/usr/include/deal.II/lac/constraint_matrix.h is in libdeal.ii-dev 8.1.0-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 | // ---------------------------------------------------------------------
// $Id: constraint_matrix.h 31932 2013-12-08 02:15:54Z heister $
//
// Copyright (C) 1998 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__constraint_matrix_h
#define __deal2__constraint_matrix_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/index_set.h>
#include <deal.II/base/subscriptor.h>
#include <deal.II/base/template_constraints.h>
#include <deal.II/base/thread_local_storage.h>
#include <deal.II/lac/vector.h>
#include <vector>
#include <map>
#include <set>
#include <utility>
#include <complex>
#include <boost/scoped_ptr.hpp>
DEAL_II_NAMESPACE_OPEN
template<int dim, class T> class Table;
template <typename> class FullMatrix;
class SparsityPattern;
class CompressedSparsityPattern;
class CompressedSetSparsityPattern;
class CompressedSimpleSparsityPattern;
class BlockSparsityPattern;
class BlockCompressedSparsityPattern;
class BlockCompressedSetSparsityPattern;
class BlockCompressedSimpleSparsityPattern;
template <typename number> class SparseMatrix;
template <typename number> class BlockSparseMatrix;
class BlockIndices;
template <typename MatrixType> struct IsBlockMatrix;
namespace internals
{
class GlobalRowsFromLocal;
}
//TODO[WB]: We should have a function of the kind
// ConstraintMatrix::add_constraint (const size_type constrained_dof,
// const std::vector<std::pair<size_type, double> > &entries,
// const double inhomogeneity = 0);
// rather than building up constraints piecemeal through add_line/add_entry
// etc. This would also eliminate the possibility of accidentally changing
// existing constraints into something pointless, see the discussion on the
// mailing list on "Tiny bug in interpolate_boundary_values" in Sept. 2010.
/**
* This class implements dealing with linear (possibly inhomogeneous)
* constraints on degrees of freedom. The concept and origin of such
* constraints is extensively described in the @ref constraints module. The
* class is meant to deal with a limited number of constraints relative to the
* total number of degrees of freedom, for example a few per cent up to maybe
* 30 per cent; and with a linear combination of <i>M</i> other degrees of freedom
* where <i>M</i> is also relatively small (no larger than at most around the
* average number of entries per row of a linear system). It is <em>not</em>
* meant to describe full rank linear systems.
*
* The algorithms used in the implementation of this class are described in
* some detail in the @ref hp_paper "hp paper". There is also a significant
* amount of documentation on how to use this class in the
* @ref constraints module.
*
*
* <h3>Description of constraints</h3>
*
* Each "line" in objects of this class corresponds to one constrained degree
* of freedom, with the number of the line being <i>i</i>, entered by
* using add_line() or add_lines(). The entries in
* this line are pairs of the form
* (<i>j</i>,<i>a<sub>ij</sub></i>), which are added by add_entry() or
* add_entries(). The organization is essentially a
* SparsityPattern, but with only a few lines containing nonzero
* elements, and therefore no data wasted on the others. For each
* line, which has been added by the mechanism above, an elimination
* of the constrained degree of freedom of the form
* @f[
* x_i = \sum_j a_{ij} x_j + b_i
* @f]
* is performed, where <i>b<sub>i</sub></i> is optional and set by
* set_inhomogeneity(). Thus, if a constraint is formulated for
* instance as a zero mean value of several degrees of freedom, one of
* the degrees has to be chosen to be eliminated.
*
* Note that the constraints are linear
* in the <i>x<sub>i</sub></i>, and that there might be a constant (non-homogeneous) term in
* the constraint. This is exactly the form we need for hanging node
* constraints, where we need to constrain one degree of freedom in terms of
* others. There are other conditions of this form possible, for example for
* implementing mean value conditions as is done in the step-11
* tutorial program. The name of the class stems from the fact that these
* constraints can be represented in matrix form as <b>X</b> <i>x</i> = <i>b</i>, and this object
* then describes the matrix <b>X</b> (and the vector <i>b</i>;
* originally, the ConstraintMatrix class was only meant to handle homogenous
* constraints where <i>b</i>=0, thus the name). The most frequent way to
* create/fill objects of this type is using the
* DoFTools::make_hanging_node_constraints() function. The use of these
* objects is first explained in step-6.
*
* Objects of the present type are organized in lines (rows), but only those
* lines are stored where constraints are present. New constraints are added
* by adding new lines using the add_line() function, and then populating it
* using the add_entry() function to a given line, or add_entries() to add
* more than one entry at a time. The right hand side element, if nonzero, can
* be set using the set_inhomogeneity() function. After all constraints have
* been added, you need to call close(), which compresses the storage format
* and sorts the entries.
*
* @note Many of the algorithms this class implements are discussed in
* the @ref hp_paper . The algorithms are also related to those shown
* in <i>M. S. Shephard: Linear multipoint constraints applied via
* transformation as part of a direct stiffness assembly process. Int. J.
* Numer. Meth. Engrg., vol. 20 (1984), pp. 2107-2112.</i>, with the
* difference that the algorithms shown there completely eliminated
* constrained degrees of freedom, whereas we usually keep them as part
* of the linear system.
*
* @ingroup dofs
* @ingroup constraints
* @author Wolfgang Bangerth, Martin Kronbichler, 1998, 2004, 2008, 2009
*/
class ConstraintMatrix : public Subscriptor
{
public:
/**
* Declare the type for container size.
*/
typedef types::global_dof_index size_type;
/**
* An enum that describes what should happen if the two ConstraintMatrix
* objects involved in a call to the merge() function happen to have
* constraints on the same degrees of freedom.
*/
enum MergeConflictBehavior
{
/**
* Throw an exception if the two objects concerned have conflicting
* constraints on the same degree of freedom.
*/
no_conflicts_allowed,
/**
* In an operation <code>cm1.merge(cm2)</code>, if <code>cm1</code> and
* <code>cm2</code> have constraints on the same degree of freedom, take
* the one from <code>cm1</code>.
*/
left_object_wins,
/**
* In an operation <code>cm1.merge(cm2)</code>, if <code>cm1</code> and
* <code>cm2</code> have constraints on the same degree of freedom, take
* the one from <code>cm2</code>.
*/
right_object_wins
};
/**
* Constructor. The supplied IndexSet defines which indices might be
* constrained inside this ConstraintMatrix. In a calculation with a
* parallel::distributed::DoFHandler one should use
* locally_relevant_dofs. The IndexSet allows the ConstraintMatrix to safe
* memory. Otherwise internal data structures for all possible indices will
* be created.
*/
ConstraintMatrix (const IndexSet &local_constraints = IndexSet());
/**
* Copy constructor
*/
ConstraintMatrix (const ConstraintMatrix &constraint_matrix);
/**
* Reinit the ConstraintMatrix object and supply an IndexSet with lines that
* may be constrained. This function is only relevant in the distributed
* case to supply a different IndexSet. Otherwise this routine is equivalent
* to calling clear(). See the constructor for details.
*/
void reinit (const IndexSet &local_constraints = IndexSet());
/**
* Determines if we can store a constraint for the given @p line_index. This
* routine only matters in the distributed case and checks if the IndexSet
* allows storage of this line. Always returns true if not in the
* distributed case.
*/
bool can_store_line (const size_type line_index) const;
/**
* Returns the index set describing locally relevant lines if any are
* present. Note that if no local lines were given, this represents an empty
* IndexSet, whereas otherwise it contains the global problem size and the
* local range.
*/
const IndexSet &get_local_lines() const;
/**
* This function copies the content of @p constraints_in with DoFs that are
* element of the IndexSet @p filter. Elements that are not present in the
* IndexSet are ignored. All DoFs will be transformed to local index space
* of the filter, both the constrained DoFs and the other DoFs these entries
* are constrained to. The local index space of the filter is a contiguous
* numbering of all (global) DoFs that are elements in the filter.
*
* If, for example, the filter represents the range <tt>[10,20)</tt>, and
* the constraint matrix @p constraints_in includes the global indices
* <tt>{7,13,14}</tt>, the indices <tt>{3,4}</tt> are added to the calling
* constraint matrix (since 13 and 14 are elements in the filter and element
* 13 is the fourth element in the index, and 14 is the fifth).
*
* This function provides an easy way to create a ConstraintMatrix for
* certain vector components in a vector-valued problem from a full
* ConstraintMatrix, i.e. extracting a diagonal subblock from a larger
* ConstraintMatrix. The block is specified by the IndexSet argument.
*/
void add_selected_constraints (const ConstraintMatrix &constraints_in,
const IndexSet &filter);
/**
* @name Adding constraints
* @{
*/
/**
* Add a new line to the matrix. If the line already exists, then the
* function simply returns without doing anything.
*/
void add_line (const size_type line);
/**
* Call the first add_line() function for every index <code>i</code> for
* which <code>lines[i]</code> is true.
*
* This function essentially exists to allow adding several constraints of
* the form <i>x<sub>i</sub></i>=0 all at once, where the set of indices
* <i>i</i> for which these constraints should be added are given by the
* argument of this function. On the other hand, just as if the
* single-argument add_line() function were called repeatedly, the
* constraints can later be modified to include linear dependencies using
* the add_entry() function as well as inhomogeneities using
* set_inhomogeneity().
*/
void add_lines (const std::vector<bool> &lines);
/**
* Call the first add_line() function for every index <code>i</code> that
* appears in the argument.
*
* This function essentially exists to allow adding several constraints of
* the form <i>x<sub>i</sub></i>=0 all at once, where the set of indices
* <i>i</i> for which these constraints should be added are given by the
* argument of this function. On the other hand, just as if the
* single-argument add_line() function were called repeatedly, the
* constraints can later be modified to include linear dependencies using
* the add_entry() function as well as inhomogeneities using
* set_inhomogeneity().
*/
void add_lines (const std::set<size_type> &lines);
/**
* Call the first add_line() function for every index <code>i</code> that
* appears in the argument.
*
* This function essentially exists to allow adding several constraints of
* the form <i>x<sub>i</sub></i>=0 all at once, where the set of indices
* <i>i</i> for which these constraints should be added are given by the
* argument of this function. On the other hand, just as if the
* single-argument add_line() function were called repeatedly, the
* constraints can later be modified to include linear dependencies using
* the add_entry() function as well as inhomogeneities using
* set_inhomogeneity().
*/
void add_lines (const IndexSet &lines);
/**
* Add an entry to a given line. The list of lines is searched from the back
* to the front, so clever programming would add a new line (which is pushed
* to the back) and immediately afterwards fill the entries of that
* line. This way, no expensive searching is needed.
*
* If an entry with the same indices as the one this function call denotes
* already exists, then this function simply returns provided that the value
* of the entry is the same. Thus, it does no harm to enter a constraint
* twice.
*/
void add_entry (const size_type line,
const size_type column,
const double value);
/**
* Add a whole series of entries, denoted by pairs of column indices and
* values, to a line of constraints. This function is equivalent to calling
* the preceding function several times, but is faster.
*/
void add_entries (const size_type line,
const std::vector<std::pair<size_type,double> > &col_val_pairs);
/**
* Set an imhomogeneity to the constraint line <i>i</i>, according to the
* discussion in the general class description.
*
* @note the line needs to be added with one of the add_line() calls first.
*/
void set_inhomogeneity (const size_type line,
const double value);
/**
* Close the filling of entries. Since the lines of a matrix of this type
* are usually filled in an arbitrary order and since we do not want to use
* associative constainers to store the lines, we need to sort the lines and
* within the lines the columns before usage of the matrix. This is done
* through this function.
*
* Also, zero entries are discarded, since they are not needed.
*
* After closing, no more entries are accepted. If the object was already
* closed, then this function returns immediately.
*
* This function also resolves chains of constraints. For example, degree of
* freedom 13 may be constrained to $u_{13} = \frac{u_3}{2} + \frac{u_7}{2}$
* while degree of freedom 7 is itself constrained as $u_{7} = \frac{u_2}{2}
* + \frac{u_4}{2}$. Then, the resolution will be that $u_{13} =
* \frac{u_3}{2} + \frac{u_2}{4} + \frac{u_4}{4}$. Note, however, that
* cycles in this graph of constraints are not allowed, i.e. for example
* $u_4$ may not be constrained, directly or indirectly, to $u_{13}$ again.
*/
void close ();
/**
* Merge the constraints represented by the object given as argument into
* the constraints represented by this object. Both objects may or may not
* be closed (by having their function close() called before). If this
* object was closed before, then it will be closed afterwards as
* well. Note, however, that if the other argument is closed, then merging
* may be significantly faster.
*
* Using the default value of the second arguments, the constraints in each
* of the two objects (the old one represented by this object and the
* argument) may not refer to the same degree of freedom, i.e. a degree of
* freedom that is constrained in one object may not be constrained in the
* second. If this is nevertheless the case, an exception is
* thrown. However, this behavior can be changed by providing a different
* value for the second argument.
*/
void merge (const ConstraintMatrix &other_constraints,
const MergeConflictBehavior merge_conflict_behavior = no_conflicts_allowed);
/**
* Shift all entries of this matrix down @p offset rows and over @p offset
* columns.
*
* This function is useful if you are building block matrices, where all
* blocks are built by the same DoFHandler object, i.e. the matrix size is
* larger than the number of degrees of freedom. Since several matrix rows
* and columns correspond to the same degrees of freedom, you'd generate
* several constraint objects, then shift them, and finally merge() them
* together again.
*/
void shift (const size_type offset);
/**
* Clear all entries of this matrix. Reset the flag determining whether new
* entries are accepted or not.
*
* This function may be called also on objects which are empty or already
* cleared.
*/
void clear ();
/**
* @}
*/
/**
* @name Querying constraints
* @{
*/
/**
* Return number of constraints stored in this matrix.
*/
size_type n_constraints () const;
/**
* Return whether the degree of freedom with number @p index is a
* constrained one.
*
* Note that if close() was called before, then this function is
* significantly faster, since then the constrained degrees of freedom are
* sorted and we can do a binary search, while before close() was called, we
* have to perform a linear search through all entries.
*/
bool is_constrained (const size_type index) const;
/**
* Return whether the dof is constrained, and whether it is constrained to
* only one other degree of freedom with weight one. The function therefore
* returns whether the degree of freedom would simply be eliminated in favor
* of exactly one other degree of freedom.
*
* The function returns @p false if either the degree of freedom is not
* constrained at all, or if it is constrained to more than one other degree
* of freedom, or if it is constrained to only one degree of freedom but
* with a weight different from one.
*/
bool is_identity_constrained (const size_type index) const;
/**
* Return whether the two given degrees of freedom are linked by an equality
* constraint that either constrains index1 to be so that
* <code>index1=index2</code> or constrains index2 so that
* <code>index2=index1</code>.
*/
bool are_identity_constrained (const size_type index1,
const size_type index2) const;
/**
* Return the maximum number of other dofs that one dof is constrained
* to. For example, in 2d a hanging node is constrained only to its two
* neighbors, so the returned value would be 2. However, for higher order
* elements and/or higher dimensions, or other types of constraints, this
* number is no more obvious.
*
* The name indicates that within the system matrix, references to a
* constrained node are indirected to the nodes it is constrained to.
*/
size_type max_constraint_indirections () const;
/**
* Returns <tt>true</tt> in case the dof is constrained and there is a
* non-trivial inhomogeneous valeus set to the dof.
*/
bool is_inhomogeneously_constrained (const size_type index) const;
/**
* Returns <tt>false</tt> if all constraints in the ConstraintMatrix are
* homogeneous ones, and <tt>true</tt> if there is at least one
* inhomogeneity.
*/
bool has_inhomogeneities () const;
/**
* Returns a pointer to the the vector of entries if a line is constrained,
* and a zero pointer in case the dof is not constrained.
*/
const std::vector<std::pair<size_type,double> > *
get_constraint_entries (const size_type line) const;
/**
* Returns the value of the inhomogeneity stored in the constrained dof @p
* line. Unconstrained dofs also return a zero value.
*/
double get_inhomogeneity (const size_type line) const;
/**
* Print the constraint lines. Mainly for debugging purposes.
*
* This function writes out all entries in the constraint matrix lines with
* their value in the form <tt>row col : value</tt>. Unconstrained lines
* containing only one identity entry are not stored in this object and are
* not printed.
*/
void print (std::ostream &) const;
/**
* Write the graph of constraints in 'dot' format. 'dot' is a program that
* can take a list of nodes and produce a graphical representation of the
* graph of constrained degrees of freedom and the degrees of freedom they
* are constrained to.
*
* The output of this function can be used as input to the 'dot' program
* that can convert the graph into a graphical representation in postscript,
* png, xfig, and a number of other formats.
*
* This function exists mostly for debugging purposes.
*/
void write_dot (std::ostream &) const;
/**
* Determine an estimate for the memory consumption (in bytes) of this
* object.
*/
std::size_t memory_consumption () const;
/**
* Add the constraint indices associated to the indices in the given vector.
* After a call to this function, the indices vector contains the initial
* elements and all the associated constrained indices. This function sorts
* the elements and suppresses duplicates.
*/
void resolve_indices(std::vector<types::global_dof_index> &indices) const;
/**
* @}
*/
/**
* @name Eliminating constraints from linear systems after their creation
* @{
*/
/**
* Condense a given sparsity pattern. This function assumes the uncondensed
* matrix struct to be compressed and the one to be filled to be empty. The
* condensed structure is compressed afterwards.
*
* The constraint matrix object must be closed to call this function.
*
* @note The hanging nodes are completely eliminated from the linear system
* referring to <tt>condensed</tt>. Therefore, the dimension of
* <tt>condensed</tt> is the dimension of <tt>uncondensed</tt> minus the
* number of constrained degrees of freedom.
*/
void condense (const SparsityPattern &uncondensed,
SparsityPattern &condensed) const;
/**
* This function does much the same as the above one, except that it
* condenses the matrix struct 'in-place'. It does not remove nonzero
* entries from the matrix but adds those needed for the process of
* distribution of the constrained degrees of freedom.
*
* Since this function adds new nonzero entries to the sparsity pattern, the
* argument must not be compressed. However the constraint matrix must be
* closed. The matrix struct is compressed at the end of the function.
*/
void condense (SparsityPattern &sparsity) const;
/**
* Same function as above, but condenses square block sparsity patterns.
*/
void condense (BlockSparsityPattern &sparsity) const;
/**
* Same function as above, but condenses square compressed sparsity
* patterns.
*
* Given the data structure used by CompressedSparsityPattern, this function
* becomes quadratic in the number of degrees of freedom for large problems
* and can dominate setting up linear systems when several hundred thousand
* or millions of unknowns are involved and for problems with many nonzero
* elements per row (for example for vector-valued problems or hp finite
* elements). In this case, it is advisable to use the
* CompressedSetSparsityPattern class instead, see for example @ref step_27
* "step-27", or to use the CompressedSimpleSparsityPattern class, see for
* example @ref step_31 "step-31".
*/
void condense (CompressedSparsityPattern &sparsity) const;
/**
* Same function as above, but condenses compressed sparsity patterns, which
* are based on the std::set container.
*/
void condense (CompressedSetSparsityPattern &sparsity) const;
/**
* Same function as above, but condenses compressed sparsity patterns, which
* are based on the ''simple'' aproach.
*/
void condense (CompressedSimpleSparsityPattern &sparsity) const;
/**
* Same function as above, but condenses square compressed sparsity
* patterns.
*
* Given the data structure used by BlockCompressedSparsityPattern, this
* function becomes quadratic in the number of degrees of freedom for large
* problems and can dominate setting up linear systems when several hundred
* thousand or millions of unknowns are involved and for problems with many
* nonzero elements per row (for example for vector-valued problems or hp
* finite elements). In this case, it is advisable to use the
* BlockCompressedSetSparsityPattern class instead, see for example @ref
* step_27 "step-27" and @ref step_31 "step-31".
*/
void condense (BlockCompressedSparsityPattern &sparsity) const;
/**
* Same function as above, but condenses square compressed sparsity
* patterns.
*/
void condense (BlockCompressedSetSparsityPattern &sparsity) const;
/**
* Same function as above, but condenses square compressed sparsity
* patterns.
*/
void condense (BlockCompressedSimpleSparsityPattern &sparsity) const;
/**
* Condense a given matrix. The associated matrix struct should be condensed
* and compressed. It is the user's responsibility to guarantee that all
* entries in the @p condensed matrix be zero!
*
* The constraint matrix object must be closed to call this function.
*
* @deprecated The functions converting an uncondensed matrix into
* its condensed form are deprecated. Use the functions doing the
* in-place condensation leaving the size of the linear system unchanged.
*/
template<typename number>
void condense (const SparseMatrix<number> &uncondensed,
SparseMatrix<number> &condensed) const DEAL_II_DEPRECATED;
/**
* This function does much the same as the above one, except that it
* condenses the matrix 'in-place'. See the general documentation of this
* class for more detailed information.
*/
template<typename number>
void condense (SparseMatrix<number> &matrix) const;
/**
* Same function as above, but condenses square block sparse matrices.
*/
template <typename number>
void condense (BlockSparseMatrix<number> &matrix) const;
/**
* Condense the given vector @p uncondensed into @p condensed. It is the
* user's responsibility to guarantee that all entries of @p condensed be
* zero. Note that this function does not take any inhomogeneity into
* account and throws an exception in case there are any
* inhomogeneities. Use the function using both a matrix and vector for that
* case.
*
* The @p VectorType may be a Vector<float>, Vector<double>,
* BlockVector<tt><...></tt>, a PETSc or Trilinos vector wrapper class, or
* any other type having the same interface.
*
* @deprecated The functions converting an uncondensed matrix into
* its condensed form are deprecated. Use the functions doing the
* in-place condensation leaving the size of the linear system unchanged.
*/
template <class VectorType>
void condense (const VectorType &uncondensed,
VectorType &condensed) const DEAL_II_DEPRECATED;
/**
* Condense the given vector in-place. The @p VectorType may be a
* Vector<float>, Vector<double>, BlockVector<tt><...></tt>, a PETSc or
* Trilinos vector wrapper class, or any other type having the same
* interface. Note that this function does not take any inhomogeneity into
* account and throws an exception in case there are any
* inhomogeneities. Use the function using both a matrix and vector for that
* case.
*/
template <class VectorType>
void condense (VectorType &vec) const;
/**
* Condense a given matrix and a given vector. The associated matrix struct
* should be condensed and compressed. It is the user's responsibility to
* guarantee that all entries in the @p condensed matrix and vector be zero!
* This function is the appropriate choice for applying inhomogeneous
* constraints.
*
* The constraint matrix object must be closed to call this function.
*
* @deprecated The functions converting an uncondensed matrix into
* its condensed form are deprecated. Use the functions doing the
* in-place condensation leaving the size of the linear system unchanged.
*/
template<typename number, class VectorType>
void condense (const SparseMatrix<number> &uncondensed_matrix,
const VectorType &uncondensed_vector,
SparseMatrix<number> &condensed_matrix,
VectorType &condensed_vector) const DEAL_II_DEPRECATED;
/**
* This function does much the same as the above one, except that it
* condenses matrix and vector 'in-place'. See the general documentation of
* this class for more detailed information.
*/
template<typename number, class VectorType>
void condense (SparseMatrix<number> &matrix,
VectorType &vector) const;
/**
* Same function as above, but condenses square block sparse matrices and
* vectors.
*/
template <typename number, class BlockVectorType>
void condense (BlockSparseMatrix<number> &matrix,
BlockVectorType &vector) const;
/**
* Sets the values of all constrained DoFs in a vector to zero. The @p
* VectorType may be a Vector<float>, Vector<double>,
* BlockVector<tt><...></tt>, a PETSc or Trilinos vector wrapper class, or
* any other type having the same interface.
*/
template <class VectorType>
void set_zero (VectorType &vec) const;
/**
* @}
*/
/**
* @name Eliminating constraints from linear systems during their creation
* @{
*/
/**
* This function takes a vector of local contributions (@p local_vector)
* corresponding to the degrees of freedom indices given in @p
* local_dof_indices and distributes them to the global vector. In most
* cases, these local contributions will be the result of an integration
* over a cell or face of a cell. However, as long as @p local_vector and @p
* local_dof_indices have the same number of elements, this function is
* happy with whatever it is given.
*
* In contrast to the similar function in the DoFAccessor class, this
* function also takes care of constraints, i.e. if one of the elements of
* @p local_dof_indices belongs to a constrained node, then rather than
* writing the corresponding element of @p local_vector into @p
* global_vector, the element is distributed to the entries in the global
* vector to which this particular degree of freedom is constrained.
*
* Thus, by using this function to distribute local contributions to the
* global object, one saves the call to the condense function after the
* vectors and matrices are fully assembled. On the other hand, by
* consequence, the function does not only write into the entries enumerated
* by the @p local_dof_indices array, but also (possibly) others as
* necessary.
*
* Note that this function will apply all constraints as if they were
* homogeneous. For correctly setting inhomogeneous constraints, use the
* similar function with a matrix argument or the function with both matrix
* and vector arguments.
*
* @note This function in itself is thread-safe, i.e., it works properly
* also when several threads call it simultaneously. However, the function
* call is only thread-safe if the underlying global vector allows
* for simultaneous access and the access is not to rows with the same
* global index at the same time. This needs to be made sure from the
* caller's site. There is no locking mechanism inside this method to
* prevent data races.
*/
template <class InVector, class OutVector>
void
distribute_local_to_global (const InVector &local_vector,
const std::vector<size_type> &local_dof_indices,
OutVector &global_vector) const;
/**
* This function takes a vector of local contributions (@p local_vector)
* corresponding to the degrees of freedom indices given in @p
* local_dof_indices and distributes them to the global vector. In most
* cases, these local contributions will be the result of an integration
* over a cell or face of a cell. However, as long as @p local_vector and @p
* local_dof_indices have the same number of elements, this function is
* happy with whatever it is given.
*
* In contrast to the similar function in the DoFAccessor class, this
* function also takes care of constraints, i.e. if one of the elements of
* @p local_dof_indices belongs to a constrained node, then rather than
* writing the corresponding element of @p local_vector into @p
* global_vector, the element is distributed to the entries in the global
* vector to which this particular degree of freedom is constrained.
*
* Thus, by using this function to distribute local contributions to the
* global object, one saves the call to the condense function after the
* vectors and matrices are fully assembled. On the other hand, by
* consequence, the function does not only write into the entries enumerated
* by the @p local_dof_indices array, but also (possibly) others as
* necessary. This includes writing into diagonal elements of the matrix if
* the corresponding degree of freedom is constrained.
*
* The fourth argument <tt>local_matrix</tt> is intended to be used in case
* one wants to apply inhomogeneous constraints on the vector only. Such a
* situation could be where one wants to assemble of a right hand side
* vector on a problem with inhomogeneous constraints, but the global matrix
* has been assembled previously. A typical example of this is a time
* stepping algorithm where the stiffness matrix is assembled once, and the
* right hand side updated every time step. Note that, however, the entries
* in the columns of the local matrix have to be exactly the same as those
* that have been written into the global matrix. Otherwise, this function
* will not be able to correctly handle inhomogeneities.
*
* @note This function in itself is thread-safe, i.e., it works properly
* also when several threads call it simultaneously. However, the function
* call is only thread-safe if the underlying global vector allows
* for simultaneous access and the access is not to rows with the same
* global index at the same time. This needs to be made sure from the
* caller's site. There is no locking mechanism inside this method to
* prevent data races.
*/
template <typename VectorType>
void
distribute_local_to_global (const Vector<double> &local_vector,
const std::vector<size_type> &local_dof_indices,
VectorType &global_vector,
const FullMatrix<double> &local_matrix) const;
/**
* Enter a single value into a result vector, obeying constraints.
*/
template <class VectorType>
void
distribute_local_to_global (const size_type index,
const double value,
VectorType &global_vector) const;
/**
* This function takes a pointer to a vector of local contributions (@p
* local_vector) corresponding to the degrees of freedom indices given in @p
* local_dof_indices and distributes them to the global vector. In most
* cases, these local contributions will be the result of an integration
* over a cell or face of a cell. However, as long as the entries in @p
* local_dof_indices indicate reasonable global vector entries, this
* function is happy with whatever it is given.
*
* If one of the elements of @p local_dof_indices belongs to a constrained
* node, then rather than writing the corresponding element of @p
* local_vector into @p global_vector, the element is distributed to the
* entries in the global vector to which this particular degree of freedom
* is constrained.
*
* Thus, by using this function to distribute local contributions to the
* global object, one saves the call to the condense function after the
* vectors and matrices are fully assembled. Note that this function
* completely ignores inhomogeneous constraints.
*
* @note This function in itself is thread-safe, i.e., it works properly
* also when several threads call it simultaneously. However, the function
* call is only thread-safe if the underlying global vector allows
* for simultaneous access and the access is not to rows with the same
* global index at the same time. This needs to be made sure from the
* caller's site. There is no locking mechanism inside this method to
* prevent data races.
*/
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
void
distribute_local_to_global (ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end,
ForwardIteratorInd local_indices_begin,
VectorType &global_vector) const;
/**
* This function takes a matrix of local contributions (@p local_matrix)
* corresponding to the degrees of freedom indices given in @p
* local_dof_indices and distributes them to the global matrix. In most
* cases, these local contributions will be the result of an integration
* over a cell or face of a cell. However, as long as @p local_matrix and @p
* local_dof_indices have the same number of elements, this function is
* happy with whatever it is given.
*
* In contrast to the similar function in the DoFAccessor class, this
* function also takes care of constraints, i.e. if one of the elements of
* @p local_dof_indices belongs to a constrained node, then rather than
* writing the corresponding element of @p local_matrix into @p
* global_matrix, the element is distributed to the entries in the global
* matrix to which this particular degree of freedom is constrained.
*
* With this scheme, we never write into rows or columns of constrained
* degrees of freedom. In order to make sure that the resulting matrix can
* still be inverted, we need to do something with the diagonal elements
* corresponding to constrained nodes. Thus, if a degree of freedom in @p
* local_dof_indices is constrained, we distribute the corresponding entries
* in the matrix, but also add the absolute value of the diagonal entry of
* the local matrix to the corresponding entry in the global matrix. Since
* the exact value of the diagonal element is not important (the value of
* the respective degree of freedom will be overwritten by the distribute()
* call later on anyway), this guarantees that the diagonal entry is always
* non-zero, positive, and of the same order of magnitude as the other
* entries of the matrix.
*
* Thus, by using this function to distribute local contributions to the
* global object, one saves the call to the condense function after the
* vectors and matrices are fully assembled.
*
* @note This function in itself is thread-safe, i.e., it works properly
* also when several threads call it simultaneously. However, the function
* call is only thread-safe if the underlying global matrix allows
* for simultaneous access and the access is not to rows with the same
* global index at the same time. This needs to be made sure from the
* caller's site. There is no locking mechanism inside this method to
* prevent data races.
*/
template <typename MatrixType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const std::vector<size_type> &local_dof_indices,
MatrixType &global_matrix) const;
/**
* Does the same as the function above but can treat non quadratic matrices.
*/
template <typename MatrixType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const std::vector<size_type> &row_indices,
const std::vector<size_type> &col_indices,
MatrixType &global_matrix) const;
/**
* This function simultaneously writes elements into matrix and vector,
* according to the constraints specified by the calling
* ConstraintMatrix. This function can correctly handle inhomogeneous
* constraints as well. For the parameter use_inhomogeneities_for_rhs see
* the documentation in @ref constraints module.
*
* @note This function in itself is thread-safe, i.e., it works properly
* also when several threads call it simultaneously. However, the function
* call is only thread-safe if the underlying global matrix and vector allow
* for simultaneous access and the access is not to rows with the same
* global index at the same time. This needs to be made sure from the
* caller's site. There is no locking mechanism inside this method to
* prevent data races.
*/
template <typename MatrixType, typename VectorType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const Vector<double> &local_vector,
const std::vector<size_type> &local_dof_indices,
MatrixType &global_matrix,
VectorType &global_vector,
bool use_inhomogeneities_for_rhs = false) const;
/**
* Do a similar operation as the distribute_local_to_global() function that
* distributes writing entries into a matrix for constrained degrees of
* freedom, except that here we don't write into a matrix but only allocate
* sparsity pattern entries.
*
* As explained in the @ref hp_paper "hp paper" and in step-27, first
* allocating a sparsity pattern and later coming back and allocating
* additional entries for those matrix entries that will be written to due
* to the elimination of constrained degrees of freedom (using
* ConstraintMatrix::condense() ), can be a very expensive procedure. It is
* cheaper to allocate these entries right away without having to do a
* second pass over the sparsity pattern object. This function does exactly
* that.
*
* Because the function only allocates entries in a sparsity pattern, all it
* needs to know are the degrees of freedom that couple to each
* other. Unlike the previous function, no actual values are written, so the
* second input argument is not necessary here.
*
* The third argument to this function, keep_constrained_entries determines
* whether the function shall allocate entries in the sparsity pattern at
* all for entries that will later be set to zero upon condensation of the
* matrix. These entries are necessary if the matrix is built unconstrained,
* and only later condensed. They are not necessary if the matrix is built
* using the distribute_local_to_global() function of this class which
* distributes entries right away when copying a local matrix into a global
* object. The default of this argument is true, meaning to allocate the few
* entries that may later be set to zero.
*
* By default, the function adds entries for all pairs of indices given in
* the first argument to the sparsity pattern (unless
* keep_constrained_entries is false). However, sometimes one would like to
* only add a subset of all of these pairs. In that case, the last argument
* can be used which specifies a boolean mask which of the pairs of indices
* should be considered. If the mask is false for a pair of indices, then no
* entry will be added to the sparsity pattern for this pair, irrespective
* of whether one or both of the indices correspond to constrained degrees
* of freedom.
*
* This function is not typically called from user code, but is used in the
* DoFTools::make_sparsity_pattern() function when passed a constraint
* matrix object.
*
* @note This function in itself is thread-safe, i.e., it works properly
* also when several threads call it simultaneously. However, the function
* call is only thread-safe if the underlying global sparsity pattern allows
* for simultaneous access and the access is not to rows with the same
* global index at the same time. This needs to be made sure from the
* caller's site. There is no locking mechanism inside this method to
* prevent data races.
*/
template <typename SparsityType>
void
add_entries_local_to_global (const std::vector<size_type> &local_dof_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries = true,
const Table<2,bool> &dof_mask = default_empty_table) const;
/**
* Similar to the other function, but for non-quadratic sparsity patterns.
*/
template <typename SparsityType>
void
add_entries_local_to_global (const std::vector<size_type> &row_indices,
const std::vector<size_type> &col_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries = true,
const Table<2,bool> &dof_mask = default_empty_table) const;
/**
* This function imports values from a global vector (@p global_vector) by
* applying the constraints to a vector of local values, expressed in
* iterator format. In most cases, the local values will be identified by
* the local dof values on a cell. However, as long as the entries in @p
* local_dof_indices indicate reasonable global vector entries, this
* function is happy with whatever it is given.
*
* If one of the elements of @p local_dof_indices belongs to a constrained
* node, then rather than writing the corresponding element of @p
* global_vector into @p local_vector, the constraints are resolved as the
* respective distribute function does, i.e., the local entry is constructed
* from the global entries to which this particular degree of freedom is
* constrained.
*
* In contrast to the similar function get_dof_values in the DoFAccessor
* class, this function does not need the constrained values to be correctly
* set (i.e., distribute to be called).
*/
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
void
get_dof_values (const VectorType &global_vector,
ForwardIteratorInd local_indices_begin,
ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end) const;
/**
* @}
*/
/**
* @name Dealing with constraints after solving a linear system
* @{
*/
/**
* Re-distribute the elements of the vector @p condensed to @p
* uncondensed. It is the user's responsibility to guarantee that all
* entries of @p uncondensed be zero!
*
* This function undoes the action of @p condense somehow, but it should be
* noted that it is not the inverse of @p condense.
*
* The @p VectorType may be a Vector<float>, Vector<double>,
* BlockVector<tt><...></tt>, a PETSc or Trilinos vector wrapper class, or
* any other type having the same interface.
*/
template <class VectorType>
void distribute (const VectorType &condensed,
VectorType &uncondensed) const;
/**
* Re-distribute the elements of the vector in-place. The @p VectorType may
* be a Vector<float>, Vector<double>, BlockVector<tt><...></tt>, a PETSc or
* Trilinos vector wrapper class, or any other type having the same
* interface.
*
* Note that if called with a TrilinosWrappers::MPI::Vector it may not
* contain ghost elements.
*/
template <class VectorType>
void distribute (VectorType &vec) const;
/**
* @}
*/
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException0 (ExcMatrixIsClosed);
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException0 (ExcMatrixNotClosed);
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException1 (ExcLineInexistant,
size_type,
<< "The specified line " << arg1
<< " does not exist.");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException4 (ExcEntryAlreadyExists,
size_type, size_type, double, double,
<< "The entry for the indices " << arg1 << " and "
<< arg2 << " already exists, but the values "
<< arg3 << " (old) and " << arg4 << " (new) differ "
<< "by " << (arg4-arg3) << ".");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException2 (ExcDoFConstrainedToConstrainedDoF,
int, int,
<< "You tried to constrain DoF " << arg1
<< " to DoF " << arg2
<< ", but that one is also constrained. This is not allowed!");
/**
* Exception.
*
* @ingroup Exceptions
*/
DeclException1 (ExcDoFIsConstrainedFromBothObjects,
size_type,
<< "Degree of freedom " << arg1
<< " is constrained from both object in a merge operation.");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException1 (ExcDoFIsConstrainedToConstrainedDoF,
size_type,
<< "In the given argument a degree of freedom is constrained "
<< "to another DoF with number " << arg1
<< ", which however is constrained by this object. This is not"
<< " allowed.");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException1 (ExcRowNotStoredHere,
size_type,
<< "The index set given to this constraint matrix indicates "
<< "constraints for degree of freedom " << arg1
<< " should not be stored by this object, but a constraint "
<< "is being added.");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException2 (ExcIncorrectConstraint,
int, int,
<< "While distributing the constraint for DoF "
<< arg1 << ", it turns out that one of the processors "
<< "who own the " << arg2
<< " degrees of freedom that x_" << arg1
<< " is constrained against does not know about "
<< "the constraint on x_" << arg1
<< ". Did you not initialize the ConstraintMatrix "
<< "with the appropriate locally_relevant set so "
<< "that every processor who owns a DoF that constrains "
<< "another DoF also knows about this constraint?");
private:
/**
* This class represents one line of a constraint matrix.
*/
struct ConstraintLine
{
/**
* A data type in which we store the list of entries that make up the
* homogenous part of a constraint.
*/
typedef std::vector<std::pair<size_type,double> > Entries;
/**
* Number of this line. Since only very few lines are stored, we can not
* assume a specific order and have to store the line number explicitly.
*/
size_type line;
/**
* Row numbers and values of the entries in this line.
*
* For the reason why we use a vector instead of a map and the
* consequences thereof, the same applies as what is said for
* ConstraintMatrix::lines.
*/
Entries entries;
/**
* Value of the inhomogeneity.
*/
double inhomogeneity;
/**
* This operator is a bit weird and unintuitive: it compares the line
* numbers of two lines. We need this to sort the lines; in fact we could
* do this using a comparison predicate. However, this way, it is easier,
* albeit unintuitive since two lines really have no god-given order
* relation.
*/
bool operator < (const ConstraintLine &) const;
/**
* This operator is likewise weird: it checks whether the line indices of
* the two operands are equal, irrespective of the fact that the contents
* of the line may be different.
*/
bool operator == (const ConstraintLine &) const;
/**
* Determine an estimate for the memory consumption (in bytes) of this
* object.
*/
std::size_t memory_consumption () const;
};
/**
* Store the lines of the matrix. Entries are usually appended in an
* arbitrary order and insertion into a vector is done best at the end, so
* the order is unspecified after all entries are inserted. Sorting of the
* entries takes place when calling the <tt>close()</tt> function.
*
* We could, instead of using a vector, use an associative array, like a map
* to store the lines. This, however, would mean a much more fractioned heap
* since it allocates many small objects, and would additionally make usage
* of this matrix much slower.
*/
std::vector<ConstraintLine> lines;
/**
* A list of size_type that contains the position of the ConstraintLine of a
* constrained degree of freedom, or numbers::invalid_size_type if the
* degree of freedom is not constrained. The numbers::invalid_size_type
* return value returns thus whether there is a constraint line for a given
* degree of freedom index. Note that this class has no notion of how many
* degrees of freedom there really are, so if we check whether there is a
* constraint line for a given degree of freedom, then this vector may
* actually be shorter than the index of the DoF we check for.
*
* This field exists since when adding a new constraint line we have to
* figure out whether it already exists. Previously, we would simply walk
* the unsorted list of constraint lines until we either hit the end or
* found it. This algorithm is O(N) if N is the number of constraints, which
* makes it O(N^2) when inserting all constraints. For large problems with
* many constraints, this could easily take 5-10 per cent of the total run
* time. With this field, we can save this time since we find any constraint
* in O(1) time or get to know that it a certain degree of freedom is not
* constrained.
*
* To make things worse, traversing the list of existing constraints
* requires reads from many different places in memory. Thus, in large 3d
* applications, the add_line() function showed up very prominently in the
* overall compute time, mainly because it generated a lot of cache
* misses. This should also be fixed by using the O(1) algorithm to access
* the fields of this array.
*
* The field is useful in a number of other contexts as well, e.g. when one
* needs random access to the constraints as in all the functions that apply
* constraints on the fly while add cell contributions into vectors and
* matrices.
*/
std::vector<size_type> lines_cache;
/**
* This IndexSet is used to limit the lines to save in the ConstraintMatrix
* to a subset. This is necessary, because the lines_cache vector would
* become too big in a distributed calculation.
*/
IndexSet local_lines;
/**
* Store whether the arrays are sorted. If so, no new entries can be added.
*/
bool sorted;
/**
* Internal function to calculate the index of line @p line in the vector
* lines_cache using local_lines.
*/
size_type calculate_line_index (const size_type line) const;
/**
* Return @p true if the weight of an entry (the second element of the pair)
* equals zero. This function is used to delete entries with zero weight.
*/
static bool check_zero_weight (const std::pair<size_type, double> &p);
/**
* Dummy table that serves as default argument for function
* <tt>add_entries_local_to_global()</tt>.
*/
static const Table<2,bool> default_empty_table;
/**
* This function actually implements the local_to_global function for
* standard (non-block) matrices.
*/
template <typename MatrixType, typename VectorType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const Vector<double> &local_vector,
const std::vector<size_type> &local_dof_indices,
MatrixType &global_matrix,
VectorType &global_vector,
bool use_inhomogeneities_for_rhs,
internal::bool2type<false>) const;
/**
* This function actually implements the local_to_global function for block
* matrices.
*/
template <typename MatrixType, typename VectorType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const Vector<double> &local_vector,
const std::vector<size_type> &local_dof_indices,
MatrixType &global_matrix,
VectorType &global_vector,
bool use_inhomogeneities_for_rhs,
internal::bool2type<true>) const;
/**
* This function actually implements the local_to_global function for
* standard (non-block) sparsity types.
*/
template <typename SparsityType>
void
add_entries_local_to_global (const std::vector<size_type> &local_dof_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries,
const Table<2,bool> &dof_mask,
internal::bool2type<false>) const;
/**
* This function actually implements the local_to_global function for block
* sparsity types.
*/
template <typename SparsityType>
void
add_entries_local_to_global (const std::vector<size_type> &local_dof_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries,
const Table<2,bool> &dof_mask,
internal::bool2type<true>) const;
/**
* Internal helper function for distribute_local_to_global function.
*
* Creates a list of affected global rows for distribution, including the
* local rows where the entries come from. The list is sorted according to
* the global row indices.
*/
void
make_sorted_row_list (const std::vector<size_type> &local_dof_indices,
internals::GlobalRowsFromLocal &global_rows) const;
/**
* Internal helper function for add_entries_local_to_global function.
*
* Creates a list of affected rows for distribution without any additional
* information, otherwise similar to the other make_sorted_row_list()
* function.
*/
void
make_sorted_row_list (const std::vector<size_type> &local_dof_indices,
std::vector<size_type> &active_dofs) const;
/**
* Internal helper function for distribute_local_to_global function.
*/
double
resolve_vector_entry (const size_type i,
const internals::GlobalRowsFromLocal &global_rows,
const Vector<double> &local_vector,
const std::vector<size_type> &local_dof_indices,
const FullMatrix<double> &local_matrix) const;
};
/* ---------------- template and inline functions ----------------- */
inline
ConstraintMatrix::ConstraintMatrix (const IndexSet &local_constraints)
:
lines (),
local_lines (local_constraints),
sorted (false)
{
// make sure the IndexSet is compressed. Otherwise this can lead to crashes
// that are hard to find (only happen in release mode).
// see tests/mpi/constraint_matrix_crash_01
local_lines.compress();
}
inline
ConstraintMatrix::ConstraintMatrix (const ConstraintMatrix &constraint_matrix)
:
Subscriptor (),
lines (constraint_matrix.lines),
lines_cache (constraint_matrix.lines_cache),
local_lines (constraint_matrix.local_lines),
sorted (constraint_matrix.sorted)
{}
inline
void
ConstraintMatrix::add_line (const size_type line)
{
Assert (sorted==false, ExcMatrixIsClosed());
// the following can happen when we compute with distributed meshes and dof
// handlers and we constrain a degree of freedom whose number we don't have
// locally. if we don't abort here the program will try to allocate several
// terabytes of memory to resize the various arrays below :-)
Assert (line != numbers::invalid_size_type,
ExcInternalError());
const size_type line_index = calculate_line_index (line);
// check whether line already exists; it may, in which case we can just quit
if (is_constrained(line))
return;
// if necessary enlarge vector of existing entries for cache
if (line_index >= lines_cache.size())
lines_cache.resize (std::max(2*static_cast<size_type>(lines_cache.size()),
line_index+1),
numbers::invalid_size_type);
// push a new line to the end of the list
lines.push_back (ConstraintLine());
lines.back().line = line;
lines.back().inhomogeneity = 0.;
lines_cache[line_index] = lines.size()-1;
}
inline
void
ConstraintMatrix::add_entry (const size_type line,
const size_type column,
const double value)
{
Assert (sorted==false, ExcMatrixIsClosed());
Assert (line != column,
ExcMessage ("Can't constrain a degree of freedom to itself"));
// if in debug mode, check whether an entry for this column already exists
// and if it's the same as the one entered at present
//
// in any case: exit the function if an entry for this column already
// exists, since we don't want to enter it twice
Assert (lines_cache[calculate_line_index(line)] != numbers::invalid_size_type,
ExcInternalError());
ConstraintLine *line_ptr = &lines[lines_cache[calculate_line_index(line)]];
Assert (line_ptr->line == line, ExcInternalError());
for (ConstraintLine::Entries::const_iterator
p=line_ptr->entries.begin();
p != line_ptr->entries.end(); ++p)
if (p->first == column)
{
Assert (std::fabs(p->second - value) < 1.e-14,
ExcEntryAlreadyExists(line, column, p->second, value));
return;
}
line_ptr->entries.push_back (std::make_pair(column,value));
}
inline
void
ConstraintMatrix::set_inhomogeneity (const size_type line,
const double value)
{
const size_type line_index = calculate_line_index(line);
Assert( line_index < lines_cache.size() &&
lines_cache[line_index] != numbers::invalid_size_type,
ExcMessage("call add_line() before calling set_inhomogeneity()"));
Assert(lines_cache[line_index] < lines.size(), ExcInternalError());
ConstraintLine *line_ptr = &lines[lines_cache[line_index]];
line_ptr->inhomogeneity = value;
}
inline
types::global_dof_index
ConstraintMatrix::n_constraints () const
{
return lines.size();
}
inline
bool
ConstraintMatrix::is_constrained (const size_type index) const
{
const size_type line_index = calculate_line_index(index);
return ((line_index < lines_cache.size())
&&
(lines_cache[line_index] != numbers::invalid_size_type));
}
inline
bool
ConstraintMatrix::is_inhomogeneously_constrained (const size_type index) const
{
// check whether the entry is constrained. could use is_constrained, but
// that means computing the line index twice
const size_type line_index = calculate_line_index(index);
if (line_index >= lines_cache.size() ||
lines_cache[line_index] == numbers::invalid_size_type)
return false;
else
{
Assert(lines_cache[line_index] < lines.size(), ExcInternalError());
return !(lines[lines_cache[line_index]].inhomogeneity == 0);
}
}
inline
const std::vector<std::pair<types::global_dof_index,double> > *
ConstraintMatrix::get_constraint_entries (const size_type line) const
{
// check whether the entry is constrained. could use is_constrained, but
// that means computing the line index twice
const size_type line_index = calculate_line_index(line);
if (line_index >= lines_cache.size() ||
lines_cache[line_index] == numbers::invalid_size_type)
return 0;
else
return &lines[lines_cache[line_index]].entries;
}
inline
double
ConstraintMatrix::get_inhomogeneity (const size_type line) const
{
// check whether the entry is constrained. could use is_constrained, but
// that means computing the line index twice
const size_type line_index = calculate_line_index(line);
if (line_index >= lines_cache.size() ||
lines_cache[line_index] == numbers::invalid_size_type)
return 0;
else
return lines[lines_cache[line_index]].inhomogeneity;
}
inline types::global_dof_index
ConstraintMatrix::calculate_line_index (const size_type line) const
{
//IndexSet is unused (serial case)
if (!local_lines.size())
return line;
Assert(local_lines.is_element(line),
ExcRowNotStoredHere(line));
return local_lines.index_within_set(line);
}
inline bool
ConstraintMatrix::can_store_line (size_type line_index) const
{
return !local_lines.size() || local_lines.is_element(line_index);
}
inline
const IndexSet &
ConstraintMatrix::get_local_lines () const
{
return local_lines;
}
template <class VectorType>
inline
void ConstraintMatrix::distribute_local_to_global (
const size_type index,
const double value,
VectorType &global_vector) const
{
Assert (lines.empty() || sorted == true, ExcMatrixNotClosed());
if (is_constrained(index) == false)
global_vector(index) += value;
else
{
const ConstraintLine &position =
lines[lines_cache[calculate_line_index(index)]];
for (size_type j=0; j<position.entries.size(); ++j)
global_vector(position.entries[j].first)
+= value * position.entries[j].second;
}
}
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
inline
void ConstraintMatrix::distribute_local_to_global (
ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end,
ForwardIteratorInd local_indices_begin,
VectorType &global_vector) const
{
Assert (lines.empty() || sorted == true, ExcMatrixNotClosed());
for ( ; local_vector_begin != local_vector_end;
++local_vector_begin, ++local_indices_begin)
{
if (is_constrained(*local_indices_begin) == false)
global_vector(*local_indices_begin) += *local_vector_begin;
else
{
const ConstraintLine &position =
lines[lines_cache[calculate_line_index(*local_indices_begin)]];
for (size_type j=0; j<position.entries.size(); ++j)
global_vector(position.entries[j].first)
+= *local_vector_begin * position.entries[j].second;
}
}
}
template <class InVector, class OutVector>
inline
void
ConstraintMatrix::distribute_local_to_global (
const InVector &local_vector,
const std::vector<size_type> &local_dof_indices,
OutVector &global_vector) const
{
Assert (local_vector.size() == local_dof_indices.size(),
ExcDimensionMismatch(local_vector.size(), local_dof_indices.size()));
distribute_local_to_global (local_vector.begin(), local_vector.end(),
local_dof_indices.begin(), global_vector);
}
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
inline
void ConstraintMatrix::get_dof_values (const VectorType &global_vector,
ForwardIteratorInd local_indices_begin,
ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end) const
{
Assert (lines.empty() || sorted == true, ExcMatrixNotClosed());
for ( ; local_vector_begin != local_vector_end;
++local_vector_begin, ++local_indices_begin)
{
if (is_constrained(*local_indices_begin) == false)
*local_vector_begin = global_vector(*local_indices_begin);
else
{
const ConstraintLine &position =
lines[lines_cache[calculate_line_index(*local_indices_begin)]];
typename VectorType::value_type value = position.inhomogeneity;
for (size_type j=0; j<position.entries.size(); ++j)
value += (global_vector(position.entries[j].first) *
position.entries[j].second);
*local_vector_begin = value;
}
}
}
template <typename MatrixType>
inline
void
ConstraintMatrix::
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const std::vector<size_type> &local_dof_indices,
MatrixType &global_matrix) const
{
// create a dummy and hand on to the function actually implementing this
// feature in the cm.templates.h file.
Vector<double> dummy(0);
distribute_local_to_global (local_matrix, dummy, local_dof_indices,
global_matrix, dummy, false,
internal::bool2type<IsBlockMatrix<MatrixType>::value>());
}
template <typename MatrixType, typename VectorType>
inline
void
ConstraintMatrix::
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const Vector<double> &local_vector,
const std::vector<size_type> &local_dof_indices,
MatrixType &global_matrix,
VectorType &global_vector,
bool use_inhomogeneities_for_rhs) const
{
// enter the internal function with the respective block information set,
// the actual implementation follows in the cm.templates.h file.
distribute_local_to_global (local_matrix, local_vector, local_dof_indices,
global_matrix, global_vector, use_inhomogeneities_for_rhs,
internal::bool2type<IsBlockMatrix<MatrixType>::value>());
}
template <typename SparsityType>
inline
void
ConstraintMatrix::
add_entries_local_to_global (const std::vector<size_type> &local_dof_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries,
const Table<2,bool> &dof_mask) const
{
// enter the internal function with the respective block information set,
// the actual implementation follows in the cm.templates.h file.
add_entries_local_to_global (local_dof_indices, sparsity_pattern,
keep_constrained_entries, dof_mask,
internal::bool2type<IsBlockMatrix<SparsityType>::value>());
}
DEAL_II_NAMESPACE_CLOSE
#endif
|