DataOperators.cpp

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/** file DataOperators.cpp
 
  \brief implementation of Data Operators for Forces and Sources
 
*/
 
/* This file is part of MoFEM.
 * MoFEM is free software: you can redistribute it and/or modify it under
 * the terms of the GNU Lesser General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or (at your
 * option) any later version.
 *
 * MoFEM is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 * License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with MoFEM. If not, see <http://www.gnu.org/licenses/>. */
 
#ifdef __cplusplus
extern "C" {
#endif
#include <cblas.h>
#include <lapack_wrap.h>
#include <gm_rule.h>
#ifdef __cplusplus
}
#endif
 
namespace MoFEM {
 
DataOperator::DataOperator(const bool symm)
    :
 
      sYmm(symm),
 
      doEntities{true, true, true, true, true, true,
                 true, true, true, true, true, true},
 
      doVertices(doEntities[MBVERTEX]), doEdges(doEntities[MBEDGE]),
      doQuads(doEntities[MBQUAD]), doTris(doEntities[MBTRI]),
      doTets(doEntities[MBTET]), doPrisms(doEntities[MBPRISM]) {
 
  /// This not yet implemented, switch off.
  doEntities[MBPOLYGON] = false;
  doEntities[MBPYRAMID] = false;
  doEntities[MBKNIFE] = false;
  doEntities[MBHEX] = false;
  doEntities[MBPOLYHEDRON] = false;
}
 
template <bool Symm>
MoFEMErrorCode DataOperator::opLhs(DataForcesAndSourcesCore &row_data,
                                   DataForcesAndSourcesCore &col_data) {
  MoFEMFunctionBeginHot;
 
  auto do_col_entity =
      [&](boost::ptr_vector<DataForcesAndSourcesCore::EntData> &row_ent_data,
          const int ss, const EntityType row_type, const EntityType low_type,
          const EntityType hi_type) {
        MoFEMFunctionBegin;
        for (EntityType col_type = low_type; col_type != hi_type; ++col_type) {
          auto &col_ent_data = col_data.dataOnEntities[col_type];
          for (size_t SS = 0; SS != col_ent_data.size(); SS++) {
            if (col_ent_data[SS].getFieldData().size())
              CHKERR doWork(ss, SS, row_type, col_type, row_ent_data[ss],
                            col_ent_data[SS]);
          }
        }
        MoFEMFunctionReturn(0);
      };
 
  auto do_row_entity = [&](const EntityType type) {
    MoFEMFunctionBegin;
    auto &row_ent_data = row_data.dataOnEntities[type];
    for (size_t ss = 0; ss != row_ent_data.size(); ++ss) {
      size_t SS = 0;
      if (Symm)
        SS = ss;
      for (; SS < col_data.dataOnEntities[type].size(); SS++) {
        CHKERR doWork(ss, SS, type, type, row_ent_data[ss],
                      col_data.dataOnEntities[type][SS]);
      }
      if (!Symm)
        CHKERR do_col_entity(row_ent_data, ss, type, MBVERTEX, type);
      CHKERR do_col_entity(row_ent_data, ss, type,
                           static_cast<EntityType>(type + 1), MBMAXTYPE);
    }
    MoFEMFunctionReturn(0);
  };
 
  for (EntityType row_type = MBVERTEX; row_type != MBENTITYSET; ++row_type) {
    if (doEntities[row_type]) {
      CHKERR do_row_entity(row_type);
    }
  }
 
  if (doEntities[MBENTITYSET]) {
    for (unsigned int mm = 0; mm != row_data.dataOnEntities[MBENTITYSET].size();
         ++mm) {
      if (!row_data.dataOnEntities[MBENTITYSET][mm].getFieldData().empty()) {
        CHKERR do_row_entity(MBENTITYSET);
      }
    }
  }
 
  MoFEMFunctionReturnHot(0);
}
 
MoFEMErrorCode DataOperator::opLhs(DataForcesAndSourcesCore &row_data,
                                   DataForcesAndSourcesCore &col_data) {
  if (getSymm())
    return opLhs<true>(row_data, col_data);
  else
    return opLhs<false>(row_data, col_data);
}
 
template <bool ErrorIfNoBase>
MoFEMErrorCode
DataOperator::opRhs(DataForcesAndSourcesCore &data,
                    const std::array<bool, MBMAXTYPE> &do_entities) {
  MoFEMFunctionBegin;
 
  auto do_entity = [&](auto type) {
    MoFEMFunctionBegin;
 
    auto &ent_data = data.dataOnEntities[type];
    const size_t size = ent_data.size();
    for (size_t ss = 0; ss != size; ++ss) {
 
      auto &side_data = ent_data[ss];
 
      if (ErrorIfNoBase) {
        if (side_data.getFieldData().size() &&
            (side_data.getBase() == NOBASE ||
             side_data.getBase() == LASTBASE)) {
          for (VectorDofs::iterator it = side_data.getFieldDofs().begin();
               it != side_data.getFieldDofs().end(); it++)
            if ((*it) && (*it)->getActive())
              SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "No base on");
        }
      }
 
      CHKERR doWork(ss, type, side_data);
    }
 
    MoFEMFunctionReturn(0);
  };
 
  for (EntityType row_type = MBVERTEX; row_type != MBENTITYSET; ++row_type) {
    if (do_entities[row_type]) {
      CHKERR do_entity(row_type);
    }
  }
 
  if (do_entities[MBENTITYSET]) {
    // This is odd behaviour, diffrent than for other entities. Should be
    // changed that behaviour is consistent,
    for (unsigned int mm = 0; mm != data.dataOnEntities[MBENTITYSET].size();
         ++mm) {
      if (!data.dataOnEntities[MBENTITYSET][mm].getFieldData().empty()) {
        CHKERR doWork(mm, MBENTITYSET, data.dataOnEntities[MBENTITYSET][mm]);
      }
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode DataOperator::opRhs(DataForcesAndSourcesCore &data,
                                   const bool error_if_no_base) {
  if (error_if_no_base)
    return opRhs<true>(data, doEntities);
  else
    return opRhs<false>(data, doEntities);
}
 
template <>
MoFEMErrorCode invertTensor3by3<3, double, ublas::row_major, DoubleAllocator>(
    MatrixDouble &jac_data, VectorDouble &det_data,
    MatrixDouble &inv_jac_data) {
  MoFEMFunctionBegin;
  auto A = getFTensor2FromMat<3, 3>(jac_data);
  int nb_gauss_pts = jac_data.size2();
  det_data.resize(nb_gauss_pts, false);
  inv_jac_data.resize(3, nb_gauss_pts, false);
  auto det = getFTensor0FromVec(det_data);
  auto I = getFTensor2FromMat<3, 3>(inv_jac_data);
  for (int gg = 0; gg != nb_gauss_pts; ++gg) {
    CHKERR determinantTensor3by3(A, det);
    CHKERR invertTensor3by3(A, det, I);
    ++A;
    ++det;
    ++I;
  }
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpSetInvJacH1::doWork(int side, EntityType type,
                                     DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  auto transform_base = [&](MatrixDouble &diff_n,
                            const bool diff_at_gauss_ptr) {
    MoFEMFunctionBeginHot;
 
    if (!diff_n.size1())
      MoFEMFunctionReturnHot(0);
    if (!diff_n.size2())
      MoFEMFunctionReturnHot(0);
 
    const int nb_base_functions =
        (diff_at_gauss_ptr || type != MBVERTEX) ? diff_n.size2() / 3 : 4;
    const int nb_gauss_pts =
        (diff_at_gauss_ptr || type != MBVERTEX) ? diff_n.size1() : 1;
    diffNinvJac.resize(diff_n.size1(), diff_n.size2(), false);
 
    double *t_diff_n_ptr = &*diff_n.data().begin();
    FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_diff_n(
        t_diff_n_ptr, &t_diff_n_ptr[1], &t_diff_n_ptr[2]);
    double *t_inv_n_ptr = &*diffNinvJac.data().begin();
    FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_inv_diff_n(
        t_inv_n_ptr, &t_inv_n_ptr[1], &t_inv_n_ptr[2]);
 
    switch (type) {
 
    case MBVERTEX:
    case MBEDGE:
    case MBTRI:
    case MBTET: {
      for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
        for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
          t_inv_diff_n(i) = t_diff_n(j) * tInvJac(j, i);
          ++t_diff_n;
          ++t_inv_diff_n;
        }
      }
 
    } break;
    default:
      SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED, "not implemented");
    }
 
    diff_n.data().swap(diffNinvJac.data());
 
    MoFEMFunctionReturnHot(0);
  };
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
    CHKERR transform_base(data.getDiffN(base), false);
  }
 
  switch (type) {
  case MBVERTEX:
    for (auto &m : data.getBBDiffNMap())
      CHKERR transform_base(*(m.second), true);
    break;
  default:
    for (auto &ptr : data.getBBDiffNByOrderArray())
      if (ptr)
        CHKERR transform_base(*ptr, true);
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode
OpSetInvJacHdivAndHcurl::doWork(int side, EntityType type,
                                DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBEDGE && type != MBTRI && type != MBTET)
    MoFEMFunctionReturnHot(0);
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
 
    const unsigned int nb_gauss_pts = data.getDiffN(base).size1();
    const unsigned int nb_base_functions = data.getDiffN(base).size2() / 9;
    if (!nb_base_functions)
      continue;
 
    diffHdivInvJac.resize(nb_gauss_pts, data.getDiffN(base).size2(), false);
 
    auto t_diff_n = data.getFTensor2DiffN<3, 3>(base);
    double *t_inv_diff_n_ptr = &*diffHdivInvJac.data().begin();
    FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3> t_inv_diff_n(
        t_inv_diff_n_ptr, &t_inv_diff_n_ptr[HVEC0_1],
        &t_inv_diff_n_ptr[HVEC0_2],
 
        &t_inv_diff_n_ptr[HVEC1_0], &t_inv_diff_n_ptr[HVEC1_1],
        &t_inv_diff_n_ptr[HVEC1_2],
 
        &t_inv_diff_n_ptr[HVEC2_0], &t_inv_diff_n_ptr[HVEC2_1],
        &t_inv_diff_n_ptr[HVEC2_2]);
 
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
        t_inv_diff_n(k, i) = t_diff_n(k, j) * tInvJac(j, i);
        ++t_diff_n;
        ++t_inv_diff_n;
      }
    }
 
    data.getDiffN(base).data().swap(diffHdivInvJac.data());
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpSetContravariantPiolaTransform::doWork(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBTRI && type != MBTET)
    MoFEMFunctionReturnHot(0);
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
 
    const unsigned int nb_base_functions = data.getN(base).size2() / 3;
    if (!nb_base_functions)
      continue;
 
    const double c = 1. / 6.;
    const unsigned int nb_gauss_pts = data.getN(base).size1();
 
    double const a = c / vOlume;
 
    piolaN.resize(nb_gauss_pts, data.getN(base).size2(), false);
    if (data.getN(base).size2() > 0) {
      auto t_n = data.getFTensor1N<3>(base);
      double *t_transformed_n_ptr = &*piolaN.data().begin();
      FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_transformed_n(
          t_transformed_n_ptr, // HVEC0
          &t_transformed_n_ptr[HVEC1], &t_transformed_n_ptr[HVEC2]);
      for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
        for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
          t_transformed_n(i) = a * tJac(i, k) * t_n(k);
          ++t_n;
          ++t_transformed_n;
        }
      }
      data.getN(base).data().swap(piolaN.data());
    }
 
    piolaDiffN.resize(nb_gauss_pts, data.getDiffN(base).size2(), false);
    if (data.getDiffN(base).size2() > 0) {
      auto t_diff_n = data.getFTensor2DiffN<3, 3>(base);
      double *t_transformed_diff_n_ptr = &*piolaDiffN.data().begin();
      FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3>
          t_transformed_diff_n(t_transformed_diff_n_ptr,
                               &t_transformed_diff_n_ptr[HVEC0_1],
                               &t_transformed_diff_n_ptr[HVEC0_2],
                               &t_transformed_diff_n_ptr[HVEC1_0],
                               &t_transformed_diff_n_ptr[HVEC1_1],
                               &t_transformed_diff_n_ptr[HVEC1_2],
                               &t_transformed_diff_n_ptr[HVEC2_0],
                               &t_transformed_diff_n_ptr[HVEC2_1],
                               &t_transformed_diff_n_ptr[HVEC2_2]);
      for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
        for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
          t_transformed_diff_n(i, k) = a * tJac(i, j) * t_diff_n(j, k);
          ++t_diff_n;
          ++t_transformed_diff_n;
        }
      }
      data.getDiffN(base).data().swap(piolaDiffN.data());
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode
OpSetCovariantPiolaTransform::doWork(int side, EntityType type,
                                     DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBEDGE && type != MBTRI && type != MBTET)
    MoFEMFunctionReturnHot(0);
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
 
    const unsigned int nb_base_functions = data.getN(base).size2() / 3;
    if (!nb_base_functions)
      continue;
 
    const unsigned int nb_gauss_pts = data.getN(base).size1();
    piolaN.resize(nb_gauss_pts, data.getN(base).size2(), false);
    piolaDiffN.resize(nb_gauss_pts, data.getDiffN(base).size2(), false);
 
    auto t_n = data.getFTensor1N<3>(base);
    double *t_transformed_n_ptr = &*piolaN.data().begin();
    FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_transformed_n(
        t_transformed_n_ptr, &t_transformed_n_ptr[HVEC1],
        &t_transformed_n_ptr[HVEC2]);
    auto t_diff_n = data.getFTensor2DiffN<3, 3>(base);
    double *t_transformed_diff_n_ptr = &*piolaDiffN.data().begin();
    FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3> t_transformed_diff_n(
        t_transformed_diff_n_ptr, &t_transformed_diff_n_ptr[HVEC0_1],
        &t_transformed_diff_n_ptr[HVEC0_2], &t_transformed_diff_n_ptr[HVEC1_0],
        &t_transformed_diff_n_ptr[HVEC1_1], &t_transformed_diff_n_ptr[HVEC1_2],
        &t_transformed_diff_n_ptr[HVEC2_0], &t_transformed_diff_n_ptr[HVEC2_1],
        &t_transformed_diff_n_ptr[HVEC2_2]);
 
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
        t_transformed_n(i) = tInvJac(k, i) * t_n(k);
        t_transformed_diff_n(i, k) = tInvJac(j, i) * t_diff_n(j, k);
        ++t_n;
        ++t_transformed_n;
        ++t_diff_n;
        ++t_transformed_diff_n;
      }
    }
    data.getN(base).data().swap(piolaN.data());
    data.getDiffN(base).data().swap(piolaDiffN.data());
  }
 
  // data.getBase() = base;
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode
OpSetHoInvJacH1::doWork(int side, EntityType type,
                        DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (invHoJac.size2() != 9)
    SETERRQ1(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
             "It looks that ho inverse of Jacobian is not calculated %d != 9",
             invHoJac.size2());
 
  auto transform_base = [&](MatrixDouble &diff_n) {
    MoFEMFunctionBeginHot;
 
    unsigned int nb_gauss_pts = diff_n.size1();
    if (nb_gauss_pts == 0)
      MoFEMFunctionReturnHot(0);
 
    if (invHoJac.size1() == nb_gauss_pts) {
 
      unsigned int nb_base_functions = diff_n.size2() / 3;
      if (nb_base_functions == 0)
        MoFEMFunctionReturnHot(0);
 
      double *t_inv_jac_ptr = &*invHoJac.data().begin();
      FTensor::Tensor2<double *, 3, 3> t_inv_jac(
          t_inv_jac_ptr, &t_inv_jac_ptr[1], &t_inv_jac_ptr[2],
          &t_inv_jac_ptr[3], &t_inv_jac_ptr[4], &t_inv_jac_ptr[5],
          &t_inv_jac_ptr[6], &t_inv_jac_ptr[7], &t_inv_jac_ptr[8], 9);
 
      diffNinvJac.resize(nb_gauss_pts, 3 * nb_base_functions, false);
 
      double *t_diff_n_ptr = &*diff_n.data().begin();
      FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_diff_n(
          t_diff_n_ptr, &t_diff_n_ptr[1], &t_diff_n_ptr[2]);
      double *t_inv_n_ptr = &*diffNinvJac.data().begin();
      FTensor::Tensor1<double *, 3> t_inv_diff_n(t_inv_n_ptr, &t_inv_n_ptr[1],
                                                 &t_inv_n_ptr[2], 3);
 
      switch (type) {
      case MBVERTEX:
      case MBEDGE:
      case MBTRI:
      case MBTET: {
        for (unsigned int gg = 0; gg < nb_gauss_pts; ++gg) {
          for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
            t_inv_diff_n(i) = t_diff_n(j) * t_inv_jac(j, i);
            ++t_diff_n;
            ++t_inv_diff_n;
          }
          ++t_inv_jac;
        }
      } break;
      default:
        SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED, "not implemented");
      }
 
      diff_n.data().swap(diffNinvJac.data());
    }
    MoFEMFunctionReturnHot(0);
  };
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
    CHKERR transform_base(data.getDiffN(base));
  }
 
  switch (type) {
  case MBVERTEX:
    for (auto &m : data.getBBDiffNMap())
      CHKERR transform_base(*(m.second));
    break;
  default:
    for (auto &ptr : data.getBBDiffNByOrderArray())
      if (ptr)
        CHKERR transform_base(*ptr);
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode
OpSetHoInvJacHdivAndHcurl::doWork(int side, EntityType type,
                                  DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBEDGE && type != MBTRI && type != MBTET)
    MoFEMFunctionReturnHot(0);
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
 
    diffHdivInvJac.resize(data.getDiffN(base).size1(),
                          data.getDiffN(base).size2(), false);
 
    unsigned int nb_gauss_pts = data.getDiffN(base).size1();
    unsigned int nb_base_functions = data.getDiffN(base).size2() / 9;
    if (nb_base_functions == 0)
      continue;
 
    auto t_diff_n = data.getFTensor2DiffN<3, 3>(base);
    double *t_inv_diff_n_ptr = &*diffHdivInvJac.data().begin();
    FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3> t_inv_diff_n(
        t_inv_diff_n_ptr, &t_inv_diff_n_ptr[HVEC0_1],
        &t_inv_diff_n_ptr[HVEC0_2], &t_inv_diff_n_ptr[HVEC1_0],
        &t_inv_diff_n_ptr[HVEC1_1], &t_inv_diff_n_ptr[HVEC1_2],
        &t_inv_diff_n_ptr[HVEC2_0], &t_inv_diff_n_ptr[HVEC2_1],
        &t_inv_diff_n_ptr[HVEC2_2]);
    double *t_inv_jac_ptr = &*invHoJac.data().begin();
    FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3> t_inv_jac(
        t_inv_jac_ptr, &t_inv_jac_ptr[1], &t_inv_jac_ptr[2], &t_inv_jac_ptr[3],
        &t_inv_jac_ptr[4], &t_inv_jac_ptr[5], &t_inv_jac_ptr[6],
        &t_inv_jac_ptr[7], &t_inv_jac_ptr[8]);
 
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
        t_inv_diff_n(i, j) = t_inv_jac(k, j) * t_diff_n(i, k);
        ++t_diff_n;
        ++t_inv_diff_n;
      }
      ++t_inv_jac;
    }
 
    data.getDiffN(base).data().swap(diffHdivInvJac.data());
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpSetHoContravariantPiolaTransform::doWork(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBTRI && type != MBTET)
    MoFEMFunctionReturnHot(0);
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
 
    unsigned int nb_gauss_pts = data.getN(base).size1();
    unsigned int nb_base_functions = data.getN(base).size2() / 3;
    piolaN.resize(nb_gauss_pts, data.getN(base).size2(), false);
    piolaDiffN.resize(nb_gauss_pts, data.getDiffN(base).size2(), false);
 
    auto t_n = data.getFTensor1N<3>(base);
    double *t_transformed_n_ptr = &*piolaN.data().begin();
    FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_transformed_n(
        t_transformed_n_ptr, // HVEC0
        &t_transformed_n_ptr[HVEC1], &t_transformed_n_ptr[HVEC2]);
    auto t_diff_n = data.getFTensor2DiffN<3, 3>(base);
    double *t_transformed_diff_n_ptr = &*piolaDiffN.data().begin();
    FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3> t_transformed_diff_n(
        t_transformed_diff_n_ptr, &t_transformed_diff_n_ptr[HVEC0_1],
        &t_transformed_diff_n_ptr[HVEC0_2], &t_transformed_diff_n_ptr[HVEC1_0],
        &t_transformed_diff_n_ptr[HVEC1_1], &t_transformed_diff_n_ptr[HVEC1_2],
        &t_transformed_diff_n_ptr[HVEC2_0], &t_transformed_diff_n_ptr[HVEC2_1],
        &t_transformed_diff_n_ptr[HVEC2_2]);
 
    FTensor::Tensor0<double *> t_det(&*detHoJac.data().begin());
    double *t_jac_ptr = &*hoJac.data().begin();
    FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3> t_jac(
        t_jac_ptr, &t_jac_ptr[1], &t_jac_ptr[2], &t_jac_ptr[3], &t_jac_ptr[4],
        &t_jac_ptr[5], &t_jac_ptr[6], &t_jac_ptr[7], &t_jac_ptr[8]);
 
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
        const double a = 1. / t_det;
        t_transformed_n(i) = a * t_jac(i, k) * t_n(k);
        t_transformed_diff_n(i, k) = a * t_jac(i, j) * t_diff_n(j, k);
        ++t_n;
        ++t_transformed_n;
        ++t_diff_n;
        ++t_transformed_diff_n;
      }
      ++t_det;
      ++t_jac;
    }
 
    data.getN(base).data().swap(piolaN.data());
    data.getDiffN(base).data().swap(piolaDiffN.data());
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpSetHoCovariantPiolaTransform::doWork(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBEDGE && type != MBTRI && type != MBTET)
    MoFEMFunctionReturnHot(0);
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
 
    unsigned int nb_gauss_pts = data.getN(base).size1();
    unsigned int nb_base_functions = data.getN(base).size2() / 3;
    piolaN.resize(nb_gauss_pts, data.getN(base).size2(), false);
    piolaDiffN.resize(nb_gauss_pts, data.getDiffN(base).size2(), false);
 
    auto t_n = data.getFTensor1N<3>(base);
    double *t_transformed_n_ptr = &*piolaN.data().begin();
    FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_transformed_n(
        t_transformed_n_ptr, // HVEC0
        &t_transformed_n_ptr[HVEC1], &t_transformed_n_ptr[HVEC2]);
    auto t_diff_n = data.getFTensor2DiffN<3, 3>(base);
    double *t_transformed_diff_n_ptr = &*piolaDiffN.data().begin();
    FTensor::Tensor2<FTensor::PackPtr<double *, 9>, 3, 3> t_transformed_diff_n(
        t_transformed_diff_n_ptr, &t_transformed_diff_n_ptr[HVEC0_1],
        &t_transformed_diff_n_ptr[HVEC0_2], &t_transformed_diff_n_ptr[HVEC1_0],
        &t_transformed_diff_n_ptr[HVEC1_1], &t_transformed_diff_n_ptr[HVEC1_2],
        &t_transformed_diff_n_ptr[HVEC2_0], &t_transformed_diff_n_ptr[HVEC2_1],
        &t_transformed_diff_n_ptr[HVEC2_2]);
 
    double *t_inv_jac_ptr = &*hoInvJac.data().begin();
    FTensor::Tensor2<double *, 3, 3> t_inv_jac(
        t_inv_jac_ptr, &t_inv_jac_ptr[1], &t_inv_jac_ptr[2], &t_inv_jac_ptr[3],
        &t_inv_jac_ptr[4], &t_inv_jac_ptr[5], &t_inv_jac_ptr[6],
        &t_inv_jac_ptr[7], &t_inv_jac_ptr[8], 9);
 
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      for (unsigned int bb = 0; bb != nb_base_functions; ++bb) {
        t_transformed_n(i) = t_inv_jac(k, i) * t_n(k);
        t_transformed_diff_n(i, k) = t_inv_jac(j, i) * t_diff_n(j, k);
        ++t_n;
        ++t_transformed_n;
        ++t_diff_n;
        ++t_transformed_diff_n;
      }
      ++t_inv_jac;
    }
 
    data.getN(base).data().swap(piolaN.data());
    data.getDiffN(base).data().swap(piolaDiffN.data());
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode
OpGetCoordsAndNormalsOnFace::doWork(int side, EntityType type,
                                    DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBeginHot;
 
  unsigned int nb_dofs = data.getFieldData().size();
  if (nb_dofs == 0)
    MoFEMFunctionReturnHot(0);
 
  int nb_gauss_pts = data.getN().size1();
  cOords_at_GaussPt.resize(nb_gauss_pts, 3, false);
  tAngent1_at_GaussPt.resize(nb_gauss_pts, 3, false);
  tAngent2_at_GaussPt.resize(nb_gauss_pts, 3, false);
 
  auto get_ftensor1 = [](MatrixDouble &m) {
    return FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3>(
        &m(0, 0), &m(0, 1), &m(0, 2));
  };
  auto t_coords = get_ftensor1(cOords_at_GaussPt);
  auto t_t1 = get_ftensor1(tAngent1_at_GaussPt);
  auto t_t2 = get_ftensor1(tAngent2_at_GaussPt);
  FTensor::Index<'i', 3> i;
  FTensor::Number<0> N0;
  FTensor::Number<1> N1;
 
  switch (type) {
  case MBVERTEX: {
    cOords_at_GaussPt.clear();
    tAngent1_at_GaussPt.clear();
    tAngent2_at_GaussPt.clear();
  }
  case MBEDGE:
  case MBTRI:
  case MBQUAD: {
    if (2 * data.getN().size2() != data.getDiffN().size2()) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "data inconsistency");
    }
    if (nb_dofs % 3 != 0) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "data inconsistency");
    }
    if (nb_dofs > 3 * data.getN().size2()) {
      unsigned int nn = 0;
      for (; nn != nb_dofs; nn++) {
        if (!data.getFieldDofs()[nn]->getActive())
          break;
      }
      if (nn > 3 * data.getN().size2()) {
        SETERRQ1(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                 "data inconsistency for base %s",
                 ApproximationBaseNames[data.getBase()]);
      } else {
        nb_dofs = nn;
        if (!nb_dofs)
          MoFEMFunctionReturnHot(0);
      }
    }
    const int nb_base_functions = data.getN().size2();
    auto t_base = data.getFTensor0N();
    auto t_diff_base = data.getFTensor1DiffN<2>();
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      auto t_data = data.getFTensor1FieldData<3>();
      int bb = 0;
      for (; bb != nb_dofs / 3; ++bb) {
        t_coords(i) += t_base * t_data(i);
        t_t1(i) += t_data(i) * t_diff_base(N0);
        t_t2(i) += t_data(i) * t_diff_base(N1);
        ++t_data;
        ++t_base;
        ++t_diff_base;
      }
      for (; bb != nb_base_functions; ++bb) {
        ++t_base;
        ++t_diff_base;
      }
      ++t_coords;
      ++t_t1;
      ++t_t2;
    }
  } break;
  default:
    SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED, "not implemented");
  }
 
  MoFEMFunctionReturnHot(0);
}
 
MoFEMErrorCode OpGetCoordsAndNormalsOnFace::calculateNormals() {
  MoFEMFunctionBeginHot;
 
  nOrmals_at_GaussPt.resize(tAngent1_at_GaussPt.size1(), 3, false);
 
  auto get_ftensor1 = [](MatrixDouble &m) {
    return FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3>(
        &m(0, 0), &m(0, 1), &m(0, 2));
  };
  auto t_normal = get_ftensor1(nOrmals_at_GaussPt);
  auto t_t1 = get_ftensor1(tAngent1_at_GaussPt);
  auto t_t2 = get_ftensor1(tAngent2_at_GaussPt);
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
 
  for (unsigned int gg = 0; gg != tAngent1_at_GaussPt.size1(); ++gg) {
    t_normal(j) = FTensor::levi_civita(i, j, k) * t_t1(k) * t_t2(i);
    ++t_normal;
    ++t_t1;
    ++t_t2;
  }
 
  MoFEMFunctionReturnHot(0);
}
 
MoFEMErrorCode
OpGetCoordsAndNormalsOnPrism::doWork(int side, EntityType type,
                                     DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (data.getFieldData().size() == 0)
    MoFEMFunctionReturnHot(0);
  const int valid_edges3[] = {1, 1, 1, 0, 0, 0, 0, 0, 0};
  const int valid_faces3[] = {0, 0, 0, 1, 0, 0, 0, 0, 0};
  const int valid_edges4[] = {0, 0, 0, 0, 0, 0, 1, 1, 1};
  const int valid_faces4[] = {0, 0, 0, 0, 1, 0, 0, 0, 0};
 
  if (type == MBEDGE) {
    if (!valid_edges3[side] || valid_edges4[side])
      MoFEMFunctionReturnHot(0);
  } else if (type == MBTRI) {
    if (!valid_faces3[side] || valid_faces4[side])
      MoFEMFunctionReturnHot(0);
  }
 
  switch (type) {
  case MBVERTEX: {
    for (unsigned int gg = 0; gg < data.getN().size1(); ++gg) {
      for (int dd = 0; dd < 3; dd++) {
        cOords_at_GaussPtF3(gg, dd) =
            cblas_ddot(3, &data.getN(gg)[0], 1, &data.getFieldData()[dd], 3);
        tAngent1_at_GaussPtF3(gg, dd) = cblas_ddot(
            3, &data.getDiffN()(gg, 0), 2, &data.getFieldData()[dd], 3);
        tAngent2_at_GaussPtF3(gg, dd) = cblas_ddot(
            3, &data.getDiffN()(gg, 1), 2, &data.getFieldData()[dd], 3);
        cOords_at_GaussPtF4(gg, dd) = cblas_ddot(
            3, &data.getN(gg)[0], 1, &data.getFieldData()[9 + dd], 3);
        tAngent1_at_GaussPtF4(gg, dd) = cblas_ddot(
            3, &data.getDiffN()(gg, 6 + 0), 2, &data.getFieldData()[9 + dd], 3);
        tAngent2_at_GaussPtF4(gg, dd) = cblas_ddot(
            3, &data.getDiffN()(gg, 6 + 1), 2, &data.getFieldData()[9 + dd], 3);
      }
    }
  } break;
  case MBEDGE:
  case MBTRI: {
    if (2 * data.getN().size2() != data.getDiffN().size2()) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "data inconsistency");
    }
    unsigned int nb_dofs = data.getFieldData().size();
    if (nb_dofs % 3 != 0) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY, "data inconsistency");
    }
    if (nb_dofs > 3 * data.getN().size2()) {
      SETERRQ2(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
               "data inconsistency, side %d type %d", side, type);
    }
    for (unsigned int gg = 0; gg < data.getN().size1(); ++gg) {
      for (int dd = 0; dd < 3; dd++) {
        if ((type == MBTRI && valid_faces3[side]) ||
            (type == MBEDGE && valid_edges3[side])) {
          cOords_at_GaussPtF3(gg, dd) += cblas_ddot(
              nb_dofs / 3, &data.getN(gg)[0], 1, &data.getFieldData()[dd], 3);
          tAngent1_at_GaussPtF3(gg, dd) +=
              cblas_ddot(nb_dofs / 3, &data.getDiffN()(gg, 0), 2,
                         &data.getFieldData()[dd], 3);
          tAngent2_at_GaussPtF3(gg, dd) +=
              cblas_ddot(nb_dofs / 3, &data.getDiffN()(gg, 1), 2,
                         &data.getFieldData()[dd], 3);
        } else if ((type == MBTRI && valid_faces4[side]) ||
                   (type == MBEDGE && valid_edges4[side])) {
          cOords_at_GaussPtF4(gg, dd) += cblas_ddot(
              nb_dofs / 3, &data.getN(gg)[0], 1, &data.getFieldData()[dd], 3);
          tAngent1_at_GaussPtF4(gg, dd) +=
              cblas_ddot(nb_dofs / 3, &data.getDiffN()(gg, 0), 2,
                         &data.getFieldData()[dd], 3);
          tAngent2_at_GaussPtF4(gg, dd) +=
              cblas_ddot(nb_dofs / 3, &data.getDiffN()(gg, 1), 2,
                         &data.getFieldData()[dd], 3);
        }
      }
    }
  } break;
  default:
    SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED, "not implemented");
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpGetCoordsAndNormalsOnPrism::calculateNormals() {
  MoFEMFunctionBegin;
 
  sPin.resize(3, 3);
  sPin.clear();
  nOrmals_at_GaussPtF3.resize(tAngent1_at_GaussPtF3.size1(), 3, false);
  for (unsigned int gg = 0; gg < tAngent1_at_GaussPtF3.size1(); ++gg) {
    ierr = Spin(&*sPin.data().begin(), &tAngent1_at_GaussPtF3(gg, 0));
    CHKERRG(ierr);
    cblas_dgemv(CblasRowMajor, CblasNoTrans, 3, 3, 1., &*sPin.data().begin(), 3,
                &tAngent2_at_GaussPtF3(gg, 0), 1, 0.,
                &nOrmals_at_GaussPtF3(gg, 0), 1);
  }
  sPin.clear();
  nOrmals_at_GaussPtF4.resize(tAngent1_at_GaussPtF4.size1(), 3, false);
  for (unsigned int gg = 0; gg < tAngent1_at_GaussPtF4.size1(); ++gg) {
    ierr = Spin(&*sPin.data().begin(), &tAngent1_at_GaussPtF4(gg, 0));
    CHKERRG(ierr);
    cblas_dgemv(CblasRowMajor, CblasNoTrans, 3, 3, 1., &*sPin.data().begin(), 3,
                &tAngent2_at_GaussPtF4(gg, 0), 1, 0.,
                &nOrmals_at_GaussPtF4(gg, 0), 1);
  }
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpSetContravariantPiolaTransformOnFace::doWork(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  FTensor::Index<'i', 3> i;
  MoFEMFunctionBegin;
 
  if (type != MBTRI)
    MoFEMFunctionReturnHot(0);
 
  if (normalRawPtr == nullptr && normalsAtGaussPtsRawPtr == nullptr)
    SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA,
            "Pointer to normal/normals not set");
 
  bool normal_is_at_gauss_pts = (normalsAtGaussPtsRawPtr != nullptr);
  if (normal_is_at_gauss_pts)
    normal_is_at_gauss_pts = (normalsAtGaussPtsRawPtr->size1() != 0);
 
  auto apply_transform_linear_geometry = [&](auto base, auto nb_gauss_pts,
                                             auto nb_base_functions) {
    MoFEMFunctionBegin;
    const auto &normal = *normalRawPtr;
    auto t_normal = FTensor::Tensor1<double, 3>{normal[normalShift + 0],
                                                normal[normalShift + 1],
                                                normal[normalShift + 2]};
    const auto l02 = t_normal(i) * t_normal(i);
    auto t_base = data.getFTensor1N<3>(base);
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      for (int bb = 0; bb != nb_base_functions; ++bb) {
        const auto v = t_base(0);
        t_base(i) = (v / l02) * t_normal(i);
        ++t_base;
      }
    }
    MoFEMFunctionReturn(0);
  };
 
  auto apply_transform_nonlinear_geometry = [&](auto base, auto nb_gauss_pts,
                                                auto nb_base_functions) {
    MoFEMFunctionBegin;
    const MatrixDouble &normals_at_pts = *normalsAtGaussPtsRawPtr;
    auto t_normal = FTensor::Tensor1<FTensor::PackPtr<const double *, 3>, 3>(
        &normals_at_pts(0, 0), &normals_at_pts(0, 1), &normals_at_pts(0, 2));
    auto t_base = data.getFTensor1N<3>(base);
    for (int gg = 0; gg != nb_gauss_pts; ++gg) {
      for (int bb = 0; bb != nb_base_functions; ++bb) {
        const auto v = t_base(0);
        const auto l2 = t_normal(i) * t_normal(i);
        t_base(i) = (v / l2) * t_normal(i);
        ++t_base;
      }
      ++t_normal;
    }
    MoFEMFunctionReturn(0);
  };
 
  if (normal_is_at_gauss_pts) {
    for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
      FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
      const auto &base_functions = data.getN(base);
      const auto nb_gauss_pts = base_functions.size1();
 
      if (nb_gauss_pts) {
 
        if (normalsAtGaussPtsRawPtr->size1() != nb_gauss_pts)
          SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
                  "normalsAtGaussPtsRawPtr has inconsistent number of "
                  "integration "
                  "points");
 
        const auto nb_base_functions = base_functions.size2() / 3;
        CHKERR apply_transform_nonlinear_geometry(base, nb_gauss_pts,
                                                  nb_base_functions);
      }
    }
  } else {
    for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
      FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
      const auto &base_functions = data.getN(base);
      const auto nb_gauss_pts = base_functions.size1();
 
      if (nb_gauss_pts) {
        const auto nb_base_functions = base_functions.size2() / 3;
        CHKERR apply_transform_linear_geometry(base, nb_gauss_pts,
                                               nb_base_functions);
      }
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpSetCovariantPiolaTransformOnFace::doWork(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  if (type != MBEDGE && type != MBTRI)
    MoFEMFunctionReturnHot(0);
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 2> k;
 
  FTensor::Tensor2<const double *, 3, 3> t_m(
      &tAngent0[0], &tAngent1[0], &nOrmal[0],
 
      &tAngent0[1], &tAngent1[1], &nOrmal[1],
 
      &tAngent0[2], &tAngent1[2], &nOrmal[2],
 
      3);
  double det;
  FTensor::Tensor2<double, 3, 3> t_inv_m;
  CHKERR determinantTensor3by3(t_m, det);
  CHKERR invertTensor3by3(t_m, det, t_inv_m);
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; ++b) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
 
    auto &baseN = data.getN(base);
    auto &diffBaseN = data.getDiffN(base);
 
    int nb_dofs = baseN.size2() / 3;
    int nb_gauss_pts = baseN.size1();
 
    MatrixDouble piola_n(baseN.size1(), baseN.size2());
    MatrixDouble diff_piola_n(diffBaseN.size1(), diffBaseN.size2());
 
    if (nb_dofs > 0 && nb_gauss_pts > 0) {
 
      FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_h_curl(
          &baseN(0, HVEC0), &baseN(0, HVEC1), &baseN(0, HVEC2));
      FTensor::Tensor2<FTensor::PackPtr<double *, 6>, 3, 2> t_diff_h_curl(
          &diffBaseN(0, HVEC0_0), &diffBaseN(0, HVEC0_1),
          &diffBaseN(0, HVEC1_0), &diffBaseN(0, HVEC1_1),
          &diffBaseN(0, HVEC2_0), &diffBaseN(0, HVEC2_1));
      FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_transformed_h_curl(
          &piola_n(0, HVEC0), &piola_n(0, HVEC1), &piola_n(0, HVEC2));
      FTensor::Tensor2<FTensor::PackPtr<double *, 6>, 3, 2>
          t_transformed_diff_h_curl(
              &diff_piola_n(0, HVEC0_0), &diff_piola_n(0, HVEC0_1),
              &diff_piola_n(0, HVEC1_0), &diff_piola_n(0, HVEC1_1),
              &diff_piola_n(0, HVEC2_0), &diff_piola_n(0, HVEC2_1));
 
      int cc = 0;
      if (normalsAtGaussPts.size1() == (unsigned int)nb_gauss_pts) {
        // HO geometry is set, so jacobian is different at each gauss point
        FTensor::Tensor2<const double *, 3, 3> t_m_at_pts(
            &tangent0AtGaussPt(0, 0), &tangent1AtGaussPt(0, 0),
            &normalsAtGaussPts(0, 0), &tangent0AtGaussPt(0, 1),
            &tangent1AtGaussPt(0, 1), &normalsAtGaussPts(0, 1),
            &tangent0AtGaussPt(0, 2), &tangent1AtGaussPt(0, 2),
            &normalsAtGaussPts(0, 2), 3);
        for (int gg = 0; gg < nb_gauss_pts; ++gg) {
          CHKERR determinantTensor3by3(t_m_at_pts, det);
          CHKERR invertTensor3by3(t_m_at_pts, det, t_inv_m);
          for (int ll = 0; ll != nb_dofs; ll++) {
            t_transformed_h_curl(i) = t_inv_m(j, i) * t_h_curl(j);
            t_transformed_diff_h_curl(i, k) =
                t_inv_m(j, i) * t_diff_h_curl(j, k);
            ++t_h_curl;
            ++t_transformed_h_curl;
            ++t_diff_h_curl;
            ++t_transformed_diff_h_curl;
            ++cc;
          }
          ++t_m_at_pts;
        }
      } else {
        for (int gg = 0; gg < nb_gauss_pts; ++gg) {
          for (int ll = 0; ll != nb_dofs; ll++) {
            t_transformed_h_curl(i) = t_inv_m(j, i) * t_h_curl(j);
            t_transformed_diff_h_curl(i, k) =
                t_inv_m(j, i) * t_diff_h_curl(j, k);
            ++t_h_curl;
            ++t_transformed_h_curl;
            ++t_diff_h_curl;
            ++t_transformed_diff_h_curl;
            ++cc;
          }
        }
      }
      if (cc != nb_gauss_pts * nb_dofs)
        SETERRQ(PETSC_COMM_SELF, MOFEM_IMPOSIBLE_CASE, "Data inconsistency");
 
      baseN.data().swap(piola_n.data());
      diffBaseN.data().swap(diff_piola_n.data());
    }
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode
OpGetHoTangentOnEdge::doWork(int side, EntityType type,
                             DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBegin;
 
  int nb_dofs = data.getFieldData().size();
  if (nb_dofs == 0)
    MoFEMFunctionReturnHot(0);
 
  int nb_gauss_pts = data.getN().size1();
  tAngent.resize(nb_gauss_pts, 3, false);
 
  int nb_approx_fun = data.getN().size2();
  double *diff = &*data.getDiffN().data().begin();
  double *dofs[] = {&data.getFieldData()[0], &data.getFieldData()[1],
                    &data.getFieldData()[2]};
 
  tAngent.resize(nb_gauss_pts, 3, false);
 
  switch (type) {
  case MBVERTEX:
    for (int dd = 0; dd != 3; dd++) {
      for (int gg = 0; gg != nb_gauss_pts; ++gg) {
        tAngent(gg, dd) = cblas_ddot(2, diff, 1, dofs[dd], 3);
      }
    }
    break;
  case MBEDGE:
    if (nb_dofs % 3) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_IMPOSIBLE_CASE,
              "Approximated field should be rank 3, i.e. vector in 3d space");
    }
    for (int dd = 0; dd != 3; dd++) {
      for (int gg = 0; gg != nb_gauss_pts; ++gg) {
        tAngent(gg, dd) +=
            cblas_ddot(nb_dofs / 3, &diff[gg * nb_approx_fun], 1, dofs[dd], 3);
      }
    }
    break;
  default:
    SETERRQ(PETSC_COMM_SELF, MOFEM_IMPOSIBLE_CASE,
            "This operator can calculate tangent vector only on edge");
  }
 
  MoFEMFunctionReturn(0);
}
 
MoFEMErrorCode OpSetCovariantPiolaTransformOnEdge::doWork(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBeginHot;
 
  if (type != MBEDGE)
    MoFEMFunctionReturnHot(0);
 
  FTensor::Index<'i', 3> i;
  FTensor::Tensor1<FTensor::PackPtr<const double *, 0>, 3> t_m(
      &tAngent[0], &tAngent[1], &tAngent[2]);
  const double l0 = t_m(i) * t_m(i);
 
  auto get_base_at_pts = [&](auto base) {
    FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_h_curl(
        &data.getN(base)(0, HVEC0), &data.getN(base)(0, HVEC1),
        &data.getN(base)(0, HVEC2));
    return t_h_curl;
  };
 
  auto get_tangent_at_pts = [&]() {
    FTensor::Tensor1<FTensor::PackPtr<const double *, 3>, 3> t_m_at_pts(
        &tangentAtGaussPt(0, 0), &tangentAtGaussPt(0, 1),
        &tangentAtGaussPt(0, 2));
    return t_m_at_pts;
  };
 
  auto calculate_squared_edge_length = [&]() {
    std::vector<double> l1;
    int nb_gauss_pts = tangentAtGaussPt.size1();
    if (nb_gauss_pts) {
      l1.resize(nb_gauss_pts);
      auto t_m_at_pts = get_tangent_at_pts();
      for (size_t gg = 0; gg != nb_gauss_pts; ++gg) {
        l1[gg] = t_m_at_pts(i) * t_m_at_pts(i);
        ++t_m_at_pts;
      }
    }
    return l1;
  };
 
  auto l1 = calculate_squared_edge_length();
 
  for (int b = AINSWORTH_LEGENDRE_BASE; b != LASTBASE; b++) {
 
    FieldApproximationBase base = static_cast<FieldApproximationBase>(b);
    const size_t nb_gauss_pts = data.getN(base).size1();
    const size_t nb_dofs = data.getN(base).size2() / 3;
    if (nb_gauss_pts && nb_dofs) {
      auto t_h_curl = get_base_at_pts(base);
      int cc = 0;
      if (tangentAtGaussPt.size1() == nb_gauss_pts) {
        auto t_m_at_pts = get_tangent_at_pts();
        for (int gg = 0; gg != nb_gauss_pts; ++gg) {
          const double l0 = l1[gg];
          for (int ll = 0; ll != nb_dofs; ll++) {
            const double val = t_h_curl(0);
            const double a = val / l0;
            t_h_curl(i) = t_m_at_pts(i) * a;
            ++t_h_curl;
            ++cc;
          }
          ++t_m_at_pts;
        }
      } else {
        for (int gg = 0; gg != nb_gauss_pts; ++gg) {
          for (int ll = 0; ll != nb_dofs; ll++) {
            const double val = t_h_curl(0);
            const double a = val / l0;
            t_h_curl(i) = t_m(i) * a;
            ++t_h_curl;
            ++cc;
          }
        }
      }
 
      if (cc != nb_gauss_pts * nb_dofs)
        SETERRQ(PETSC_COMM_SELF, MOFEM_IMPOSIBLE_CASE, "Data inconsistency");
    }
  }
 
  MoFEMFunctionReturnHot(0);
}
 
template <>
template <>
FTensor::Tensor1<double *, 3>
OpGetDataAndGradient<3, 3>::getValAtGaussPtsTensor<3>(MatrixDouble &data) {
  double *ptr = &*data.data().begin();
  return FTensor::Tensor1<double *, 3>(ptr, &ptr[1], &ptr[2], 3);
}
 
template <>
template <>
FTensor::Tensor2<double *, 3, 3>
OpGetDataAndGradient<3, 3>::getGradAtGaussPtsTensor<3, 3>(MatrixDouble &data) {
  double *ptr = &*data.data().begin();
  return FTensor::Tensor2<double *, 3, 3>(ptr, &ptr[1], &ptr[2], &ptr[3],
                                          &ptr[4], &ptr[5], &ptr[6], &ptr[7],
                                          &ptr[8], 9);
}
 
template <>
MoFEMErrorCode OpGetDataAndGradient<3, 3>::calculateValAndGrad(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBeginHot;
  if (data.getBase() == NOBASE)
    MoFEMFunctionReturnHot(0);
  const unsigned int nb_gauss_pts = data.getN().size1();
  const unsigned int nb_base_functions = data.getN().size2();
  const unsigned int nb_dofs = data.getFieldData().size();
  if (!nb_dofs)
    MoFEMFunctionReturnHot(0);
  auto t_n = data.getFTensor0N();
  auto t_val = getValAtGaussPtsTensor<3>(dataAtGaussPts);
  auto t_grad = getGradAtGaussPtsTensor<3, 3>(dataGradAtGaussPts);
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  if (type == MBVERTEX &&
      data.getDiffN().data().size() == 3 * nb_base_functions) {
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      auto t_data = data.getFTensor1FieldData<3>();
      auto t_diff_n = data.getFTensor1DiffN<3>();
      unsigned int bb = 0;
      for (; bb != nb_dofs / 3; ++bb) {
        t_val(i) += t_data(i) * t_n;
        t_grad(i, j) += t_data(i) * t_diff_n(j);
        ++t_n;
        ++t_diff_n;
        ++t_data;
      }
      ++t_val;
      ++t_grad;
      for (; bb != nb_base_functions; ++bb) {
        ++t_n;
      }
    }
  } else {
    auto t_diff_n = data.getFTensor1DiffN<3>();
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      auto t_data = data.getFTensor1FieldData<3>();
      unsigned int bb = 0;
      for (; bb != nb_dofs / 3; ++bb) {
        t_val(i) += t_data(i) * t_n;
        t_grad(i, j) += t_data(i) * t_diff_n(j);
        ++t_n;
        ++t_diff_n;
        ++t_data;
      }
      ++t_val;
      ++t_grad;
      for (; bb != nb_base_functions; ++bb) {
        ++t_n;
        ++t_diff_n;
      }
    }
  }
  MoFEMFunctionReturnHot(0);
}
 
template <>
MoFEMErrorCode OpGetDataAndGradient<1, 3>::calculateValAndGrad(
    int side, EntityType type, DataForcesAndSourcesCore::EntData &data) {
  MoFEMFunctionBeginHot;
  const unsigned int nb_gauss_pts = data.getN().size1();
  const unsigned int nb_base_functions = data.getN().size2();
  // bool constant_diff = false;
  const unsigned int nb_dofs = data.getFieldData().size();
  auto t_n = data.getFTensor0N();
  FTensor::Tensor0<double *> t_val =
      FTensor::Tensor0<double *>(&*dataAtGaussPts.data().begin(), 1);
  double *ptr = &*dataGradAtGaussPts.data().begin();
  FTensor::Tensor1<FTensor::PackPtr<double *, 3>, 3> t_grad(ptr, &ptr[1],
                                                            &ptr[2]);
  FTensor::Index<'i', 3> i;
  if (type == MBVERTEX &&
      data.getDiffN().data().size() == 3 * nb_base_functions) {
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      auto t_data = data.getFTensor0FieldData();
      auto t_diff_n = data.getFTensor1DiffN<3>();
      unsigned int bb = 0;
      for (; bb != nb_dofs / 3; ++bb) {
        t_val += t_data * t_n;
        t_grad(i) += t_data * t_diff_n(i);
        ++t_n;
        ++t_diff_n;
        ++t_data;
      }
      ++t_val;
      ++t_grad;
      for (; bb != nb_base_functions; ++bb) {
        ++t_n;
      }
    }
  } else {
    auto t_diff_n = data.getFTensor1DiffN<3>();
    for (unsigned int gg = 0; gg != nb_gauss_pts; ++gg) {
      auto t_data = data.getFTensor0FieldData();
      unsigned int bb = 0;
      for (; bb != nb_dofs / 3; ++bb) {
        t_val = t_data * t_n;
        t_grad(i) += t_data * t_diff_n(i);
        ++t_n;
        ++t_diff_n;
        ++t_data;
      }
      ++t_val;
      ++t_grad;
      for (; bb != nb_base_functions; ++bb) {
        ++t_n;
        ++t_diff_n;
      }
    }
  }
  MoFEMFunctionReturnHot(0);
}
} // namespace MoFEM