bgeot_sparse_tensors.h

Go to the documentation of this file.

/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2000-2020 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.
 
 As a special exception, you  may use  this file  as it is a part of a free
 software  library  without  restriction.  Specifically,  if   other  files
 instantiate  templates  or  use macros or inline functions from this file,
 or  you compile this  file  and  link  it  with other files  to produce an
 executable, this file  does  not  by itself cause the resulting executable
 to be covered  by the GNU Lesser General Public License.  This   exception
 does not  however  invalidate  any  other  reasons why the executable file
 might be covered by the GNU Lesser General Public License.
 
===========================================================================*/
 
/**@file bgeot_sparse_tensors.h
   @author  Julien Pommier <Julien.Pommier@insa-toulouse.fr>
   @date January 2003.
   @brief Sparse tensors, used during the assembly.
 
   "sparse" tensors: these are not handled like sparse matrices
 
   As an example, let say that we have a tensor t(i,j,k,l) of
   dimensions 4x2x3x3, with t(i,j,k,l!=k) == 0.
 
   Then the tensor shape will be represented by a set of 3 objects of type
     'tensor_mask':
   mask1: {i}, "1111"
   mask2: {j}, "11"
   mask3: {k,l}, "100"
                 "010"
                 "001"
   They contain a binary tensor indicating the non-null elements.
 
   The set of these three masks define the shape of the tensor
   (class tensor_shape)
 
   If we add information about the location of the non-null elements
   (by mean of strides), then we have an object of type 'tensor_ref'
 
   Iteration on the data of one or more tensor should be done via the
   'multi_tensor_iterator', which can iterate over common non-null
   elements of a set of tensors.
 
 
   maximum (virtual) number of elements in a tensor : 2^31
   maximum number of dimensions : 254
 
   "ought to be enough for anybody"
*/
#ifndef BGEOT_SPARSE_TENSORS
#define BGEOT_SPARSE_TENSORS
 
#include "gmm/gmm_except.h"
#include "bgeot_config.h"
#include "dal_bit_vector.h"
// #include "gmm/gmm_kernel.h" // for i/o on vectors it is convenient
#include <iostream>
#include <bitset>
 
namespace bgeot {
  typedef gmm::uint32_type index_type;
  typedef gmm::int32_type stride_type; /* signé! */
 
  //  typedef std::vector<index_type> tensor_ranges;
  class tensor_ranges : public std::vector<index_type> {
  public:
    tensor_ranges() : std::vector<index_type>() {}
    tensor_ranges(size_type n) : std::vector<index_type>(n) {}
    tensor_ranges(size_type n, index_type V) : std::vector<index_type>(n,V) {}
    bool is_zero_size() const
    {
      for (dim_type i=0; i < this->size(); ++i)
        if ((*this)[i] == 0)
          return true;
      return false;
    }
  };
  typedef std::vector<stride_type> tensor_strides;
  typedef std::vector<dim_type> index_set;
 
  typedef scalar_type * TDIter;
 
  std::ostream& operator<<(std::ostream& o, const tensor_ranges& r);
 
  /* stupid && inefficient loop structure */
  struct tensor_ranges_loop {
    tensor_ranges sz;
    tensor_ranges cnt;
    bool finished_;
  public:
    tensor_ranges_loop(const tensor_ranges& t) : sz(t), cnt(t.size()), finished_(t.size() == 0) {
      std::fill(cnt.begin(), cnt.end(), 0);
    }
    index_type index(dim_type i) { return cnt[i]; }
    bool finished() const { return finished_; }
    bool next() {
      index_type i = 0;
      while (++cnt[i] >= sz[i]) {
        cnt[i] = 0; i++; if (i >= sz.size()) { finished_ = true; break; }
      }
      return finished_;
    }
  };
 
  /* handle a binary mask over a given number of indices */
  class tensor_mask {
    tensor_ranges r;
    index_set idxs;
    std::vector<bool> m;
    tensor_strides s; /* strides in m */
    mutable index_type card_; /* finally i should have kept m as a dal::bit_vector ... */
    mutable bool card_uptodate;
  public:
    tensor_mask() { set_card(0); }
    explicit tensor_mask(const tensor_ranges& r_, const index_set& idxs_) {
      assign(r_,idxs_);
    }
    /* constructeur par fusion */
    explicit tensor_mask(const tensor_mask& tm1, const tensor_mask& tm2, bool and_op);
    explicit tensor_mask(const std::vector<const tensor_mask*>& tm);
    explicit tensor_mask(const std::vector<const tensor_mask*> tm1,
                         const std::vector<const tensor_mask*> tm2, bool and_op);
    void swap(tensor_mask &tm) {
      r.swap(tm.r); idxs.swap(tm.idxs);
      m.swap(tm.m); s.swap(tm.s);
      std::swap(card_, tm.card_);
      std::swap(card_uptodate, tm.card_uptodate);
    }
    void assign(const tensor_ranges& r_, const index_set& idxs_) {
      r = r_; idxs = idxs_; eval_strides(); m.assign(size(),false);
      set_card(0);
    }
    void assign(const tensor_mask& tm) {
      r = tm.r;
      idxs = tm.idxs;
      m = tm.m;
      s = tm.s;
      card_ = tm.card_; card_uptodate = tm.card_uptodate;
    }
    void assign(const std::vector<const tensor_mask* >& tm);
    void assign(const tensor_mask& tm1, const tensor_mask& tm2, bool and_op);
 
    void clear() { r.resize(0); idxs.resize(0); m.clear(); s.resize(0); set_card(0); }
    const tensor_ranges& ranges() const { return r; }
    const index_set& indexes() const { return idxs; }
    const tensor_strides& strides() const { return s; }
    index_set& indexes() { return idxs; }
    void eval_strides() {
      s.resize(r.size()+1); s[0]=1;
      for (index_type i=0; i < r.size(); ++i) {
        s[i+1]=s[i]*r[i];
      }
    }
    index_type ndim() const { return index_type(r.size()); }
    index_type size() const { return s[r.size()]; }
    void set_card(index_type c) const { card_ = c; card_uptodate = true; }
    void unset_card() const { card_uptodate = false; }
    index_type card(bool just_look=false) const {
      if (!card_uptodate || just_look) {
        index_type c = index_type(std::count_if(m.begin(), m.end(),
                                  [](const auto &x) {return x == true;}));
        if (just_look) return c;
        card_ = c;
      }
      return card_;
    }
    index_type pos(tensor_ranges& global_r) const {
      index_type p = 0;
      for (index_type i=0; i < r.size(); ++i)
        p+= s[i]*global_r[idxs[i]];
      return p;
    }
    index_type lpos(tensor_ranges& local_r) const {
      index_type p = 0;
      for (index_type i=0; i < r.size(); ++i)
        p+= s[i]*local_r[i];
      return p;
    }
    bool operator()(tensor_ranges& global_r) const {
      return m[pos(global_r)];
    }
    bool operator()(stride_type p) const { return m[p]; }
    void set_mask_val(stride_type p, bool v) { m[p]=v; card_uptodate = false; }
    struct Slice {
      dim_type dim;
      index_type i0;
      Slice(dim_type d, index_type i0_) : dim(d), i0(i0_) {}
    };
 
    /* cree un masque de tranche */
    void set_slice(index_type dim, index_type range, index_type islice) {
      r.resize(1); r[0] = range;
      idxs.resize(1); idxs[0] = dim_type(dim);
      m.clear(); m.assign(range,false); m[islice] = 1; set_card(1);
      eval_strides();
    }
    explicit tensor_mask(index_type range, Slice slice) {
      set_slice(slice.dim, range, slice.i0);
    }
 
    struct Diagonal {
      dim_type i0, i1;
      Diagonal(dim_type i0_, dim_type i1_) : i0(i0_), i1(i1_) {}
    };
 
    /* cree un masque diagonal */
    void set_diagonal(index_type n, index_type i0, index_type i1) {
      assert(n);
      r.resize(2); r[0] = r[1] = n;
      idxs.resize(2); idxs[0] = dim_type(i0); idxs[1] = dim_type(i1);
      m.assign(n*n, false);
      for (index_type i=0; i < n; ++i) m[n*i+i]=true;
      set_card(n);
      eval_strides();
    }
    explicit tensor_mask(index_type n, Diagonal diag) {
      set_diagonal(n, diag.i0, diag.i1);
    }
    void set_triangular(index_type n, index_type i0, index_type i1) {
      assert(n);
      r.resize(2); r[0] = r[1] = n;
      idxs.resize(2); idxs[0] = dim_type(i0); idxs[1] = dim_type(i1);
      m.assign(n*n,false); unset_card();
      for (index_type i=0; i < n; ++i)
        for (index_type j=i; j < n; ++j) m[i*n+j]=true;
      eval_strides();
    }
    void set_full(index_type dim, index_type range) {
      // assert(range); // not sure if permitting range==0 can have any side effects
      r.resize(1); r[0] = range;
      idxs.resize(1); idxs[0] = dim_type(dim);
      m.assign(range, true); set_card(range);
      eval_strides();
    }
    void set_empty(index_type dim, index_type range) {
      // assert(range); // not sure if permitting range==0 can have any side effects
      r.resize(1); r[0] = range;
      idxs.resize(1); idxs[0] = dim_type(dim);
      m.assign(range,false); set_card(0);
      eval_strides();
    }
    explicit tensor_mask(index_type dim, index_type range) {
      set_full(dim, range);
    }
    void set_zero() {
      m.assign(size(),false); set_card(0);
    }
    void shift_dim_num_ge(dim_type dim, int shift) {
      for (dim_type i=0; i < idxs.size(); ++i) {
        if (idxs[i] >= dim) idxs[i] = dim_type(idxs[i] + shift);
      }
      check_assertions();
    }
    void gen_mask_pos(tensor_strides& p) const {
      check_assertions();
      p.resize(card());
      index_type i = 0;
      for (tensor_ranges_loop l(r); !l.finished(); l.next()) {
        if (m[lpos(l.cnt)]) p[i++] = lpos(l.cnt);
      }
      assert(i==card());
    }
    void unpack_strides(const tensor_strides& packed, tensor_strides& unpacked) const;
 
    /* c'est mieux que celle ci renvoie un int ..
       ou alors un unsigned mais dim_type c'est dangereux */
    int max_dim() const {
      index_set::const_iterator it = std::max_element(idxs.begin(),idxs.end());
      return (it == idxs.end() ? -1 : *it);
    }
    void check_assertions() const;
    void print(std::ostream &o) const;
    void print_() const { print(cerr); }
  };
 
 
 
  typedef std::vector<tensor_mask> tensor_mask_container;
 
  struct tensor_index_to_mask {
    short_type mask_num;
    short_type mask_dim;
    tensor_index_to_mask() : mask_num(short_type(-1)),
                             mask_dim(short_type(-1)) {}
    bool is_valid() { return mask_num != short_type(-1) &&
        mask_dim != short_type(-1); }
  };
 
 
  /*
     defini une "forme" de tenseur creux
     la fonction merge permet de faire des unions / intersections entre ces formes
  */
  class tensor_shape {
    mutable std::vector<tensor_index_to_mask> idx2mask;
    tensor_mask_container masks_;
 
    /* verifie si un masque est completement vide,
       si c'est le cas alors tous les autres masques sont vidés
       (le tenseur est identiquement nul) */
    void check_empty_mask() {
      if (card() == 0) {
        for (dim_type i=0; i < masks_.size(); ++i) {
          masks_[i].set_zero();
        }
      }
    }
 
    static void find_linked_masks(dim_type mnum, const tensor_shape &ts1, const tensor_shape &ts2,
                                  dal::bit_vector& treated1, dal::bit_vector& treated2,
                                  std::vector<const tensor_mask*>& lstA,
                                  std::vector<const tensor_mask*>& lstB) {
      // gare aux boucles infinies si aucun des indices n'est valide
      assert(mnum < ts1.masks().size());
      assert(!treated1[mnum]);
      treated1.add(mnum);
      lstA.push_back(&ts1.mask(mnum));
      for (dim_type i=0; i < ts1.mask(mnum).indexes().size(); ++i) {
        dim_type ii = ts1.mask(mnum).indexes()[i];
        if (ts2.index_is_valid(ii) && !treated2[ts2.index_to_mask_num(ii)])
          find_linked_masks(ts2.index_to_mask_num(ii),ts2,ts1,treated2,treated1,lstB,lstA);
      }
    }
 
  protected:
    dim_type index_to_mask_num(dim_type ii) const {
      if (index_is_valid(ii))
        return dim_type(idx2mask[ii].mask_num); else return dim_type(-1);
    }
  public:
    void clear() { masks_.resize(0); idx2mask.resize(0); }
    void swap(tensor_shape& ts) {
      idx2mask.swap(ts.idx2mask);
      masks_.swap(ts.masks_);
    }
    dim_type ndim() const { return dim_type(idx2mask.size()); }
    bool index_is_valid(dim_type ii) const {
      assert(ii < idx2mask.size()); return idx2mask[ii].is_valid();
    }
    const tensor_mask& index_to_mask(dim_type ii) const {
      assert(index_is_valid(ii)); return masks_[idx2mask[ii].mask_num];
    }
    dim_type index_to_mask_dim(dim_type ii) const {
      assert(index_is_valid(ii)); return dim_type(idx2mask[ii].mask_dim);
    }
    index_type dim(dim_type ii) const
    { assert(index_is_valid(ii)); return index_to_mask(ii).ranges()[index_to_mask_dim(ii)];
    }
    tensor_mask_container& masks() { return masks_; }
    const tensor_mask_container& masks() const { return masks_; }
    const tensor_mask& mask(dim_type i) const { assert(i<masks_.size()); return masks_[i]; }
    stride_type card(bool just_look=false) const {
      stride_type n = 1;
      for (dim_type i=0; i < masks().size(); ++i)
        n *= masks()[i].card(just_look);
      return n;
    }
    void push_mask(const tensor_mask& m) { masks_.push_back(m); update_idx2mask(); }
    void remove_mask(dim_type mdim) { /* be careful with this function.. remove
                                         only useless mask ! */
      masks_.erase(masks_.begin()+mdim);
      update_idx2mask();
    }
    void remove_unused_dimensions() {
      dim_type nd = 0;
      for (dim_type i=0; i < ndim(); ++i) {
        if (index_is_valid(i))
          masks_[idx2mask[i].mask_num].indexes()[idx2mask[i].mask_dim] = nd++;
      }
      set_ndim_noclean(nd);
      update_idx2mask();
    }
 
    void update_idx2mask() const {
      /*
        dim_type N=0;
        for (dim_type i=0; i < masks_.size(); ++i)
          N = std::max(N, std::max_element(masks_.indexes().begin(), masks_.indexes.end()));
        idx2mask.resize(N);
      */
 
      std::fill(idx2mask.begin(), idx2mask.end(), tensor_index_to_mask());
      for (dim_type i=0; i < masks_.size(); ++i) {
        for (dim_type j=0; j < masks_[i].indexes().size(); ++j) {
          dim_type k = masks_[i].indexes()[j];
          GMM_ASSERT3(k < idx2mask.size() && !idx2mask[k].is_valid(), "");
          idx2mask[k].mask_num = i; idx2mask[k].mask_dim = j;
        }
      }
    }
    void assign_shape(const tensor_shape& other) {
      masks_ = other.masks_;
      idx2mask = other.idx2mask;
      //      update_idx2mask();
    }
    void set_ndim(dim_type n) {
      clear();
      idx2mask.resize(n); update_idx2mask();
    }
    void set_ndim_noclean(dim_type n) {idx2mask.resize(n);}
 
    tensor_shape() {}
 
    /* create an "empty" shape of dimensions nd */
    explicit tensor_shape(dim_type nd) : idx2mask(nd,tensor_index_to_mask()) {
      masks_.reserve(16);
    }
    explicit tensor_shape(const tensor_ranges& r) {
      masks_.reserve(16);
      set_full(r);
    }
    void set_full(const tensor_ranges& r) {
      idx2mask.resize(r.size());
      masks_.resize(r.size());
      for (dim_type i=0; i < r.size(); ++i) masks_[i].set_full(i,r[i]);
      update_idx2mask();
    }
 
    void set_empty(const tensor_ranges& r) {
      idx2mask.resize(r.size());
      masks_.resize(r.size());
      for (dim_type i=0; i < r.size(); ++i) masks_[i].set_empty(i,r[i]);
      update_idx2mask();
    }
 
 
    /* fusion d'une autre forme */
    void merge(const tensor_shape &ts2, bool and_op = true) {
      /* quelques verifs de base */
      GMM_ASSERT3(ts2.ndim() == ndim(), "");
      if (ts2.ndim()==0) return; /* c'est un scalaire */
      for (dim_type i = 0; i < ndim(); ++i)
        if (index_is_valid(i) && ts2.index_is_valid(i))
          GMM_ASSERT3(ts2.dim(i) == dim(i), "");
 
      tensor_mask_container new_mask;
      dal::bit_vector mask_treated1; mask_treated1.sup(0,masks().size());
      dal::bit_vector mask_treated2; mask_treated2.sup(0,ts2.masks().size());
      std::vector<const tensor_mask*> lstA, lstB; lstA.reserve(10); lstB.reserve(10);
      for (dim_type i = 0; i < ndim(); ++i) {
        dim_type i1 = dim_type(index_to_mask_num(i));
        dim_type i2 = dim_type(ts2.index_to_mask_num(i));
        lstA.clear(); lstB.clear();
        if (index_is_valid(i) && !mask_treated1[i1])
          find_linked_masks(i1, *this, ts2, mask_treated1, mask_treated2,
                            lstA, lstB);
        else if (ts2.index_is_valid(i) && !mask_treated2[i2])
          find_linked_masks(i2, ts2, *this, mask_treated2, mask_treated1,
                            lstB, lstA);
        else continue;
        GMM_ASSERT3(lstA.size() || lstB.size(), "");
        new_mask.push_back(tensor_mask(lstA,lstB,and_op));
      }
      masks_ = new_mask;
      update_idx2mask();
      check_empty_mask();
    }
 
    void shift_dim_num_ge(dim_type dim_num, int shift) {
      for (dim_type m = 0; m < masks().size(); ++m)
        masks()[m].shift_dim_num_ge(dim_num,shift);
    }
    /* the permutation vector might be greater than the current ndim,
       in which case some indexes will be unused (when p[i] == dim_type(-1))
    */
    void permute(const std::vector<dim_type> p, bool revert=false) {
      std::vector<dim_type> invp(ndim()); std::fill(invp.begin(), invp.end(), dim_type(-1));
 
      /* build the inverse permutation and check that this IS really a permuation */
      for (dim_type i=0; i < p.size(); ++i) {
        if (p[i] != dim_type(-1)) {
          assert(invp[p[i]] == dim_type(-1));
          invp[p[i]] = i;
        }
      }
      for (dim_type i=0; i < invp.size(); ++i) assert(invp[i] != dim_type(-1));
 
      /* do the permutation (quite simple!) */
      for (dim_type m=0; m < masks().size(); ++m) {
        for (dim_type i=0; i < masks()[m].indexes().size(); ++i) {
          if (!revert)
            masks()[m].indexes()[i] = invp[masks()[m].indexes()[i]];
          else
            masks()[m].indexes()[i] = p[masks()[m].indexes()[i]];
        }
      }
      set_ndim_noclean(dim_type(p.size()));
      update_idx2mask();
    }
 
    /* forme d'une tranche (c'est la forme qu'on applique à un tenseur pour
       en extraire la tranche) */
    tensor_shape slice_shape(tensor_mask::Slice slice) const {
      assert(slice.dim < ndim() && slice.i0 < dim(slice.dim));
      tensor_shape ts(ndim());
      ts.push_mask(tensor_mask(dim(slice.dim), slice));
      ts.merge(*this); /* le masque peut se retrouver brutalement vidé si on a tranché au mauvais endroit! */
      return ts;
    }
 
    tensor_shape diag_shape(tensor_mask::Diagonal diag) const {
      assert(diag.i1 != diag.i0 && diag.i0 < ndim() && diag.i1 < ndim());
      assert(dim(diag.i0) == dim(diag.i1));
      tensor_shape ts(ndim());
      ts.push_mask(tensor_mask(dim(diag.i0), diag));
      ts.merge(*this);
      return ts;
    }
 
    /*
      void diag(index_type i0, index_type i1) {
      assert(i0 < idx.size() && i1 < idx.size());
      assert(idx[i0].n == idx[i1].n);
      tensor_shape ts2 = *this;
      ts2.masks.resize(1);
      ts2.masks[0].set_diagonal(idx[i0].n, i0, i1);
      ts2.idx[i0].mask_num = ts2.idx[i1].mask_num = 0;
      ts2.idx[i0].mask_dim = 0;
      ts2.idx[i1].mask_dim = 1;
      }
    */
    void print(std::ostream& o) const;
    void print_() const { print(cerr); }
  };
 
 
  /* reference to a tensor:
     - a shape
     - a data pointer
     - a set of strides
  */
  class tensor_ref : public tensor_shape {
    std::vector< tensor_strides > strides_;
    TDIter *pbase_; /* pointeur sur un pointeur qui designe les données
                       ça permet de changer la base pour toute une serie
                       de tensor_ref en un coup */
 
    stride_type base_shift_;
 
    void remove_mask(dim_type mdim) {
      tensor_shape::remove_mask(mdim);
      assert(strides_[mdim].size() == 0 ||
             (strides_[mdim].size() == 1 && strides_[mdim][0] == 0)); /* sanity check.. */
      strides_.erase(strides_.begin()+mdim);
    }
  public:
    void swap(tensor_ref& tr) {
      tensor_shape::swap(tr);
      strides_.swap(tr.strides_);
      std::swap(pbase_, tr.pbase_);
      std::swap(base_shift_, tr.base_shift_);
    }
    const std::vector< tensor_strides >& strides() const { return strides_; }
    std::vector< tensor_strides >& strides() { return strides_; }
    TDIter base() const { return (pbase_ ? (*pbase_) : 0); }
    TDIter *pbase() const { return pbase_; }
    stride_type base_shift() const { return base_shift_; }
    void set_base(TDIter &new_base) { pbase_ = &new_base; base_shift_ = 0; }
 
    void clear() { strides_.resize(0); pbase_ = 0; base_shift_ = 0; tensor_shape::clear(); }
 
 
 
    /* s'assure que le stride du premier indice est toujours bien égal à zéro */
    void  ensure_0_stride() {
      for (index_type i=0; i < strides_.size(); ++i) {
        if (strides_[i].size() >= 1 && strides_[i][0] != 0) {
          stride_type s = strides_[i][0];
          base_shift_ += s;
          for (index_type j=0; j < strides_[i].size(); ++j)
            strides_[i][j] -= s;
        }
      }
    }
 
    /* constructeur à partir d'une forme : ATTENTION ce constructeur n'alloue pas la
       mémoire nécessaire pour les données !! */
    explicit tensor_ref(const tensor_shape& ts) : tensor_shape(ts), pbase_(0), base_shift_(0) {
      strides_.reserve(16);
      init_strides();
    }
    explicit tensor_ref(const tensor_ranges& r, TDIter *pbase__=0)
      : tensor_shape(r), pbase_(pbase__), base_shift_(0) {
      strides_.reserve(16);
      init_strides();
    }
    void init_strides() {
      strides_.resize(masks().size());
      stride_type s = 1;
      for (dim_type i = 0; i < strides_.size(); ++i) {
        index_type n = mask(i).card();
        strides_[i].resize(n);
        for (index_type j=0;j<n;++j)
          strides_[i][j] = j*s;
        s *= n;
      }
    }
    tensor_ref() : pbase_(0), base_shift_(0) { strides_.reserve(16); }
 
    void set_sub_tensor(const tensor_ref& tr, const tensor_shape& sub);
 
    /* constructeur à partir d'un sous-tenseur à partir d'un tenseur et d'une forme
       hypothese: la forme 'sub' doit être un sous-ensemble de la forme du tenseur
    */
    explicit tensor_ref(const tensor_ref& tr, const tensor_shape& sub) {
      set_sub_tensor(tr,sub);
    }
 
    /* slices a tensor_ref, at dimension 'dim', position 'islice'
       ... not straightforward for sparse tensors !
    */
    explicit tensor_ref(const tensor_ref& tr, tensor_mask::Slice slice);
 
    /* create a diagonal of another tensor */
    explicit tensor_ref(const tensor_ref& tr, tensor_mask::Diagonal diag) {
      set_sub_tensor(tr, tr.diag_shape(diag));
      ensure_0_stride();
    }
 
    void print(std::ostream& o) const;
 
    void print_() const { print(cerr); }
  };
 
    std::ostream& operator<<(std::ostream& o, const tensor_mask& m);
    std::ostream& operator<<(std::ostream& o, const tensor_shape& ts);
    std::ostream& operator<<(std::ostream& o, const tensor_ref& tr);
 
  /* minimalistic data for iterations */
  struct packed_range {
    const stride_type *pinc;
    const stride_type *begin, *end;
    index_type n;
    /*    index_type cnt;*/
  };
  /* additionnal data */
  struct packed_range_info {
    index_type range;
    dim_type original_masknum;
    dim_type n;
    std::vector<stride_type> mask_pos; /* pour l'iteration avec maj de la valeur des indices */
    bool operator<(const packed_range_info& pi) const {
      if (n < pi.n) return true;
      else return false;
    }
    stride_type mean_increm; /* valeur moyenne de l'increment (utilisé pour le tri) */
    tensor_strides inc; /* not strides but increments to the next index value,
                           with inc[range-1] == -sum(inc[0..range-2]) (automatic rewinding!)
                           of course, stride_type MUST be signed
                        */
    std::bitset<32> have_regular_strides;
  };
 
  /* the big one */
  class multi_tensor_iterator {
    index_type N; /* number of simultaneous tensors */
    std::vector<packed_range> pr;
    std::vector<packed_range_info> pri;
 
    std::vector<index_type> bloc_rank;
    std::vector<index_type> bloc_nelt;
 
    std::vector<TDIter> it;
    std::vector<TDIter*> pit0;
    tensor_strides itbase;
    struct  index_value_data {
      dim_type cnt_num;
      const stride_type **ppinc; /* pointe vers pr[cnt_num].pinc, initialisé par rewind()
                                    et pas avant (à cause de pbs lors de la copie de multi_tensor_iterator sinon)
                                    permet de déduire la valeur du compteur: (*ppinc - pincbase) (à diviser par nn=(pri[cnt_num].n-N))
                                 */
      const stride_type *pincbase;
      const stride_type *pposbase; /* pointe dans pri[cnt_num].mask_pos, retrouve la position dans le masque en fonction
                                      du compteur déduit ci-dessus et des champs div et mod ci-dessous */
      index_type div, mod, nn;
      stride_type pos_; /* stores the position when the indexe is not part of the pri array
                           (hence the index only has 1 value, and ppos == &pos_, and pcnt = &zero */
    };
    std::vector<index_value_data> idxval;
    std::vector<stride_type> vectorized_strides_; /* if the tensor have regular strides, the mti might be vectorizable */
    index_type vectorized_size_;                  /* the size of each vectorizable chunk */
    index_type vectorized_pr_dim;                 /* all pr[i], i >= vectorized_pr_dim, can be accessed via vectorized_strides */
  public:
    void clear() {
      N = 0; pr.clear(); pri.clear(); bloc_rank.clear(); bloc_nelt.clear();
      it.clear(); pit0.clear(); itbase.clear(); idxval.clear();
    }
    void swap(multi_tensor_iterator& m) {
      std::swap(N,m.N);  pr.swap(m.pr);  pri.swap(m.pri);
      bloc_rank.swap(m.bloc_rank); bloc_nelt.swap(m.bloc_nelt);
      it.swap(m.it); pit0.swap(m.pit0); itbase.swap(m.itbase);
      idxval.swap(m.idxval);
    }
    void rewind() {
      for (dim_type i=0; i < pr.size(); ++i) {
        pr[i].pinc = pr[i].begin = &pri[i].inc[0];
        pr[i].end = pr[i].begin+pri[i].inc.size();
      }
      for (dim_type n=0; n < N; ++n)
        it[n] = *(pit0[n]) + itbase[n];
      for (dim_type i=0; i < idxval.size(); ++i) {
        if (idxval[i].cnt_num != dim_type(-1)) {
          idxval[i].ppinc = &pr[idxval[i].cnt_num].pinc;
          idxval[i].pincbase = &pri[idxval[i].cnt_num].inc[0];
          idxval[i].pposbase = &pri[idxval[i].cnt_num].mask_pos[0];
          idxval[i].nn = (N-pri[idxval[i].cnt_num].n);
        } else {
          static const stride_type *null=0;
          idxval[i].ppinc = &null;
          idxval[i].pincbase = 0;
          idxval[i].pposbase = &idxval[i].pos_;
          idxval[i].nn = 1;
        }
      }
    }
    dim_type ndim() const { return dim_type(idxval.size()); }
    /* get back the value of an index from then current iterator position */
    index_type index(dim_type ii) {
      index_value_data& iv = idxval[ii];
      index_type cnt = index_type((*iv.ppinc - iv.pincbase)/iv.nn);
      return ((iv.pposbase[cnt]) % iv.mod)/ iv.div;
    }
    index_type vectorized_size() const { return vectorized_size_; }
    const std::vector<stride_type>& vectorized_strides() const { return vectorized_strides_; }
    bool next(unsigned i_stop = unsigned(-1), unsigned i0_ = unsigned(-2)) {//=pr.size()-1) {
      unsigned i0 = unsigned(i0_ == unsigned(-2) ? pr.size()-1 : i0_);
      while (i0 != i_stop) {
        for (unsigned n = pr[i0].n; n < N; ++n) {
          //  index_type pos = pr[i0].cnt * (N-pri[i0].n) + (n - pri[i0].n);
          it[n] += *pr[i0].pinc; pr[i0].pinc++;
        }
        if (pr[i0].pinc != pr[i0].end) {
          return true;
        } else {
          pr[i0].pinc = pr[i0].begin;
          i0--;
        }
      }
      return false;
    }
    bool vnext() { return next(unsigned(-1), vectorized_pr_dim); }
    bool bnext(dim_type b) { return next(bloc_rank[b]-1, bloc_rank[b+1]-1); }
    bool bnext_useful(dim_type b) { return bloc_rank[b] != bloc_rank[b+1]; }
    /* version speciale pour itérer sur des tenseurs de même dimensions
       (doit être un poil plus rapide) */
    bool qnext1() {
      if (pr.size() == 0) return false;
      std::vector<packed_range>::reverse_iterator p_ = pr.rbegin();
     while (p_!=pr.rend()) {
        it[0] += *(p_->pinc++);
        if (p_->pinc != p_->end) {
          return true;
        } else {
          p_->pinc = p_->begin;
          p_++;
        }
      }
      return false;
    }
 
    bool qnext2() {
      if (pr.size() == 0) return false;
      std::vector<packed_range>::reverse_iterator p_ = pr.rbegin();
      while (p_!=pr.rend()) {
        it[0] += *(p_->pinc++);
        it[1] += *(p_->pinc++);
        if (p_->pinc != p_->end) {
          return true;
        } else {
          p_->pinc = p_->begin;
          p_++;
        }
      }
      return false;
    }
 
    scalar_type& p(dim_type n) { return *it[n]; }
 
    multi_tensor_iterator() {}
    multi_tensor_iterator(std::vector<tensor_ref> trtab, bool with_index_values) {
      init(trtab, with_index_values);
    }
    void assign(std::vector<tensor_ref> trtab, bool with_index_values) {
      multi_tensor_iterator m(trtab, with_index_values);
      swap(m);
    }
    multi_tensor_iterator(const tensor_ref& tr0, bool with_index_values) {
      std::vector<tensor_ref> trtab(1); trtab[0] = tr0;
      init(trtab, with_index_values);
    }
    void assign(const tensor_ref& tr0, bool with_index_values) {
      multi_tensor_iterator m(tr0, with_index_values);
      swap(m);
    }
    multi_tensor_iterator(const tensor_ref& tr0,
                          const tensor_ref& tr1,  bool with_index_values) {
      std::vector<tensor_ref> trtab(2); trtab[0] = tr0; trtab[1] = tr1;
      init(trtab, with_index_values);
    }
    void assign(const tensor_ref& tr0, const tensor_ref& tr1,  bool with_index_values) {
      multi_tensor_iterator m(tr0, tr1, with_index_values);
      swap(m);
    }
    multi_tensor_iterator(const tensor_ref& tr0,
                          const tensor_ref& tr1,
                          const tensor_ref& tr2, bool with_index_values) {
      std::vector<tensor_ref> trtab(3); trtab[0] = tr0; trtab[1] = tr1; trtab[2] = tr2;
      init(trtab, with_index_values);
    }
    void assign(const tensor_ref& tr0, const tensor_ref& tr1, const tensor_ref& tr2,  bool with_index_values) {
      multi_tensor_iterator m(tr0, tr1, tr2, with_index_values);
      swap(m);
    }
    void init(std::vector<tensor_ref> trtab, bool with_index_values);
    void print() const;
  };
 
 
  /* handles a tree of reductions
     The tree is used if more than two tensors are reduced, i.e.
       z(:,:)=t(:,i).u(i,j).v(j,:)
     in that case, the reduction against j can be performed on u(:,j).v(j,:) = w(:,:)
     and then, z(:,:) = t(:,i).w(i,:)
  */
  struct tensor_reduction {
    struct tref_or_reduction {
      tensor_ref tr_;
      std::shared_ptr<tensor_reduction> reduction;
      tensor_ref &tr() { return tr_; }
      const tensor_ref &tr() const { return tr_; }
      explicit tref_or_reduction(const tensor_ref &tr__, const std::string& s)
        : tr_(tr__), ridx(s) {}
      explicit tref_or_reduction(const std::shared_ptr<tensor_reduction> &p, const std::string& s)
        : reduction(p), ridx(s) {
        reduction->result(tr_);
      }
      bool is_reduction() const { return reduction != 0; }
      void swap(tref_or_reduction &other) { tr_.swap(other.tr_); std::swap(reduction, other.reduction); }
      std::string ridx;      /* reduction indexes, no index can appear
                                twice in the same tensor */
      std::vector<dim_type> gdim; /* mapping to the global virtual
                                     tensor whose range is the
                                     union of the ranges of each
                                     reduced tensor */
      std::vector<dim_type> rdim; /* mapping to the dimensions of the
                                     reduced tensor ( = dim_type(-1) for
                                     dimensions i s.t. ridx[i] != ' ' ) */
 
    };
    tensor_ranges reduced_range;
    std::string reduction_chars; /* list of all indexes used for reduction */
    tensor_ref trres;
    typedef std::vector<tref_or_reduction>::iterator trtab_iterator;
    std::vector<tref_or_reduction> trtab;
    multi_tensor_iterator mti;
    std::vector<scalar_type> out_data; /* optional storage of output */
    TDIter pout_data;
  public:
    tensor_reduction() { clear(); }
    virtual ~tensor_reduction() { clear(); }
    void clear();
 
    /* renvoie les formes diagonalisées
       pour bien faire, il faudrait que cette fonction prenne en argument
       le required_shape de l'objet ATN_reducted_tensor, et fasse le merge
       avec ce qu'elle renvoie... non trivial
    */
    static void diag_shape(tensor_shape& ts, const std::string& s) {
      for (index_type i=0; i < s.length(); ++i) {
        size_type pos = s.find(s[i]);
        if (s[i] != ' ' && pos != i) // ce n'est pas de l'indice => reduction sur la diagonale
          ts = ts.diag_shape(tensor_mask::Diagonal(dim_type(pos),dim_type(i)));
      }
    }
 
    void insert(const tensor_ref& tr_, const std::string& s);
    void prepare(const tensor_ref* tr_out = NULL);
    void do_reduction();
    void result(tensor_ref& res) const {
      res=trres;
      res.remove_unused_dimensions();
    }
  private:
    void insert(const tref_or_reduction& tr_, const std::string& s);
    void update_reduction_chars();
    void pre_prepare();
    void make_sub_reductions();
    size_type find_best_sub_reduction(dal::bit_vector &best_lst, std::string &best_idxset);
  };
 
} /* namespace bgeot */
 
#endif