Reference documentation for deal.II version GIT 20f059c89a 2022-12-04 14:55:02+00:00
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full_matrix.h
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15 
16 #ifndef dealii_full_matrix_h
17 #define dealii_full_matrix_h
18 
19 
20 #include <deal.II/base/config.h>
21 
22 #include <deal.II/base/numbers.h>
23 #include <deal.II/base/table.h>
24 #include <deal.II/base/tensor.h>
25 
26 #include <deal.II/lac/exceptions.h>
28 
29 #include <cstring>
30 #include <iomanip>
31 #include <vector>
32 
34 
35 
36 // forward declarations
37 #ifndef DOXYGEN
38 template <typename number>
39 class Vector;
40 template <typename number>
41 class LAPACKFullMatrix;
42 #endif
43 
77 template <typename number>
78 class FullMatrix : public Table<2, number>
79 {
80 public:
88  static_assert(
89  std::is_arithmetic<
91  "The FullMatrix class only supports basic numeric types. In particular, it "
92  "does not support automatically differentiated numbers.");
93 
94 
98  using size_type = std::size_t;
99 
104  using value_type = number;
105 
110 
115 
120 
124  using Table<2, number>::end;
125 
136 
151  explicit FullMatrix(const size_type n = 0);
152 
156  FullMatrix(const size_type rows, const size_type cols);
157 
162  FullMatrix(const size_type rows, const size_type cols, const number *entries);
163 
185  template <typename number2>
188 
197  operator=(const number d);
198 
209 
214  template <typename number2>
217 
218 
224  template <typename MatrixType>
225  void
226  copy_from(const MatrixType &);
227 
233  template <typename MatrixType>
234  void
235  copy_transposed(const MatrixType &);
236 
244  template <int dim>
245  void
247  const unsigned int src_r_i = 0,
248  const unsigned int src_r_j = dim - 1,
249  const unsigned int src_c_i = 0,
250  const unsigned int src_c_j = dim - 1,
251  const size_type dst_r = 0,
252  const size_type dst_c = 0);
253 
261  template <int dim>
262  void
264  const size_type src_r_i = 0,
265  const size_type src_r_j = dim - 1,
266  const size_type src_c_i = 0,
267  const size_type src_c_j = dim - 1,
268  const unsigned int dst_r = 0,
269  const unsigned int dst_c = 0) const;
270 
283  template <typename MatrixType, typename index_type>
284  void
285  extract_submatrix_from(const MatrixType & matrix,
286  const std::vector<index_type> &row_index_set,
287  const std::vector<index_type> &column_index_set);
288 
301  template <typename MatrixType, typename index_type>
302  void
303  scatter_matrix_to(const std::vector<index_type> &row_index_set,
304  const std::vector<index_type> &column_index_set,
305  MatrixType & matrix) const;
306 
317  template <typename number2>
318  void
320  const size_type dst_offset_i = 0,
321  const size_type dst_offset_j = 0,
322  const size_type src_offset_i = 0,
323  const size_type src_offset_j = 0);
324 
325 
329  template <typename number2>
330  void
331  fill(const number2 *);
332 
344  template <typename number2>
345  void
347  const std::vector<size_type> &p_rows,
348  const std::vector<size_type> &p_cols);
349 
360  void
361  set(const size_type i, const size_type j, const number value);
375  bool
377 
382  size_type
383  m() const;
384 
389  size_type
390  n() const;
391 
397  bool
398  all_zero() const;
399 
415  template <typename number2>
416  number2
418 
428  template <typename number2>
429  number2
431  const Vector<number2> &v) const;
432 
437  real_type
438  l1_norm() const;
439 
444  real_type
445  linfty_norm() const;
446 
454  real_type
455  frobenius_norm() const;
456 
465  real_type
467 
473  number
474  determinant() const;
475 
481  number
482  trace() const;
483 
490  template <class StreamType>
491  void
492  print(StreamType & s,
493  const unsigned int width = 5,
494  const unsigned int precision = 2) const;
495 
518  void
519  print_formatted(std::ostream & out,
520  const unsigned int precision = 3,
521  const bool scientific = true,
522  const unsigned int width = 0,
523  const char * zero_string = " ",
524  const double denominator = 1.,
525  const double threshold = 0.) const;
526 
531  std::size_t
533 
543  iterator
544  begin(const size_type r);
545 
549  iterator
550  end(const size_type r);
551 
556  begin(const size_type r) const;
557 
562  end(const size_type r) const;
563 
573  FullMatrix &
574  operator*=(const number factor);
575 
579  FullMatrix &
580  operator/=(const number factor);
581 
589  template <typename number2>
590  void
591  add(const number a, const FullMatrix<number2> &A);
592 
600  template <typename number2>
601  void
602  add(const number a,
603  const FullMatrix<number2> &A,
604  const number b,
605  const FullMatrix<number2> &B);
606 
615  template <typename number2>
616  void
617  add(const number a,
618  const FullMatrix<number2> &A,
619  const number b,
620  const FullMatrix<number2> &B,
621  const number c,
622  const FullMatrix<number2> &C);
623 
635  template <typename number2>
636  void
638  const number factor,
639  const size_type dst_offset_i = 0,
640  const size_type dst_offset_j = 0,
641  const size_type src_offset_i = 0,
642  const size_type src_offset_j = 0);
643 
649  template <typename number2>
650  void
651  Tadd(const number s, const FullMatrix<number2> &B);
652 
664  template <typename number2>
665  void
667  const number factor,
668  const size_type dst_offset_i = 0,
669  const size_type dst_offset_j = 0,
670  const size_type src_offset_i = 0,
671  const size_type src_offset_j = 0);
672 
676  void
677  add(const size_type row, const size_type column, const number value);
678 
688  template <typename number2, typename index_type>
689  void
690  add(const size_type row,
691  const size_type n_cols,
692  const index_type *col_indices,
693  const number2 * values,
694  const bool elide_zero_values = true,
695  const bool col_indices_are_sorted = false);
696 
700  void
701  add_row(const size_type i, const number s, const size_type j);
702 
707  void
709  const number s,
710  const size_type j,
711  const number t,
712  const size_type k);
713 
717  void
718  add_col(const size_type i, const number s, const size_type j);
719 
724  void
726  const number s,
727  const size_type j,
728  const number t,
729  const size_type k);
730 
734  void
735  swap_row(const size_type i, const size_type j);
736 
740  void
741  swap_col(const size_type i, const size_type j);
742 
747  void
748  diagadd(const number s);
749 
753  template <typename number2>
754  void
755  equ(const number a, const FullMatrix<number2> &A);
756 
760  template <typename number2>
761  void
762  equ(const number a,
763  const FullMatrix<number2> &A,
764  const number b,
765  const FullMatrix<number2> &B);
766 
770  template <typename number2>
771  void
772  equ(const number a,
773  const FullMatrix<number2> &A,
774  const number b,
775  const FullMatrix<number2> &B,
776  const number c,
777  const FullMatrix<number2> &C);
778 
785  void
787 
802  void
804 
811  template <typename number2>
812  void
814 
823  template <typename number2>
824  void
826 
831  template <typename number2>
832  void
834 
840  template <typename number2>
841  void
843 
849  template <typename number2>
850  void
852 
877  template <typename number2>
878  void
880  const FullMatrix<number2> &B,
881  const bool adding = false) const;
882 
901  template <typename number2>
902  void
904  const FullMatrix<number2> &B,
905  const bool adding = false) const;
906 
925  template <typename number2>
926  void
928  const FullMatrix<number2> &B,
929  const bool adding = false) const;
930 
950  template <typename number2>
951  void
953  const FullMatrix<number2> &B,
954  const bool adding = false) const;
955 
966  void
968  const FullMatrix<number> &B,
969  const FullMatrix<number> &D,
970  const bool transpose_B = false,
971  const bool transpose_D = false,
972  const number scaling = number(1.));
973 
986  template <typename number2>
987  void
989  const Vector<number2> &v,
990  const bool adding = false) const;
991 
997  template <typename number2>
998  void
1000 
1014  template <typename number2>
1015  void
1017  const Vector<number2> &v,
1018  const bool adding = false) const;
1019 
1026  template <typename number2>
1027  void
1029 
1035  template <typename somenumber>
1036  void
1038  const Vector<somenumber> &src,
1039  const number omega = 1.) const;
1040 
1047  template <typename number2, typename number3>
1048  number
1050  const Vector<number2> &x,
1051  const Vector<number3> &b) const;
1052 
1063  template <typename number2>
1064  void
1065  forward(Vector<number2> &dst, const Vector<number2> &src) const;
1066 
1074  template <typename number2>
1075  void
1076  backward(Vector<number2> &dst, const Vector<number2> &src) const;
1077 
1089 
1094  ExcNotRegular,
1095  number,
1096  << "The maximal pivot is " << arg1
1097  << ", which is below the threshold. The matrix may be singular.");
1102  size_type,
1103  size_type,
1104  size_type,
1105  << "Target region not in matrix: size in this direction="
1106  << arg1 << ", size of new matrix=" << arg2
1107  << ", offset=" << arg3);
1112  "You are attempting an operation on two vectors that "
1113  "are the same object, but the operation requires that the "
1114  "two objects are in fact different.");
1120 };
1121 
1124 #ifndef DOXYGEN
1125 /*-------------------------Inline functions -------------------------------*/
1126 
1127 
1128 
1129 template <typename number>
1130 inline typename FullMatrix<number>::size_type
1131 FullMatrix<number>::m() const
1132 {
1133  return this->n_rows();
1134 }
1135 
1136 
1137 
1138 template <typename number>
1139 inline typename FullMatrix<number>::size_type
1140 FullMatrix<number>::n() const
1141 {
1142  return this->n_cols();
1143 }
1144 
1145 
1146 
1147 template <typename number>
1149 FullMatrix<number>::operator=(const number d)
1150 {
1151  Assert(d == number(0), ExcScalarAssignmentOnlyForZeroValue());
1152  (void)d; // removes -Wunused-parameter warning in optimized mode
1153 
1154  if (this->n_elements() != 0)
1155  this->reset_values();
1156 
1157  return *this;
1158 }
1159 
1160 
1161 
1162 template <typename number>
1163 template <typename number2>
1164 inline void
1165 FullMatrix<number>::fill(const number2 *src)
1166 {
1168 }
1169 
1170 
1171 
1172 template <typename number>
1173 template <typename MatrixType>
1174 void
1175 FullMatrix<number>::copy_from(const MatrixType &M)
1176 {
1177  this->reinit(M.m(), M.n());
1178 
1179  // loop over the elements of the argument matrix row by row, as suggested
1180  // in the documentation of the sparse matrix iterator class, and
1181  // copy them into the current object
1182  for (size_type row = 0; row < M.m(); ++row)
1183  {
1184  const typename MatrixType::const_iterator end_row = M.end(row);
1185  for (typename MatrixType::const_iterator entry = M.begin(row);
1186  entry != end_row;
1187  ++entry)
1188  this->el(row, entry->column()) = entry->value();
1189  }
1190 }
1191 
1192 
1193 
1194 template <typename number>
1195 template <typename MatrixType>
1196 void
1197 FullMatrix<number>::copy_transposed(const MatrixType &M)
1198 {
1199  this->reinit(M.n(), M.m());
1200 
1201  // loop over the elements of the argument matrix row by row, as suggested
1202  // in the documentation of the sparse matrix iterator class, and
1203  // copy them into the current object
1204  for (size_type row = 0; row < M.m(); ++row)
1205  {
1206  const typename MatrixType::const_iterator end_row = M.end(row);
1207  for (typename MatrixType::const_iterator entry = M.begin(row);
1208  entry != end_row;
1209  ++entry)
1210  this->el(entry->column(), row) = entry->value();
1211  }
1212 }
1213 
1214 
1215 
1216 template <typename number>
1217 template <typename MatrixType, typename index_type>
1218 inline void
1220  const MatrixType & matrix,
1221  const std::vector<index_type> &row_index_set,
1222  const std::vector<index_type> &column_index_set)
1223 {
1224  AssertDimension(row_index_set.size(), this->n_rows());
1225  AssertDimension(column_index_set.size(), this->n_cols());
1226 
1227  const size_type n_rows_submatrix = row_index_set.size();
1228  const size_type n_cols_submatrix = column_index_set.size();
1229 
1230  for (size_type sub_row = 0; sub_row < n_rows_submatrix; ++sub_row)
1231  for (size_type sub_col = 0; sub_col < n_cols_submatrix; ++sub_col)
1232  (*this)(sub_row, sub_col) =
1233  matrix.el(row_index_set[sub_row], column_index_set[sub_col]);
1234 }
1235 
1236 
1237 
1238 template <typename number>
1239 template <typename MatrixType, typename index_type>
1240 inline void
1242  const std::vector<index_type> &row_index_set,
1243  const std::vector<index_type> &column_index_set,
1244  MatrixType & matrix) const
1245 {
1246  AssertDimension(row_index_set.size(), this->n_rows());
1247  AssertDimension(column_index_set.size(), this->n_cols());
1248 
1249  const size_type n_rows_submatrix = row_index_set.size();
1250  const size_type n_cols_submatrix = column_index_set.size();
1251 
1252  for (size_type sub_row = 0; sub_row < n_rows_submatrix; ++sub_row)
1253  for (size_type sub_col = 0; sub_col < n_cols_submatrix; ++sub_col)
1254  matrix.set(row_index_set[sub_row],
1255  column_index_set[sub_col],
1256  (*this)(sub_row, sub_col));
1257 }
1258 
1259 
1260 template <typename number>
1261 inline void
1263  const size_type j,
1264  const number value)
1265 {
1266  (*this)(i, j) = value;
1267 }
1268 
1269 
1270 
1271 template <typename number>
1272 template <typename number2>
1273 void
1275  const Vector<number2> &v) const
1276 {
1277  vmult(w, v, true);
1278 }
1279 
1280 
1281 template <typename number>
1282 template <typename number2>
1283 void
1285  const Vector<number2> &v) const
1286 {
1287  Tvmult(w, v, true);
1288 }
1289 
1290 
1291 //---------------------------------------------------------------------------
1292 template <typename number>
1293 inline typename FullMatrix<number>::iterator
1295 {
1296  AssertIndexRange(r, m());
1297  return iterator(this, r, 0);
1298 }
1299 
1300 
1301 
1302 template <typename number>
1303 inline typename FullMatrix<number>::iterator
1305 {
1306  AssertIndexRange(r, m());
1307  return iterator(this, r + 1, 0);
1308 }
1309 
1310 
1311 
1312 template <typename number>
1313 inline typename FullMatrix<number>::const_iterator
1314 FullMatrix<number>::begin(const size_type r) const
1315 {
1316  AssertIndexRange(r, m());
1317  return const_iterator(this, r, 0);
1318 }
1319 
1320 
1321 
1322 template <typename number>
1323 inline typename FullMatrix<number>::const_iterator
1324 FullMatrix<number>::end(const size_type r) const
1325 {
1326  AssertIndexRange(r, m());
1327  return const_iterator(this, r + 1, 0);
1328 }
1329 
1330 
1331 
1332 template <typename number>
1333 inline void
1334 FullMatrix<number>::add(const size_type r, const size_type c, const number v)
1335 {
1336  AssertIndexRange(r, this->m());
1337  AssertIndexRange(c, this->n());
1338 
1339  this->operator()(r, c) += v;
1340 }
1341 
1342 
1343 
1344 template <typename number>
1345 template <typename number2, typename index_type>
1346 inline void
1348  const size_type n_cols,
1349  const index_type *col_indices,
1350  const number2 * values,
1351  const bool,
1352  const bool)
1353 {
1354  AssertIndexRange(row, this->m());
1355  for (size_type col = 0; col < n_cols; ++col)
1356  {
1357  AssertIndexRange(col_indices[col], this->n());
1358  this->operator()(row, col_indices[col]) += values[col];
1359  }
1360 }
1361 
1362 
1363 template <typename number>
1364 template <class StreamType>
1365 inline void
1366 FullMatrix<number>::print(StreamType & s,
1367  const unsigned int w,
1368  const unsigned int p) const
1369 {
1370  Assert(!this->empty(), ExcEmptyMatrix());
1371 
1372  // save the state of out stream
1373  const std::streamsize old_precision = s.precision(p);
1374  const std::streamsize old_width = s.width(w);
1375 
1376  for (size_type i = 0; i < this->m(); ++i)
1377  {
1378  for (size_type j = 0; j < this->n(); ++j)
1379  {
1380  s.width(w);
1381  s.precision(p);
1382  s << this->el(i, j);
1383  }
1384  s << std::endl;
1385  }
1386 
1387  // reset output format
1388  s.precision(old_precision);
1389  s.width(old_width);
1390 }
1391 
1392 
1393 #endif // DOXYGEN
1394 
1396 
1397 #endif
typename numbers::NumberTraits< number >::real_type real_type
Definition: full_matrix.h:135
typename Table< 2, number >::const_iterator const_iterator
Definition: full_matrix.h:114
void triple_product(const FullMatrix< number > &A, const FullMatrix< number > &B, const FullMatrix< number > &D, const bool transpose_B=false, const bool transpose_D=false, const number scaling=number(1.))
void TmTmult(FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
FullMatrix(const size_type rows, const size_type cols)
number residual(Vector< number2 > &dst, const Vector< number2 > &x, const Vector< number3 > &b) const
std::size_t memory_consumption() const
void diagadd(const number s)
void fill_permutation(const FullMatrix< number2 > &src, const std::vector< size_type > &p_rows, const std::vector< size_type > &p_cols)
void add_row(const size_type i, const number s, const size_type j)
void mmult(FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
real_type relative_symmetry_norm2() const
void add(const size_type row, const size_type column, const number value)
void copy_from(const Tensor< 2, dim > &T, const unsigned int src_r_i=0, const unsigned int src_r_j=dim - 1, const unsigned int src_c_i=0, const unsigned int src_c_j=dim - 1, const size_type dst_r=0, const size_type dst_c=0)
void symmetrize()
void equ(const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B)
number trace() const
void right_invert(const FullMatrix< number2 > &M)
std::size_t size_type
Definition: full_matrix.h:98
void set(const size_type i, const size_type j, const number value)
size_type n() const
void add_row(const size_type i, const number s, const size_type j, const number t, const size_type k)
FullMatrix< number > & operator=(const FullMatrix< number2 > &)
number value_type
Definition: full_matrix.h:104
typename Table< 2, number >::iterator iterator
Definition: full_matrix.h:109
void add(const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B, const number c, const FullMatrix< number2 > &C)
FullMatrix & operator/=(const number factor)
void Tadd(const number s, const FullMatrix< number2 > &B)
void vmult(Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const
bool all_zero() const
void add_col(const size_type i, const number s, const size_type j, const number t, const size_type k)
void scatter_matrix_to(const std::vector< index_type > &row_index_set, const std::vector< index_type > &column_index_set, MatrixType &matrix) const
void swap_row(const size_type i, const size_type j)
void add(const FullMatrix< number2 > &src, const number factor, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0)
void copy_to(Tensor< 2, dim > &T, const size_type src_r_i=0, const size_type src_r_j=dim - 1, const size_type src_c_i=0, const size_type src_c_j=dim - 1, const unsigned int dst_r=0, const unsigned int dst_c=0) const
number2 matrix_norm_square(const Vector< number2 > &v) const
void equ(const number a, const FullMatrix< number2 > &A)
const_iterator end(const size_type r) const
FullMatrix(const size_type rows, const size_type cols, const number *entries)
bool operator==(const FullMatrix< number > &) const
void Tvmult(Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const
void Tmmult(FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
number2 matrix_scalar_product(const Vector< number2 > &u, const Vector< number2 > &v) const
void gauss_jordan()
void add(const size_type row, const size_type n_cols, const index_type *col_indices, const number2 *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false)
void add_col(const size_type i, const number s, const size_type j)
void precondition_Jacobi(Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1.) const
FullMatrix(const IdentityMatrix &id)
void vmult_add(Vector< number2 > &w, const Vector< number2 > &v) const
FullMatrix< number > & operator=(const IdentityMatrix &id)
void invert(const FullMatrix< number2 > &M)
void cholesky(const FullMatrix< number2 > &A)
void fill(const FullMatrix< number2 > &src, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0)
void add(const number a, const FullMatrix< number2 > &A)
FullMatrix & operator*=(const number factor)
FullMatrix< number > & operator=(const number d)
number determinant() const
void equ(const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B, const number c, const FullMatrix< number2 > &C)
void fill(const number2 *)
void copy_transposed(const MatrixType &)
void print(StreamType &s, const unsigned int width=5, const unsigned int precision=2) const
void print_formatted(std::ostream &out, const unsigned int precision=3, const bool scientific=true, const unsigned int width=0, const char *zero_string=" ", const double denominator=1., const double threshold=0.) const
void Tvmult_add(Vector< number2 > &w, const Vector< number2 > &v) const
void mTmult(FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
void left_invert(const FullMatrix< number2 > &M)
iterator begin(const size_type r)
iterator end(const size_type r)
void add(const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B)
void outer_product(const Vector< number2 > &V, const Vector< number2 > &W)
real_type frobenius_norm() const
void forward(Vector< number2 > &dst, const Vector< number2 > &src) const
void Tadd(const FullMatrix< number2 > &src, const number factor, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0)
FullMatrix< number > & operator=(const LAPACKFullMatrix< number2 > &)
FullMatrix(const size_type n=0)
size_type m() const
void swap_col(const size_type i, const size_type j)
void extract_submatrix_from(const MatrixType &matrix, const std::vector< index_type > &row_index_set, const std::vector< index_type > &column_index_set)
void backward(Vector< number2 > &dst, const Vector< number2 > &src) const
void copy_from(const MatrixType &)
const_iterator begin(const size_type r) const
real_type l1_norm() const
real_type linfty_norm() const
Definition: vector.h:109
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:458
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:459
#define DeclException0(Exception0)
Definition: exceptions.h:464
static ::ExceptionBase & ExcSourceEqualsDestination()
static ::ExceptionBase & ExcScalarAssignmentOnlyForZeroValue()
#define Assert(cond, exc)
Definition: exceptions.h:1501
static ::ExceptionBase & ExcInvalidDestination(size_type arg1, size_type arg2, size_type arg3)
static ::ExceptionBase & ExcNotRegular(number arg1)
#define AssertDimension(dim1, dim2)
Definition: exceptions.h:1695
#define AssertIndexRange(index, range)
Definition: exceptions.h:1760
#define DeclExceptionMsg(Exception, defaulttext)
Definition: exceptions.h:487
#define DeclException3(Exception3, type1, type2, type3, outsequence)
Definition: exceptions.h:555
static ::ExceptionBase & ExcMatrixNotPositiveDefinite()
static ::ExceptionBase & ExcEmptyMatrix()
#define DeclException1(Exception1, type1, outsequence)
Definition: exceptions.h:509
@ matrix
Contents is actually a matrix.
static const char A
static const char T
static const char V
types::global_dof_index size_type
Definition: cuda_kernels.h:45
SymmetricTensor< 2, dim, Number > C(const Tensor< 2, dim, Number > &F)
SymmetricTensor< 2, dim, Number > d(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
Tensor< 2, dim, Number > w(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
SymmetricTensor< 2, dim, Number > b(const Tensor< 2, dim, Number > &F)
void reinit(MatrixBlock< MatrixType > &v, const BlockSparsityPattern &p)
Definition: matrix_block.h:618