of the license can be found in the file LICENSE.md at
12// the top level directory of deal.II.
13//
14// ---------------------------------------------------------------------
15
18
21
22#include <algorithm>
23#include <cmath>
24#include <functional>
25#include <numeric>
26#include <set>
27
29
30
31
32template <typename ForwardIterator>
33void
35 ForwardIterator end,
36 const bool indices_are_sorted)
37{
38 const int n_elements = end - begin;
39 if (n_elements <= 0)
40 return;
41
42 const size_type stop_size = entries.size() + n_elements;
43
44 if (indices_are_sorted == true && n_elements > 3)
45 {
46 // in debug mode, check whether the
47 // indices really are sorted.
48#ifdef DEBUG
49 {
50 ForwardIterator test = begin, test1 = begin;
51 ++test1;
52 for (; test1 != end; ++test, ++test1)
53 Assert(*test1 > *test, ExcInternalError());
54 }
55#endif
56
57 if (entries.size() == 0 || entries.back() < *begin)
58 {
59 entries.insert(entries.end(), begin, end);
60 return;
61 }
62
63 // find a possible insertion point for
64 // the first entry. check whether the
65 // first entry is a duplicate before
66 // actually doing something.
67 ForwardIterator my_it = begin;
68 size_type col = *my_it;
69 std::vector<size_type>::iterator it =
70 Utilities::lower_bound(entries.begin(), entries.end(), col);
71 while (*it == col)
72 {
73 ++my_it;
74 if (my_it == end)
75 break;
76 col = *my_it;
77 // check the very next entry in the
78 // current array
79 ++it;
80 if (it == entries.end())
81 break;
82 if (*it > col)
83 break;
84 if (*it == col)
85 continue;
86 // ok, it wasn't the very next one, do a
87 // binary search to find the insert point
88 it = Utilities::lower_bound(it, entries.end(), col);
89 if (it == entries.end())
90 break;
91 }
92 // all input entries were duplicates.
93 if (my_it == end)
94 return;
95
96 // resize vector by just inserting the
97 // list
98 const size_type pos1 = it - entries.begin();
99 Assert(pos1 <= entries.size(), ExcInternalError());
100 entries.insert(it, my_it, end);
101 it = entries.begin() + pos1;
102 Assert(entries.size() >= static_cast<size_type>(it - entries.begin()),
104
105 // now merge the two lists.
106 std::vector<size_type>::iterator it2 = it + (end - my_it);
107
108 // as long as there are indices both in
109 // the end of the entries list and in the
110 // input list
111 while (my_it != end && it2 != entries.end())
112 {
113 if (*my_it < *it2)
114 *it++ = *my_it++;
115 else if (*my_it == *it2)
116 {
117 *it++ = *it2++;
118 ++my_it;
119 }
120 else
121 *it++ = *it2++;
122 }
123 // in case there are indices left in the
124 // input list
125 while (my_it != end)
126 *it++ = *my_it++;
127
128 // in case there are indices left in the
129 // end of entries
130 while (it2 != entries.end())
131 *it++ = *it2++;
132
133 // resize and return
134 const size_type new_size = it - entries.begin();
135 Assert(new_size <= stop_size, ExcInternalError());
136 entries.resize(new_size);
137 return;
138 }
139
140 // unsorted case or case with too few
141 // elements
142 ForwardIterator my_it = begin;
143
144 // If necessary, increase the size of the
145 // array.
146 if (stop_size > entries.capacity())
147 entries.reserve(stop_size);
148
149 size_type col = *my_it;
150 std::vector<size_type>::iterator it, it2;
151 // insert the first element as for one
152 // entry only first check the last
153 // element (or if line is still empty)
154 if ((entries.size() == 0) || (entries.back() < col))
155 {
156 entries.push_back(col);
157 it = entries.end() - 1;
158 }
159 else
160 {
161 // do a binary search to find the place
162 // where to insert:
163 it2 = Utilities::lower_bound(entries.begin(), entries.end(), col);
164
165 // If this entry is a duplicate, continue
166 // immediately Insert at the right place
167 // in the vector. Vector grows
168 // automatically to fit elements. Always
169 // doubles its size.
170 if (*it2 != col)
171 it = entries.insert(it2, col);
172 else
173 it = it2;
174 }
175
176 ++my_it;
177 // Now try to be smart and insert with
178 // bias in the direction we are
179 // walking. This has the advantage that
180 // for sorted lists, we always search in
181 // the right direction, what should
182 // decrease the work needed in here.
183 for (; my_it != end; ++my_it)
184 {
185 col = *my_it;
186 // need a special insertion command when
187 // we're at the end of the list
188 if (col > entries.back())
189 {
190 entries.push_back(col);
191 it = entries.end() - 1;
192 }
193 // search to the right (preferred search
194 // direction)
195 else if (col > *it)
196 {
197 it2 = Utilities::lower_bound(it++, entries.end(), col);
198 if (*it2 != col)
199 it = entries.insert(it2, col);
200 }
201 // search to the left
202 else if (col < *it)
203 {
204 it2 = Utilities::lower_bound(entries.begin(), it, col);
205 if (*it2 != col)
206 it = entries.insert(it2, col);
207 }
208 // if we're neither larger nor smaller,
209 // then this was a duplicate and we can
210 // just continue.
211 }
212}
213
214
217{
218 return entries.capacity() * sizeof(size_type) + sizeof(Line);
219}
220
221
223 : have_entries(false)
224 , rows(0)
225 , cols(0)
226 , rowset(0)
227{}
228
229
230
232 : Subscriptor()
233 , have_entries(false)
234 , rows(0)
235 , cols(0)
236 , rowset(0)
237{
238 (void)s;
239 Assert(s.rows == 0 && s.cols == 0,
241 "This constructor can only be called if the provided argument "
242 "is the sparsity pattern for an empty matrix. This constructor can "
243 "not be used to copy-construct a non-empty sparsity pattern."));
244}
245
246
247
249 const size_type n,
250 const IndexSet &rowset_)
251 : have_entries(false)
252 , rows(0)
253 , cols(0)
254 , rowset(0)
255{
256 reinit(m, n, rowset_);
257}
258
259
261 : have_entries(false)
262 , rows(0)
263 , cols(0)
264 , rowset(0)
265{
266 reinit(rowset_.size(), rowset_.size(), rowset_);
267}
268
269
271 : have_entries(false)
272 , rows(0)
273 , cols(0)
274 , rowset(0)
275{
276 reinit(n, n);
277}
278
279
280
283{
284 (void)s;
285 Assert(s.rows == 0 && s.cols == 0,
287 "This operator can only be called if the provided argument "
288 "is the sparsity pattern for an empty matrix. This operator can "
289 "not be used to copy a non-empty sparsity pattern."));
290
291 Assert(rows == 0 && cols == 0,
292 ExcMessage("This operator can only be called if the current object is "
293 "empty."));
294
295 return *this;
296}
297
298
299
300void
302 const size_type n,
303 const IndexSet &rowset_)
304{
305 have_entries = false;
306 rows = m;
307 cols = n;
308 rowset = rowset_;
309
310 Assert(rowset.size() == 0 || rowset.size() == m,
312 "The IndexSet argument to this function needs to either "
313 "be empty (indicating the complete set of rows), or have size "
314 "equal to the desired number of rows as specified by the "
315 "first argument to this function. (Of course, the number "
316 "of indices in this IndexSet may be less than the number "
317 "of rows, but the *size* of the IndexSet must be equal.)"));
318
319 std::vector<Line> new_lines(rowset.size() == 0 ? rows : rowset.n_elements());
320 lines.swap(new_lines);
321}
322
323
324
325void
327{}
328
329
330
331bool
333{
334 return ((rows == 0) && (cols == 0));
335}
336
337
338
341{
342 if (!have_entries)
343 return 0;
344
345 size_type m = 0;
346 for (const auto &line : lines)
347 {
348 m = std::max(m, static_cast<size_type>(line.entries.size()));
349 }
350
351 return m;
352}
353
354
355
356bool
358{
361 Assert(
362 rowset.size() == 0 || rowset.is_element(i),
364 "The row IndexSet does not contain the index i. This sparsity pattern "
365 "object cannot know whether the entry (i, j) exists or not."));
366
367 // Avoid a segmentation fault in below code if the row index happens to
368 // not be present in the IndexSet rowset:
369 if (!(rowset.size() == 0 || rowset.is_element(i)))
370 return false;
371
372 if (!have_entries)
373 return false;
374
375 const size_type rowindex =
376 rowset.size() == 0 ? i : rowset.index_within_set(i);
377
378 return std::binary_search(lines[rowindex].entries.begin(),
379 lines[rowindex].entries.end(),
380 j);
381}
382
383
384
385void
387{
389
390 // loop over all elements presently in the sparsity pattern and add the
391 // transpose element. note:
392 //
393 // 1. that the sparsity pattern changes which we work on, but not the present
394 // row
395 //
396 // 2. that the @p{add} function can be called on elements that already exist
397 // without any harm
398 for (size_type row = 0; row < lines.size(); ++row)
399 {
400 const size_type rowindex =
401 rowset.size() == 0 ? row : rowset.nth_index_in_set(row);
402
403 for (const size_type row_entry : lines[row].entries)
404 // add the transpose entry if this is not the diagonal
405 if (rowindex != row_entry)
406 add(row_entry, rowindex);
407 }
408}
409
410
411
412void
414{
415 AssertIndexRange(row, n_rows());
416 if (!have_entries)
417 return;
418
419 if (rowset.size() > 0 && !rowset.is_element(row))
420 return;
421
422 const size_type rowindex =
423 rowset.size() == 0 ? row : rowset.index_within_set(row);
424
425 AssertIndexRange(rowindex, lines.size());
426 lines[rowindex].entries = std::vector<size_type>();
427}
428
429
430
433{
435 view.reinit(rows.n_elements(), this->n_cols());
436 AssertDimension(rows.size(), this->n_rows());
437
438 const auto end = rows.end();
440 for (auto it = rows.begin(); it != end; ++it, ++view_row)
441 {
442 const size_type rowindex =
443 rowset.size() == 0 ? *it : rowset.index_within_set(*it);
444
445 view.lines[view_row].entries = lines[rowindex].entries;
446 view.have_entries |= (lines[rowindex].entries.size() > 0);
447 }
448 return view;
449}
450
451
452
453template <typename SparsityPatternTypeLeft, typename SparsityPatternTypeRight>
454void
456 const SparsityPatternTypeLeft & sp_A,
457 const SparsityPatternTypeRight &sp_B)
458{
459 Assert(sp_A.n_rows() == sp_B.n_rows(),
460 ExcDimensionMismatch(sp_A.n_rows(), sp_B.n_rows()));
461
462 this->reinit(sp_A.n_cols(), sp_B.n_cols());
463 // we will go through all the
464 // rows in the matrix A, and for each column in a row we add the whole
465 // row of matrix B with that row number. This means that we will insert
466 // a lot of entries to each row, which is best handled by the
467 // DynamicSparsityPattern class.
468
469 std::vector<size_type> new_cols;
470 new_cols.reserve(sp_B.max_entries_per_row());
471
472 // C_{kl} = A_{ik} B_{il}
473 for (size_type i = 0; i < sp_A.n_rows(); ++i)
474 {
475 // get all column numbers from sp_B in a temporary vector:
476 new_cols.resize(sp_B.row_length(i));
477 {
478 const auto last_il = sp_B.end(i);
479 auto * col_ptr = new_cols.data();
480 for (auto il = sp_B.begin(i); il != last_il; ++il)
481 *col_ptr++ = il->column();
482 }
483 std::sort(new_cols.begin(), new_cols.end());
484
485 // now for each k, add new_cols to the target sparsity
486 const auto last_ik = sp_A.end(i);
487 for (auto ik = sp_A.begin(i); ik != last_ik; ++ik)
488 this->add_entries(ik->column(), new_cols.begin(), new_cols.end(), true);
489 }
490}
491
492
493
494template <typename SparsityPatternTypeLeft, typename SparsityPatternTypeRight>
495void
497 const SparsityPatternTypeLeft & left,
498 const SparsityPatternTypeRight &right)
499{
500 Assert(left.n_cols() == right.n_rows(),
501 ExcDimensionMismatch(left.n_cols(), right.n_rows()));
502
503 this->reinit(left.n_rows(), right.n_cols());
504
505 typename SparsityPatternTypeLeft::iterator it_left = left.begin(),
506 end_left = left.end();
507 for (; it_left != end_left; ++it_left)
508 {
509 const unsigned int j = it_left->column();
510
511 // We are sitting on entry (i,j) of the left sparsity pattern. We then
512 // need to add all entries (i,k) to the final sparsity pattern where (j,k)
513 // exists in the right sparsity pattern -- i.e., we need to iterate over
514 // row j.
515 typename SparsityPatternTypeRight::iterator it_right = right.begin(j),
516 end_right = right.end(j);
517 for (; it_right != end_right; ++it_right)
518 this->add(it_left->row(), it_right->column());
519 }
520}
521
522
523
524void
525DynamicSparsityPattern::print(std::ostream &out) const
526{
527 for (size_type row = 0; row < lines.size(); ++row)
528 {
529 out << '[' << (rowset.size() == 0 ? row : rowset.nth_index_in_set(row));
530
531 for (const auto entry : lines[row].entries)
532 out << ',' << entry;
533
534 out << ']' << std::endl;
535 }
536
537 AssertThrow(out.fail() == false, ExcIO());
538}
539
540
541
542void
544{
545 for (size_type row = 0; row < lines.size(); ++row)
546 {
547 const size_type rowindex =
548 rowset.size() == 0 ? row : rowset.nth_index_in_set(row);
549
550 for (const auto entry : lines[row].entries)
551 // while matrix entries are usually
552 // written (i,j), with i vertical and
553 // j horizontal, gnuplot output is
554 // x-y, that is we have to exchange
555 // the order of output
556 out << entry << " " << -static_cast<signed int>(rowindex) << std::endl;
557 }
558
559
560 AssertThrow(out.fail() == false, ExcIO());
561}
562
563
564
567{
568 size_type b = 0;
569 for (size_type row = 0; row < lines.size(); ++row)
570 {
571 const size_type rowindex =
572 rowset.size() == 0 ? row : rowset.nth_index_in_set(row);
573
574 for (const auto entry : lines[row].entries)
575 if (static_cast<size_type>(
576 std::abs(static_cast<int>(rowindex - entry))) > b)
577 b = std::abs(static_cast<signed int>(rowindex - entry));
578 }
579
580 return b;
581}
582
583
584
587{
588 if (!have_entries)
589 return 0;
590
591 size_type n = 0;
592 for (const auto &line : lines)
593 {
594 n += line.entries.size();
595 }
596
597 return n;
598}
599
600
601
604{
605 std::set<types::global_dof_index> cols;
606 for (const auto &line : lines)
607 cols.insert(line.entries.begin(), line.entries.end());
608
609 IndexSet res(this->n_cols());
610 res.add_indices(cols.begin(), cols.end());
611 return res;
612}
613
614
615
618{
619 const IndexSet all_rows = complete_index_set(this->n_rows());
620 const IndexSet &locally_stored_rows = rowset.size() == 0 ? all_rows : rowset;
621
622 std::vector<types::global_dof_index> rows;
623 auto line = lines.begin();
624 AssertDimension(locally_stored_rows.n_elements(), lines.size());
625 for (const auto row : locally_stored_rows)
626 {
627 if (line->entries.size() > 0)
628 rows.push_back(row);
629
630 ++line;
631 }
632
633 IndexSet res(this->n_rows());
634 res.add_indices(rows.begin(), rows.end());
635 return res;
636}
637
638
639
642{
643 size_type mem = sizeof(DynamicSparsityPattern) +
645 sizeof(rowset);
646
647 for (const auto &line : lines)
649
650 return mem;
651}
652
653
654
658 const DynamicSparsityPattern::size_type col) const
659{
660 AssertIndexRange(row, n_rows());
661 AssertIndexRange(col, n_cols());
663
664 const DynamicSparsityPattern::size_type local_row =
665 rowset.size() != 0u ? rowset.index_within_set(row) : row;
666
667 // now we need to do a binary search. Note that col indices are assumed to
668 // be sorted.
669 const auto &cols = lines[local_row].entries;
670 auto it = Utilities::lower_bound(cols.begin(), cols.end(), col);
671
672 if ((it != cols.end()) && (*it == col))
673 return (it - cols.begin());
674 else
676}
677
678
679
680// explicit instantiations
681template void
683template void
685 const size_type *,
686 const bool);
687#ifndef DEAL_II_VECTOR_ITERATOR_IS_POINTER
688template void
689DynamicSparsityPattern::Line::add_entries(std::vector<size_type>::iterator,
690 std::vector<size_type>::iterator,
691 const bool);
692template void
694 std::vector<size_type>::const_iterator,
695 std::vector<size_type>::const_iterator,
696 const bool);
697#endif
698
699template void
701 const DynamicSparsityPattern &);
702template void
704 const SparsityPattern &);
705template void
707 const DynamicSparsityPattern &);
708template void
710 const SparsityPattern &);
711
712template void
714 const SparsityPattern &);
715template void
717 const SparsityPattern &);
718template void
720 const DynamicSparsityPattern &);
721template void
723 const DynamicSparsityPattern &);
724
size_type size() const
Definition: index_set.h:1636
size_type index_within_set(const size_type global_index) const
Definition: index_set.h:1923
size_type n_elements() const
Definition: index_set.h:1834
bool is_element(const size_type index) const
Definition: index_set.h:1767
size_type nth_index_in_set(const size_type local_index) const
Definition: index_set.h:1882
void add_indices(const ForwardIterator &begin, const ForwardIterator &end)
Definition: index_set.h:1705
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:442
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:443
static ::ExceptionBase & ExcIO()
#define Assert(cond, exc)
Definition: exceptions.h:1473
#define AssertDimension(dim1, dim2)
Definition: exceptions.h:1667
#define AssertIndexRange(index, range)
Definition: exceptions.h:1732
static ::ExceptionBase & ExcInternalError()
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
static ::ExceptionBase & ExcNotQuadratic()
static ::ExceptionBase & ExcMessage(std::string arg1)
#define AssertThrow(cond, exc)
Definition: exceptions.h:1583
void add_entries(const size_type row, ForwardIterator begin, ForwardIterator end, const bool indices_are_unique_and_sorted=false)
DynamicSparsityPattern get_view(const IndexSet &rows) const
void add_entries(ForwardIterator begin, ForwardIterator end, const bool indices_are_sorted)
types::global_dof_index size_type
void compute_mmult_pattern(const SparsityPatternTypeLeft &left, const SparsityPatternTypeRight &right)
size_type column_index(const size_type row, const size_type col) const
DynamicSparsityPattern & operator=(const DynamicSparsityPattern &)
void print(std::ostream &out) const
void reinit(const size_type m, const size_type n, const IndexSet &rowset=IndexSet())
void clear_row(const size_type row)
void print_gnuplot(std::ostream &out) const
void compute_Tmmult_pattern(const SparsityPatternTypeLeft &left, const SparsityPatternTypeRight &right)
bool exists(const size_type i, const size_type j) const
void add(const size_type i, const size_type j)
IndexSet complete_index_set(const IndexSet::size_type N)
Definition: index_set.h:1014
types::global_dof_index size_type
Definition: cuda_kernels.h:45
std::enable_if< std::is_fundamental< T >::value, std::size_t >::type memory_consumption(const T &t)
SymmetricTensor< 2, dim, Number > b(const Tensor< 2, dim, Number > &F)
VectorType::value_type * end(VectorType &V)
VectorType::value_type * begin(VectorType &V)
Iterator lower_bound(Iterator first, Iterator last, const T &val)
Definition: utilities.h:1153
const types::global_dof_index invalid_size_type
Definition: types.h:210
::VectorizedArray< Number, width > max(const ::VectorizedArray< Number, width > &, const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > abs(const ::VectorizedArray< Number, width > &)