getfem_assembling_tensors.cc

/*===========================================================================

 Copyright (C) 2003-2017 Julien Pommier

 This file is a part of GetFEM++

 GetFEM++  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 along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
 This program  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 and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.

===========================================================================*/

#include "gmm/gmm_blas_interface.h"
#include "getfem/getfem_arch_config.h"
#include "getfem/getfem_assembling_tensors.h"
#include "getfem/getfem_mat_elem.h"

namespace getfem {
  size_type vdim_specif_list::nb_mf() const {
    return std::count_if(begin(),end(),
      std::mem_fun_ref(&vdim_specif::is_mf_ref));
  }
  size_type vdim_specif_list::nbelt() const {
    size_type sz = 1;
    for (const_iterator it = begin(); it != end(); ++it) sz *= (*it).dim;
    return sz;
  }
  void vdim_specif_list::build_strides_for_cv
    (size_type cv, tensor_ranges& r, std::vector<tensor_strides >& str) const {
      stride_type s = 1, cnt = 0;
      str.resize(size());
      r.resize(size());
      for (const_iterator it = begin(); it != end(); ++it, ++cnt) {
        if ((*it).is_mf_ref()) {
          r[cnt] = unsigned((*it).pmf->nb_basic_dof_of_element(cv));
          //mesh_fem::ind_dof_ct::const_iterator ii
          //       = (*it).pmf->ind_basic_dof_of_element(cv).begin();
          str[cnt].resize(r[cnt]);
          for (index_type j=0; j < r[cnt]; ++j) {
            str[cnt][j] = int((*it).pmf->ind_basic_dof_of_element(cv)[j]*s);
          }
        } else {
          r[cnt] = int((*it).dim);
          str[cnt].resize(r[cnt]);
          for (index_type j=0; j < (*it).dim; ++j) {
            str[cnt][j] = j*s;
          }
        }
        s *= stride_type((*it).dim);
      }
  }

  void ATN::update_childs_required_shape() {
    for (dim_type i=0; i < nchilds(); ++i) {
      child(i).merge_required_shape(tensor_shape(child(i).ranges()));
    }
  }
  void ATN::set_number(unsigned &gcnt) {
    if (number_ == unsigned(-1)) {
      for (unsigned i=0; i < nchilds(); ++i) child(i).set_number(gcnt);
      number_ = ++gcnt;
    }
  }

  bool ATN::is_zero_size() {
    return child(0).is_zero_size();
  }

  /*
  general class for tensor who store their data
  */
  class ATN_tensor_w_data : public ATN_tensor {
    TDIter data_base;
  protected:
    std::vector<scalar_type> data;
    void reinit_();
    void reinit0()
    { ATN_tensor_w_data::reinit_(); std::fill(data.begin(), data.end(),0); }
  };

  /* note that the data is NOT filled with zeros */
  void ATN_tensor_w_data::reinit_() {
    tr.assign_shape(req_shape);
    tr.init_strides();
    if (tr.card() > 10000000) {
      cerr << "warning, a tensor of size " << tr.card()
        << " will be created, it needs "
        << tr.card()*sizeof(scalar_type) << " bytes of memory\n";
    }
    if (tr.card() == 0) {
      cerr << "WARNING: tensor " << name()
        << " will be created with a size of "
        << ranges() << " and 0 non-null elements!" << endl;
    }
    data.resize(tr.card());
    data_base = &data[0];
    tr.set_base(data_base);
  }


  /*
  general class for the computation of a reduced product of tensors
  (templated by the number of product tensors)

  should be very effective.
  */
  typedef std::vector<std::pair<ATN_tensor*,std::string> >
    reduced_tensor_arg_type;

  class ATN_reduced_tensor : public ATN_tensor_w_data {
    /* used for specification of tensors and reduction indices , see below */
    reduced_tensor_arg_type red;
    bgeot::tensor_reduction tred;
  public:
    void check_shape_update(size_type , dim_type) {
      shape_updated_ = false;
      for (dim_type i=0; i < nchilds(); ++i) {
        if (child(i).is_shape_updated()) {
          shape_updated_ = true;
        }
      }
      if (shape_updated_) {
        r_.resize(0);
        for (dim_type i=0; i < nchilds(); ++i) {
          std::string s = red_n(i);
          if (s.size() != child(i).ranges().size()) {
            ASM_THROW_TENSOR_ERROR("wrong number of indexes for the "
              << int(i+1)
              << "th argument of the reduction "
              << name()
              << " (ranges=" << child(i).ranges() << ")");
          }
          for (size_type j=0; j < s.length(); ++j) {
            if (s[j] == ' ') r_.push_back(child(i).ranges()[j]);
          }
        }
      }
    }
    void update_childs_required_shape() {
      /* pourrait etre mieux, cf les commentaires de la fonction
      tensor_reduction::required_shape */
      for (dim_type n=0; n < nchilds(); ++n) {
        tensor_shape ts(child(n).ranges());
        tensor_ranges rn(child(n).ranges());
        const std::string &s = red[n].second;
        GMM_ASSERT1(rn.size() == s.size(), "Wrong size !");
        for (unsigned i=0; i < rn.size(); ++i)
          if (s[i] != ' ') {
            size_type p = s.find(s[i]);
            if (p != size_type(-1) && p < i && rn[p] != rn[i])
              ASM_THROW_TENSOR_ERROR("can't reduce the diagonal of a tensor "
              "of size " << rn << " with '"
              << s << "'");
          }
          //cerr << "ts = " << child(n).ranges() << ", red="
          //     << red[n].second << "\n";
          bgeot::tensor_reduction::diag_shape(ts, red[n].second);
          // cerr << "REDUCTION '" << red[n].second
          //        << "' -> sending required to child#" << int(n)
          //        << " " << child(n).name() << ":" << endl;
          // cerr << ts << endl;
          child(n).merge_required_shape(ts);
          // cerr << "------>required shape is now: "
          //      << child(n).required_shape() << endl;
      }
    }

    /*
    r is a container of pair<vtensor&,std::string>
    where the strings specify the reduction indices:

    if a_{ik}b_{kjl} is reduced against k and l, then the strings are
    " k" and "k l"
    */
    ATN_reduced_tensor(reduced_tensor_arg_type& r) : red(r) {
      for (size_type i=0; i < r.size(); ++i) add_child(*red[i].first);
    }

    std::string red_n(size_type n) {
      std::string s = red[n].second;
      if (s.length() == 0)
        s.append(red[n].first->ranges().size(), ' ');
      return s;
    }

  private:
    void reinit_() {
      tred.clear();
      for (dim_type i=0; i < red.size(); ++i) {
        // cerr << "ATN_reduced_tensor::reinit : insertion of r(" << red_n(i)
        //      << "), tr[" << red[i].first->ranges() << "\n"
        //      << red[i].first->tensor() << endl;*/
        // if (red[i].first->ranges().size() != red_n(i).length()) {
        // ASM_THROW_TENSOR_ERROR("wrong number of indexes for the "
        //                        << int(i+1)
        //                        << "th argument of the reduction " << name()
        //                        << " (ranges=" << red[i].first->ranges()
        //                        << ")");
        // }
        tred.insert(red[i].first->tensor(), red_n(i));
      }
      /* reserve the memory for the output
      the memory is set to zero since the reduction may only affect a
      subset of this tensor hence a part of it would not be initialized
      */
      ATN_tensor_w_data::reinit0();
      /* on fournit notre propre tenseur pour stocker les resultats */
      tred.prepare(&tensor());
    }

    void exec_(size_type , dim_type ) {
      std::fill(data.begin(), data.end(), 0.); /* do_reduction ne peut pas */
      /* le faire puisque ce n'est pas lui le proprietaire du tenseur de   */
      /* sortie. */
      tred.do_reduction();
    }
  };


  /* slice tensor:
  no need of a temporary storage for the slice, since direct access
  can be provided via strides.
  */
  class ATN_sliced_tensor : public ATN_tensor {
    dim_type slice_dim;
    size_type slice_idx;
  public:
    ATN_sliced_tensor(ATN_tensor& a, dim_type slice_dim_,
      size_type slice_idx_) :
    slice_dim(slice_dim_), slice_idx(slice_idx_)  { add_child(a); }
    void check_shape_update(size_type , dim_type) {
      if ((shape_updated_ = child(0).is_shape_updated())) {
        if (slice_dim >= child(0).ranges().size() ||
          slice_idx >= child(0).ranges()[slice_dim]) {
            ASM_THROW_TENSOR_ERROR("can't slice tensor " << child(0).ranges()
              << " at index " << int(slice_idx)
              << " of dimension " << int(slice_dim));
        }
        r_ = child(0).ranges(); r_.erase(r_.begin()+slice_dim);
      }
    }
    void update_childs_required_shape() {
      tensor_shape ts = req_shape;
      ts.set_ndim_noclean(dim_type(ts.ndim()+1));
      ts.shift_dim_num_ge(slice_dim,+1);
      ts.push_mask(tensor_mask(child(0).ranges()[slice_dim],
        tensor_mask::Slice(slice_dim, index_type(slice_idx))));
      child(0).merge_required_shape(ts);
    }
  private:
    void reinit_() {
      tensor() = tensor_ref(child(0).tensor(),
        tensor_mask::Slice(slice_dim, index_type(slice_idx)));
    }
    void exec_(size_type, dim_type) {}
  };

  /* tensor with reoderer indices:
  t{i,j,k} -> t{j,i,k}
  reorder=   0 1 2       1 0 2
  */
  class ATN_permuted_tensor : public ATN_tensor {
    std::vector<dim_type> reorder;
  public:
    /* attention on ne s'assure pas que reorder est une permutation */
    ATN_permuted_tensor(ATN_tensor& a, const std::vector<dim_type>& reorder_) :
      reorder(reorder_)  { add_child(a); }
  private:
    void check_shape_update(size_type , dim_type) {
      if ((shape_updated_ = child(0).is_shape_updated())) {
        if (reorder.size() != child(0).ranges().size())
          ASM_THROW_TENSOR_ERROR("can't reorder tensor '" << name()
                                 << "' of dimensions " << child(0).ranges()
                                 << " with this permutation: " << vref(reorder));
        r_.resize(reorder.size());
        std::fill(r_.begin(), r_.end(), dim_type(-1));

        /*
        --- TODO: A VERIFIER !!!!! ---
        */
        for (size_type i=0; i < reorder.size(); ++i)
          r_[i] = child(0).ranges()[reorder[i]];
      }
    }
    void update_childs_required_shape() {
      tensor_shape ts = req_shape;
      ts.permute(reorder, true);
      child(0).merge_required_shape(ts);
    }
    void reinit_() {
      tensor() = child(0).tensor();
      tensor().permute(reorder);
    }
    void exec_(size_type, dim_type) {}
  };

  /* diagonal tensor: take the "diagonal" of a tensor
  (ie diag(t(i,j,k), {i,k}) == t(i,j,i))

  /!\ the number of dimensions DO NOT change
  */
  class ATN_diagonal_tensor : public ATN_tensor {
    dim_type i1, i2;
  public:
    ATN_diagonal_tensor(ATN_tensor& a, dim_type i1_, dim_type i2_) :
      i1(i1_), i2(i2_) { add_child(a); }
  private:
    void check_shape_update(size_type , dim_type) {
      if ((shape_updated_ = child(0).is_shape_updated())) {
        if (i1 >= child(0).ranges().size() || i2 >= child(0).ranges().size() ||
          i1 == i2 || child(0).ranges()[i1] != child(0).ranges()[i2])
          ASM_THROW_TENSOR_ERROR("can't take the diagonal of a tensor of "
          "sizes " << child(0).ranges() <<
          " at indexes " << int(i1) << " and "
          << int(i2));
        r_ = child(0).ranges();
      }
    }
    void update_childs_required_shape() {
      tensor_shape ts = req_shape.diag_shape(tensor_mask::Diagonal(i1,i2));
      child(0).merge_required_shape(ts);
    }
    void reinit_() {
      tensor() = tensor_ref(child(0).tensor(), tensor_mask::Diagonal(i1,i2));
    }
    void exec_(size_type, dim_type) {}
  };

  /* called (if possible, i.e. if not an exact integration) for each
  integration point during mat_elem->compute() */
  struct computed_tensor_integration_callback
    : public mat_elem_integration_callback {
      bgeot::tensor_reduction red;
      bool was_called;
      std::vector<TDIter> tensor_bases; /* each tref of 'red' has a   */
      /* reference into this vector */
      virtual void exec(bgeot::base_tensor &t, bool first, scalar_type c) {
        if (first) {
          resize_t(t);
          std::fill(t.begin(), t.end(), 0.);
          was_called = true;
        }
        assert(t.size());
        for (unsigned k=0; k!=eltm.size(); ++k) { /* put in the 'if (first)' ? */
          tensor_bases[k] = const_cast<TDIter>(&(*eltm[k]->begin()));
        }
        red.do_reduction();
        long one = 1, n = int(red.out_data.size()); assert(n);
        gmm::daxpy_(&n, &c, const_cast<double*>(&(red.out_data[0])),
                    &one, (double*)&(t[0]), &one);
      }
      void resize_t(bgeot::base_tensor &t) {
        bgeot::multi_index r;
        if (red.reduced_range.size())
          r.assign(red.reduced_range.begin(), red.reduced_range.end());
        else { r.resize(1); r[0]=1; }
        t.adjust_sizes(r);
      }
  };

  /*
  ATN_computed_tensor , the largest of all

  This object has become quite complex. It is the glue with the
  mat_elem_*.  It is able to perform an inline reduction (i.e. a
  reduction applied during the mat_elem->compute()) when it is
  allowed (i.e. no exact integration), or do the same reduction
  after the mat_elem->compute().
  The reduction may also involve other ATN_tensors.
  */

  struct mf_comp_vect;

  struct mf_comp {
    pnonlinear_elem_term nlt;
    const mesh_fem* pmf; /* always defined except when op_type == NORMAL */
    mf_comp_vect *owner;

    ATN_tensor *data;
    std::vector<const mesh_fem*> auxmf; /* used only by nonlinear terms */
    typedef enum { BASE=1, GRAD=2, HESS=3, NORMAL=4, GRADGT=5, GRADGTINV=6,
      NONLIN=7, DATA=8 } op_type;
    typedef enum { PLAIN_SHAPE = 0, VECTORIZED_SHAPE = 1,
      MATRIXIZED_SHAPE = 2 } field_shape_type;
    op_type op; /* the numerical values indicates the number
                of dimensions in the tensor */
    field_shape_type vshape; /* VECTORIZED_SHAPE if vectorization was required
                             (adds an addiational dimension to the tensor
                             which represents the component number.
                             MATRIXIZED_SHAPE for "matricization" of the
                             field.
                             */
    std::string reduction;
    /*
    vectorization of non-vector FEM:

    phi1  0    0
    0   phi1   0
    0     0  phi1
    phi2  0    0
    0   phi2   0
    0     0  phi2
    ...
    */
    mf_comp(mf_comp_vect *ow, const mesh_fem* pmf_, op_type op_,
      field_shape_type fst) :
    nlt(0), pmf(pmf_), owner(ow), data(0), op(op_), vshape(fst) { }
    mf_comp(mf_comp_vect *ow, const std::vector<const mesh_fem*> vmf,
      pnonlinear_elem_term nlt_) :
    nlt(nlt_), pmf(vmf[0]), owner(ow), data(0),
      auxmf(vmf.begin()+1, vmf.end()), op(NONLIN),
      vshape(PLAIN_SHAPE) { }
    mf_comp(mf_comp_vect *ow, ATN_tensor *t) :
      nlt(0), pmf(0), owner(ow), data(t), op(DATA), vshape(PLAIN_SHAPE) {}
    void push_back_dimensions(size_type cv, tensor_ranges &rng,
      bool only_reduced=false) const;
    bool reduced(unsigned i) const {
      if (i >= reduction.size()) return false;
      else return reduction[i] != ' ';
    }
  };

  struct mf_comp_vect : public std::vector<mf_comp> {
    const mesh_im *main_im;
  public:
    mf_comp_vect() : std::vector<mf_comp>(), main_im(0) { }
    mf_comp_vect(const mf_comp_vect &other)
      : std::vector<mf_comp>(other), main_im(other.main_im) {
        for (size_type i=0; i < size(); ++i) (*this)[i].owner = this;
    }
    void set_im(const mesh_im &mim) { main_im = &mim; }
    const mesh_im& get_im() const { return *main_im; }
  private:
    mf_comp_vect& operator=(const mf_comp_vect &other);
  };

  void mf_comp::push_back_dimensions(size_type cv, tensor_ranges &rng,
    bool only_reduced) const {
      switch (op) {
      case NONLIN:
        {
          const bgeot::multi_index &sizes = nlt->sizes(cv);
          for (unsigned j=0; j < sizes.size(); ++j)
            if (!only_reduced || !reduced(j))
              rng.push_back(short_type(sizes[j]));
        }
        break;
      case DATA:
        for (unsigned i=0; i < data->ranges().size(); ++i)
          if (!only_reduced || !reduced(i))
            rng.push_back(data->ranges()[i]);
        break;
      case NORMAL:
        assert(pmf==0);
        assert(&owner->get_im());
        assert(owner->get_im().linked_mesh().dim() != dim_type(-1));
        rng.push_back(owner->get_im().linked_mesh().dim());
        break;
      case GRADGT:
      case GRADGTINV:
        assert(pmf==0);
        assert(&owner->get_im());
        rng.push_back(owner->get_im().linked_mesh().dim()); // N
        rng.push_back(owner->get_im().linked_mesh().structure_of_convex(cv)->dim()); // P
        break;
      default:
        unsigned d = 0;
        if (!only_reduced || !reduced(d))
          rng.push_back(unsigned(pmf->nb_basic_dof_of_element(cv)));
        ++d;
        if (vshape == mf_comp::VECTORIZED_SHAPE) {
          if (!only_reduced || !reduced(d)) rng.push_back(pmf->get_qdim());
          ++d;
        }
        if (vshape == mf_comp::MATRIXIZED_SHAPE) {
          if (!only_reduced || !reduced(d)) {
            GMM_ASSERT1(pmf->get_qdims().size() == 2, "Non matrix field");
            rng.push_back(dim_type(pmf->get_qdims()[0]));
          }
          ++d;
          if (!only_reduced || !reduced(d)) rng.push_back(dim_type(pmf->get_qdims()[1]));
          ++d;
        }

        if (op == GRAD || op == HESS) {
          if (!only_reduced || !reduced(d))
            rng.push_back(pmf->linked_mesh().dim());
          ++d;
        }
        if (op == HESS) {
          if (!only_reduced || !reduced(d))
            rng.push_back(pmf->linked_mesh().dim());
          ++d;
        }
        break;
      }
  }


  class ATN_computed_tensor : public ATN_tensor {
    mf_comp_vect mfcomp;
    mat_elem_pool mep;
    pmat_elem_computation pmec;
    pmat_elem_type pme;
    pintegration_method pim;
    bgeot::pgeometric_trans pgt;
    base_tensor t;
    std::vector<scalar_type> data;
    TDIter data_base;
    stride_type tsize;
    dal::bit_vector req_bv;  /* bit_vector of values the mat_elem has to compute
                             (useful when only a subset is required from the
                             possibly very large elementary tensor) */
    bool has_inline_reduction; /* true if used with reductions inside the comp, for example:
                               "comp(Grad(#1)(:,i).Grad(#2)(:,i))" */
    computed_tensor_integration_callback icb; /* callback for inline reductions */

    /* if inline reduction are to be done, but were not possible (i.e. if exact
    integration was used) then a fallback is used: apply the reduction
    afterward, on the large expanded tensor */
    bgeot::tensor_reduction fallback_red;
    bool fallback_red_uptodate;
    TDIter fallback_base;

    size_type cv_shape_update;
    //mat_elem_inline_reduction inline_red;
  public:
    ATN_computed_tensor(const mf_comp_vect &mfcomp_) :
      mfcomp(mfcomp_), pmec(0), pme(0), pim(0), pgt(0), data_base(0) {
        has_inline_reduction = false;
        bool in_data = false;
        for (size_type i=0; i < mfcomp.size(); ++i) {
          if (mfcomp[i].reduction.size() || mfcomp[i].op == mf_comp::DATA) {
            has_inline_reduction = true;
            if (mfcomp[i].op == mf_comp::DATA) { add_child(*mfcomp[i].data); in_data = true; }
          }
          if (mfcomp[i].op != mf_comp::DATA && in_data) {
            /* constraint of fallback 'do_post_reduction' */
            ASM_THROW_ERROR("data tensors inside comp() cannot be intermixed with Grad() and Base() etc., they must appear LAST");
          }
        }
    }

  private:
    /* mostly for non-linear terms, such as a 3x3x3x3 tensor which may have
    many symmetries or many null elements..  in that case, it is preferable
    for getfem_mat_elem to handle only a sufficient subset of the tensor,
    and build back the full tensor via adequate strides and masks */

    /* append a dimension (full) to tref */
    stride_type add_dim(const tensor_ranges& rng, dim_type d, stride_type s, tensor_ref &tref) {
      assert(d < rng.size());
      tensor_strides v;
      index_type r = rng[d];
      tensor_mask m; m.set_full(d, r);
      v.resize(r);
      for (index_type i=0; i < r; ++i) v[i] = s*i;
      assert(tref.masks().size() == tref.strides().size());
      tref.set_ndim_noclean(dim_type(tref.ndim()+1));
      tref.push_mask(m);
      tref.strides().push_back(v);
      return s*r;
    }

    /* append a vectorized dimension to tref -- works also for cases
    where target_dim > 1
    */
    stride_type add_vdim(const tensor_ranges& rng, dim_type d,
      index_type target_dim, stride_type s,
      tensor_ref &tref) {
        assert(d < rng.size()-1);
        index_type r = rng[d], q=rng[d+1];
        index_type qmult = q/target_dim;
        assert(r%qmult == 0); assert(q%qmult==0);

        tensor_strides v;
        tensor_ranges trng(2); trng[0] = q; trng[1] = r;
        index_set ti(2); ti[0] = dim_type(d+1); ti[1] = d;
        tensor_mask m(trng,ti);
        v.resize(r*target_dim);
        tensor_ranges cnt(2);
        for (cnt[1]=0; cnt[1] < r; cnt[1]++) {
          for (index_type k=0; k < target_dim; ++k) {
            cnt[0] = k*qmult + (cnt[1]%qmult); //(cnt[1] % qmult)*target_dim + k;
            m.set_mask_val(m.lpos(cnt), true);
            v[cnt[1]*target_dim+k] = s*( k * r/qmult + cnt[1]/qmult); //s*((cnt[1]/qmult)*target_dim + k);
          }
        }
        assert(tref.masks().size() == tref.strides().size());
        tref.set_ndim_noclean(dim_type(tref.ndim()+2));
        tref.push_mask(m);
        tref.strides().push_back(v);
        return s*(r/qmult)*target_dim;
    }

    /* append a matrixized dimension to tref -- works also for cases
    where target_dim > 1 (in that case the rows are "vectorized")

    for example, the Base(RT0) in 2D (3 dof, target_dim=2) is:
    [0 1 2;
    3 4 5]


    if we set it in a mesh_fem of qdim = 3x2 , we produce the sparse
    elementary tensor 9x3x2 =

    x x x y y y
    0 . . 3 . . <- phi1
    . 0 . . 3 . <- phi2
    . . 0 . . 3 <- phi3
    1 . . 4 . . <- phi4
    . 1 . . 4 . <- phi5
    . . 1 . . 4 <- phi6
    2 . . 5 . . <- phi7
    . 2 . . 5 . <- phi8
    . . 2 . . 5 <- phi9

    */
    stride_type add_mdim(const tensor_ranges& rng, dim_type d,
      index_type target_dim, stride_type s, tensor_ref &tref) {
        assert(d < rng.size()-2);

        /* r = nb_dof, q = nb_rows, p = nb_cols */
        index_type r = rng[d], q=rng[d+1], p=rng[d+2];
        index_type qmult = (q*p)/target_dim;

        assert(r % q == 0);
        assert(p % target_dim == 0);
        assert(r % (p/target_dim) == 0);

        tensor_strides v;
        tensor_ranges trng(3); trng[0] = q; trng[1] = p; trng[2] = r;
        index_set ti(3); ti[0] = dim_type(d+1); ti[1] = dim_type(d+2); ti[2] = d;
        tensor_mask m(trng,ti);
        v.resize(r*target_dim);
        tensor_ranges cnt(3);
        for (cnt[2]=0; cnt[2] < r; cnt[2]++) { // loop over virtual dof number {
          for (index_type k=0; k < target_dim; ++k) {
            unsigned pos = (cnt[2]*target_dim+k) % (q*p);
            //unsigned ii = (pos%q), jj = (pos/q);
            unsigned ii = (pos/p), jj = (pos%p);
            cnt[0] = ii; cnt[1] = jj;
            //cerr << " set_mask_val(lpos(" << cnt[0] << "," << cnt[1] << "," << cnt[2] << ") = " << m.lpos(cnt) << ")\n";
            m.set_mask_val(m.lpos(cnt), true);
            v[cnt[2]*target_dim+k] = s*(k * r/qmult + cnt[2]/qmult); //s*((cnt[2]/qmult)*target_dim + k);
          }
        }
        assert(tref.masks().size() == tref.strides().size());
        tref.set_ndim_noclean(dim_type(tref.ndim()+3));
        tref.push_mask(m);
        // cerr << "rng = " << rng << "\nr=" << r << ", q=" << q << ", p="
        //      << p << ", qmult =" << qmult << ", target_dim= " << target_dim
        //      << "\n" << "m = " << m << "\nv=" << v << "\n";
        tref.strides().push_back(v);
        return s*(r/qmult)*target_dim;
    }


    /* called when the FEM has changed */
    void update_pmat_elem(size_type cv) {
      pme = 0;
      for (size_type i=0; i < mfcomp.size(); ++i) {
        if (mfcomp[i].op == mf_comp::DATA) continue;
        pfem fem = (mfcomp[i].pmf ? mfcomp[i].pmf->fem_of_element(cv)
          : NULL);
        pmat_elem_type pme2 = 0;
        switch (mfcomp[i].op) {
        case mf_comp::BASE: pme2 = mat_elem_base(fem); break;
        case mf_comp::GRAD: pme2 = mat_elem_grad(fem); break;
        case mf_comp::HESS: pme2 = mat_elem_hessian(fem); break;
        case mf_comp::NORMAL: pme2 = mat_elem_unit_normal(); break;
        case mf_comp::GRADGT:
        case mf_comp::GRADGTINV:
          pme2 = mat_elem_grad_geotrans(mfcomp[i].op == mf_comp::GRADGTINV);
          break;
        case mf_comp::NONLIN: {
          std::vector<pfem> ftab(1+mfcomp[i].auxmf.size());
          ftab[0] = fem;
          for (unsigned k=0; k < mfcomp[i].auxmf.size(); ++k)
            ftab[k+1] = mfcomp[i].auxmf[k]->fem_of_element(cv);
          pme2 = mat_elem_nonlinear(mfcomp[i].nlt, ftab);
                              } break;
        case mf_comp::DATA: /*ignore*/;
        }
        if (pme == 0) pme = pme2;
        else pme = mat_elem_product(pme, pme2);
      }

      if (pme == 0) pme = mat_elem_empty();
      //ASM_THROW_ERROR("no Base() or Grad() or etc!");
    }



    size_type
      push_back_mfcomp_dimensions(size_type cv, const mf_comp& mc,
      unsigned &d, const bgeot::tensor_ranges &rng,
      bgeot::tensor_ref &tref, size_type tsz=1) {
        if (mc.op == mf_comp::NONLIN) {
          for (size_type j=0; j < mc.nlt->sizes(cv).size(); ++j)
            tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
        } else if (mc.op == mf_comp::DATA) {
          assert(tsz == 1);
          tref = mc.data->tensor();
          tsz *= tref.card();
          d += tref.ndim();
        } else if (mc.op == mf_comp::NORMAL) {
          tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
        } else if (mc.op == mf_comp::GRADGT ||
          mc.op == mf_comp::GRADGTINV) {
            tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
            tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
        } else {
          size_type target_dim = mc.pmf->fem_of_element(cv)->target_dim();
          size_type qdim = mc.pmf->get_qdim();

          //cerr << "target_dim = " << target_dim << ", qdim = " << qdim << ", vectorize=" << mc.vectorize << ", rng=" << rng << " d=" << d << ", tsz=" << tsz << "\n";
          if (mc.vshape == mf_comp::VECTORIZED_SHAPE) {
            if (target_dim == qdim) {
              tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
              tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
            } else {
              tsz = add_vdim(rng,dim_type(d),index_type(target_dim),
                stride_type(tsz), tref);
              d += 2;
            }
          } else if (mc.vshape == mf_comp::MATRIXIZED_SHAPE) {
            if (target_dim == qdim) {
              tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
              tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
              tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
            } else {
              tsz = add_mdim(rng, dim_type(d), index_type(target_dim),
                stride_type(tsz), tref);
              d += 3;
            }
          } else tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
          if (mc.op == mf_comp::GRAD || mc.op == mf_comp::HESS) {
            tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
          }
          if (mc.op == mf_comp::HESS) {
            tsz = add_dim(rng, dim_type(d++), stride_type(tsz), tref);
          }
        }
        return tsz;
    }

    void update_shape_with_inline_reduction(size_type cv) {
      fallback_red_uptodate = false;
      icb.tensor_bases.resize(mfcomp.size()); /* todo : resize(nb_mfcomp_not_data) */
      icb.red.clear();
      for (size_type i=0; i < mfcomp.size(); ++i) {
        tensor_ref tref;
        tensor_ranges rng;
        unsigned d = 0;
        mfcomp[i].push_back_dimensions(cv,rng);
        push_back_mfcomp_dimensions(cv,mfcomp[i], d, rng, tref);
        assert(tref.ndim() == rng.size() && d == rng.size());
        if (mfcomp[i].reduction.size() == 0)
          mfcomp[i].reduction.insert(size_type(0), tref.ndim(), ' ');
        if (mfcomp[i].op != mf_comp::DATA) /* should already have the correct base */
          tref.set_base(icb.tensor_bases[i]);
        tref.update_idx2mask();
        if (mfcomp[i].reduction.size() != tref.ndim()) {
          ASM_THROW_TENSOR_ERROR("wrong number of indices for the "<< int(i+1)
            << "th argument of the reduction "<< name()
            << " (expected " << int(tref.ndim())
            << " indexes, got "
            << mfcomp[i].reduction.size());
        }
        icb.red.insert(tref, mfcomp[i].reduction);
      }
      icb.red.prepare();
      icb.red.result(tensor());
      r_.resize(tensor().ndim());
      for (dim_type i=0; i < tensor().ndim(); ++i) r_[i] = tensor().dim(i);
      tsize = tensor().card();
      //cerr << "update_shape_with_inline_reduction: tensor=" << tensor()
      //     << "\nr_=" << r_ << ", tsize=" << tsize << "\n";
    }

    void update_shape_with_expanded_tensor(size_type cv) {
      icb.red.clear();
      unsigned d = 0;
      for (size_type i=0; i < mfcomp.size(); ++i) {
        tsize = stride_type(push_back_mfcomp_dimensions(cv, mfcomp[i], d, r_, tensor(), tsize));
      }
      assert(d == r_.size());
      tensor().update_idx2mask();
    }

    void check_shape_update(size_type cv, dim_type) {
      const mesh_im& mi = mfcomp.get_im();
      pintegration_method pim2;
      bgeot::pgeometric_trans pgt2;
      bool fem_changed = false;
      pgt2 = mi.linked_mesh().trans_of_convex(cv);
      pim2 = mi.int_method_of_element(cv);
      // cerr << "computed tensor cv=" << cv << " f=" << int(face) << "\n";
      /* shape is considered for update only if the FEM changes,
      changes of pgt or integration method does not affect shape
      (only the mat_elem) */
      cv_shape_update = cv;
      shape_updated_ = (pme == 0); //false;
      for (size_type i=0; i < nchilds(); ++i)
        shape_updated_ = shape_updated_ || child(i).is_shape_updated();
      for (size_type i=0; shape_updated_ == false && i < mfcomp.size(); ++i) {
        if (mfcomp[i].pmf == 0) continue;
        if  (current_cv == size_type(-1)) {
          shape_updated_ = true; fem_changed = true;
        } else {
          fem_changed = fem_changed ||
            (mfcomp[i].pmf->fem_of_element(current_cv) !=
            mfcomp[i].pmf->fem_of_element(cv));
          /* for FEM with non-constant nb_dof.. */
          shape_updated_ = shape_updated_ ||
            (mfcomp[i].pmf->nb_basic_dof_of_element(current_cv) !=
            mfcomp[i].pmf->nb_basic_dof_of_element(cv));
        }
      }
      if (shape_updated_) {
        r_.resize(0);
        /* get the new ranges */
        for (unsigned i=0; i < mfcomp.size(); ++i)
          mfcomp[i].push_back_dimensions(cv, r_, true);
      }
      if (fem_changed || shape_updated_) {
        /* build the new mat_elem structure */
        update_pmat_elem(cv);
      }
      if (shape_updated_ || fem_changed || pgt != pgt2 || pim != pim2) {
        pgt = pgt2; pim = pim2;
        pmec = mep(pme, pim, pgt, has_inline_reduction);
      }
    }

    void reinit_() {
      if (!shape_updated_) return;
      tensor().clear();
      tsize = 1;
      if (has_inline_reduction) {
        update_shape_with_inline_reduction(cv_shape_update);
      } else {
        update_shape_with_expanded_tensor(cv_shape_update);
      }
      data_base = 0;
      tensor().set_base(data_base);
    }
    void update_childs_required_shape() {
    }

    /* fallback when inline reduction is not possible:
    do the reduction after evaluation of the mat_elem */
    void do_post_reduction(size_type cv) {
      if (!fallback_red_uptodate) {
        fallback_red_uptodate = true;
        std::string s;
        size_type sz = 1;
        tensor_ref tref; tensor_ranges r;
        unsigned cnt, d=0;
        /* insert the tensorial product of Grad() etc */
        for (cnt=0; cnt < mfcomp.size() && mfcomp[cnt].op != mf_comp::DATA; ++cnt) {
          mfcomp[cnt].push_back_dimensions(cv,r);
          sz = push_back_mfcomp_dimensions(cv, mfcomp[cnt], d, r, tref, sz);
          s += mfcomp[cnt].reduction;
        }
        fallback_red.clear();
        tref.set_base(fallback_base);
        fallback_red.insert(tref, s);
        /* insert the optional data tensors */
        for ( ; cnt < mfcomp.size(); ++cnt) {
          assert(mfcomp[cnt].op == mf_comp::DATA);
          fallback_red.insert(mfcomp[cnt].data->tensor(), mfcomp[cnt].reduction);
        }
        fallback_red.prepare();
        fallback_red.result(tensor()); /* this SHOULD NOT, IN ANY CASE change the shape or strides of tensor() .. */
        assert(icb.red.reduced_range == fallback_red.reduced_range);
      }
      icb.resize_t(t);
      fallback_base = &(*t.begin());
      fallback_red.do_reduction();
    }

    void exec_(size_type cv, dim_type face) {
      const mesh_im& mim = mfcomp.get_im();
      for (unsigned i=0; i < mfcomp.size(); ++i) {
        if (mfcomp[i].op == mf_comp::DATA) {
          size_type fullsz = 1;
          for (unsigned j=0; j < mfcomp[i].data->ranges().size(); ++j)
            fullsz *= mfcomp[i].data->ranges()[j];
          if (fullsz != size_type(mfcomp[i].data->tensor().card()))
            ASM_THROW_TENSOR_ERROR("aaarg inline reduction will explode with non-full tensors. "
            "Complain to the author, I was too lazy to do that properly");
        }
      }
      icb.was_called = false;
      if (face == dim_type(-1)) {
        pmec->gen_compute(t, mim.linked_mesh().points_of_convex(cv), cv,
          has_inline_reduction ? &icb : 0);
      } else {
        pmec->gen_compute_on_face(t, mim.linked_mesh().points_of_convex(cv), face, cv,
          has_inline_reduction ? &icb : 0);
      }

      if (has_inline_reduction && icb.was_called == false) {
        do_post_reduction(cv);
        data_base = &fallback_red.out_data[0];
      } else data_base = &(*t.begin());
      GMM_ASSERT1(t.size() == size_type(tsize),
        "Internal error: bad size " << t.size() << " should be " << tsize);
    }
  };


  /* extract data for each dof of the convex */
  class ATN_tensor_from_dofs_data : public ATN_tensor_w_data {
    const base_asm_data *basm; //scalar_type* global_array;
    vdim_specif_list vdim;
    multi_tensor_iterator mti;
    tensor_ranges e_r;
    std::vector< tensor_strides > e_str;
  public:
    ATN_tensor_from_dofs_data(const base_asm_data *basm_,
      const vdim_specif_list& d) :
    basm(basm_), vdim(d) {
    }
    void check_shape_update(size_type cv, dim_type) {
      shape_updated_ = false;
      r_.resize(vdim.size());
      for (dim_type i=0; i < vdim.size(); ++i) {
        if (vdim[i].is_mf_ref()) {
          size_type nbde = vdim[i].pmf->nb_basic_dof_of_element(cv);
          if (nbde != ranges()[i])
          { r_[i] = unsigned(nbde); shape_updated_ = true; }
        } else if (vdim[i].dim != ranges()[i]) {
          r_[i] = unsigned(vdim[i].dim);
          shape_updated_ = true;
        }
      }
    }
    virtual void init_required_shape() { req_shape = tensor_shape(ranges()); }

  private:
    void reinit_() {
      ATN_tensor_w_data::reinit_();
      mti.assign(tensor(), true);
    }
    void exec_(size_type cv, dim_type ) {
      vdim.build_strides_for_cv(cv, e_r, e_str);
      assert(e_r == ranges());
      mti.rewind();
      basm->copy_with_mti(e_str, mti, (vdim.nb_mf() >= 1) ? vdim[0].pmf : 0);
    }
  };

  /* enforce symmetry of a 2D tensor
  (requiring only the upper-triangle of its child and
  duplicating it) */
  class ATN_symmetrized_tensor : public ATN_tensor_w_data {
    multi_tensor_iterator mti;
  public:
    ATN_symmetrized_tensor(ATN_tensor& a) { add_child(a); }
    void check_shape_update(size_type , dim_type) {
      if ((shape_updated_ = child(0).is_shape_updated())) {
        if (child(0).ranges().size() != 2 ||
          child(0).ranges()[0] != child(0).ranges()[1])
          ASM_THROW_TENSOR_ERROR("can't symmetrize a non-square tensor "
          "of sizes " << child(0).ranges());
        r_ = child(0).ranges();
      }
    }
    void update_childs_required_shape() {
      tensor_shape ts = req_shape;
      tensor_shape ts2 = req_shape;
      index_set perm(2); perm[0] = 1; perm[1] = 0; ts2.permute(perm);
      ts.merge(ts2, false);
      tensor_mask dm; dm.set_triangular(ranges()[0],0,1);
      tensor_shape tsdm(2); tsdm.push_mask(dm);
      ts.merge(tsdm, true);
      child(0).merge_required_shape(ts);
    }

  private:
    void reinit_() {
      req_shape.set_full(ranges()); // c'est plus simple comme ca
      ATN_tensor_w_data::reinit0();
      mti.assign(child(0).tensor(),true);
    }
    void exec_(size_type, dim_type) {
      std::fill(data.begin(), data.end(), 0.);
      mti.rewind();
      index_type n = ranges()[0];
      do {
        index_type i=mti.index(0), j=mti.index(1);
        data[i*n+j]=data[j*n+i]=mti.p(0);
      } while (mti.qnext1());
    }
  };


  template<class UnaryOp> class ATN_unary_op_tensor
    : public ATN_tensor_w_data {
      multi_tensor_iterator mti;
  public:
    ATN_unary_op_tensor(ATN_tensor& a) { add_child(a); }
    void check_shape_update(size_type , dim_type) {
      if ((shape_updated_ = (ranges() != child(0).ranges())))
        r_ = child(0).ranges();
    }
  private:
    void reinit_() {
      ATN_tensor_w_data::reinit0();
      mti.assign(tensor(), child(0).tensor(),false);
    }
    void update_cv_(size_type, dim_type) {
      mti.rewind();
      do {
        mti.p(0) = UnaryOp()(mti.p(1));
      } while (mti.qnext2());
    }
  };

  /* sum AND scalar scaling */
  class ATN_tensors_sum_scaled : public ATN_tensor_w_data {
    std::vector<multi_tensor_iterator> mti;
    std::vector<scalar_type> scales; /* utile pour des somme "scaled" du genre 0.5*t1 + 0.5*t2 */
  public:
    ATN_tensors_sum_scaled(ATN_tensor& t1, scalar_type s1) {
      add_child(t1);
      scales.resize(1); scales[0]=s1;
    }
    void push_scaled_tensor(ATN_tensor& t, scalar_type s) {
      add_child(t); scales.push_back(s);
    }
    void check_shape_update(size_type , dim_type) {
      if ((shape_updated_ = child(0).is_shape_updated()))
        r_ = child(0).ranges();
      for (size_type i=1; i < nchilds(); ++i)
        if (ranges() != child(i).ranges())
          ASM_THROW_TENSOR_ERROR("can't add two tensors of sizes " <<
          ranges() << " and " << child(i).ranges());
    }
    void apply_scale(scalar_type s) {
      for (size_type i=0; i < scales.size(); ++i) scales[i] *= s;
    }
    ATN_tensors_sum_scaled* is_tensors_sum_scaled() { return this; }
  private:
    void reinit_() {
      ATN_tensor_w_data::reinit0();
      mti.resize(nchilds());
      for (size_type i=0; i < nchilds(); ++i)
        mti[i].assign(tensor(), child(i).tensor(),false);
    }
    void exec_(size_type, dim_type) {
      //if (cv == 0) {
      // cerr << "ATN_tensors_sum["<< name() << "] req_shape="
      //      << req_shape << endl;
      //}
      std::fill(data.begin(), data.end(), 0.);
      mti[0].rewind();
      do {
        mti[0].p(0) = mti[0].p(1)*scales[0];
      } while (mti[0].qnext2());
      for (size_type i=1; i < nchilds(); ++i) {
        mti[i].rewind();
        do {
          mti[i].p(0) = mti[i].p(0)+mti[i].p(1)*scales[i];
        } while (mti[i].qnext2());
      }
    }
  };

  class ATN_tensor_scalar_add : public ATN_tensor_w_data {
    scalar_type v;
    multi_tensor_iterator mti;
    int sgn; /* v+t or v-t ? */
  public:
    ATN_tensor_scalar_add(ATN_tensor& a, scalar_type v_, int sgn_) :
      v(v_), sgn(sgn_) { add_child(a); }
    void check_shape_update(size_type , dim_type) {
      if ((shape_updated_ = child(0).is_shape_updated()))
        r_ = child(0).ranges();
    }
  private:
    void reinit_() {
      ATN_tensor_w_data::reinit_();
      mti.assign(tensor(), child(0).tensor(),false);
    }
    void exec_(size_type, dim_type) {
      std::fill(data.begin(), data.end(), v);
      mti.rewind();
      do {
        if (sgn > 0)
          mti.p(0) += mti.p(1);
        else mti.p(0) -= mti.p(1);
      } while (mti.qnext2());
    }
  };

  class ATN_print_tensor : public ATN {
    std::string name;
  public:
    ATN_print_tensor(ATN_tensor& a, std::string n_)
      : name(n_) { add_child(a); }
  private:
    void reinit_() {}
    void exec_(size_type cv, dim_type face) {
      multi_tensor_iterator mti(child(0).tensor(), true);
      cout << "------- > evaluation of " << name << ", at" << endl;
      cout << "convex " << cv;
      if (face != dim_type(-1)) cout << ", face " << int(face);
      cout << endl;
      cout << "  size   = " << child(0).ranges() << endl;
      mti.rewind();
      do {
        cout << " @[";
        for (size_type i=0; i < child(0).ranges().size(); ++i)
          cout <<(i>0 ? "," : "") << mti.index(dim_type(i));
        cout << "] = " << mti.p(0) << endl;
      } while (mti.qnext1());
    }
  };


  /*
  -------------------
  analysis of the supplied string
  -----------------
  */

  std::string asm_tokenizer::syntax_err_print() {
    std::string s;
    if (tok_pos - err_msg_mark > 80) err_msg_mark = tok_pos - 40;
    if (str.length() - err_msg_mark < 80) s = tok_substr(err_msg_mark, str.length());
    else { s = tok_substr(err_msg_mark,err_msg_mark+70); s.append(" ... (truncated)"); }
    s += "\n" + std::string(std::max(int(tok_pos - err_msg_mark),0), '-') + "^^";
    return s;
  }

  void asm_tokenizer::get_tok() {
    gmm::standard_locale sl;
    curr_tok_ival = -1;
    while (tok_pos < str.length() && isspace(str[tok_pos])) ++tok_pos;
    if (tok_pos == str.length()) {
      curr_tok_type = END; tok_len = 0;
    } else if (strchr("{}(),;:=-.*/+", str[tok_pos])) {
      curr_tok_type = tok_type_enum(str[tok_pos]); tok_len = 1;
    } else if (str[tok_pos] == '$' || str[tok_pos] == '#' || str[tok_pos] == '%') {
      curr_tok_type = str[tok_pos] == '$' ? ARGNUM_SELECTOR :
        (str[tok_pos] == '#' ? MFREF : IMREF);
    tok_len = 1;
    curr_tok_ival = 0;
    while (isdigit(str[tok_pos+tok_len])) {
      curr_tok_ival*=10;
      curr_tok_ival += str[tok_pos+tok_len] - '0';
      ++tok_len;
    }
    curr_tok_ival--;
    } else if (isalpha(str[tok_pos])) {
      curr_tok_type = IDENT;
      tok_len = 0;
      while (isalnum(str[tok_pos+tok_len]) || str[tok_pos+tok_len] == '_') ++tok_len;
    } else if (isdigit(str[tok_pos])) {
      curr_tok_type = NUMBER;
      char *p;
      curr_tok_dval = strtod(&str[0]+tok_pos, &p);
      tok_len = p - &str[0] - tok_pos;
    }
    if (tok_pos < str.length())
      curr_tok = str.substr(tok_pos, tok_len);
    else
      curr_tok.clear();
  }

  const mesh_fem& generic_assembly::do_mf_arg_basic() {
    if (tok_type() != MFREF) ASM_THROW_PARSE_ERROR("expecting mesh_fem reference");
    if (tok_mfref_num() >= mftab.size())
      ASM_THROW_PARSE_ERROR("reference to a non-existant mesh_fem #" << tok_mfref_num()+1);
    const mesh_fem& mf_ = *mftab[tok_mfref_num()]; advance();
    return mf_;
  }

  const mesh_fem& generic_assembly::do_mf_arg(std::vector<const mesh_fem*> * multimf) {
    if (!multimf) advance(); // special hack for NonLin$i(#a,#b,..)
    accept(OPEN_PAR,"expecting '('");
    const mesh_fem &mf_ = do_mf_arg_basic();
    if (multimf) {
      multimf->resize(1); (*multimf)[0] = &mf_;
      while (advance_if(COMMA)) {
        if (tok_type() != MFREF) ASM_THROW_PARSE_ERROR("expecting mesh_fem reference");
        if (tok_mfref_num() >= mftab.size())
          ASM_THROW_PARSE_ERROR("reference to a non-existant mesh_fem #" << tok_mfref_num()+1);
        multimf->push_back(mftab[tok_mfref_num()]); advance();
      }
    }
    accept(CLOSE_PAR, "expecting ')'");
    return mf_;
  }

  /* "inline" reduction operations inside comp(..) */
  std::string generic_assembly::do_comp_red_ops() {
    std::string s;
    if (advance_if(OPEN_PAR)) {
      size_type j = 0;
      do {
        if (tok_type() == COLON) {
          s.push_back(' '); advance(); j++;
        } else if (tok_type() == IDENT) {
          if ((tok().length()==1 && isalpha(tok()[0])) || islower(tok()[0])) {
            s.push_back(tok()[0]); advance(); j++;
          } else ASM_THROW_PARSE_ERROR("invalid reduction index '" << tok() <<
            "', only lower case characters allowed");
        }
      } while (advance_if(COMMA));
      accept(CLOSE_PAR, "expecting ')'");
    }
    return s;
  }

  static mf_comp::field_shape_type get_shape(const std::string &s) {
    if (s[0] == 'v') return mf_comp::VECTORIZED_SHAPE;
    else if (s[0] == 'm') return mf_comp::MATRIXIZED_SHAPE;
    else return mf_comp::PLAIN_SHAPE;
  }

  ATN_tensor* generic_assembly::do_comp() {
    accept(OPEN_PAR, "expecting '('");
    mf_comp_vect what;
    bool in_data = false;
    /* the first optional argument is the "main" mesh_im, i.e. the one
    whose integration methods are used, (and whose linked_mesh is
    used for mf_comp::NORMAL, mf_comp::GRADGT etc computations). If
    not given, then the first mesh_im pushed is used (then expect
    problems when assembling simultaneously on two different
    meshes).
    */
    if (tok_type() == IMREF) {
      if (tok_imref_num() >= imtab.size())
        ASM_THROW_PARSE_ERROR("reference to a non-existant mesh_im %" << tok_imref_num()+1);
      what.set_im(*imtab[tok_imref_num()]); advance();
      accept(COMMA, "expecting ','");
    } else {
      what.set_im(*imtab[0]);
    }
    do {
      if (tok_type() == CLOSE_PAR) break;
      if (tok_type() != IDENT) ASM_THROW_PARSE_ERROR("expecting Base or Grad or Hess, Normal, etc..");
      std::string f = tok();
      const mesh_fem *pmf = 0;
      if (f.compare("Base")==0 || f.compare("vBase")==0 || f.compare("mBase")==0) {
        pmf = &do_mf_arg();
        what.push_back(mf_comp(&what, pmf, mf_comp::BASE, get_shape(f)));
      } else if (f.compare("Grad")==0 || f.compare("vGrad")==0 || f.compare("mGrad")==0) {
        pmf = &do_mf_arg();
        what.push_back(mf_comp(&what, pmf, mf_comp::GRAD, get_shape(f)));
      } else if (f.compare("Hess")==0 || f.compare("vHess")==0 || f.compare("mHess")==0) {
        pmf = &do_mf_arg();
        what.push_back(mf_comp(&what, pmf, mf_comp::HESS, get_shape(f)));
      } else if (f.compare("NonLin")==0) {
        size_type num = 0; /* default value */
        advance();
        if (tok_type() == ARGNUM_SELECTOR) { num = tok_argnum(); advance(); }
        if (num >= innonlin.size()) ASM_THROW_PARSE_ERROR("NonLin$" << num << " does not exist");
        std::vector<const mesh_fem*> allmf;
        pmf = &do_mf_arg(&allmf); what.push_back(mf_comp(&what, allmf, innonlin[num]));
      } else if (f.compare("Normal") == 0) {
        advance();
        accept(OPEN_PAR,"expecting '('"); accept(CLOSE_PAR,"expecting ')'");
        pmf = 0; what.push_back(mf_comp(&what, pmf, mf_comp::NORMAL, mf_comp::PLAIN_SHAPE));
      } else if (f.compare("GradGT") == 0 ||
        f.compare("GradGTInv") == 0) {
          advance();
          accept(OPEN_PAR,"expecting '('"); accept(CLOSE_PAR,"expecting ')'");
          pmf = 0;
          what.push_back(mf_comp(&what, pmf,
            f.compare("GradGT") == 0 ?
            mf_comp::GRADGT :
          mf_comp::GRADGTINV, mf_comp::PLAIN_SHAPE));
      } else {
        if (vars.find(f) != vars.end()) {
          what.push_back(mf_comp(&what, vars[f]));
          in_data = true;
          advance();
        } else {
          ASM_THROW_PARSE_ERROR("expecting Base, Grad, vBase, NonLin ...");
        }
      }

      if (!in_data && f[0] != 'v' && f[0] != 'm' && pmf && pmf->get_qdim() != 1 && f.compare("NonLin")!=0) {
        ASM_THROW_PARSE_ERROR("Attempt to use a vector mesh_fem as a scalar mesh_fem");
      }
      what.back().reduction = do_comp_red_ops();
    } while (advance_if(PRODUCT));
    accept(CLOSE_PAR, "expecting ')'");

    return record(std::make_unique<ATN_computed_tensor>(what));
  }

  void generic_assembly::do_dim_spec(vdim_specif_list& lst) {
    lst.resize(0);
    accept(OPEN_PAR, "expecting '('");
    while (true) {
      if (tok_type() == IDENT) {
        if (tok().compare("mdim")==0) lst.push_back(vdim_specif(do_mf_arg().linked_mesh().dim()));
        else if (tok().compare("qdim")==0) lst.push_back(vdim_specif(do_mf_arg().get_qdim()));
        else ASM_THROW_PARSE_ERROR("expecting mdim(#mf) or qdim(#mf) or a number or a mesh_fem #id");
      } else if (tok_type() == NUMBER) {
        lst.push_back(vdim_specif(tok_number_ival()+1));
        advance();
      } else if (tok_type() == MFREF) {
        lst.push_back(vdim_specif(&do_mf_arg_basic()));
      } else if (tok_type() != CLOSE_PAR) ASM_THROW_PARSE_ERROR("expecting mdim(#mf) or qdim(#mf) or a number or a mesh_fem #id");
      /*      if (mfcnt && !lst.back().is_mf_ref())
      ASM_THROW_PARSE_ERROR("#mf argument must be given after numeric dimensions");*/
      if (advance_if(CLOSE_PAR)) break;
      accept(COMMA,"expecting ',' or ')'");
    }
  }


  ATN_tensor* generic_assembly::do_data() {
    //    ATN_tensor *t;
    size_type datanum = 0; /* par defaut */
    if (tok_type() != OPEN_PAR) { /* on peut oublier le numero de dataset */
      if (tok_type() != ARGNUM_SELECTOR)
        ASM_THROW_PARSE_ERROR("expecting dataset number");
      datanum = tok_argnum();
      advance();
    }
    if (datanum >= indata.size())
      ASM_THROW_PARSE_ERROR("wrong dataset number: " << datanum);

    vdim_specif_list sz;
    do_dim_spec(sz);

    if (sz.nbelt() != indata[datanum]->vect_size())
      ASM_THROW_PARSE_ERROR("invalid size for data argument " << datanum+1 <<
      " real size is " << indata[datanum]->vect_size()
      << " expected size is " << sz.nbelt());
    return record(std::make_unique<ATN_tensor_from_dofs_data>(indata[datanum].get(), sz));
  }

  std::pair<ATN_tensor*, std::string>
    generic_assembly::do_red_ops(ATN_tensor* t) {
      std::string s;

      if (advance_if(OPEN_PAR)) {
        size_type j = 0;
        do {
          if (tok_type() == COLON) {
            s.push_back(' '); advance(); j++;
          } else if (tok_type() == NUMBER) {
            t = record(std::make_unique<ATN_sliced_tensor>(*t, dim_type(j),
              tok_number_ival())); advance();
          } else if (tok_type() == IDENT) {
            if ((tok().length()==1 && isalpha(tok()[0])) || islower(tok()[0])) {
              s.push_back(tok()[0]); advance(); j++;
            } else ASM_THROW_PARSE_ERROR("invalid reduction index '" << tok() <<
              "', only lower case chars allowed");
          }
        } while (advance_if(COMMA));
        accept(CLOSE_PAR, "expecting ')'");
      }
      return std::pair<ATN_tensor*,std::string>(t,s);
  }

  /*
  ( expr )
  variable
  comp(..)
  data(data)
  */
  tnode generic_assembly::do_tens() {
    tnode t;
    push_mark();
    if (advance_if(OPEN_PAR)) {
      t = do_expr();
      accept(CLOSE_PAR, "expecting ')'");
    } else if (tok_type() == NUMBER) {
      t.assign(tok_number_dval()); advance();
    } else if (tok_type() == IDENT) {
      if (vars.find(tok()) != vars.end()) {
        t.assign(vars[tok()]); advance();
      } else if (tok().compare("comp")==0) {
        advance(); t.assign(do_comp());
      } else if (tok().compare("data")==0) {
        advance(); t.assign(do_data());
      } else if (tok().compare("sym")==0) {
        advance();
        tnode t2 = do_expr();
        if (t2.type() != tnode::TNTENSOR)
          ASM_THROW_PARSE_ERROR("can't symmetrise a scalar!");
        t.assign(record(std::make_unique<ATN_symmetrized_tensor>(*t2.tensor())));
      } else ASM_THROW_PARSE_ERROR("unknown identifier: " << tok());
    } else ASM_THROW_PARSE_ERROR("unexpected token: " << tok());
    pop_mark();
    return t;
  }

  /*
  handle tensorial product/reduction

  a(:,i).b(j,i).(c)(1,:,i)
  */
  tnode generic_assembly::do_prod() {
    reduced_tensor_arg_type ttab;

    do {
      tnode t = do_tens();
      if (t.type() == tnode::TNCONST) {
        if (ttab.size() == 0) return t;
        else ASM_THROW_PARSE_ERROR("can't mix tensor and scalar into a "
          "reduction expression");
      }
      ttab.push_back(do_red_ops(t.tensor()));
    } while (advance_if(PRODUCT));
    if (ttab.size() == 1 && ttab[0].second.length() == 0) {
      return tnode(ttab[0].first);
    } else {
      return tnode(record(std::make_unique<ATN_reduced_tensor>(ttab)));
    }
  }

  /* calls do_prod() once,
  and handle successive reordering/diagonals transformations */
  tnode generic_assembly::do_prod_trans() {
    tnode t = do_prod();
    while (advance_if(OPEN_BRACE)) {
      index_set reorder;
      size_type j = 0;
      dal::bit_vector check_permut;
      if (t.type() != tnode::TNTENSOR)
        ASM_THROW_PARSE_ERROR("can't use reorder braces on a constant!");
      for (;; ++j) {
        size_type i;
        if (tok_type() == COLON) i = j;
        else if (tok_type() == NUMBER) i = tok_number_ival(1000);
        else ASM_THROW_PARSE_ERROR("only numbers or colons allowed here");
        if (check_permut.is_in(i)) { /* on prend la diagonale du tenseur */
          t = tnode(record(std::make_unique<ATN_diagonal_tensor>(*t.tensor(), dim_type(i),
            dim_type(j))));
          check_permut.add(j);
          reorder.push_back(dim_type(j));
        } else {
          check_permut.add(i);
          reorder.push_back(dim_type(i));
        }
        advance();
        if (advance_if(CLOSE_BRACE)) break;
        accept(COMMA, "expecting ','");
      }
      if (check_permut.first_false() != reorder.size()) {
        cerr << check_permut << endl;
        cerr << vref(reorder) << endl;
        ASM_THROW_PARSE_ERROR("you did not give a real permutation:"
                              << vref(reorder));
      }
      t = tnode(record(std::make_unique<ATN_permuted_tensor>(*t.tensor(), reorder)));
    }
    return t;
  }

  /*
  term := prod_trans*prod_trans/prod_trans ...
  */
  tnode generic_assembly::do_term() {
    push_mark();
    err_set_mark();
    tnode t = do_prod_trans();
    while (true) {
      bool mult;
      if (advance_if(MULTIPLY)) mult = true;
      else if (advance_if(DIVIDE)) mult = false;
      else break;
      tnode t2 = do_prod();
      if (mult == false && t.type() == tnode::TNCONST
        && t2.type() == tnode::TNTENSOR)
        ASM_THROW_PARSE_ERROR("can't divide a constant by a tensor");
      if (t.type() == tnode::TNTENSOR && t2.type() == tnode::TNTENSOR) {
        ASM_THROW_PARSE_ERROR("tensor term-by-term productor division not "
          "implemented yet! are you sure you need it ?");
      } else if (t.type() == tnode::TNCONST && t2.type() == tnode::TNCONST) {
        if (mult)
          t.assign(t.xval()*t2.xval());
        else {
          t2.check0();
          t.assign(t.xval()/t2.xval());
        }
      } else {
        if (t.type() != tnode::TNTENSOR) std::swap(t,t2);
        scalar_type v = t2.xval();
        if (!mult) {
          if (v == 0.) { ASM_THROW_PARSE_ERROR("can't divide by zero"); }
          else v = 1./v;
        }
        if (t.tensor()->is_tensors_sum_scaled() && !t.tensor()->is_frozen()) {
          t.tensor()->is_tensors_sum_scaled()->apply_scale(v);
        } else {
          t.assign(record(std::make_unique<ATN_tensors_sum_scaled>(*t.tensor(), v)));
        }
      }
    }
    pop_mark();
    return t;
  }

  /*
  expr := term + term - term + ...
  suboptimal for things like t1+1-2-1 (which gives (((t1+1)-2)-1) )
  ... could be fixed but noone needs that i guess
  */
  tnode generic_assembly::do_expr() {
    bool negt=false;
    push_mark();
    if (advance_if(MINUS)) negt = true;
    tnode t = do_term();
    if (negt) {
      if (t.type() == tnode::TNCONST) t.assign(-t.xval());
      else t.assign(record(std::make_unique<ATN_tensor_scalar_add>(*t.tensor(), 0., -1)));
    }
    while (true) {
      int plus;
      if (advance_if(PLUS)) plus = +1;
      else if (advance_if(MINUS)) plus = -1;
      else break;
      tnode t2 = do_term();
      if (t.type() == tnode::TNTENSOR && t2.type() == tnode::TNTENSOR) {
        if (!t.tensor()->is_tensors_sum_scaled() || t.tensor()->is_frozen()) {
          t.assign(record(std::make_unique<ATN_tensors_sum_scaled>(*t.tensor(), +1)));
        }
        t.tensor()->is_tensors_sum_scaled()
          ->push_scaled_tensor(*t2.tensor(), scalar_type(plus));
      } else if (t.type() == tnode::TNCONST && t2.type() == tnode::TNCONST) {
        t.assign(t.xval()+t2.xval()*plus);
      } else {
        int tsgn = 1;
        if (t.type() != tnode::TNTENSOR)
        { std::swap(t,t2); if (plus<0) tsgn = -1; }
        else if (plus<0) t2.assign(-t2.xval());
        t.assign(record(std::make_unique<ATN_tensor_scalar_add>(*t.tensor(), t2.xval(),
          tsgn)));
      }
    }
    pop_mark();
    return t;
  }

  /* instr := ident '=' expr |
  print expr |
  M(#mf,#mf) '+=' expr |
  V(#mf) '+=' expr */
  void generic_assembly::do_instr() {
    enum { wALIAS, wOUTPUT_ARRAY, wOUTPUT_MATRIX, wPRINT, wERROR }
    what = wERROR;
    std::string ident;

    /* get the rhs */
    if (tok_type() != IDENT) ASM_THROW_PARSE_ERROR("expecting identifier");
    if (vars.find(tok()) != vars.end())
      ASM_THROW_PARSE_ERROR("redefinition of identifier " << tok());

    push_mark();
    ident = tok();
    advance();

    size_type print_mark = 0;
    size_type arg_num = size_type(-1);

    vdim_specif_list vds;

    if (ident.compare("print") == 0) {
      print_mark = tok_mark();
      what = wPRINT;
    } else if (tok_type() == ARGNUM_SELECTOR ||
      tok_type() == OPEN_PAR) {
        if (tok_type() == ARGNUM_SELECTOR) {
          arg_num = tok_argnum();
          advance();
        } else { arg_num = 0; }

        do_dim_spec(vds);

        /* check the validity of the output statement */
        if (ident.compare("V")==0) {
          what = wOUTPUT_ARRAY;
          if (arg_num >= outvec.size())
          { outvec.resize(arg_num+1); outvec[arg_num] = 0; }
          /* if we are allowed to dynamically create vectors */
          if (outvec[arg_num] == 0) {
            if (vec_fact != 0) {
              tensor_ranges r(vds.size());
              for (size_type i=0; i < vds.size(); ++i)
                r[i] = unsigned(vds[i].dim);
              outvec[arg_num] = std::shared_ptr<base_asm_vec>(std::shared_ptr<base_asm_vec>(), vec_fact->create_vec(r));
            }
            else ASM_THROW_PARSE_ERROR("output vector $" << arg_num+1
              << " does not exist");
          }
        } else if (vds.nb_mf()==2 && vds.size() == 2 && ident.compare("M")==0) {
          what = wOUTPUT_MATRIX;
          if (arg_num >= outmat.size())
          { outmat.resize(arg_num+1); outmat[arg_num] = 0; }
          /* if we are allowed to dynamically create matrices */
          if (outmat[arg_num] == 0) {
            if (mat_fact != 0)
              outmat[arg_num] = std::shared_ptr<base_asm_mat>
                                (std::shared_ptr<base_asm_mat>(),
                                 mat_fact->create_mat(vds[0].pmf->nb_dof(),
                                                      vds[1].pmf->nb_dof()));
            else ASM_THROW_PARSE_ERROR("output matrix $" << arg_num+1
              << " does not exist");
          }
        } else ASM_THROW_PARSE_ERROR("not a valid output statement");

        accept(PLUS);
        accept(EQUAL);
    } else if (advance_if(EQUAL)) {
      what = wALIAS;
    } else ASM_THROW_PARSE_ERROR("missing '=' or ':='");

    tnode t = do_expr();
    if (t.type() != tnode::TNTENSOR)
      ASM_THROW_PARSE_ERROR("left hand side is a constant, not a tensor!");

    switch (what) {
    case wPRINT: {
      record_out(std::make_unique<ATN_print_tensor>(*t.tensor(), tok_substr(print_mark,
        tok_mark())));
                 } break;
    case wOUTPUT_ARRAY: {
      record_out(outvec[arg_num]->build_output_tensor(*t.tensor(), vds));
                        } break;
    case wOUTPUT_MATRIX: {
      record_out(outmat[arg_num]->build_output_tensor(*t.tensor(),
                                                      *vds[0].pmf,
                                                      *vds[1].pmf));
                         } break;
    case wALIAS: {
      vars[ident] = t.tensor(); t.tensor()->freeze();
                 } break;
    default: GMM_ASSERT3(false, ""); break;
    }
    pop_mark();
  }

  struct atn_number_compare {
    bool operator()(const std::unique_ptr<ATN_tensor> &a,
                    const std::unique_ptr<ATN_tensor> &b) {
      assert(a.get() && b.get());
      return (a->number() < b->number());
    }
  };

  struct outvar_compare {
    bool operator()(const std::unique_ptr<ATN> &a,
                    const std::unique_ptr<ATN> &b) {
      assert(a.get() && b.get());
      return (a->number() < b->number());
    }
  };

  void generic_assembly::parse() {
    if (parse_done) return;
    do {
      if (tok_type() == END) break;
      do_instr();
    } while (advance_if(SEMICOLON));
    if (tok_type() != END) ASM_THROW_PARSE_ERROR("unexpected token: '"
      << tok() << "'");
    if (outvars.size() == 0) cerr << "warning: assembly without output\n";

    /* reordering of atn_tensors and outvars */
    unsigned gcnt = 0;
    for (size_type i=0; i < outvars.size(); ++i)
      outvars[i]->set_number(gcnt);

    std::sort(atn_tensors.begin(), atn_tensors.end(), atn_number_compare());
    std::sort(outvars.begin(), outvars.end(), outvar_compare());

    /* remove non-numbered (ie unused) atn_tensors */
    while (atn_tensors.size()
      && atn_tensors.back()->number() == unsigned(-1)) {
        cerr << "warning: the expression " << atn_tensors.back()->name()
          << " won't be evaluated since it is not used!\n";
        atn_tensors.pop_back();
    }
    parse_done = true;
  }

  /* caution: the order of the loops is really important */
  void generic_assembly::exec(size_type cv, dim_type face) {
    bool update_shapes = false;
    for (size_type i=0; i < atn_tensors.size(); ++i) {
      atn_tensors[i]->check_shape_update(cv,face);
      update_shapes =  (update_shapes || atn_tensors[i]->is_shape_updated());
      /* if (atn_tensors[i]->is_shape_updated()) {
      cerr << "[cv=" << cv << ",f=" << int(face) << "], shape_updated: "
      << typeid(*atn_tensors[i]).name()
      << " [" << atn_tensors[i]->name()
      << "]\n  -> r=" << atn_tensors[i]->ranges() << "\n    ";
      }
      */
    }

    if (update_shapes) {

      /*cerr << "updated shapes: cv=" << cv << " face=" << int(face) << ": ";
      for (size_type k=0; k < mftab.size(); ++k)
      cerr << mftab[k]->nb_basic_dof_of_element(cv) << " "; cerr << "\n";
      */

      for (auto &&t : atn_tensors)
        t->init_required_shape();

      for (auto &&v : outvars)
        v->update_childs_required_shape();

      for (size_type i=atn_tensors.size()-1; i!=size_type(-1); --i)
        atn_tensors[i]->update_childs_required_shape();

      for (auto &&t : atn_tensors)
        t->reinit();

      for (auto &&v : outvars)
        v->reinit();
    }
    for (auto &&t : atn_tensors)
      t->exec(cv,face);
    for (auto &&v : outvars)
      v->exec(cv, face);
  }

  struct cv_fem_compare {
    const std::vector<const mesh_fem *> &mf;
    cv_fem_compare(const std::vector<const mesh_fem *>& mf_) : mf(mf_) {}
    bool operator()(size_type a, size_type b) const {
      for (size_type i=0; i < mf.size(); ++i) {
        pfem pfa(mf[i]->fem_of_element(a));
        pfem pfb(mf[i]->fem_of_element(b));
        /* sort by nb_dof and then by fem */
        unsigned nba = unsigned(pfa->nb_dof(a));
        unsigned nbb = unsigned(pfb->nb_dof(b));
        if (nba < nbb) {
          return true;
        } else if (nba > nbb) {
          return false;
        } else if (pfa < pfb) {
          return true;
        }
      }
      return false;
    }
  };

  /* reorder the convexes in order to minimize the number of
  shape modifications during the assembly (since this can be
  very expensive) */
  static void get_convex_order(const dal::bit_vector& cvlst,
    const std::vector<const mesh_im *>& imtab,
    const std::vector<const mesh_fem *>& mftab,
    const dal::bit_vector& candidates,
    std::vector<size_type>& cvorder) {
      cvorder.reserve(candidates.card()); cvorder.resize(0);

      for (dal::bv_visitor cv(candidates); !cv.finished(); ++cv) {
        if (cvlst.is_in(cv) &&
          imtab[0]->int_method_of_element(cv) != im_none()) {
            bool ok = true;
            for (size_type i=0; i < mftab.size(); ++i) {
              if (!mftab[i]->convex_index().is_in(cv)) {
                ok = false;
                // ASM_THROW_ERROR("the convex " << cv << " has no FEM for the #"
                //                               << i+1 << " mesh_fem");
              }
            }
            if (ok) {
              cvorder.push_back(cv);
            }
        } else if (!imtab[0]->linked_mesh().convex_index().is_in(cv)) {
          ASM_THROW_ERROR("the convex " << cv << " is not part of the mesh");
        } else {
          /* skip convexes without integration method */
        }
      }
      //std::sort(cvorder.begin(), cvorder.end(), cv_fem_compare(mftab));
  }

  void generic_assembly::consistency_check() {
    //if (mftab.size() == 0) ASM_THROW_ERROR("no mesh_fem for assembly!");
    if (imtab.size() == 0)
      ASM_THROW_ERROR("no mesh_im (integration methods) given for assembly!");
    const mesh& m = imtab[0]->linked_mesh();
    for (unsigned i=0; i < mftab.size(); ++i) {
      if (&mftab[i]->linked_mesh() != &m)
        ASM_THROW_ERROR("the mesh_fem/mesh_im live on different meshes!");
    }
    for (unsigned i=0; i < imtab.size(); ++i) {
      if (&imtab[i]->linked_mesh() != &m)
        ASM_THROW_ERROR("the mesh_fem/mesh_im live on different meshes!");
    }
    if (imtab.size() == 0)
      ASM_THROW_ERROR("no integration method !");
  }

  void generic_assembly::assembly(const mesh_region &r) {
    std::vector<size_type> cv;
    r.from_mesh(imtab.at(0)->linked_mesh());
    r.error_if_not_homogeneous();


    consistency_check();
    get_convex_order(imtab.at(0)->convex_index(), imtab, mftab, r.index(), cv);
    parse();

    for (size_type i=0; i < cv.size(); ++i) {
      mesh_region::face_bitset nf = r[cv[i]];
      dim_type f = dim_type(-1);
      while (nf.any())
      {
        if (nf[0]) exec(cv[i],f);
        nf >>= 1;
        f++;
      }
    }
  }
} /* end of namespace */