#include <language/algorithms/HeatDiamondAlgorithm.hpp>

#include <algebra/CRSMatrix.hpp>
#include <algebra/LeastSquareSolver.hpp>
#include <algebra/LinearSolver.hpp>
#include <algebra/LocalRectangularMatrix.hpp>
#include <algebra/SparseMatrixDescriptor.hpp>
#include <algebra/TinyVector.hpp>
#include <algebra/Vector.hpp>
#include <language/utils/InterpolateItemValue.hpp>
#include <mesh/Connectivity.hpp>
#include <mesh/ConnectivityToDiamondDualConnectivityDataMapper.hpp>
#include <mesh/DiamondDualConnectivityManager.hpp>
#include <mesh/DiamondDualMeshManager.hpp>
#include <mesh/Mesh.hpp>
#include <mesh/MeshData.hpp>
#include <mesh/MeshDataManager.hpp>
#include <mesh/MeshNodeBoundary.hpp>
#include <mesh/SubItemValuePerItem.hpp>
#include <output/VTKWriter.hpp>
#include <scheme/DirichletBoundaryConditionDescriptor.hpp>
#include <scheme/FourierBoundaryConditionDescriptor.hpp>
#include <scheme/NeumannBoundaryConditionDescriptor.hpp>
#include <scheme/SymmetryBoundaryConditionDescriptor.hpp>
#include <utils/Timer.hpp>

template <size_t Dimension>
HeatDiamondScheme<Dimension>::HeatDiamondScheme(
  std::shared_ptr<const IMesh> i_mesh,
  const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>& bc_descriptor_list,
  const FunctionSymbolId& T_id,
  const FunctionSymbolId& kappa_id,
  const FunctionSymbolId& f_id)
{
  using ConnectivityType = Connectivity<Dimension>;
  using MeshType         = Mesh<ConnectivityType>;
  using MeshDataType     = MeshData<Dimension>;

  constexpr ItemType FaceType = [] {
    if constexpr (Dimension > 1) {
      return ItemType::face;
    } else {
      return ItemType::node;
    }
  }();

  using BoundaryCondition = std::variant<DirichletBoundaryCondition, FourierBoundaryCondition, NeumannBoundaryCondition,
                                         SymmetryBoundaryCondition>;

  using BoundaryConditionList = std::vector<BoundaryCondition>;

  BoundaryConditionList boundary_condition_list;

  std::cout << "number of bc descr = " << bc_descriptor_list.size() << '\n';
  std::shared_ptr mesh = std::dynamic_pointer_cast<const MeshType>(i_mesh);

  for (const auto& bc_descriptor : bc_descriptor_list) {
    bool is_valid_boundary_condition = true;

    switch (bc_descriptor->type()) {
    case IBoundaryConditionDescriptor::Type::symmetry: {
      throw NotImplementedError("NIY");
      break;
    }
    case IBoundaryConditionDescriptor::Type::dirichlet: {
      const DirichletBoundaryConditionDescriptor& dirichlet_bc_descriptor =
        dynamic_cast<const DirichletBoundaryConditionDescriptor&>(*bc_descriptor);
      if constexpr (Dimension > 1) {
        for (size_t i_ref_face_list = 0;
             i_ref_face_list < mesh->connectivity().template numberOfRefItemList<FaceType>(); ++i_ref_face_list) {
          const auto& ref_face_list = mesh->connectivity().template refItemList<FaceType>(i_ref_face_list);
          const RefId& ref          = ref_face_list.refId();
          if (ref == dirichlet_bc_descriptor.boundaryDescriptor()) {
            MeshNodeBoundary<Dimension> mesh_node_boundary{mesh, ref_face_list};

            const FunctionSymbolId g_id = dirichlet_bc_descriptor.rhsSymbolId();
            MeshDataType& mesh_data     = MeshDataManager::instance().getMeshData(*mesh);

            Array<const FaceId> face_list = ref_face_list.list();
            Array<const double> value_list =
              InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::face>(g_id,
                                                                                                        mesh_data.xl(),
                                                                                                        face_list);
            boundary_condition_list.push_back(DirichletBoundaryCondition{face_list, value_list});
          }
        }
      }
      break;
    }
    case IBoundaryConditionDescriptor::Type::fourier: {
      throw NotImplementedError("NIY");
      break;
    }
    case IBoundaryConditionDescriptor::Type::neumann: {
      const NeumannBoundaryConditionDescriptor& neumann_bc_descriptor =
        dynamic_cast<const NeumannBoundaryConditionDescriptor&>(*bc_descriptor);

      for (size_t i_ref_face_list = 0; i_ref_face_list < mesh->connectivity().template numberOfRefItemList<FaceType>();
           ++i_ref_face_list) {
        const auto& ref_face_list = mesh->connectivity().template refItemList<FaceType>(i_ref_face_list);
        const RefId& ref          = ref_face_list.refId();
        if (ref == neumann_bc_descriptor.boundaryDescriptor()) {
          const FunctionSymbolId g_id = neumann_bc_descriptor.rhsSymbolId();

          if constexpr (Dimension > 1) {
            MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*mesh);

            Array<const FaceId> face_list = ref_face_list.list();
            Array<const double> value_list =
              InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::face>(g_id,
                                                                                                        mesh_data.xl(),
                                                                                                        face_list);
            boundary_condition_list.push_back(NeumannBoundaryCondition{face_list, value_list});
          }
        }
      }
      break;
    }
    default: {
      is_valid_boundary_condition = false;
    }
    }
    if (not is_valid_boundary_condition) {
      std::ostringstream error_msg;
      error_msg << *bc_descriptor << " is an invalid boundary condition for heat equation";
      throw NormalError(error_msg.str());
    }
  }

  if constexpr (Dimension > 1) {
    const CellValue<const size_t> cell_dof_number = [&] {
      CellValue<size_t> compute_cell_dof_number{mesh->connectivity()};
      parallel_for(
        mesh->numberOfCells(), PUGS_LAMBDA(CellId cell_id) { compute_cell_dof_number[cell_id] = cell_id; });
      return compute_cell_dof_number;
    }();
    size_t number_of_dof = mesh->numberOfCells();

    const FaceValue<const size_t> face_dof_number = [&] {
      FaceValue<size_t> compute_face_dof_number{mesh->connectivity()};
      compute_face_dof_number.fill(std::numeric_limits<size_t>::max());
      for (const auto& boundary_condition : boundary_condition_list) {
        std::visit(
          [&](auto&& bc) {
            using T = std::decay_t<decltype(bc)>;
            if constexpr ((std::is_same_v<T, NeumannBoundaryCondition>) or
                          (std::is_same_v<T, FourierBoundaryCondition>) or
                          (std::is_same_v<T, SymmetryBoundaryCondition>) or
                          (std::is_same_v<T, DirichletBoundaryCondition>)) {
              const auto& face_list = bc.faceList();

              for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                const FaceId face_id = face_list[i_face];
                if (compute_face_dof_number[face_id] != std::numeric_limits<size_t>::max()) {
                  std::ostringstream os;
                  os << "The face " << face_id << " is used at least twice for boundary conditions";
                  throw NormalError(os.str());
                } else {
                  compute_face_dof_number[face_id] = number_of_dof++;
                }
              }
            }
          },
          boundary_condition);
      }

      return compute_face_dof_number;
    }();

    const FaceValue<const bool> primal_face_is_neumann = [&] {
      FaceValue<bool> face_is_neumann{mesh->connectivity()};
      face_is_neumann.fill(false);
      for (const auto& boundary_condition : boundary_condition_list) {
        std::visit(
          [&](auto&& bc) {
            using T = std::decay_t<decltype(bc)>;
            if constexpr ((std::is_same_v<T, NeumannBoundaryCondition>) or
                          (std::is_same_v<T, FourierBoundaryCondition>) or
                          (std::is_same_v<T, SymmetryBoundaryCondition>)) {
              const auto& face_list = bc.faceList();

              for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                const FaceId face_id     = face_list[i_face];
                face_is_neumann[face_id] = true;
              }
            }
          },
          boundary_condition);
      }

      return face_is_neumann;
    }();

    const auto& primal_face_to_node_matrix = mesh->connectivity().faceToNodeMatrix();
    const auto& face_to_cell_matrix        = mesh->connectivity().faceToCellMatrix();
    NodeValue<bool> primal_node_is_on_boundary(mesh->connectivity());
    if (parallel::size() > 1) {
      throw NotImplementedError("Calculation of node_is_on_boundary is incorrect");
    }

    primal_node_is_on_boundary.fill(false);
    for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
      if (face_to_cell_matrix[face_id].size() == 1) {
        for (size_t i_node = 0; i_node < primal_face_to_node_matrix[face_id].size(); ++i_node) {
          NodeId node_id                      = primal_face_to_node_matrix[face_id][i_node];
          primal_node_is_on_boundary[node_id] = true;
        }
      }
    }

    FaceValue<bool> primal_face_is_on_boundary(mesh->connectivity());
    if (parallel::size() > 1) {
      throw NotImplementedError("Calculation of face_is_on_boundary is incorrect");
    }

    primal_face_is_on_boundary.fill(false);
    for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
      if (face_to_cell_matrix[face_id].size() == 1) {
        primal_face_is_on_boundary[face_id] = true;
      }
    }

    FaceValue<bool> primal_face_is_dirichlet(mesh->connectivity());
    if (parallel::size() > 1) {
      throw NotImplementedError("Calculation of face_is_neumann is incorrect");
    }

    primal_face_is_dirichlet.fill(false);
    for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
      primal_face_is_dirichlet[face_id] = (primal_face_is_on_boundary[face_id] && (!primal_face_is_neumann[face_id]));
    }

    MeshDataType& mesh_data = MeshDataManager::instance().getMeshData(*mesh);

    CellValue<double> Tj =
      InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(T_id, mesh_data.xj());
    FaceValue<double> Tl =
      InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::face>(T_id, mesh_data.xl());
    NodeValue<double> Tr(mesh->connectivity());
    const NodeValue<const TinyVector<Dimension>>& xr = mesh->xr();

    const FaceValue<const TinyVector<Dimension>>& xl = mesh_data.xl();
    const CellValue<const TinyVector<Dimension>>& xj = mesh_data.xj();
    const auto& node_to_cell_matrix                  = mesh->connectivity().nodeToCellMatrix();
    const auto& node_to_face_matrix                  = mesh->connectivity().nodeToFaceMatrix();
    CellValuePerNode<double> w_rj{mesh->connectivity()};
    FaceValuePerNode<double> w_rl{mesh->connectivity()};

    for (size_t i = 0; i < w_rl.numberOfValues(); ++i) {
      w_rl[i] = std::numeric_limits<double>::signaling_NaN();
    }

    for (NodeId i_node = 0; i_node < mesh->numberOfNodes(); ++i_node) {
      Vector<double> b{Dimension + 1};
      b[0] = 1;
      for (size_t i = 1; i < Dimension + 1; i++) {
        b[i] = xr[i_node][i - 1];
      }
      const auto& node_to_cell = node_to_cell_matrix[i_node];

      if (not primal_node_is_on_boundary[i_node]) {
        LocalRectangularMatrix<double> A{Dimension + 1, node_to_cell.size()};
        for (size_t j = 0; j < node_to_cell.size(); j++) {
          A(0, j) = 1;
        }
        for (size_t i = 1; i < Dimension + 1; i++) {
          for (size_t j = 0; j < node_to_cell.size(); j++) {
            const CellId J = node_to_cell[j];
            A(i, j)        = xj[J][i - 1];
          }
        }
        Vector<double> x{node_to_cell.size()};
        x = 0;

        LeastSquareSolver ls_solver;
        ls_solver.solveLocalSystem(A, x, b);

        Tr[i_node] = 0;
        for (size_t j = 0; j < node_to_cell.size(); j++) {
          Tr[i_node] += x[j] * Tj[node_to_cell[j]];
          w_rj(i_node, j) = x[j];
        }
      } else {
        int nb_face_used = 0;
        for (size_t i_face = 0; i_face < node_to_face_matrix[i_node].size(); ++i_face) {
          FaceId face_id = node_to_face_matrix[i_node][i_face];
          if (primal_face_is_on_boundary[face_id]) {
            nb_face_used++;
          }
        }
        LocalRectangularMatrix<double> A{Dimension + 1, node_to_cell.size() + nb_face_used};
        for (size_t j = 0; j < node_to_cell.size() + nb_face_used; j++) {
          A(0, j) = 1;
        }
        for (size_t i = 1; i < Dimension + 1; i++) {
          for (size_t j = 0; j < node_to_cell.size(); j++) {
            const CellId J = node_to_cell[j];
            A(i, j)        = xj[J][i - 1];
          }
        }
        for (size_t i = 1; i < Dimension + 1; i++) {
          int cpt_face = 0;
          for (size_t i_face = 0; i_face < node_to_face_matrix[i_node].size(); ++i_face) {
            FaceId face_id = node_to_face_matrix[i_node][i_face];
            if (primal_face_is_on_boundary[face_id]) {
              A(i, node_to_cell.size() + cpt_face) = xl[face_id][i - 1];
              cpt_face++;
            }
          }
        }

        Vector<double> x{node_to_cell.size() + nb_face_used};
        x = 0;

        LeastSquareSolver ls_solver;
        ls_solver.solveLocalSystem(A, x, b);

        Tr[i_node] = 0;
        for (size_t j = 0; j < node_to_cell.size(); j++) {
          Tr[i_node] += x[j] * Tj[node_to_cell[j]];
          w_rj(i_node, j) = x[j];
        }
        int cpt_face = node_to_cell.size();
        for (size_t i_face = 0; i_face < node_to_face_matrix[i_node].size(); ++i_face) {
          FaceId face_id = node_to_face_matrix[i_node][i_face];
          if (primal_face_is_on_boundary[face_id]) {
            w_rl(i_node, i_face) = x[cpt_face++];
            Tr[i_node] += w_rl(i_node, i_face) * Tl[face_id];
          }
        }
      }
    }

    {
      VTKWriter vtk_writer("T_" + std::to_string(Dimension), 0.01);

      vtk_writer.write(mesh,
                       {NamedItemValue{"Tr", Tr}, NamedItemValue{"temperature", Tj},
                        NamedItemValue{"coords", mesh->xr()}, NamedItemValue{"xj", mesh_data.xj()},
                        NamedItemValue{"cell_owner", mesh->connectivity().cellOwner()},
                        NamedItemValue{"node_owner", mesh->connectivity().nodeOwner()}},
                       0, true);   // forces last output
    }

    {
      std::shared_ptr diamond_mesh = DiamondDualMeshManager::instance().getDiamondDualMesh(mesh);

      MeshDataType& diamond_mesh_data = MeshDataManager::instance().getMeshData(*diamond_mesh);

      std::shared_ptr mapper =
        DiamondDualConnectivityManager::instance().getConnectivityToDiamondDualConnectivityDataMapper(
          mesh->connectivity());

      NodeValue<double> Trd{diamond_mesh->connectivity()};

      mapper->toDualNode(Tr, Tj, Trd);

      CellValue<double> kappaj =
        InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(kappa_id,
                                                                                                  mesh_data.xj());

      CellValue<double> dual_kappaj =
        InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(kappa_id,
                                                                                                  diamond_mesh_data
                                                                                                    .xj());

      VTKWriter vtk_writer("D_" + std::to_string(Dimension), 0.01);

      vtk_writer.write(diamond_mesh,
                       {NamedItemValue{"kappaj", dual_kappaj}, NamedItemValue{"coords", diamond_mesh->xr()},
                        NamedItemValue{"Vj", diamond_mesh_data.Vj()}, NamedItemValue{"xj", diamond_mesh_data.xj()}},
                       0, true);   // forces last output

      const CellValue<const double> dual_Vj = diamond_mesh_data.Vj();

      const FaceValue<const double> mes_l = [&] {
        if constexpr (Dimension == 1) {
          FaceValue<double> compute_mes_l{mesh->connectivity()};
          compute_mes_l.fill(1);
          return compute_mes_l;
        } else {
          return mesh_data.ll();
        }
      }();

      const CellValue<const double> dual_mes_l_j = [=] {
        CellValue<double> compute_mes_j{diamond_mesh->connectivity()};
        mapper->toDualCell(mes_l, compute_mes_j);

        return compute_mes_j;
      }();

      FaceValue<const CellId> face_dual_cell_id = [=]() {
        FaceValue<CellId> computed_face_dual_cell_id{mesh->connectivity()};
        CellValue<CellId> dual_cell_id{diamond_mesh->connectivity()};
        parallel_for(
          diamond_mesh->numberOfCells(), PUGS_LAMBDA(CellId cell_id) { dual_cell_id[cell_id] = cell_id; });

        mapper->fromDualCell(dual_cell_id, computed_face_dual_cell_id);

        return computed_face_dual_cell_id;
      }();

      NodeValue<const NodeId> dual_node_primal_node_id = [=]() {
        CellValue<NodeId> cell_ignored_id{mesh->connectivity()};
        cell_ignored_id.fill(NodeId{std::numeric_limits<unsigned int>::max()});

        NodeValue<NodeId> node_primal_id{mesh->connectivity()};

        parallel_for(
          mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) { node_primal_id[node_id] = node_id; });

        NodeValue<NodeId> computed_dual_node_primal_node_id{diamond_mesh->connectivity()};

        mapper->toDualNode(node_primal_id, cell_ignored_id, computed_dual_node_primal_node_id);

        return computed_dual_node_primal_node_id;
      }();

      CellValue<NodeId> primal_cell_dual_node_id = [=]() {
        CellValue<NodeId> cell_id{mesh->connectivity()};
        NodeValue<NodeId> node_ignored_id{mesh->connectivity()};
        node_ignored_id.fill(NodeId{std::numeric_limits<unsigned int>::max()});

        NodeValue<NodeId> dual_node_id{diamond_mesh->connectivity()};

        parallel_for(
          diamond_mesh->numberOfNodes(), PUGS_LAMBDA(NodeId node_id) { dual_node_id[node_id] = node_id; });

        CellValue<NodeId> computed_primal_cell_dual_node_id{mesh->connectivity()};

        mapper->fromDualNode(dual_node_id, node_ignored_id, cell_id);

        return cell_id;
      }();
      Timer my_timer;
      const auto& dual_Cjr                     = diamond_mesh_data.Cjr();
      FaceValue<TinyVector<Dimension>> dualClj = [&] {
        FaceValue<TinyVector<Dimension>> computedClj{mesh->connectivity()};
        const auto& dual_node_to_cell_matrix = diamond_mesh->connectivity().nodeToCellMatrix();
        const auto& dual_cell_to_node_matrix = diamond_mesh->connectivity().cellToNodeMatrix();
        parallel_for(
          mesh->numberOfFaces(), PUGS_LAMBDA(FaceId face_id) {
            const auto& primal_face_to_cell = face_to_cell_matrix[face_id];
            for (size_t i = 0; i < primal_face_to_cell.size(); i++) {
              CellId cell_id            = primal_face_to_cell[i];
              const NodeId dual_node_id = primal_cell_dual_node_id[cell_id];
              for (size_t i_dual_cell = 0; i_dual_cell < dual_node_to_cell_matrix[dual_node_id].size(); i_dual_cell++) {
                const CellId dual_cell_id = dual_node_to_cell_matrix[dual_node_id][i_dual_cell];
                if (face_dual_cell_id[face_id] == dual_cell_id) {
                  for (size_t i_dual_node = 0; i_dual_node < dual_cell_to_node_matrix[dual_cell_id].size();
                       i_dual_node++) {
                    const NodeId final_dual_node_id = dual_cell_to_node_matrix[dual_cell_id][i_dual_node];
                    if (final_dual_node_id == dual_node_id) {
                      computedClj[face_id] = dual_Cjr(dual_cell_id, i_dual_node);
                    }
                  }
                }
              }
            }
          });
        return computedClj;
      }();

      FaceValue<TinyVector<Dimension>> nlj = [&] {
        FaceValue<TinyVector<Dimension>> computedNlj{mesh->connectivity()};
        parallel_for(
          mesh->numberOfFaces(),
          PUGS_LAMBDA(FaceId face_id) { computedNlj[face_id] = 1. / l2Norm(dualClj[face_id]) * dualClj[face_id]; });
        return computedNlj;
      }();

      FaceValue<const double> alpha_l = [&] {
        CellValue<double> alpha_j{diamond_mesh->connectivity()};

        parallel_for(
          diamond_mesh->numberOfCells(), PUGS_LAMBDA(CellId diamond_cell_id) {
            alpha_j[diamond_cell_id] = dual_kappaj[diamond_cell_id] / dual_Vj[diamond_cell_id];
          });

        FaceValue<double> computed_alpha_l{mesh->connectivity()};
        mapper->fromDualCell(alpha_j, computed_alpha_l);
        VTKWriter vtk_writer("DD_" + std::to_string(Dimension), 0.01);

        vtk_writer.write(diamond_mesh,
                         {NamedItemValue{"alphaj", alpha_j}, NamedItemValue{"xj", diamond_mesh_data.xj()},
                          NamedItemValue{"Vl", diamond_mesh_data.Vj()}, NamedItemValue{"|l|", dual_mes_l_j}},
                         0,
                         true);   // forces last output

        return computed_alpha_l;
      }();

      SparseMatrixDescriptor S{number_of_dof};
      for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
        const auto& primal_face_to_cell = face_to_cell_matrix[face_id];
        // const double beta_l             = 1. / Dimension * alpha_l[face_id] * mes_l[face_id];
        const double beta_l = l2Norm(dualClj[face_id]) * alpha_l[face_id] * mes_l[face_id];
        for (size_t i_cell = 0; i_cell < primal_face_to_cell.size(); ++i_cell) {
          const CellId cell_id1 = primal_face_to_cell[i_cell];
          for (size_t j_cell = 0; j_cell < primal_face_to_cell.size(); ++j_cell) {
            const CellId cell_id2 = primal_face_to_cell[j_cell];
            if (i_cell == j_cell) {
              S(cell_dof_number[cell_id1], cell_dof_number[cell_id2]) += beta_l;
              if (primal_face_is_neumann[face_id]) {
                S(face_dof_number[face_id], cell_dof_number[cell_id2]) -= beta_l;
              }
            } else {
              S(cell_dof_number[cell_id1], cell_dof_number[cell_id2]) -= beta_l;
            }
          }
        }
      }

      const auto& dual_cell_to_node_matrix = diamond_mesh->connectivity().cellToNodeMatrix();

      const auto& primal_node_to_cell_matrix = mesh->connectivity().nodeToCellMatrix();
      for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
        const double alpha_face_id = mes_l[face_id] * alpha_l[face_id];

        for (size_t i_face_cell = 0; i_face_cell < face_to_cell_matrix[face_id].size(); ++i_face_cell) {
          CellId i_id                            = face_to_cell_matrix[face_id][i_face_cell];
          const bool is_face_reversed_for_cell_i = ((dualClj[face_id], xl[face_id] - xj[i_id]) < 0);

          for (size_t i_node = 0; i_node < primal_face_to_node_matrix[face_id].size(); ++i_node) {
            NodeId node_id = primal_face_to_node_matrix[face_id][i_node];

            const TinyVector<Dimension> nil = [&] {
              if (is_face_reversed_for_cell_i) {
                return -nlj[face_id];
              } else {
                return nlj[face_id];
              }
            }();

            CellId dual_cell_id = face_dual_cell_id[face_id];

            for (size_t i_dual_node = 0; i_dual_node < dual_cell_to_node_matrix[dual_cell_id].size(); ++i_dual_node) {
              const NodeId dual_node_id = dual_cell_to_node_matrix[dual_cell_id][i_dual_node];
              if (dual_node_primal_node_id[dual_node_id] == node_id) {
                const TinyVector<Dimension> Clr = dual_Cjr(dual_cell_id, i_dual_node);

                const double a_ir = alpha_face_id * (nil, Clr);

                for (size_t j_cell = 0; j_cell < primal_node_to_cell_matrix[node_id].size(); ++j_cell) {
                  CellId j_id = primal_node_to_cell_matrix[node_id][j_cell];
                  S(cell_dof_number[i_id], cell_dof_number[j_id]) -= w_rj(node_id, j_cell) * a_ir;
                  if (primal_face_is_neumann[face_id]) {
                    S(face_dof_number[face_id], cell_dof_number[j_id]) += w_rj(node_id, j_cell) * a_ir;
                  }
                }
                if (primal_node_is_on_boundary[node_id]) {
                  for (size_t l_face = 0; l_face < node_to_face_matrix[node_id].size(); ++l_face) {
                    FaceId l_id = node_to_face_matrix[node_id][l_face];
                    if (primal_face_is_on_boundary[l_id]) {
                      S(cell_dof_number[i_id], face_dof_number[l_id]) -= w_rl(node_id, l_face) * a_ir;
                      if (primal_face_is_neumann[face_id]) {
                        S(face_dof_number[face_id], face_dof_number[l_id]) += w_rl(node_id, l_face) * a_ir;
                      }
                    }
                  }
                }
              }
            }
          }
        }
      }
      for (FaceId face_id = 0; face_id < mesh->numberOfFaces(); ++face_id) {
        if (primal_face_is_dirichlet[face_id]) {
          S(face_dof_number[face_id], face_dof_number[face_id]) += 1;
        }
      }

      CellValue<double> fj =
        InterpolateItemValue<double(TinyVector<Dimension>)>::template interpolate<ItemType::cell>(f_id, mesh_data.xj());

      const CellValue<const double> primal_Vj = mesh_data.Vj();
      CRSMatrix A{S};
      Vector<double> b{number_of_dof};

      for (CellId cell_id = 0; cell_id < mesh->numberOfCells(); ++cell_id) {
        b[cell_dof_number[cell_id]] = fj[cell_id] * primal_Vj[cell_id];
      }
      // Dirichlet on b^L_D
      {
        for (const auto& boundary_condition : boundary_condition_list) {
          std::visit(
            [&](auto&& bc) {
              using T = std::decay_t<decltype(bc)>;
              if constexpr (std::is_same_v<T, DirichletBoundaryCondition>) {
                const auto& face_list  = bc.faceList();
                const auto& value_list = bc.valueList();
                for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                  const FaceId face_id = face_list[i_face];
                  b[face_dof_number[face_id]] += value_list[i_face];   // sign
                }
              }
            },
            boundary_condition);
        }
      }
      // EL b^L
      for (const auto& boundary_condition : boundary_condition_list) {
        std::visit(
          [&](auto&& bc) {
            using T = std::decay_t<decltype(bc)>;
            if constexpr ((std::is_same_v<T, NeumannBoundaryCondition>) or
                          (std::is_same_v<T, FourierBoundaryCondition>)) {
              const auto& face_list  = bc.faceList();
              const auto& value_list = bc.valueList();
              for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                FaceId face_id = face_list[i_face];
                Assert(face_to_cell_matrix[face_id].size() == 1);
                b[face_dof_number[face_id]] += mes_l[face_id] * value_list[i_face];   // sign
              }
            }
          },
          boundary_condition);
      }

      Vector<double> T{number_of_dof};
      T = 1;

      LinearSolver solver;
      solver.solveLocalSystem(A, T, b);

      CellValue<double> Temperature{mesh->connectivity()};
      FaceValue<double> Temperature_face{mesh->connectivity()};
      parallel_for(
        mesh->numberOfCells(), PUGS_LAMBDA(CellId cell_id) { Temperature[cell_id] = T[cell_dof_number[cell_id]]; });
      parallel_for(
        mesh->numberOfFaces(), PUGS_LAMBDA(FaceId face_id) {
          if (primal_face_is_neumann[face_id]) {
            Temperature_face[face_id] = T[face_dof_number[face_id]];
          } else {
            Temperature_face[face_id] = Tl[face_id];
          }
        });
      Vector<double> error{mesh->numberOfCells()};
      CellValue<double> cell_error{mesh->connectivity()};
      Vector<double> face_error{mesh->numberOfFaces()};
      double error_max = 0.;
      size_t cell_max  = 0;
      parallel_for(
        mesh->numberOfCells(), PUGS_LAMBDA(CellId cell_id) {
          error[cell_id]      = (Temperature[cell_id] - Tj[cell_id]) * sqrt(primal_Vj[cell_id]);
          cell_error[cell_id] = (Temperature[cell_id] - Tj[cell_id]);
        });
      parallel_for(
        mesh->numberOfFaces(), PUGS_LAMBDA(FaceId face_id) {
          if (primal_face_is_on_boundary[face_id]) {
            face_error[face_id] = (Temperature_face[face_id] - Tl[face_id]) * sqrt(mes_l[face_id]);
          } else {
            face_error[face_id] = 0;
          }
        });
      for (CellId cell_id = 0; cell_id < mesh->numberOfCells(); cell_id++) {
        if (error_max < std::abs(cell_error[cell_id])) {
          error_max = std::abs(cell_error[cell_id]);
          cell_max  = cell_id;
        }
      }

      std::cout << " ||Error||_max (cell)= " << error_max << " on cell " << cell_max << "\n";
      std::cout << "||Error||_2 (cell)= " << std::sqrt((error, error)) << "\n";
      std::cout << "||Error||_2 (face)= " << std::sqrt((face_error, face_error)) << "\n";
      std::cout << "||Error||_2 (total)= " << std::sqrt((error, error)) + std::sqrt((face_error, face_error)) << "\n";

      {
        VTKWriter vtk_writer("Temperature_" + std::to_string(Dimension), 0.01);

        vtk_writer.write(mesh,
                         {NamedItemValue{"T", Temperature}, NamedItemValue{"Vj", primal_Vj},
                          NamedItemValue{"Texact", Tj}, NamedItemValue{"error", cell_error}},
                         0,
                         true);   // forces last output
      }
    }
  } else {
    throw NotImplementedError("not done in 1d");
  }
}

template <size_t Dimension>
class HeatDiamondScheme<Dimension>::DirichletBoundaryCondition
{
 private:
  const Array<const double> m_value_list;
  const Array<const FaceId> m_face_list;

 public:
  const Array<const FaceId>&
  faceList() const
  {
    return m_face_list;
  }

  const Array<const double>&
  valueList() const
  {
    return m_value_list;
  }

  DirichletBoundaryCondition(const Array<const FaceId>& face_list, const Array<const double>& value_list)
    : m_value_list{value_list}, m_face_list{face_list}
  {
    Assert(m_value_list.size() == m_face_list.size());
  }

  ~DirichletBoundaryCondition() = default;
};

template <size_t Dimension>
class HeatDiamondScheme<Dimension>::NeumannBoundaryCondition
{
 private:
  const Array<const double> m_value_list;
  const Array<const FaceId> m_face_list;

 public:
  const Array<const FaceId>&
  faceList() const
  {
    return m_face_list;
  }

  const Array<const double>&
  valueList() const
  {
    return m_value_list;
  }

  NeumannBoundaryCondition(const Array<const FaceId>& face_list, const Array<const double>& value_list)
    : m_value_list{value_list}, m_face_list{face_list}
  {
    Assert(m_value_list.size() == m_face_list.size());
  }

  ~NeumannBoundaryCondition() = default;
};

template <size_t Dimension>
class HeatDiamondScheme<Dimension>::FourierBoundaryCondition
{
 private:
  const Array<const double> m_coef_list;
  const Array<const double> m_value_list;
  const Array<const FaceId> m_face_list;

 public:
  const Array<const FaceId>&
  faceList() const
  {
    return m_face_list;
  }

  const Array<const double>&
  valueList() const
  {
    return m_value_list;
  }

  const Array<const double>&
  coefList() const
  {
    return m_coef_list;
  }

 public:
  FourierBoundaryCondition(const Array<const FaceId>& face_list,
                           const Array<const double>& coef_list,
                           const Array<const double>& value_list)
    : m_coef_list{coef_list}, m_value_list{value_list}, m_face_list{face_list}
  {
    Assert(m_coef_list.size() == m_face_list.size());
    Assert(m_value_list.size() == m_face_list.size());
  }

  ~FourierBoundaryCondition() = default;
};

template <size_t Dimension>
class HeatDiamondScheme<Dimension>::SymmetryBoundaryCondition
{
 private:
  const Array<const FaceId> m_face_list;

 public:
  const Array<const FaceId>&
  faceList() const
  {
    return m_face_list;
  }

 public:
  SymmetryBoundaryCondition(const Array<const FaceId>& face_list) : m_face_list{face_list} {}

  ~SymmetryBoundaryCondition() = default;
};

template HeatDiamondScheme<1>::HeatDiamondScheme(
  std::shared_ptr<const IMesh>,
  const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>&,
  const FunctionSymbolId&,
  const FunctionSymbolId&,
  const FunctionSymbolId&);

template HeatDiamondScheme<2>::HeatDiamondScheme(
  std::shared_ptr<const IMesh>,
  const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>&,
  const FunctionSymbolId&,
  const FunctionSymbolId&,
  const FunctionSymbolId&);

template HeatDiamondScheme<3>::HeatDiamondScheme(
  std::shared_ptr<const IMesh>,
  const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>&,
  const FunctionSymbolId&,
  const FunctionSymbolId&,
  const FunctionSymbolId&);