bgeot_sparse_tensors.h

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/**@file bgeot_sparse_tensors.h
   @author  Julien Pommier <[email protected]>
   @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