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finite-element.h
1 // Copyright (c) 2020 Chris Richardson
2 // FEniCS Project
3 // SPDX-License-Identifier: MIT
4 
5 #pragma once
6 
7 #include "cell.h"
8 #include "element-families.h"
9 #include "maps.h"
10 #include "mdspan.hpp"
11 #include "precompute.h"
12 #include <array>
13 #include <functional>
14 #include <map>
15 #include <numeric>
16 #include <span>
17 #include <string>
18 #include <tuple>
19 #include <vector>
20 
22 namespace basix
23 {
24 
25 namespace impl
26 {
27 using mdspan2_t
28  = std::experimental::mdspan<double,
29  std::experimental::dextents<std::size_t, 2>>;
30 using mdspan4_t
31  = std::experimental::mdspan<double,
32  std::experimental::dextents<std::size_t, 4>>;
33 using cmdspan2_t
34  = std::experimental::mdspan<const double,
35  std::experimental::dextents<std::size_t, 2>>;
36 using cmdspan3_t
37  = std::experimental::mdspan<const double,
38  std::experimental::dextents<std::size_t, 3>>;
39 using cmdspan4_t
40  = std::experimental::mdspan<const double,
41  std::experimental::dextents<std::size_t, 4>>;
42 
43 using mdarray2_t
44  = std::experimental::mdarray<double,
45  std::experimental::dextents<std::size_t, 2>>;
46 using mdarray4_t
47  = std::experimental::mdarray<double,
48  std::experimental::dextents<std::size_t, 4>>;
49 
52 inline std::array<std::vector<cmdspan2_t>, 4>
53 to_mdspan(std::array<std::vector<mdarray2_t>, 4>& x)
54 {
55  std::array<std::vector<cmdspan2_t>, 4> x1;
56  for (std::size_t i = 0; i < x.size(); ++i)
57  for (std::size_t j = 0; j < x[i].size(); ++j)
58  x1[i].emplace_back(x[i][j].data(), x[i][j].extents());
59 
60  return x1;
61 }
62 
65 inline std::array<std::vector<cmdspan4_t>, 4>
66 to_mdspan(std::array<std::vector<mdarray4_t>, 4>& M)
67 {
68  std::array<std::vector<cmdspan4_t>, 4> M1;
69  for (std::size_t i = 0; i < M.size(); ++i)
70  for (std::size_t j = 0; j < M[i].size(); ++j)
71  M1[i].emplace_back(M[i][j].data(), M[i][j].extents());
72 
73  return M1;
74 }
75 
78 inline std::array<std::vector<cmdspan2_t>, 4>
79 to_mdspan(const std::array<std::vector<std::vector<double>>, 4>& x,
80  const std::array<std::vector<std::array<std::size_t, 2>>, 4>& shape)
81 {
82  std::array<std::vector<cmdspan2_t>, 4> x1;
83  for (std::size_t i = 0; i < x.size(); ++i)
84  for (std::size_t j = 0; j < x[i].size(); ++j)
85  x1[i].push_back(cmdspan2_t(x[i][j].data(), shape[i][j]));
86 
87  return x1;
88 }
89 
92 inline std::array<std::vector<cmdspan4_t>, 4>
93 to_mdspan(const std::array<std::vector<std::vector<double>>, 4>& M,
94  const std::array<std::vector<std::array<std::size_t, 4>>, 4>& shape)
95 {
96  std::array<std::vector<cmdspan4_t>, 4> M1;
97  for (std::size_t i = 0; i < M.size(); ++i)
98  for (std::size_t j = 0; j < M[i].size(); ++j)
99  M1[i].push_back(cmdspan4_t(M[i][j].data(), shape[i][j]));
100 
101  return M1;
102 }
103 
104 } // namespace impl
105 
106 namespace element
107 {
109 using cmdspan2_t = impl::cmdspan2_t;
111 using cmdspan4_t = impl::cmdspan4_t;
112 
128 std::tuple<std::array<std::vector<std::vector<double>>, 4>,
129  std::array<std::vector<std::array<std::size_t, 2>>, 4>,
130  std::array<std::vector<std::vector<double>>, 4>,
131  std::array<std::vector<std::array<std::size_t, 4>>, 4>>
132 make_discontinuous(const std::array<std::vector<cmdspan2_t>, 4>& x,
133  const std::array<std::vector<cmdspan4_t>, 4>& M,
134  std::size_t tdim, std::size_t value_size);
135 
136 } // namespace element
137 
143 class FiniteElement
144 {
145  using cmdspan2_t
146  = std::experimental::mdspan<const double,
147  std::experimental::dextents<std::size_t, 2>>;
148  using cmdspan4_t
149  = std::experimental::mdspan<const double,
150  std::experimental::dextents<std::size_t, 4>>;
151 
152 public:
322  FiniteElement(
323  element::family family, cell::type cell_type, int degree,
324  const std::vector<std::size_t>& value_shape, const cmdspan2_t& wcoeffs,
325  const std::array<std::vector<cmdspan2_t>, 4>& x,
326  const std::array<std::vector<cmdspan4_t>, 4>& M,
327  int interpolation_nderivs, maps::type map_type, bool discontinuous,
328  int highest_complete_degree, int highest_degree,
329  element::lagrange_variant lvariant, element::dpc_variant dvariant,
330  std::vector<std::tuple<std::vector<FiniteElement>, std::vector<int>>>
331  tensor_factors
332  = {});
333 
335  FiniteElement(
336  element::family family, cell::type cell_type, int degree,
337  const std::vector<std::size_t>& value_shape, const cmdspan2_t& wcoeffs,
338  const std::array<std::vector<cmdspan2_t>, 4>& x,
339  const std::array<std::vector<cmdspan4_t>, 4>& M,
340  int interpolation_nderivs, maps::type map_type, bool discontinuous,
341  int highest_complete_degree, int highest_degree,
342  element::lagrange_variant lvariant,
343  std::vector<std::tuple<std::vector<FiniteElement>, std::vector<int>>>
344  tensor_factors
345  = {});
346 
348  FiniteElement(
349  element::family family, cell::type cell_type, int degree,
350  const std::vector<std::size_t>& value_shape, const cmdspan2_t& wcoeffs,
351  const std::array<std::vector<cmdspan2_t>, 4>& x,
352  const std::array<std::vector<cmdspan4_t>, 4>& M,
353  int interpolation_nderivs, maps::type map_type, bool discontinuous,
354  int highest_complete_degree, int highest_degree,
355  element::dpc_variant dvariant,
356  std::vector<std::tuple<std::vector<FiniteElement>, std::vector<int>>>
357  tensor_factors
358  = {});
359 
361  FiniteElement(
362  element::family family, cell::type cell_type, int degree,
363  const std::vector<std::size_t>& value_shape, const cmdspan2_t& wcoeffs,
364  const std::array<std::vector<cmdspan2_t>, 4>& x,
365  const std::array<std::vector<cmdspan4_t>, 4>& M,
366  int interpolation_nderivs, maps::type map_type, bool disccontinuous,
367  int highest_complete_degree, int highest_degree,
368  std::vector<std::tuple<std::vector<FiniteElement>, std::vector<int>>>
369  tensor_factors
370  = {});
371 
373  FiniteElement(const FiniteElement& element) = default;
374 
376  FiniteElement(FiniteElement&& element) = default;
377 
379  ~FiniteElement() = default;
380 
382  FiniteElement& operator=(const FiniteElement& element) = default;
383 
385  FiniteElement& operator=(FiniteElement&& element) = default;
386 
391  bool operator==(const FiniteElement& e) const;
392 
402  std::array<std::size_t, 4> tabulate_shape(std::size_t nd,
403  std::size_t num_points) const;
404 
426  std::pair<std::vector<double>, std::array<std::size_t, 4>>
427  tabulate(int nd, impl::cmdspan2_t x) const;
428 
452  std::pair<std::vector<double>, std::array<std::size_t, 4>>
453  tabulate(int nd, const std::span<const double>& x,
454  std::array<std::size_t, 2> shape) const;
455 
481  void tabulate(int nd, impl::cmdspan2_t x, impl::mdspan4_t basis) const;
482 
508  void tabulate(int nd, const std::span<const double>& x,
509  std::array<std::size_t, 2> xshape,
510  const std::span<double>& basis) const;
511 
514  cell::type cell_type() const;
515 
518  int degree() const;
519 
524  int highest_degree() const;
525 
529  int highest_complete_degree() const;
530 
534  const std::vector<std::size_t>& value_shape() const;
535 
539  int dim() const;
540 
543  element::family family() const;
544 
547  element::lagrange_variant lagrange_variant() const;
548 
551  element::dpc_variant dpc_variant() const;
552 
555  maps::type map_type() const;
556 
560  bool discontinuous() const;
561 
564  bool dof_transformations_are_permutations() const;
565 
568  bool dof_transformations_are_identity() const;
569 
583  std::pair<std::vector<double>, std::array<std::size_t, 3>>
584  push_forward(impl::cmdspan3_t U, impl::cmdspan3_t J,
585  std::span<const double> detJ, impl::cmdspan3_t K) const;
586 
594  std::pair<std::vector<double>, std::array<std::size_t, 3>>
595  pull_back(impl::cmdspan3_t u, impl::cmdspan3_t J,
596  std::span<const double> detJ, impl::cmdspan3_t K) const;
597 
629  template <typename O, typename P, typename Q, typename R>
630  std::function<void(O&, const P&, const Q&, double, const R&)> map_fn() const
631  {
632  switch (_map_type)
633  {
634  case maps::type::identity:
635  return [](O& u, const P& U, const Q&, double, const R&)
636  {
637  assert(U.extent(0) == u.extent(0));
638  assert(U.extent(1) == u.extent(1));
639  for (std::size_t i = 0; i < U.extent(0); ++i)
640  for (std::size_t j = 0; j < U.extent(1); ++j)
641  u(i, j) = U(i, j);
642  };
643  case maps::type::covariantPiola:
644  return [](O& u, const P& U, const Q& J, double detJ, const R& K)
645  { maps::covariant_piola(u, U, J, detJ, K); };
646  case maps::type::contravariantPiola:
647  return [](O& u, const P& U, const Q& J, double detJ, const R& K)
648  { maps::contravariant_piola(u, U, J, detJ, K); };
649  case maps::type::doubleCovariantPiola:
650  return [](O& u, const P& U, const Q& J, double detJ, const R& K)
651  { maps::double_covariant_piola(u, U, J, detJ, K); };
652  case maps::type::doubleContravariantPiola:
653  return [](O& u, const P& U, const Q& J, double detJ, const R& K)
654  { maps::double_contravariant_piola(u, U, J, detJ, K); };
655  default:
656  throw std::runtime_error("Map not implemented");
657  }
658  }
659 
666  const std::vector<std::vector<std::vector<int>>>& entity_dofs() const;
667 
675  const std::vector<std::vector<std::vector<int>>>& entity_closure_dofs() const;
676 
758  std::pair<std::vector<double>, std::array<std::size_t, 3>>
759  base_transformations() const;
760 
765  std::map<cell::type,
766  std::pair<std::vector<double>, std::array<std::size_t, 3>>>
767  entity_transformations() const;
768 
776  void permute_dofs(const std::span<std::int32_t>& dofs,
777  std::uint32_t cell_info) const;
778 
786  void unpermute_dofs(const std::span<std::int32_t>& dofs,
787  std::uint32_t cell_info) const;
788 
797  template <typename T>
798  void apply_dof_transformation(const std::span<T>& data, int block_size,
799  std::uint32_t cell_info) const;
800 
809  template <typename T>
810  void apply_transpose_dof_transformation(const std::span<T>& data,
811  int block_size,
812  std::uint32_t cell_info) const;
813 
822  template <typename T>
823  void apply_inverse_transpose_dof_transformation(
824  const std::span<T>& data, int block_size, std::uint32_t cell_info) const;
825 
834  template <typename T>
835  void apply_inverse_dof_transformation(const std::span<T>& data,
836  int block_size,
837  std::uint32_t cell_info) const;
838 
847  template <typename T>
848  void apply_dof_transformation_to_transpose(const std::span<T>& data,
849  int block_size,
850  std::uint32_t cell_info) const;
851 
860  template <typename T>
861  void apply_transpose_dof_transformation_to_transpose(
862  const std::span<T>& data, int block_size, std::uint32_t cell_info) const;
863 
873  template <typename T>
874  void apply_inverse_transpose_dof_transformation_to_transpose(
875  const std::span<T>& data, int block_size, std::uint32_t cell_info) const;
876 
885  template <typename T>
886  void apply_inverse_dof_transformation_to_transpose(
887  const std::span<T>& data, int block_size, std::uint32_t cell_info) const;
888 
893  const std::pair<std::vector<double>, std::array<std::size_t, 2>>&
894  points() const;
895 
948  const std::pair<std::vector<double>, std::array<std::size_t, 2>>&
949  interpolation_matrix() const;
950 
956  const std::pair<std::vector<double>, std::array<std::size_t, 2>>&
957  dual_matrix() const;
958 
993  const std::pair<std::vector<double>, std::array<std::size_t, 2>>&
994  wcoeffs() const;
995 
1000  const std::array<
1001  std::vector<std::pair<std::vector<double>, std::array<std::size_t, 2>>>,
1002  4>&
1003  x() const;
1004 
1041  const std::array<
1042  std::vector<std::pair<std::vector<double>, std::array<std::size_t, 4>>>,
1043  4>&
1044  M() const;
1045 
1051  const std::pair<std::vector<double>, std::array<std::size_t, 2>>&
1052  coefficient_matrix() const;
1053 
1061  bool has_tensor_product_factorisation() const;
1062 
1074  std::vector<std::tuple<std::vector<FiniteElement>, std::vector<int>>>
1075  get_tensor_product_representation() const;
1076 
1079  bool interpolation_is_identity() const;
1080 
1082  int interpolation_nderivs() const;
1083 
1084 private:
1085  // Cell type
1086  cell::type _cell_type;
1087 
1088  // Topological dimension of the cell
1089  std::size_t _cell_tdim;
1090 
1091  // Topological dimension of the cell
1092  std::vector<std::vector<cell::type>> _cell_subentity_types;
1093 
1094  // Finite element family
1095  element::family _family;
1096 
1097  // Lagrange variant
1098  element::lagrange_variant _lagrange_variant;
1099 
1100  // Lagrange variant
1101  element::dpc_variant _dpc_variant;
1102 
1103  // Degree that was input when creating the element
1104  int _degree;
1105 
1106  // Degree
1107  int _interpolation_nderivs;
1108 
1109  // Highest degree polynomial in element's polyset
1110  int _highest_degree;
1111 
1112  // Highest degree space that is a subspace of element's polyset
1113  int _highest_complete_degree;
1114 
1115  // Value shape
1116  std::vector<std::size_t> _value_shape;
1117 
1119  maps::type _map_type;
1120 
1121  // Shape function coefficient of expansion sets on cell. If shape
1122  // function is given by @f$\psi_i = \sum_{k} \phi_{k}
1123  // \alpha^{i}_{k}@f$, then _coeffs(i, j) = @f$\alpha^i_k@f$. ie
1124  // _coeffs.row(i) are the expansion coefficients for shape function i
1125  // (@f$\psi_{i}@f$).
1126  std::pair<std::vector<double>, std::array<std::size_t, 2>> _coeffs;
1127 
1128  // Dofs associated with each cell (sub-)entity
1129  std::vector<std::vector<std::vector<int>>> _edofs;
1130 
1131  // Dofs associated with the closdure of each cell (sub-)entity
1132  std::vector<std::vector<std::vector<int>>> _e_closure_dofs;
1133 
1134  using array2_t = std::pair<std::vector<double>, std::array<std::size_t, 2>>;
1135  using array3_t = std::pair<std::vector<double>, std::array<std::size_t, 3>>;
1136 
1137  // Entity transformations
1138  std::map<cell::type, array3_t> _entity_transformations;
1139 
1140  // Set of points used for point evaluation
1141  // Experimental - currently used for an implementation of
1142  // "tabulate_dof_coordinates" Most useful for Lagrange. This may change or go
1143  // away. For non-Lagrange elements, these points will be used in combination
1144  // with _interpolation_matrix to perform interpolation
1145  std::pair<std::vector<double>, std::array<std::size_t, 2>> _points;
1146 
1147  // Interpolation points on the cell. The shape is (entity_dim, num
1148  // entities of given dimension, num_points, tdim)
1149  std::array<
1150  std::vector<std::pair<std::vector<double>, std::array<std::size_t, 2>>>,
1151  4>
1152  _x;
1153 
1155  std::pair<std::vector<double>, std::array<std::size_t, 2>> _matM;
1156 
1157  // Indicates whether or not the DOF transformations are all
1158  // permutations
1159  bool _dof_transformations_are_permutations;
1160 
1161  // Indicates whether or not the DOF transformations are all identity
1162  bool _dof_transformations_are_identity;
1163 
1164  // The entity permutations (factorised). This will only be set if
1165  // _dof_transformations_are_permutations is True and
1166  // _dof_transformations_are_identity is False
1167  std::map<cell::type, std::vector<std::vector<std::size_t>>> _eperm;
1168 
1169  // The reverse entity permutations (factorised). This will only be set
1170  // if _dof_transformations_are_permutations is True and
1171  // _dof_transformations_are_identity is False
1172  std::map<cell::type, std::vector<std::vector<std::size_t>>> _eperm_rev;
1173 
1174  using trans_data_t
1175  = std::vector<std::pair<std::vector<std::size_t>, array2_t>>;
1176 
1177  // The entity transformations in precomputed form
1178  std::map<cell::type, trans_data_t> _etrans;
1179 
1180  // The transposed entity transformations in precomputed form
1181  std::map<cell::type, trans_data_t> _etransT;
1182 
1183  // The inverse entity transformations in precomputed form
1184  std::map<cell::type, trans_data_t> _etrans_inv;
1185 
1186  // The inverse transpose entity transformations in precomputed form
1187  std::map<cell::type, trans_data_t> _etrans_invT;
1188 
1189  // Indicates whether or not this is the discontinuous version of the
1190  // element
1191  bool _discontinuous;
1192 
1193  // The dual matrix
1194  std::pair<std::vector<double>, std::array<std::size_t, 2>> _dual_matrix;
1195 
1196  // Tensor product representation
1197  // Entries of tuple are (list of elements on an interval, permutation
1198  // of DOF numbers)
1199  // @todo: For vector-valued elements, a tensor product type and a
1200  // scaling factor may additionally be needed.
1201  std::vector<std::tuple<std::vector<FiniteElement>, std::vector<int>>>
1202  _tensor_factors;
1203 
1204  // Is the interpolation matrix an identity?
1205  bool _interpolation_is_identity;
1206 
1207  // The coefficients that define the polynomial set in terms of the
1208  // orthonormal polynomials
1209  std::pair<std::vector<double>, std::array<std::size_t, 2>> _wcoeffs;
1210 
1211  // Interpolation matrices for each entity
1212  using array4_t
1213  = std::vector<std::pair<std::vector<double>, std::array<std::size_t, 4>>>;
1214  std::array<array4_t, 4> _M;
1215  // std::array<
1216  // std::vector<std::pair<std::vector<double>, std::array<std::size_t,
1217  // 4>>>, 4> _M;
1218 };
1219 
1243 FiniteElement create_custom_element(
1244  cell::type cell_type, const std::vector<std::size_t>& value_shape,
1245  const impl::cmdspan2_t& wcoeffs,
1246  const std::array<std::vector<impl::cmdspan2_t>, 4>& x,
1247  const std::array<std::vector<impl::cmdspan4_t>, 4>& M,
1248  int interpolation_nderivs, maps::type map_type, bool discontinuous,
1249  int highest_complete_degree, int highest_degree);
1250 
1260 FiniteElement create_element(element::family family, cell::type cell,
1261  int degree, element::lagrange_variant lvariant,
1262  bool discontinuous);
1263 
1274 FiniteElement create_element(element::family family, cell::type cell,
1275  int degree, element::lagrange_variant lvariant,
1276  element::dpc_variant dvariant, bool discontinuous);
1277 
1287 FiniteElement create_element(element::family family, cell::type cell,
1288  int degree, element::dpc_variant dvariant,
1289  bool discontinuous);
1290 
1301 FiniteElement create_element(element::family family, cell::type cell,
1302  int degree, bool discontinuous);
1303 
1311 FiniteElement create_element(element::family family, cell::type cell,
1312  int degree, element::lagrange_variant lvariant);
1313 
1323 FiniteElement create_element(element::family family, cell::type cell,
1324  int degree, element::lagrange_variant lvariant,
1325  element::dpc_variant dvariant);
1326 
1334 FiniteElement create_element(element::family family, cell::type cell,
1335  int degree, element::dpc_variant dvariant);
1336 
1343 FiniteElement create_element(element::family family, cell::type cell,
1344  int degree);
1345 
1348 std::string version();
1349 
1350 //-----------------------------------------------------------------------------
1351 template <typename T>
1352 void FiniteElement::apply_dof_transformation(const std::span<T>& data,
1353  int block_size,
1354  std::uint32_t cell_info) const
1355 {
1356  if (_dof_transformations_are_identity)
1357  return;
1358 
1359  if (_cell_tdim >= 2)
1360  {
1361  // This assumes 3 bits are used per face. This will need updating if
1362  // 3D cells with faces with more than 4 sides are implemented
1363  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1364  int dofstart = 0;
1365  for (auto& edofs0 : _edofs[0])
1366  dofstart += edofs0.size();
1367 
1368  // Transform DOFs on edges
1369  {
1370  auto& [v_size_t, matrix] = _etrans.at(cell::type::interval)[0];
1371  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1372  {
1373  // Reverse an edge
1374  if (cell_info >> (face_start + e) & 1)
1375  {
1376  precompute::apply_matrix(
1377  std::span(v_size_t),
1378  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1379  block_size);
1380  }
1381  dofstart += _edofs[1][e].size();
1382  }
1383  }
1384 
1385  if (_cell_tdim == 3)
1386  {
1387  // Permute DOFs on faces
1388  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1389  {
1390  auto& trans = _etrans.at(_cell_subentity_types[2][f]);
1391 
1392  // Reflect a face
1393  if (cell_info >> (3 * f) & 1)
1394  {
1395  const auto& m = trans[1];
1396  const auto& v_size_t = std::get<0>(m);
1397  const auto& matrix = std::get<1>(m);
1398  precompute::apply_matrix(
1399  std::span(v_size_t),
1400  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1401  block_size);
1402  }
1403 
1404  // Rotate a face
1405  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1406  {
1407  const auto& m = trans[0];
1408  const auto& v_size_t = std::get<0>(m);
1409  const auto& matrix = std::get<1>(m);
1410  precompute::apply_matrix(
1411  std::span(v_size_t),
1412  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1413  block_size);
1414  }
1415 
1416  dofstart += _edofs[2][f].size();
1417  }
1418  }
1419  }
1420 }
1421 //-----------------------------------------------------------------------------
1422 template <typename T>
1423 void FiniteElement::apply_transpose_dof_transformation(
1424  const std::span<T>& data, int block_size, std::uint32_t cell_info) const
1425 {
1426  if (_dof_transformations_are_identity)
1427  return;
1428 
1429  if (_cell_tdim >= 2)
1430  {
1431  // This assumes 3 bits are used per face. This will need updating if
1432  // 3D cells with faces with more than 4 sides are implemented
1433  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1434  int dofstart = 0;
1435  for (auto& edofs0 : _edofs[0])
1436  dofstart += edofs0.size();
1437 
1438  // Transform DOFs on edges
1439  {
1440  auto& [v_size_t, matrix] = _etransT.at(cell::type::interval)[0];
1441  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1442  {
1443  // Reverse an edge
1444  if (cell_info >> (face_start + e) & 1)
1445  {
1446  precompute::apply_matrix(
1447  std::span(v_size_t),
1448  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1449  block_size);
1450  }
1451  dofstart += _edofs[1][e].size();
1452  }
1453  }
1454 
1455  if (_cell_tdim == 3)
1456  {
1457  // Permute DOFs on faces
1458  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1459  {
1460  auto& trans = _etransT.at(_cell_subentity_types[2][f]);
1461 
1462  // Rotate a face
1463  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1464  {
1465  auto& m = trans[0];
1466  auto& v_size_t = std::get<0>(m);
1467  auto& matrix = std::get<1>(m);
1468  precompute::apply_matrix(
1469  std::span(v_size_t),
1470  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1471  block_size);
1472  }
1473 
1474  // Reflect a face
1475  if (cell_info >> (3 * f) & 1)
1476  {
1477  auto& m = trans[1];
1478  auto& v_size_t = std::get<0>(m);
1479  auto& matrix = std::get<1>(m);
1480  precompute::apply_matrix(
1481  std::span(v_size_t),
1482  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1483  block_size);
1484  }
1485  dofstart += _edofs[2][f].size();
1486  }
1487  }
1488  }
1489 }
1490 //-----------------------------------------------------------------------------
1491 template <typename T>
1492 void FiniteElement::apply_inverse_transpose_dof_transformation(
1493  const std::span<T>& data, int block_size, std::uint32_t cell_info) const
1494 {
1495  if (_dof_transformations_are_identity)
1496  return;
1497 
1498  if (_cell_tdim >= 2)
1499  {
1500  // This assumes 3 bits are used per face. This will need updating if
1501  // 3D cells with faces with more than 4 sides are implemented
1502  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1503  int dofstart = 0;
1504  for (auto& edofs0 : _edofs[0])
1505  dofstart += edofs0.size();
1506 
1507  // Transform DOFs on edges
1508  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1509  {
1510  // Reverse an edge
1511  if (cell_info >> (face_start + e) & 1)
1512  {
1513  auto& [v_size_t, matrix] = _etrans_invT.at(cell::type::interval)[0];
1514  precompute::apply_matrix(std::span(v_size_t),
1515  cmdspan2_t(matrix.first.data(), matrix.second),
1516  data, dofstart, block_size);
1517  }
1518  dofstart += _edofs[1][e].size();
1519  }
1520 
1521  if (_cell_tdim == 3)
1522  {
1523  // Permute DOFs on faces
1524  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1525  {
1526  auto& trans = _etrans_invT.at(_cell_subentity_types[2][f]);
1527 
1528  // Reflect a face
1529  if (cell_info >> (3 * f) & 1)
1530  {
1531  auto& m = trans[1];
1532  auto& v_size_t = std::get<0>(m);
1533  auto& matrix = std::get<1>(m);
1534  precompute::apply_matrix(
1535  std::span(v_size_t),
1536  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1537  block_size);
1538  }
1539 
1540  // Rotate a face
1541  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1542  {
1543  const auto& m = trans[0];
1544  const auto& v_size_t = std::get<0>(m);
1545  const auto& matrix = std::get<1>(m);
1546  precompute::apply_matrix(
1547  std::span(v_size_t),
1548  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1549  block_size);
1550  }
1551 
1552  dofstart += _edofs[2][f].size();
1553  }
1554  }
1555  }
1556 }
1557 //-----------------------------------------------------------------------------
1558 template <typename T>
1559 void FiniteElement::apply_inverse_dof_transformation(
1560  const std::span<T>& data, int block_size, std::uint32_t cell_info) const
1561 {
1562  if (_dof_transformations_are_identity)
1563  return;
1564 
1565  if (_cell_tdim >= 2)
1566  {
1567  // This assumes 3 bits are used per face. This will need updating if
1568  // 3D cells with faces with more than 4 sides are implemented
1569  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1570  int dofstart = 0;
1571  for (auto& edofs0 : _edofs[0])
1572  dofstart += edofs0.size();
1573 
1574  // Transform DOFs on edges
1575  {
1576  auto& [v_size_t, matrix] = _etrans_inv.at(cell::type::interval)[0];
1577  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1578  {
1579  // Reverse an edge
1580  if (cell_info >> (face_start + e) & 1)
1581  {
1582  precompute::apply_matrix(
1583  std::span(v_size_t),
1584  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1585  block_size);
1586  }
1587  dofstart += _edofs[1][e].size();
1588  }
1589  }
1590 
1591  if (_cell_tdim == 3)
1592  {
1593  // Permute DOFs on faces
1594  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1595  {
1596  auto& trans = _etrans_inv.at(_cell_subentity_types[2][f]);
1597 
1598  // Rotate a face
1599  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1600  {
1601  auto& m = trans[0];
1602  auto& v_size_t = std::get<0>(m);
1603  auto& matrix = std::get<1>(m);
1604  precompute::apply_matrix(
1605  std::span(v_size_t),
1606  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1607  block_size);
1608  }
1609 
1610  // Reflect a face
1611  if (cell_info >> (3 * f) & 1)
1612  {
1613  auto& m = trans[1];
1614  auto& v_size_t = std::get<0>(m);
1615  auto& matrix = std::get<1>(m);
1616  precompute::apply_matrix(
1617  std::span(v_size_t),
1618  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1619  block_size);
1620  }
1621 
1622  dofstart += _edofs[2][f].size();
1623  }
1624  }
1625  }
1626 }
1627 //-----------------------------------------------------------------------------
1628 template <typename T>
1629 void FiniteElement::apply_dof_transformation_to_transpose(
1630  const std::span<T>& data, int block_size, std::uint32_t cell_info) const
1631 {
1632  if (_dof_transformations_are_identity)
1633  return;
1634 
1635  if (_cell_tdim >= 2)
1636  {
1637  // This assumes 3 bits are used per face. This will need updating if
1638  // 3D cells with faces with more than 4 sides are implemented
1639  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1640  int dofstart = 0;
1641  for (auto& edofs0 : _edofs[0])
1642  dofstart += edofs0.size();
1643 
1644  // Transform DOFs on edges
1645  {
1646  auto& [v_size_t, matrix] = _etrans.at(cell::type::interval)[0];
1647  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1648  {
1649  // Reverse an edge
1650  if (cell_info >> (face_start + e) & 1)
1651  {
1652  precompute::apply_matrix_to_transpose(
1653  std::span(v_size_t),
1654  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1655  block_size);
1656  }
1657 
1658  dofstart += _edofs[1][e].size();
1659  }
1660  }
1661 
1662  if (_cell_tdim == 3)
1663  {
1664  // Permute DOFs on faces
1665  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1666  {
1667  auto& trans = _etrans.at(_cell_subentity_types[2][f]);
1668 
1669  // Reflect a face
1670  if (cell_info >> (3 * f) & 1)
1671  {
1672  auto& m = trans[1];
1673  auto& v_size_t = std::get<0>(m);
1674  auto& matrix = std::get<1>(m);
1675  precompute::apply_matrix_to_transpose(
1676  std::span(v_size_t),
1677  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1678  block_size);
1679  }
1680 
1681  // Rotate a face
1682  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1683  {
1684  auto& m = trans[0];
1685  auto& v_size_t = std::get<0>(m);
1686  auto& matrix = std::get<1>(m);
1687  precompute::apply_matrix_to_transpose(
1688  std::span(v_size_t),
1689  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1690  block_size);
1691  }
1692  dofstart += _edofs[2][f].size();
1693  }
1694  }
1695  }
1696 }
1697 //-----------------------------------------------------------------------------
1698 template <typename T>
1699 void FiniteElement::apply_inverse_transpose_dof_transformation_to_transpose(
1700  const std::span<T>& data, int block_size, std::uint32_t cell_info) const
1701 {
1702  if (_dof_transformations_are_identity)
1703  return;
1704 
1705  if (_cell_tdim >= 2)
1706  {
1707  // This assumes 3 bits are used per face. This will need updating if
1708  // 3D cells with faces with more than 4 sides are implemented
1709  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1710  int dofstart = 0;
1711  for (auto& edofs0 : _edofs[0])
1712  dofstart += edofs0.size();
1713 
1714  // Transform DOFs on edges
1715  {
1716  auto& [v_size_t, matrix] = _etrans_invT.at(cell::type::interval)[0];
1717  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1718  {
1719  // Reverse an edge
1720  if (cell_info >> (face_start + e) & 1)
1721  {
1722  precompute::apply_matrix_to_transpose(
1723  std::span(v_size_t),
1724  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1725  block_size);
1726  }
1727  dofstart += _edofs[1][e].size();
1728  }
1729  }
1730 
1731  if (_cell_tdim == 3)
1732  {
1733  // Permute DOFs on faces
1734  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1735  {
1736  auto& trans = _etrans_invT.at(_cell_subentity_types[2][f]);
1737 
1738  // Reflect a face
1739  if (cell_info >> (3 * f) & 1)
1740  {
1741  auto& m = trans[1];
1742  auto& v_size_t = std::get<0>(m);
1743  auto& matrix = std::get<1>(m);
1744  precompute::apply_matrix_to_transpose(
1745  std::span(v_size_t),
1746  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1747  block_size);
1748  }
1749 
1750  // Rotate a face
1751  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1752  {
1753  auto& m = trans[0];
1754  auto& v_size_t = std::get<0>(m);
1755  auto& matrix = std::get<1>(m);
1756  precompute::apply_matrix_to_transpose(
1757  std::span(v_size_t),
1758  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1759  block_size);
1760  }
1761  dofstart += _edofs[2][f].size();
1762  }
1763  }
1764  }
1765 }
1766 //-----------------------------------------------------------------------------
1767 template <typename T>
1768 void FiniteElement::apply_transpose_dof_transformation_to_transpose(
1769  const std::span<T>& data, int block_size, std::uint32_t cell_info) const
1770 {
1771  if (_dof_transformations_are_identity)
1772  return;
1773 
1774  if (_cell_tdim >= 2)
1775  {
1776  // This assumes 3 bits are used per face. This will need updating if
1777  // 3D cells with faces with more than 4 sides are implemented
1778  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1779  int dofstart = 0;
1780  for (auto& edofs0 : _edofs[0])
1781  dofstart += edofs0.size();
1782 
1783  // Transform DOFs on edges
1784  {
1785  auto& [v_size_t, matrix] = _etransT.at(cell::type::interval)[0];
1786  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1787  {
1788  // Reverse an edge
1789  if (cell_info >> (face_start + e) & 1)
1790  {
1791  precompute::apply_matrix_to_transpose(
1792  std::span(v_size_t),
1793  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1794  block_size);
1795  }
1796  dofstart += _edofs[1][e].size();
1797  }
1798  }
1799 
1800  if (_cell_tdim == 3)
1801  {
1802  // Permute DOFs on faces
1803  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1804  {
1805  auto& trans = _etransT.at(_cell_subentity_types[2][f]);
1806 
1807  // Rotate a face
1808  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1809  {
1810  auto& m = trans[0];
1811  auto& v_size_t = std::get<0>(m);
1812  auto& matrix = std::get<1>(m);
1813  precompute::apply_matrix_to_transpose(
1814  std::span(v_size_t),
1815  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1816  block_size);
1817  }
1818 
1819  // Reflect a face
1820  if (cell_info >> (3 * f) & 1)
1821  {
1822  auto& m = trans[1];
1823  auto& v_size_t = std::get<0>(m);
1824  auto& matrix = std::get<1>(m);
1825  precompute::apply_matrix_to_transpose(
1826  std::span(v_size_t),
1827  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1828  block_size);
1829  }
1830  dofstart += _edofs[2][f].size();
1831  }
1832  }
1833  }
1834 }
1835 //-----------------------------------------------------------------------------
1836 template <typename T>
1837 void FiniteElement::apply_inverse_dof_transformation_to_transpose(
1838  const std::span<T>& data, int block_size, std::uint32_t cell_info) const
1839 {
1840  if (_dof_transformations_are_identity)
1841  return;
1842 
1843  if (_cell_tdim >= 2)
1844  {
1845  // This assumes 3 bits are used per face. This will need updating if
1846  // 3D cells with faces with more than 4 sides are implemented
1847  int face_start = _cell_tdim == 3 ? 3 * _edofs[2].size() : 0;
1848  int dofstart = 0;
1849  for (auto& edofs0 : _edofs[0])
1850  dofstart += edofs0.size();
1851 
1852  // Transform DOFs on edges
1853  {
1854  auto& [v_size_t, matrix] = _etrans_inv.at(cell::type::interval)[0];
1855  for (std::size_t e = 0; e < _edofs[1].size(); ++e)
1856  {
1857  // Reverse an edge
1858  if (cell_info >> (face_start + e) & 1)
1859  {
1860  precompute::apply_matrix_to_transpose(
1861  std::span(v_size_t),
1862  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1863  block_size);
1864  }
1865  dofstart += _edofs[1][e].size();
1866  }
1867  }
1868 
1869  if (_cell_tdim == 3)
1870  {
1871  // Permute DOFs on faces
1872  for (std::size_t f = 0; f < _edofs[2].size(); ++f)
1873  {
1874  auto& trans = _etrans_inv.at(_cell_subentity_types[2][f]);
1875 
1876  // Rotate a face
1877  for (std::uint32_t r = 0; r < (cell_info >> (3 * f + 1) & 3); ++r)
1878  {
1879  auto& m = trans[0];
1880  auto& v_size_t = std::get<0>(m);
1881  auto& matrix = std::get<1>(m);
1882  precompute::apply_matrix_to_transpose(
1883  std::span(v_size_t),
1884  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1885  block_size);
1886  }
1887 
1888  // Reflect a face
1889  if (cell_info >> (3 * f) & 1)
1890  {
1891  auto& m = trans[1];
1892  auto& v_size_t = std::get<0>(m);
1893  auto& matrix = std::get<1>(m);
1894  precompute::apply_matrix_to_transpose(
1895  std::span(v_size_t),
1896  cmdspan2_t(matrix.first.data(), matrix.second), data, dofstart,
1897  block_size);
1898  }
1899 
1900  dofstart += _edofs[2][f].size();
1901  }
1902  }
1903  }
1904 }
1905 //-----------------------------------------------------------------------------
1906 
1907 } // namespace basix
basix::FiniteElement::map_type
maps::type map_type() const
Definition: finite-element.cpp:1136
basix::FiniteElement::permute_dofs
void permute_dofs(const std::span< std::int32_t > &dofs, std::uint32_t cell_info) const
Definition: finite-element.cpp:1310
basix::FiniteElement::highest_complete_degree
int highest_complete_degree() const
Definition: finite-element.cpp:1122
basix::FiniteElement::dof_transformations_are_identity
bool dof_transformations_are_identity() const
Definition: finite-element.cpp:1145
basix::FiniteElement::lagrange_variant
element::lagrange_variant lagrange_variant() const
Definition: finite-element.cpp:1460
basix::element::lagrange_variant
lagrange_variant
Variants of a Lagrange space that can be created.
Definition: element-families.h:11
basix::FiniteElement::entity_transformations
std::map< cell::type, std::pair< std::vector< double >, std::array< std::size_t, 3 > > > entity_transformations() const
Definition: finite-element.cpp:1418
basix::FiniteElement::degree
int degree() const
Definition: finite-element.cpp:1118
basix::FiniteElement::interpolation_matrix
const std::pair< std::vector< double >, std::array< std::size_t, 2 > > & interpolation_matrix() const
Return a matrix of weights interpolation,.
Definition: finite-element.cpp:1151
basix::FiniteElement::~FiniteElement
~FiniteElement()=default
Destructor.
basix::FiniteElement::push_forward
std::pair< std::vector< double >, std::array< std::size_t, 3 > > push_forward(impl::cmdspan3_t U, impl::cmdspan3_t J, std::span< const double > detJ, impl::cmdspan3_t K) const
Definition: finite-element.cpp:1243
basix::FiniteElement::dpc_variant
element::dpc_variant dpc_variant() const
Definition: finite-element.cpp:1465
basix::FiniteElement::coefficient_matrix
const std::pair< std::vector< double >, std::array< std::size_t, 2 > > & coefficient_matrix() const
Definition: finite-element.cpp:1450
basix::FiniteElement::apply_transpose_dof_transformation_to_transpose
void apply_transpose_dof_transformation_to_transpose(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Definition: finite-element.h:1768
basix::FiniteElement::apply_dof_transformation_to_transpose
void apply_dof_transformation_to_transpose(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Definition: finite-element.h:1629
basix::cell::type
type
Cell type.
Definition: cell.h:19
basix::FiniteElement::base_transformations
std::pair< std::vector< double >, std::array< std::size_t, 3 > > base_transformations() const
Get the base transformations.
Definition: finite-element.cpp:1169
basix::FiniteElement::has_tensor_product_factorisation
bool has_tensor_product_factorisation() const
Definition: finite-element.cpp:1455
basix::FiniteElement::apply_transpose_dof_transformation
void apply_transpose_dof_transformation(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Definition: finite-element.h:1423
basix::create_custom_element
FiniteElement create_custom_element(cell::type cell_type, const std::vector< std::size_t > &value_shape, const impl::cmdspan2_t &wcoeffs, const std::array< std::vector< impl::cmdspan2_t >, 4 > &x, const std::array< std::vector< impl::cmdspan4_t >, 4 > &M, int interpolation_nderivs, maps::type map_type, bool discontinuous, int highest_complete_degree, int highest_degree)
Definition: finite-element.cpp:464
basix::FiniteElement::points
const std::pair< std::vector< double >, std::array< std::size_t, 2 > > & points() const
Definition: finite-element.cpp:1237
basix::FiniteElement::cell_type
cell::type cell_type() const
Definition: finite-element.cpp:1116
basix::FiniteElement::entity_dofs
const std::vector< std::vector< std::vector< int > > > & entity_dofs() const
Definition: finite-element.cpp:1157
basix::maps::double_contravariant_piola
void double_contravariant_piola(O &&r, const P &U, const Q &J, double detJ, const R &)
Double contravariant Piola map.
Definition: maps.h:107
basix::FiniteElement::discontinuous
bool discontinuous() const
Definition: finite-element.cpp:1138
basix::create_element
FiniteElement create_element(element::family family, cell::type cell, int degree, element::lagrange_variant lvariant, bool discontinuous)
Definition: finite-element.cpp:345
basix::FiniteElement::dof_transformations_are_permutations
bool dof_transformations_are_permutations() const
Definition: finite-element.cpp:1140
basix::FiniteElement::apply_inverse_dof_transformation
void apply_inverse_dof_transformation(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Definition: finite-element.h:1559
basix::element::cmdspan4_t
impl::cmdspan4_t cmdspan4_t
Typedef for mdspan.
Definition: finite-element.h:111
basix::FiniteElement::family
element::family family() const
Definition: finite-element.cpp:1134
basix::FiniteElement::get_tensor_product_representation
std::vector< std::tuple< std::vector< FiniteElement >, std::vector< int > > > get_tensor_product_representation() const
Definition: finite-element.cpp:1478
basix::FiniteElement::wcoeffs
const std::pair< std::vector< double >, std::array< std::size_t, 2 > > & wcoeffs() const
Definition: finite-element.cpp:1430
basix::element::cmdspan2_t
impl::cmdspan2_t cmdspan2_t
Typedef for mdspan.
Definition: finite-element.h:109
basix::FiniteElement::dim
int dim() const
Definition: finite-element.cpp:1132
basix::FiniteElement::operator==
bool operator==(const FiniteElement &e) const
Definition: finite-element.cpp:994
basix::FiniteElement::apply_inverse_dof_transformation_to_transpose
void apply_inverse_dof_transformation_to_transpose(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Definition: finite-element.h:1837
basix::FiniteElement::dual_matrix
const std::pair< std::vector< double >, std::array< std::size_t, 2 > > & dual_matrix() const
Definition: finite-element.cpp:1424
basix::FiniteElement::tabulate_shape
std::array< std::size_t, 4 > tabulate_shape(std::size_t nd, std::size_t num_points) const
Definition: finite-element.cpp:1028
basix::FiniteElement::FiniteElement
FiniteElement(element::family family, cell::type cell_type, int degree, const std::vector< std::size_t > &value_shape, const cmdspan2_t &wcoeffs, const std::array< std::vector< cmdspan2_t >, 4 > &x, const std::array< std::vector< cmdspan4_t >, 4 > &M, int interpolation_nderivs, maps::type map_type, bool discontinuous, int highest_complete_degree, int highest_degree, element::lagrange_variant lvariant, element::dpc_variant dvariant, std::vector< std::tuple< std::vector< FiniteElement >, std::vector< int >>> tensor_factors={})
Construct a finite element.
Definition: finite-element.cpp:603
basix::FiniteElement::highest_degree
int highest_degree() const
Definition: finite-element.cpp:1120
basix::maps::type
type
Map type.
Definition: maps.h:16
basix::FiniteElement::unpermute_dofs
void unpermute_dofs(const std::span< std::int32_t > &dofs, std::uint32_t cell_info) const
Definition: finite-element.cpp:1364
basix::FiniteElement::M
const std::array< std::vector< std::pair< std::vector< double >, std::array< std::size_t, 4 > > >, 4 > & M() const
Definition: finite-element.cpp:1444
basix::FiniteElement::interpolation_is_identity
bool interpolation_is_identity() const
Definition: finite-element.cpp:1467
basix::element::make_discontinuous
std::tuple< std::array< std::vector< std::vector< double > >, 4 >, std::array< std::vector< std::array< std::size_t, 2 > >, 4 >, std::array< std::vector< std::vector< double > >, 4 >, std::array< std::vector< std::array< std::size_t, 4 > >, 4 > > make_discontinuous(const std::array< std::vector< cmdspan2_t >, 4 > &x, const std::array< std::vector< cmdspan4_t >, 4 > &M, std::size_t tdim, std::size_t value_size)
Definition: finite-element.cpp:394
basix::maps::double_covariant_piola
void double_covariant_piola(O &&r, const P &U, const Q &J, double, const R &K)
Double covariant Piola map.
Definition: maps.h:79
basix::FiniteElement::apply_inverse_transpose_dof_transformation
void apply_inverse_transpose_dof_transformation(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Definition: finite-element.h:1492
basix::FiniteElement
A finite element.
Definition: finite-element.h:143
basix::FiniteElement::apply_dof_transformation
void apply_dof_transformation(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Definition: finite-element.h:1352
basix::maps::contravariant_piola
void contravariant_piola(O &&r, const P &U, const Q &J, double detJ, const R &)
Contravariant Piola map.
Definition: maps.h:58
basix::version
std::string version()
Definition: finite-element.cpp:1485
basix::precompute::apply_matrix
void apply_matrix(const std::span< const std::size_t > &v_size_t, const std::experimental::mdspan< const T, std::experimental::dextents< std::size_t, 2 >> &M, const std::span< E > &data, std::size_t offset=0, std::size_t block_size=1)
Apply a (precomputed) matrix.
Definition: precompute.h:207
basix::FiniteElement::interpolation_nderivs
int interpolation_nderivs() const
The number of derivatives needed when interpolating.
Definition: finite-element.cpp:1472
basix::FiniteElement::entity_closure_dofs
const std::vector< std::vector< std::vector< int > > > & entity_closure_dofs() const
Definition: finite-element.cpp:1163
basix::FiniteElement::map_fn
std::function< void(O &, const P &, const Q &, double, const R &)> map_fn() const
Definition: finite-element.h:630
basix::FiniteElement::pull_back
std::pair< std::vector< double >, std::array< std::size_t, 3 > > pull_back(impl::cmdspan3_t u, impl::cmdspan3_t J, std::span< const double > detJ, impl::cmdspan3_t K) const
Definition: finite-element.cpp:1278
basix::FiniteElement::apply_inverse_transpose_dof_transformation_to_transpose
void apply_inverse_transpose_dof_transformation_to_transpose(const std::span< T > &data, int block_size, std::uint32_t cell_info) const
Apply inverse transpose DOF transformations to some transposed data.
Definition: finite-element.h:1699
basix
Basix: FEniCS runtime basis evaluation library.
Definition: cell.h:15
basix::FiniteElement::tabulate
std::pair< std::vector< double >, std::array< std::size_t, 4 > > tabulate(int nd, impl::cmdspan2_t x) const
Compute basis values and derivatives at set of points.
Definition: finite-element.cpp:1042
basix::precompute::apply_matrix_to_transpose
void apply_matrix_to_transpose(const std::span< const std::size_t > &v_size_t, const std::experimental::mdspan< const T, std::experimental::dextents< std::size_t, 2 >> &M, const std::span< E > &data, std::size_t offset=0, std::size_t block_size=1)
Apply a (precomputed) matrix to some transposed data.
Definition: precompute.h:244
basix::FiniteElement::operator=
FiniteElement & operator=(const FiniteElement &element)=default
Assignment operator.
basix::FiniteElement::x
const std::array< std::vector< std::pair< std::vector< double >, std::array< std::size_t, 2 > > >, 4 > & x() const
Definition: finite-element.cpp:1437
basix::FiniteElement::value_shape
const std::vector< std::size_t > & value_shape() const
Definition: finite-element.cpp:1127
basix::maps::covariant_piola
void covariant_piola(O &&r, const P &U, const Q &, double, const R &K)
Covariant Piola map.
Definition: maps.h:39
basix::element::dpc_variant
dpc_variant
Definition: element-families.h:32
basix::element::family
family
Available element families.
Definition: element-families.h:45