Reference documentation for deal.II version 9.5.0
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notation.h
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1// ---------------------------------------------------------------------
2//
3// Copyright (C) 2017 - 2023 by the deal.II authors
4//
5// This file is part of the deal.II library.
6//
7// The deal.II library is free software; you can use it, redistribute
8// it, and/or modify it under the terms of the GNU Lesser General
9// Public License as published by the Free Software Foundation; either
10// version 2.1 of the License, or (at your option) any later version.
11// The full text of the license can be found in the file LICENSE.md at
12// the top level directory of deal.II.
13//
14// ---------------------------------------------------------------------
15
16#ifndef dealii_physics_notation_h
17#define dealii_physics_notation_h
18
19#include <deal.II/base/config.h>
20
21#include <deal.II/base/exceptions.h>
22#include <deal.II/base/numbers.h>
23#include <deal.II/base/symmetric_tensor.h>
24#include <deal.II/base/tensor.h>
25
26#include <deal.II/lac/full_matrix.h>
27#include <deal.II/lac/vector.h>
28
29#include <type_traits>
30
31DEAL_II_NAMESPACE_OPEN
32
33
34namespace Physics
35{
36 namespace Notation
37 {
285 namespace Kelvin
286 {
290 DeclException3(ExcNotationExcFullMatrixToTensorRowSize2,
291 int,
292 int,
293 int,
294 << "The number of rows in the input matrix is " << arg1
295 << ", but needs to be either " << arg2 << " or " << arg3
296 << '.');
297
298
302 DeclException4(ExcNotationExcFullMatrixToTensorRowSize3,
303 int,
304 int,
305 int,
306 int,
307 << "The number of rows in the input matrix is " << arg1
308 << ", but needs to be either " << arg2 << ',' << arg3
309 << ", or " << arg4 << '.');
310
311
315 DeclException3(ExcNotationExcFullMatrixToTensorColSize2,
316 int,
317 int,
318 int,
319 << "The number of columns in the input matrix is " << arg1
320 << ", but needs to be either " << arg2 << " or " << arg3
321 << '.');
322
323
327 DeclException4(ExcNotationExcFullMatrixToTensorColSize3,
328 int,
329 int,
330 int,
331 int,
332 << "The number of columns in the input matrix is " << arg1
333 << ", but needs to be either " << arg2 << ',' << arg3
334 << ", or " << arg4 << '.');
335
336
347 template <typename Number>
348 Vector<Number>
349 to_vector(const Number &s);
350
351
357 template <int dim, typename Number>
358 Vector<Number>
359 to_vector(const Tensor<0, dim, Number> &s);
360
361
367 template <int dim, typename Number>
368 Vector<Number>
369 to_vector(const Tensor<1, dim, Number> &v);
370
371
377 template <int dim, typename Number>
378 Vector<Number>
379 to_vector(const Tensor<2, dim, Number> &t);
380
381
388 template <int dim, typename Number>
389 Vector<Number>
390 to_vector(const SymmetricTensor<2, dim, Number> &st);
391
392
398 template <typename Number>
399 FullMatrix<Number>
400 to_matrix(const Number &s);
401
402
408 template <int dim, typename Number>
409 FullMatrix<Number>
410 to_matrix(const Tensor<0, dim, Number> &s);
411
412
418 template <int dim, typename Number>
419 FullMatrix<Number>
420 to_matrix(const Tensor<1, dim, Number> &v);
421
422
428 template <int dim, typename Number>
429 FullMatrix<Number>
430 to_matrix(const Tensor<2, dim, Number> &t);
431
432
442 template <int dim, typename Number>
443 FullMatrix<Number>
444 to_matrix(const SymmetricTensor<2, dim, Number> &st);
445
478 template <int dim,
479 typename SubTensor1 = Tensor<2, dim>,
480 typename SubTensor2 = Tensor<1, dim>,
481 typename Number>
482 FullMatrix<Number>
483 to_matrix(const Tensor<3, dim, Number> &t);
484
485
492 template <int dim, typename Number>
493 FullMatrix<Number>
494 to_matrix(const Tensor<4, dim, Number> &t);
495
496
504 template <int dim, typename Number>
505 FullMatrix<Number>
506 to_matrix(const SymmetricTensor<4, dim, Number> &st);
507
518 template <typename Number>
519 void
520 to_tensor(const Vector<Number> &vec, Number &s);
521
522
526 template <int dim, typename Number>
527 void
528 to_tensor(const Vector<Number> &vec, Tensor<0, dim, Number> &s);
529
530
534 template <int dim, typename Number>
535 void
536 to_tensor(const Vector<Number> &vec, Tensor<1, dim, Number> &v);
537
538
542 template <int dim, typename Number>
543 void
544 to_tensor(const Vector<Number> &vec, Tensor<2, dim, Number> &t);
545
546
550 template <int dim, typename Number>
551 void
552 to_tensor(const Vector<Number> &vec, SymmetricTensor<2, dim, Number> &st);
553
554
558 template <typename Number>
559 void
560 to_tensor(const FullMatrix<Number> &mtrx, Number &s);
561
562
566 template <int dim, typename Number>
567 void
568 to_tensor(const FullMatrix<Number> &mtrx, Tensor<0, dim, Number> &s);
569
570
574 template <int dim, typename Number>
575 void
576 to_tensor(const FullMatrix<Number> &mtrx, Tensor<1, dim, Number> &v);
577
578
582 template <int dim, typename Number>
583 void
584 to_tensor(const FullMatrix<Number> &mtrx, Tensor<2, dim, Number> &t);
585
586
590 template <int dim, typename Number>
591 void
592 to_tensor(const FullMatrix<Number> & mtrx,
593 SymmetricTensor<2, dim, Number> &st);
594
595
605 template <int dim, typename Number>
606 void
607 to_tensor(const FullMatrix<Number> &mtrx, Tensor<3, dim, Number> &t);
608
609
613 template <int dim, typename Number>
614 void
615 to_tensor(const FullMatrix<Number> &mtrx, Tensor<4, dim, Number> &t);
616
617
621 template <int dim, typename Number>
622 void
623 to_tensor(const FullMatrix<Number> & mtrx,
624 SymmetricTensor<4, dim, Number> &st);
625
626
631 template <typename TensorType, typename Number>
632 TensorType
633 to_tensor(const Vector<Number> &vec);
634
635
640 template <typename TensorType, typename Number>
641 TensorType
642 to_tensor(const FullMatrix<Number> &vec);
645 } // namespace Kelvin
646
647 } // namespace Notation
648} // namespace Physics
649
650
651#ifndef DOXYGEN
652
653
654// ------------------------- inline functions ------------------------
655
656
657namespace Physics
658{
659 namespace Notation
660 {
661 namespace Kelvin
662 {
663 namespace internal
664 {
672 template <int dim>
673 std::pair<unsigned int, unsigned int>
674 indices_from_component(const unsigned int component_n,
675 const bool symmetric);
676
677
678 template <int dim>
679 std::pair<unsigned int, unsigned int>
680 indices_from_component(const unsigned int /*component_n*/, const bool)
681 {
682 AssertThrow(false, ExcNotImplemented());
683 return std::make_pair(0u, 0u);
684 }
685
686
687 template <>
688 inline std::pair<unsigned int, unsigned int>
689 indices_from_component<1>(const unsigned int component_n, const bool)
690 {
691 AssertIndexRange(component_n, 1);
692
693 return std::make_pair(0u, 0u);
694 }
695
696
697 template <>
698 inline std::pair<unsigned int, unsigned int>
699 indices_from_component<2>(const unsigned int component_n,
700 const bool symmetric)
701 {
702 if (symmetric == true)
703 {
704 Assert(
705 (component_n < SymmetricTensor<2, 2>::n_independent_components),
706 ExcIndexRange(component_n,
707 0,
708 SymmetricTensor<2, 2>::n_independent_components));
709 }
710 else
711 {
712 Assert((component_n < Tensor<2, 2>::n_independent_components),
713 ExcIndexRange(component_n,
714 0,
715 Tensor<2, 2>::n_independent_components));
716 }
717
718 static const unsigned int indices[4][2] = {{0, 0},
719 {1, 1},
720 {0, 1},
721 {1, 0}};
722 return std::make_pair(indices[component_n][0],
723 indices[component_n][1]);
724 }
725
726
727 template <>
728 inline std::pair<unsigned int, unsigned int>
729 indices_from_component<3>(const unsigned int component_n,
730 const bool symmetric)
731 {
732 if (symmetric == true)
733 {
734 Assert(
735 (component_n < SymmetricTensor<2, 3>::n_independent_components),
736 ExcIndexRange(component_n,
737 0,
738 SymmetricTensor<2, 3>::n_independent_components));
739 }
740 else
741 {
742 Assert((component_n < Tensor<2, 3>::n_independent_components),
743 ExcIndexRange(component_n,
744 0,
745 Tensor<2, 3>::n_independent_components));
746 }
747
748 static const unsigned int indices[9][2] = {{0, 0},
749 {1, 1},
750 {2, 2},
751 {1, 2},
752 {0, 2},
753 {0, 1},
754 {1, 0},
755 {2, 0},
756 {2, 1}};
757 return std::make_pair(indices[component_n][0],
758 indices[component_n][1]);
759 }
760
761
766 template <int dim>
767 double
768 vector_component_factor(const unsigned int component_i,
769 const bool symmetric)
770 {
771 if (symmetric == false)
772 return 1.0;
773
774 if (component_i < dim)
775 return 1.0;
776 else
777 return numbers::SQRT2;
778 }
779
780
785 template <int dim>
786 double
787 matrix_component_factor(const unsigned int component_i,
788 const unsigned int component_j,
789 const bool symmetric)
790 {
791 if (symmetric == false)
792 return 1.0;
793
794 // This case check returns equivalent of this result:
795 // internal::vector_component_factor<dim>(component_i,symmetric)*internal::vector_component_factor<dim>(component_j,symmetric);
796 if (component_i < dim && component_j < dim)
797 return 1.0;
798 else if (component_i >= dim && component_j >= dim)
799 return 2.0;
800 else // ((component_i >= dim && component_j < dim) || (component_i <
801 // dim && component_j >= dim))
802 return numbers::SQRT2;
803 }
804
805 } // namespace internal
806
807
808 template <typename Number>
809 Vector<Number>
810 to_vector(const Number &s)
811 {
812 Vector<Number> out(1);
813 const unsigned int n_rows = out.size();
814 for (unsigned int r = 0; r < n_rows; ++r)
815 out(r) = s;
816 return out;
817 }
818
819
820 template <int dim, typename Number>
821 Vector<Number>
822 to_vector(const Tensor<0, dim, Number> &s)
823 {
824 return to_vector(s.operator const Number &());
825 }
826
827
828 template <int dim, typename Number>
829 Vector<Number>
830 to_vector(const Tensor<1, dim, Number> &v)
831 {
832 Vector<Number> out(v.n_independent_components);
833 const unsigned int n_rows = out.size();
834 for (unsigned int r = 0; r < n_rows; ++r)
835 {
836 const std::pair<unsigned int, unsigned int> indices =
837 internal::indices_from_component<dim>(r, false);
838 Assert(indices.first < dim, ExcInternalError());
839 const unsigned int i = indices.first;
840 out(r) = v[i];
841 }
842 return out;
843 }
844
845
846 template <int dim, typename Number>
847 Vector<Number>
848 to_vector(const Tensor<2, dim, Number> &t)
849 {
850 Vector<Number> out(t.n_independent_components);
851 const unsigned int n_rows = out.size();
852 for (unsigned int r = 0; r < n_rows; ++r)
853 {
854 const std::pair<unsigned int, unsigned int> indices =
855 internal::indices_from_component<dim>(r, false);
856 Assert(indices.first < dim, ExcInternalError());
857 Assert(indices.second < dim, ExcInternalError());
858 const unsigned int i = indices.first;
859 const unsigned int j = indices.second;
860 out(r) = t[i][j];
861 }
862 return out;
863 }
864
865
866 template <int dim, typename Number>
867 Vector<Number>
868 to_vector(const SymmetricTensor<2, dim, Number> &st)
869 {
870 Vector<Number> out(st.n_independent_components);
871 const unsigned int n_rows = out.size();
872 for (unsigned int r = 0; r < n_rows; ++r)
873 {
874 const std::pair<unsigned int, unsigned int> indices =
875 internal::indices_from_component<dim>(r, true);
876 Assert(indices.first < dim, ExcInternalError());
877 Assert(indices.second < dim, ExcInternalError());
878 Assert(indices.second >= indices.first, ExcInternalError());
879 const unsigned int i = indices.first;
880 const unsigned int j = indices.second;
881
882 const double factor =
883 internal::vector_component_factor<dim>(r, true);
884
885 out(r) = factor * st[i][j];
886 }
887 return out;
888 }
889
890
891 template <typename Number>
892 FullMatrix<Number>
893 to_matrix(const Number &s)
894 {
895 FullMatrix<Number> out(1, 1);
896 out(0, 0) = s;
897 return out;
898 }
899
900
901 template <int dim, typename Number>
902 FullMatrix<Number>
903 to_matrix(const Tensor<0, dim, Number> &s)
904 {
905 return to_matrix(s.operator const Number &());
906 }
907
908
909 template <int dim, typename Number>
910 FullMatrix<Number>
911 to_matrix(const Tensor<1, dim, Number> &v)
912 {
913 FullMatrix<Number> out(v.n_independent_components, 1);
914 const unsigned int n_rows = out.m();
915 const unsigned int n_cols = out.n();
916 for (unsigned int r = 0; r < n_rows; ++r)
917 {
918 const std::pair<unsigned int, unsigned int> indices =
919 internal::indices_from_component<dim>(r, false);
920 Assert(indices.first < dim, ExcInternalError());
921 const unsigned int i = indices.first;
922
923 for (unsigned int c = 0; c < n_cols; ++c)
924 {
925 Assert(c < 1, ExcInternalError());
926 out(r, c) = v[i];
927 }
928 }
929 return out;
930 }
931
932
933 template <int dim, typename Number>
934 FullMatrix<Number>
935 to_matrix(const Tensor<2, dim, Number> &t)
936 {
937 FullMatrix<Number> out(dim, dim);
938 const unsigned int n_rows = out.m();
939 const unsigned int n_cols = out.n();
940 for (unsigned int r = 0; r < n_rows; ++r)
941 {
942 const std::pair<unsigned int, unsigned int> indices_i =
943 internal::indices_from_component<dim>(r, false);
944 Assert(indices_i.first < dim, ExcInternalError());
945 Assert(indices_i.second < dim, ExcInternalError());
946 const unsigned int i = indices_i.first;
947
948 for (unsigned int c = 0; c < n_cols; ++c)
949 {
950 const std::pair<unsigned int, unsigned int> indices_j =
951 internal::indices_from_component<dim>(c, false);
952 Assert(indices_j.first < dim, ExcInternalError());
953 Assert(indices_j.second < dim, ExcInternalError());
954 const unsigned int j = indices_j.second;
955
956 out(r, c) = t[i][j];
957 }
958 }
959 return out;
960 }
961
962
963 template <int dim, typename Number>
964 FullMatrix<Number>
965 to_matrix(const SymmetricTensor<2, dim, Number> &st)
966 {
967 return to_matrix(Tensor<2, dim, Number>(st));
968 }
969
970
971 namespace internal
972 {
973 template <typename TensorType>
974 struct is_rank_2_symmetric_tensor : std::false_type
975 {};
976
977 template <int dim, typename Number>
978 struct is_rank_2_symmetric_tensor<SymmetricTensor<2, dim, Number>>
979 : std::true_type
980 {};
981 } // namespace internal
982
983
984 template <int dim,
985 typename SubTensor1,
986 typename SubTensor2,
987 typename Number>
988 FullMatrix<Number>
989 to_matrix(const Tensor<3, dim, Number> &t)
990 {
991 static_assert(
992 (SubTensor1::dimension == dim && SubTensor2::dimension == dim),
993 "Sub-tensor spatial dimension is different from those of the input tensor.");
994
995 static_assert(
996 (SubTensor1::rank == 2 && SubTensor2::rank == 1) ||
997 (SubTensor1::rank == 1 && SubTensor2::rank == 2),
998 "Cannot build a rank 3 tensor from the given combination of sub-tensors.");
999
1000 FullMatrix<Number> out(SubTensor1::n_independent_components,
1001 SubTensor2::n_independent_components);
1002 const unsigned int n_rows = out.m();
1003 const unsigned int n_cols = out.n();
1004
1005 if (SubTensor1::rank == 2 && SubTensor2::rank == 1)
1006 {
1007 const bool subtensor_is_rank_2_symmetric_tensor =
1008 internal::is_rank_2_symmetric_tensor<SubTensor1>::value;
1009
1010 for (unsigned int r = 0; r < n_rows; ++r)
1011 {
1012 const std::pair<unsigned int, unsigned int> indices_ij =
1013 internal::indices_from_component<dim>(
1014 r, subtensor_is_rank_2_symmetric_tensor);
1015 Assert(indices_ij.first < dim, ExcInternalError());
1016 Assert(indices_ij.second < dim, ExcInternalError());
1017 if (subtensor_is_rank_2_symmetric_tensor)
1018 {
1019 Assert(indices_ij.second >= indices_ij.first,
1020 ExcInternalError());
1021 }
1022 const unsigned int i = indices_ij.first;
1023 const unsigned int j = indices_ij.second;
1024
1025 const double factor = internal::vector_component_factor<dim>(
1026 r, subtensor_is_rank_2_symmetric_tensor);
1027
1028 for (unsigned int c = 0; c < n_cols; ++c)
1029 {
1030 const std::pair<unsigned int, unsigned int> indices_k =
1031 internal::indices_from_component<dim>(c, false);
1032 Assert(indices_k.first < dim, ExcInternalError());
1033 const unsigned int k = indices_k.first;
1034
1035 if (subtensor_is_rank_2_symmetric_tensor)
1036 out(r, c) = factor * t[i][j][k];
1037 else
1038 out(r, c) = t[i][j][k];
1039 }
1040 }
1041 }
1042 else if (SubTensor1::rank == 1 && SubTensor2::rank == 2)
1043 {
1044 const bool subtensor_is_rank_2_symmetric_tensor =
1045 internal::is_rank_2_symmetric_tensor<SubTensor2>::value;
1046
1047 for (unsigned int r = 0; r < n_rows; ++r)
1048 {
1049 const std::pair<unsigned int, unsigned int> indices_k =
1050 internal::indices_from_component<dim>(r, false);
1051 Assert(indices_k.first < dim, ExcInternalError());
1052 const unsigned int k = indices_k.first;
1053
1054 for (unsigned int c = 0; c < n_cols; ++c)
1055 {
1056 const std::pair<unsigned int, unsigned int> indices_ij =
1057 internal::indices_from_component<dim>(
1058 c, subtensor_is_rank_2_symmetric_tensor);
1059 Assert(indices_ij.first < dim, ExcInternalError());
1060 Assert(indices_ij.second < dim, ExcInternalError());
1061 if (subtensor_is_rank_2_symmetric_tensor)
1062 {
1063 Assert(indices_ij.second >= indices_ij.first,
1064 ExcInternalError());
1065 }
1066 const unsigned int i = indices_ij.first;
1067 const unsigned int j = indices_ij.second;
1068
1069 if (subtensor_is_rank_2_symmetric_tensor)
1070 {
1071 const double factor =
1072 internal::vector_component_factor<dim>(
1073 c, subtensor_is_rank_2_symmetric_tensor);
1074 out(r, c) = factor * t[k][i][j];
1075 }
1076 else
1077 out(r, c) = t[k][i][j];
1078 }
1079 }
1080 }
1081 else
1082 {
1083 AssertThrow(false, ExcNotImplemented());
1084 }
1085
1086 return out;
1087 }
1088
1089
1090 template <int dim, typename Number>
1091 FullMatrix<Number>
1092 to_matrix(const Tensor<4, dim, Number> &t)
1093 {
1094 FullMatrix<Number> out(
1095 Tensor<2, dim, Number>::n_independent_components,
1096 Tensor<2, dim, Number>::n_independent_components);
1097 const unsigned int n_rows = out.m();
1098 const unsigned int n_cols = out.n();
1099 for (unsigned int r = 0; r < n_rows; ++r)
1100 {
1101 const std::pair<unsigned int, unsigned int> indices_ij =
1102 internal::indices_from_component<dim>(r, false);
1103 Assert(indices_ij.first < dim, ExcInternalError());
1104 Assert(indices_ij.second < dim, ExcInternalError());
1105 const unsigned int i = indices_ij.first;
1106 const unsigned int j = indices_ij.second;
1107
1108 for (unsigned int c = 0; c < n_cols; ++c)
1109 {
1110 const std::pair<unsigned int, unsigned int> indices_kl =
1111 internal::indices_from_component<dim>(c, false);
1112 Assert(indices_kl.first < dim, ExcInternalError());
1113 Assert(indices_kl.second < dim, ExcInternalError());
1114 const unsigned int k = indices_kl.first;
1115 const unsigned int l = indices_kl.second;
1116
1117 out(r, c) = t[i][j][k][l];
1118 }
1119 }
1120 return out;
1121 }
1122
1123
1124 template <int dim, typename Number>
1125 FullMatrix<Number>
1126 to_matrix(const SymmetricTensor<4, dim, Number> &st)
1127 {
1128 FullMatrix<Number> out(
1129 SymmetricTensor<2, dim, Number>::n_independent_components,
1130 SymmetricTensor<2, dim, Number>::n_independent_components);
1131 const unsigned int n_rows = out.m();
1132 const unsigned int n_cols = out.n();
1133 for (unsigned int r = 0; r < n_rows; ++r)
1134 {
1135 const std::pair<unsigned int, unsigned int> indices_ij =
1136 internal::indices_from_component<dim>(r, true);
1137 Assert(indices_ij.first < dim, ExcInternalError());
1138 Assert(indices_ij.second < dim, ExcInternalError());
1139 Assert(indices_ij.second >= indices_ij.first, ExcInternalError());
1140 const unsigned int i = indices_ij.first;
1141 const unsigned int j = indices_ij.second;
1142
1143 for (unsigned int c = 0; c < n_cols; ++c)
1144 {
1145 const std::pair<unsigned int, unsigned int> indices_kl =
1146 internal::indices_from_component<dim>(c, true);
1147 Assert(indices_kl.first < dim, ExcInternalError());
1148 Assert(indices_kl.second < dim, ExcInternalError());
1149 Assert(indices_kl.second >= indices_kl.first,
1150 ExcInternalError());
1151 const unsigned int k = indices_kl.first;
1152 const unsigned int l = indices_kl.second;
1153
1154 const double factor =
1155 internal::matrix_component_factor<dim>(r, c, true);
1156
1157 out(r, c) = factor * st[i][j][k][l];
1158 }
1159 }
1160 return out;
1161 }
1162
1163
1164 template <typename Number>
1165 void
1166 to_tensor(const Vector<Number> &vec, Number &s)
1167 {
1168 Assert(vec.size() == 1, ExcDimensionMismatch(vec.size(), 1));
1169 s = vec(0);
1170 }
1171
1172
1173 template <int dim, typename Number>
1174 void
1175 to_tensor(const Vector<Number> &vec, Tensor<0, dim, Number> &s)
1176 {
1177 return to_tensor(vec, s.operator Number &());
1178 }
1179
1180
1181 template <int dim, typename Number>
1182 void
1183 to_tensor(const Vector<Number> &vec, Tensor<1, dim, Number> &v)
1184 {
1185 Assert(vec.size() == v.n_independent_components,
1186 ExcDimensionMismatch(vec.size(), v.n_independent_components));
1187 const unsigned int n_rows = vec.size();
1188 for (unsigned int r = 0; r < n_rows; ++r)
1189 {
1190 const std::pair<unsigned int, unsigned int> indices =
1191 internal::indices_from_component<dim>(r, false);
1192 Assert(indices.first < dim, ExcInternalError());
1193 const unsigned int i = indices.first;
1194 v[i] = vec(r);
1195 }
1196 }
1197
1198
1199 template <int dim, typename Number>
1200 void
1201 to_tensor(const Vector<Number> &vec, Tensor<2, dim, Number> &t)
1202 {
1203 Assert(vec.size() == t.n_independent_components,
1204 ExcDimensionMismatch(vec.size(), t.n_independent_components));
1205 const unsigned int n_rows = vec.size();
1206 for (unsigned int r = 0; r < n_rows; ++r)
1207 {
1208 const std::pair<unsigned int, unsigned int> indices =
1209 internal::indices_from_component<dim>(r, false);
1210 Assert(indices.first < dim, ExcInternalError());
1211 Assert(indices.second < dim, ExcInternalError());
1212 const unsigned int i = indices.first;
1213 const unsigned int j = indices.second;
1214 t[i][j] = vec(r);
1215 }
1216 }
1217
1218
1219 template <int dim, typename Number>
1220 void
1221 to_tensor(const Vector<Number> &vec, SymmetricTensor<2, dim, Number> &st)
1222 {
1223 Assert(vec.size() == st.n_independent_components,
1224 ExcDimensionMismatch(vec.size(), st.n_independent_components));
1225 const unsigned int n_rows = vec.size();
1226 for (unsigned int r = 0; r < n_rows; ++r)
1227 {
1228 const std::pair<unsigned int, unsigned int> indices =
1229 internal::indices_from_component<dim>(r, true);
1230 Assert(indices.first < dim, ExcInternalError());
1231 Assert(indices.second < dim, ExcInternalError());
1232 Assert(indices.second >= indices.first, ExcInternalError());
1233 const unsigned int i = indices.first;
1234 const unsigned int j = indices.second;
1235
1236 const double inv_factor =
1237 1.0 / internal::vector_component_factor<dim>(r, true);
1238
1239 st[i][j] = inv_factor * vec(r);
1240 }
1241 }
1242
1243
1244 template <typename Number>
1245 void
1246 to_tensor(const FullMatrix<Number> &mtrx, Number &s)
1247 {
1248 Assert(mtrx.m() == 1, ExcDimensionMismatch(mtrx.m(), 1));
1249 Assert(mtrx.n() == 1, ExcDimensionMismatch(mtrx.n(), 1));
1250 Assert(mtrx.n_elements() == 1,
1251 ExcDimensionMismatch(mtrx.n_elements(), 1));
1252 s = mtrx(0, 0);
1253 }
1254
1255
1256 template <int dim, typename Number>
1257 void
1258 to_tensor(const FullMatrix<Number> &mtrx, Tensor<0, dim, Number> &s)
1259 {
1260 return to_tensor(mtrx, s.operator Number &());
1261 }
1262
1263
1264 template <int dim, typename Number>
1265 void
1266 to_tensor(const FullMatrix<Number> &mtrx, Tensor<1, dim, Number> &v)
1267 {
1268 Assert(mtrx.m() == dim, ExcDimensionMismatch(mtrx.m(), dim));
1269 Assert(mtrx.n() == 1, ExcDimensionMismatch(mtrx.n(), 1));
1270 Assert(mtrx.n_elements() == v.n_independent_components,
1271 ExcDimensionMismatch(mtrx.n_elements(),
1272 v.n_independent_components));
1273
1274 const unsigned int n_rows = mtrx.m();
1275 const unsigned int n_cols = mtrx.n();
1276 for (unsigned int r = 0; r < n_rows; ++r)
1277 {
1278 const std::pair<unsigned int, unsigned int> indices =
1279 internal::indices_from_component<dim>(r, false);
1280 Assert(indices.first < dim, ExcInternalError());
1281 Assert(indices.second == 0, ExcInternalError());
1282 const unsigned int i = indices.first;
1283
1284 for (unsigned int c = 0; c < n_cols; ++c)
1285 {
1286 Assert(c < 1, ExcInternalError());
1287 v[i] = mtrx(r, c);
1288 }
1289 }
1290 }
1291
1292
1293 template <int dim, typename Number>
1294 void
1295 to_tensor(const FullMatrix<Number> &mtrx, Tensor<2, dim, Number> &t)
1296 {
1297 Assert(mtrx.m() == dim, ExcDimensionMismatch(mtrx.m(), dim));
1298 Assert(mtrx.n() == dim, ExcDimensionMismatch(mtrx.n(), dim));
1299 Assert(mtrx.n_elements() == t.n_independent_components,
1300 ExcDimensionMismatch(mtrx.n_elements(),
1301 t.n_independent_components));
1302
1303 const unsigned int n_rows = mtrx.m();
1304 const unsigned int n_cols = mtrx.n();
1305 for (unsigned int r = 0; r < n_rows; ++r)
1306 {
1307 const std::pair<unsigned int, unsigned int> indices_i =
1308 internal::indices_from_component<dim>(r, false);
1309 Assert(indices_i.first < dim, ExcInternalError());
1310 Assert(indices_i.second < dim, ExcInternalError());
1311 const unsigned int i = indices_i.first;
1312
1313 for (unsigned int c = 0; c < n_cols; ++c)
1314 {
1315 const std::pair<unsigned int, unsigned int> indices_j =
1316 internal::indices_from_component<dim>(c, false);
1317 Assert(indices_j.first < dim, ExcInternalError());
1318 Assert(indices_j.second < dim, ExcInternalError());
1319 const unsigned int j = indices_j.second;
1320
1321 t[i][j] = mtrx(r, c);
1322 }
1323 }
1324 }
1325
1326
1327 template <int dim, typename Number>
1328 void
1329 to_tensor(const FullMatrix<Number> & mtrx,
1330 SymmetricTensor<2, dim, Number> &st)
1331 {
1332 // Its impossible to fit the (dim^2 + dim)/2 entries into a square
1333 // matrix We therefore assume that its been converted to a standard
1334 // tensor format using to_matrix (SymmetricTensor<2,dim,Number>) at some
1335 // point...
1336 Assert(mtrx.m() == dim, ExcDimensionMismatch(mtrx.m(), dim));
1337 Assert(mtrx.n() == dim, ExcDimensionMismatch(mtrx.n(), dim));
1338 Assert((mtrx.n_elements() ==
1339 Tensor<2, dim, Number>::n_independent_components),
1340 ExcDimensionMismatch(
1341 mtrx.n_elements(),
1342 Tensor<2, dim, Number>::n_independent_components));
1343
1344 Tensor<2, dim, Number> tmp;
1345 to_tensor(mtrx, tmp);
1346 st = symmetrize(tmp);
1347 Assert((Tensor<2, dim, Number>(st) - tmp).norm() < 1e-12,
1348 ExcMessage(
1349 "The entries stored inside the matrix were not symmetric"));
1350 }
1351
1352
1353 template <int dim, typename Number>
1354 void
1355 to_tensor(const FullMatrix<Number> &mtrx, Tensor<3, dim, Number> &t)
1356 {
1357 Assert((mtrx.m() == Tensor<1, dim, Number>::n_independent_components) ||
1358 (mtrx.m() ==
1359 Tensor<2, dim, Number>::n_independent_components) ||
1360 (mtrx.m() ==
1361 SymmetricTensor<2, dim, Number>::n_independent_components),
1362 ExcNotationExcFullMatrixToTensorColSize3(
1363 mtrx.m(),
1364 Tensor<1, dim, Number>::n_independent_components,
1365 Tensor<2, dim, Number>::n_independent_components,
1366 SymmetricTensor<2, dim, Number>::n_independent_components));
1367 Assert((mtrx.n() == Tensor<1, dim, Number>::n_independent_components) ||
1368 (mtrx.n() ==
1369 Tensor<2, dim, Number>::n_independent_components) ||
1370 (mtrx.n() ==
1371 SymmetricTensor<2, dim, Number>::n_independent_components),
1372 ExcNotationExcFullMatrixToTensorColSize3(
1373 mtrx.n(),
1374 Tensor<1, dim, Number>::n_independent_components,
1375 Tensor<2, dim, Number>::n_independent_components,
1376 SymmetricTensor<2, dim, Number>::n_independent_components));
1377
1378 const unsigned int n_rows = mtrx.m();
1379 const unsigned int n_cols = mtrx.n();
1380 if (mtrx.n() == Tensor<1, dim, Number>::n_independent_components)
1381 {
1382 Assert(
1383 (mtrx.m() == Tensor<2, dim, Number>::n_independent_components) ||
1384 (mtrx.m() ==
1385 SymmetricTensor<2, dim, Number>::n_independent_components),
1386 ExcNotationExcFullMatrixToTensorRowSize2(
1387 mtrx.m(),
1388 Tensor<2, dim, Number>::n_independent_components,
1389 SymmetricTensor<2, dim, Number>::n_independent_components));
1390
1391 const bool subtensor_is_rank_2_symmetric_tensor =
1392 (mtrx.m() ==
1393 SymmetricTensor<2, dim, Number>::n_independent_components);
1394
1395 for (unsigned int r = 0; r < n_rows; ++r)
1396 {
1397 const std::pair<unsigned int, unsigned int> indices_ij =
1398 internal::indices_from_component<dim>(
1399 r, subtensor_is_rank_2_symmetric_tensor);
1400 Assert(indices_ij.first < dim, ExcInternalError());
1401 Assert(indices_ij.second < dim, ExcInternalError());
1402 if (subtensor_is_rank_2_symmetric_tensor)
1403 {
1404 Assert(indices_ij.second >= indices_ij.first,
1405 ExcInternalError());
1406 }
1407 const unsigned int i = indices_ij.first;
1408 const unsigned int j = indices_ij.second;
1409
1410 const double inv_factor =
1411 1.0 / internal::vector_component_factor<dim>(
1412 r, subtensor_is_rank_2_symmetric_tensor);
1413
1414 for (unsigned int c = 0; c < n_cols; ++c)
1415 {
1416 const std::pair<unsigned int, unsigned int> indices_k =
1417 internal::indices_from_component<dim>(c, false);
1418 Assert(indices_k.first < dim, ExcInternalError());
1419 const unsigned int k = indices_k.first;
1420
1421 if (subtensor_is_rank_2_symmetric_tensor)
1422 {
1423 t[i][j][k] = inv_factor * mtrx(r, c);
1424 t[j][i][k] = t[i][j][k];
1425 }
1426 else
1427 t[i][j][k] = mtrx(r, c);
1428 }
1429 }
1430 }
1431 else
1432 {
1433 Assert(
1434 (mtrx.m() == Tensor<1, dim, Number>::n_independent_components),
1435 ExcDimensionMismatch(
1436 mtrx.m(), Tensor<1, dim, Number>::n_independent_components));
1437 Assert(
1438 (mtrx.n() == Tensor<2, dim, Number>::n_independent_components) ||
1439 (mtrx.n() ==
1440 SymmetricTensor<2, dim, Number>::n_independent_components),
1441 ExcNotationExcFullMatrixToTensorColSize2(
1442 mtrx.n(),
1443 Tensor<2, dim, Number>::n_independent_components,
1444 SymmetricTensor<2, dim, Number>::n_independent_components));
1445
1446 const bool subtensor_is_rank_2_symmetric_tensor =
1447 (mtrx.n() ==
1448 SymmetricTensor<2, dim, Number>::n_independent_components);
1449
1450 for (unsigned int r = 0; r < n_rows; ++r)
1451 {
1452 const std::pair<unsigned int, unsigned int> indices_k =
1453 internal::indices_from_component<dim>(r, false);
1454 Assert(indices_k.first < dim, ExcInternalError());
1455 const unsigned int k = indices_k.first;
1456
1457 for (unsigned int c = 0; c < n_cols; ++c)
1458 {
1459 const std::pair<unsigned int, unsigned int> indices_ij =
1460 internal::indices_from_component<dim>(
1461 c, subtensor_is_rank_2_symmetric_tensor);
1462 Assert(indices_ij.first < dim, ExcInternalError());
1463 Assert(indices_ij.second < dim, ExcInternalError());
1464 if (subtensor_is_rank_2_symmetric_tensor)
1465 {
1466 Assert(indices_ij.second >= indices_ij.first,
1467 ExcInternalError());
1468 }
1469 const unsigned int i = indices_ij.first;
1470 const unsigned int j = indices_ij.second;
1471
1472 if (subtensor_is_rank_2_symmetric_tensor)
1473 {
1474 const double inv_factor =
1475 1.0 / internal::vector_component_factor<dim>(
1476 c, subtensor_is_rank_2_symmetric_tensor);
1477 t[k][i][j] = inv_factor * mtrx(r, c);
1478 t[k][j][i] = t[k][i][j];
1479 }
1480 else
1481 t[k][i][j] = mtrx(r, c);
1482 }
1483 }
1484 }
1485 }
1486
1487
1488 template <int dim, typename Number>
1489 void
1490 to_tensor(const FullMatrix<Number> &mtrx, Tensor<4, dim, Number> &t)
1491 {
1492 Assert((mtrx.m() == Tensor<2, dim, Number>::n_independent_components),
1493 ExcDimensionMismatch(
1494 mtrx.m(), Tensor<2, dim, Number>::n_independent_components));
1495 Assert((mtrx.n() == Tensor<2, dim, Number>::n_independent_components),
1496 ExcDimensionMismatch(
1497 mtrx.n(), Tensor<2, dim, Number>::n_independent_components));
1498 Assert(mtrx.n_elements() == t.n_independent_components,
1499 ExcDimensionMismatch(mtrx.n_elements(),
1500 t.n_independent_components));
1501
1502 const unsigned int n_rows = mtrx.m();
1503 const unsigned int n_cols = mtrx.n();
1504 for (unsigned int r = 0; r < n_rows; ++r)
1505 {
1506 const std::pair<unsigned int, unsigned int> indices_ij =
1507 internal::indices_from_component<dim>(r, false);
1508 Assert(indices_ij.first < dim, ExcInternalError());
1509 Assert(indices_ij.second < dim, ExcInternalError());
1510 const unsigned int i = indices_ij.first;
1511 const unsigned int j = indices_ij.second;
1512
1513 for (unsigned int c = 0; c < n_cols; ++c)
1514 {
1515 const std::pair<unsigned int, unsigned int> indices_kl =
1516 internal::indices_from_component<dim>(c, false);
1517 Assert(indices_kl.first < dim, ExcInternalError());
1518 Assert(indices_kl.second < dim, ExcInternalError());
1519 const unsigned int k = indices_kl.first;
1520 const unsigned int l = indices_kl.second;
1521
1522 t[i][j][k][l] = mtrx(r, c);
1523 }
1524 }
1525 }
1526
1527
1528 template <int dim, typename Number>
1529 void
1530 to_tensor(const FullMatrix<Number> & mtrx,
1531 SymmetricTensor<4, dim, Number> &st)
1532 {
1533 Assert((mtrx.m() ==
1534 SymmetricTensor<2, dim, Number>::n_independent_components),
1535 ExcDimensionMismatch(
1536 mtrx.m(),
1537 SymmetricTensor<2, dim, Number>::n_independent_components));
1538 Assert((mtrx.n() ==
1539 SymmetricTensor<2, dim, Number>::n_independent_components),
1540 ExcDimensionMismatch(
1541 mtrx.n(),
1542 SymmetricTensor<2, dim, Number>::n_independent_components));
1543 Assert(mtrx.n_elements() == st.n_independent_components,
1544 ExcDimensionMismatch(mtrx.n_elements(),
1545 st.n_independent_components));
1546
1547 const unsigned int n_rows = mtrx.m();
1548 const unsigned int n_cols = mtrx.n();
1549 for (unsigned int r = 0; r < n_rows; ++r)
1550 {
1551 const std::pair<unsigned int, unsigned int> indices_ij =
1552 internal::indices_from_component<dim>(r, false);
1553 Assert(indices_ij.first < dim, ExcInternalError());
1554 Assert(indices_ij.second < dim, ExcInternalError());
1555 const unsigned int i = indices_ij.first;
1556 const unsigned int j = indices_ij.second;
1557
1558 for (unsigned int c = 0; c < n_cols; ++c)
1559 {
1560 const std::pair<unsigned int, unsigned int> indices_kl =
1561 internal::indices_from_component<dim>(c, false);
1562 Assert(indices_kl.first < dim, ExcInternalError());
1563 Assert(indices_kl.second < dim, ExcInternalError());
1564 const unsigned int k = indices_kl.first;
1565 const unsigned int l = indices_kl.second;
1566
1567 const double inv_factor =
1568 1.0 / internal::matrix_component_factor<dim>(r, c, true);
1569
1570 st[i][j][k][l] = inv_factor * mtrx(r, c);
1571 }
1572 }
1573 }
1574
1575
1576 template <typename TensorType, typename Number>
1577 inline TensorType
1578 to_tensor(const Vector<Number> &vec)
1579 {
1580 TensorType out;
1581 to_tensor(vec, out);
1582 return out;
1583 }
1584
1585
1586 template <typename TensorType, typename Number>
1587 inline TensorType
1588 to_tensor(const FullMatrix<Number> &mtrx)
1589 {
1590 TensorType out;
1591 to_tensor(mtrx, out);
1592 return out;
1593 }
1594
1595 } // namespace Kelvin
1596 } // namespace Notation
1597} // namespace Physics
1598
1599
1600#endif // DOXYGEN
1601
1602
1603DEAL_II_NAMESPACE_CLOSE
1604
1605#endif
FullMatrix::n
size_type n() const
FullMatrix::m
size_type m() const
SymmetricTensor::n_independent_components
static constexpr unsigned int n_independent_components
Definition symmetric_tensor.h:743
Tensor::n_independent_components
static constexpr unsigned int n_independent_components
Definition tensor.h:541
Vector::size
size_type size() const
DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_OPEN
Definition config.h:472
DEAL_II_NAMESPACE_CLOSE
#define DEAL_II_NAMESPACE_CLOSE
Definition config.h:473
full_matrix.h
Physics::Notation::Kelvin::ExcNotationExcFullMatrixToTensorRowSize2
static ::ExceptionBase & ExcNotationExcFullMatrixToTensorRowSize2(int arg1, int arg2, int arg3)
DeclException4
#define DeclException4(Exception4, type1, type2, type3, type4, outsequence)
Definition exceptions.h:579
StandardExceptions::ExcNotImplemented
static ::ExceptionBase & ExcNotImplemented()
Assert
#define Assert(cond, exc)
Definition exceptions.h:1614
Physics::Notation::Kelvin::ExcNotationExcFullMatrixToTensorRowSize3
static ::ExceptionBase & ExcNotationExcFullMatrixToTensorRowSize3(int arg1, int arg2, int arg3, int arg4)
AssertIndexRange
#define AssertIndexRange(index, range)
Definition exceptions.h:1855
StandardExceptions::ExcInternalError
static ::ExceptionBase & ExcInternalError()
DeclException3
#define DeclException3(Exception3, type1, type2, type3, outsequence)
Definition exceptions.h:556
StandardExceptions::ExcIndexRange
static ::ExceptionBase & ExcIndexRange(std::size_t arg1, std::size_t arg2, std::size_t arg3)
StandardExceptions::ExcDimensionMismatch
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
StandardExceptions::ExcMessage
static ::ExceptionBase & ExcMessage(std::string arg1)
Physics::Notation::Kelvin::ExcNotationExcFullMatrixToTensorColSize3
static ::ExceptionBase & ExcNotationExcFullMatrixToTensorColSize3(int arg1, int arg2, int arg3, int arg4)
Physics::Notation::Kelvin::ExcNotationExcFullMatrixToTensorColSize2
static ::ExceptionBase & ExcNotationExcFullMatrixToTensorColSize2(int arg1, int arg2, int arg3)
AssertThrow
#define AssertThrow(cond, exc)
Definition exceptions.h:1703
LocalIntegrators::Divergence::norm
double norm(const FEValuesBase< dim > &fe, const ArrayView< const std::vector< Tensor< 1, dim > > > &Du)
Definition divergence.h:472
Physics::Elasticity::Kinematics::l
Tensor< 2, dim, Number > l(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
Physics::Notation::Kelvin::to_tensor
void to_tensor(const Vector< Number > &vec, Number &s)
Physics::Notation::Kelvin::to_matrix
FullMatrix< Number > to_matrix(const Number &s)
Physics::Notation::Kelvin::to_vector
Vector< Number > to_vector(const Number &s)
numbers::SQRT2
static constexpr double SQRT2
Definition numbers.h:274
symmetric_tensor.h
symmetrize
DEAL_II_HOST constexpr SymmetricTensor< 2, dim, Number > symmetrize(const Tensor< 2, dim, Number > &t)
Definition symmetric_tensor.h:3536
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