structuredInference_tpl.h

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#include <agrum/PRM/inference/structuredInference.h>

namespace gum {
  namespace prm {

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::StructuredInference(
       const PRM< GUM_SCALAR >&             prm,
       const PRMSystem< GUM_SCALAR >&       system,
       gspan::SearchStrategy< GUM_SCALAR >* strategy) :
        PRMInference< GUM_SCALAR >(prm, system),
        __gspan(0), __pdata(0), __mining(false), __dot(".") {
      GUM_CONSTRUCTOR(StructuredInference);
      __gspan = new GSpan< GUM_SCALAR >(prm, system, strategy);
      triang_time = 0.0;
      mining_time = 0.0;
      pattern_time = 0.0;
      inner_time = 0.0;
      obs_time = 0.0;
      full_time = 0.0;
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::StructuredInference(
       const StructuredInference< GUM_SCALAR >& source) :
        PRMInference< GUM_SCALAR >(source),
        __gspan(0), __pdata(0), __mining(source.__mining), __found_query(false),
        __dot(".") {
      GUM_CONS_CPY(StructuredInference);
      __gspan = new GSpan< GUM_SCALAR >(*(this->_prm), *(this->_sys));
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::~StructuredInference() {
      GUM_DESTRUCTOR(StructuredInference);
      delete this->__gspan;

      for (const auto& elt : __elim_map)
        delete elt.second;

      for (const auto& elt : __cdata_map)
        delete elt.second;

      for (const auto elt : __trash)
        delete (elt);

      for (const auto& elt : __outputs)
        delete elt.second;

      if (__pdata) delete __pdata;
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >& StructuredInference< GUM_SCALAR >::
                                       operator=(const StructuredInference< GUM_SCALAR >& source) {
      this->_prm = source._prm;
      this->_sys = source._sys;

      if (this->__gspan) delete this->__gspan;

      this->__gspan = new GSpan< GUM_SCALAR >(*(this->_prm), *(this->_sys));
      return *this;
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::_evidenceAdded(
       const typename PRMInference< GUM_SCALAR >::Chain& chain) {}

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::_evidenceRemoved(
       const typename PRMInference< GUM_SCALAR >::Chain& chain) {}

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::_marginal(
       const typename PRMInference< GUM_SCALAR >::Chain& chain,
       Potential< GUM_SCALAR >&                          m) {
      timer.reset();
      __found_query = false;
      __query = chain;
      typename StructuredInference< GUM_SCALAR >::RGData data;

      if (!this->hasEvidence() && (chain.second->cpf().nbrDim() == 1)) {
        Instantiation i(m);

        for (i.setFirst(); !i.end(); i.inc())
          m.set(i, chain.second->cpf().get(i));

        return;
      } else if (this->hasEvidence(chain)) {
        Instantiation                  i(m);
        const Potential< GUM_SCALAR >* e =
           this->evidence(__query.first)[__query.second->id()];

        for (i.setFirst(); !i.end(); i.inc())
          m.set(i, e->get(i));

        return;
      }

      __buildReduceGraph(data);
      Set< const Potential< GUM_SCALAR >* > pots;

      if (data.pool.size() > 1) {
        for (const auto pot : data.pool)
          if (pot->contains(__query.second->type().variable())) pots.insert(pot);

        if (pots.size() == 1) {
          Potential< GUM_SCALAR >* pot =
             const_cast< Potential< GUM_SCALAR >* >(*(pots.begin()));
          GUM_ASSERT(pot->contains(__query.second->type().variable()));
          GUM_ASSERT(pot->variablesSequence().size() == 1);
          Instantiation i(*pot), j(m);

          for (i.setFirst(), j.setFirst(); !i.end(); i.inc(), j.inc())
            m.set(j, pot->get(i));
        } else {
          MultiDimCombinationDefault< GUM_SCALAR, Potential > Comb(multPotential);
          Potential< GUM_SCALAR >* tmp = Comb.combine(pots);
          Instantiation            i(m), j(*tmp);

          for (i.setFirst(), j.setFirst(); !i.end(); i.inc(), j.inc())
            m.set(i, tmp->get(j));

          delete tmp;
        }
      } else {
        Potential< GUM_SCALAR >* pot = *(data.pool.begin());
        GUM_ASSERT(pot->contains(__query.second->type().variable()));
        GUM_ASSERT(pot->variablesSequence().size() == 1);
        Instantiation i(*pot), j(m);

        for (i.setFirst(), j.setFirst(); !i.end(); i.inc(), j.inc())
          m.set(j, pot->get(i));
      }

      m.normalize();

      if (__pdata) {
        delete __pdata;
        __pdata = 0;
      }

      full_time = timer.step();
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::_joint(
       const std::vector< typename PRMInference< GUM_SCALAR >::Chain >& queries,
       Potential< GUM_SCALAR >&                                         j) {
      GUM_ERROR(FatalError, "not implemented");
    }

    template < typename GUM_SCALAR >
    std::string StructuredInference< GUM_SCALAR >::info() const {
      std::stringstream s;
      s << "Triangulation time: " << triang_time << std::endl;
      s << "Pattern mining time: " << mining_time << std::endl;
      s << "Pattern elimination time: " << pattern_time << std::endl;
      s << "Inner node elimination time: " << inner_time << std::endl;
      s << "Observed node elimination time: " << obs_time << std::endl;
      s << "Full inference time: " << full_time << std::endl;
      s << "#patterns: " << __gspan->patterns().size() << std::endl;
      Size                                                   count = 0;
      typedef std::vector< gspan::Pattern* >::const_iterator Iter;

      for (Iter p = __gspan->patterns().begin(); p != __gspan->patterns().end();
           ++p) {
        if (__gspan->matches(**p).size()) {
          s << "Pattern n°" << count++
            << " match count: " << __gspan->matches(**p).size() << std::endl;
          s << "Pattern n°" << count++ << " instance count: " << (**p).size()
            << std::endl;
        }
      }

      return s.str();
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::__buildReduceGraph(
       typename StructuredInference< GUM_SCALAR >::RGData& data) {
      // Launch the pattern mining
      plopTimer.reset();

      if (__mining) __gspan->discoverPatterns();

      mining_time = plopTimer.step();
      // Reducing each used pattern
      plopTimer.reset();
      typedef std::vector< gspan::Pattern* >::const_iterator Iter;

      for (Iter p = __gspan->patterns().begin(); p != __gspan->patterns().end();
           ++p)
        if (__gspan->matches(**p).size()) __reducePattern(*p);

      pattern_time = plopTimer.step();
      // reducing instance not already reduced in a pattern
      __reduceAloneInstances(data);
      // Adding edges using the pools
      __addEdgesInReducedGraph(data);
      // Placing the query where it belongs
      NodeId id = data.var2node.second(&(__query.second->type().variable()));
      data.outputs().erase(id);
      data.queries().insert(id);
      // Triangulating, then eliminating
      PartialOrderedTriangulation t(
         &(data.reducedGraph), &(data.mods), &(data.partial_order));
      const std::vector< NodeId >& elim_order = t.eliminationOrder();

      for (size_t i = 0; i < data.outputs().size(); ++i)
        eliminateNode(data.var2node.first(elim_order[i]), data.pool, __trash);
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::__reducePattern(
       const gspan::Pattern* p) {
      Set< Potential< GUM_SCALAR >* >                   pool;
      typename StructuredInference< GUM_SCALAR >::PData data(*p,
                                                             __gspan->matches(*p));
      __buildPatternGraph(data, pool, **(data.matches.begin()));
      __removeBarrenNodes(data, pool);
      PartialOrderedTriangulation t(
         &(data.graph), &(data.mod), data.partial_order());
      const std::vector< NodeId >& elim_order = t.eliminationOrder();

      for (size_t i = 0; i < data.inners().size(); ++i)
        if (!data.barren.exists(elim_order[i]))
          eliminateNode(data.vars.second(elim_order[i]), pool, __trash);

      typename GSpan< GUM_SCALAR >::MatchedInstances                 fake_patterns;
      typename GSpan< GUM_SCALAR >::MatchedInstances::const_iterator iter =
         data.matches.begin();

      for (const auto elt : **iter)
        __reducedInstances.insert(elt);

      if (data.obs().size())
        __elim_map.insert(
           *iter,
           __eliminateObservedNodesInSource(data, pool, **iter, elim_order));
      else
        __elim_map.insert(*iter, new Set< Potential< GUM_SCALAR >* >(pool));

      ++iter;

      if (data.obs().size()) {
        for (; iter != data.matches.end(); ++iter) {
          try {
            __elim_map.insert(
               *iter, __eliminateObservedNodes(data, pool, **iter, elim_order));
          } catch (OperationNotAllowed&) { fake_patterns.insert(*iter); }
        }
      } else {
        for (; iter != data.matches.end(); ++iter) {
          try {
            __elim_map.insert(*iter, __translatePotSet(data, pool, **iter));
          } catch (OperationNotAllowed&) { fake_patterns.insert(*iter); }
        }
      }

      for (const auto pat : fake_patterns) {
        for (const auto elt : *pat)
          __reducedInstances.erase(elt);

        data.matches.erase(pat);
      }

      obs_time += plopTimer.step();

      if (data.queries().size())
        for (const auto m : data.matches)
          if (!(m->exists(
                 const_cast< PRMInstance< GUM_SCALAR >* >(__query.first))))
            eliminateNode(&(m->atPos(__query_data.first)
                               ->get(__query_data.second)
                               .type()
                               .variable()),
                          *(__elim_map[m]),
                          __trash);
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::__insertNodeInElimLists(
       typename StructuredInference< GUM_SCALAR >::PData& data,
       const Sequence< PRMInstance< GUM_SCALAR >* >&      match,
       PRMInstance< GUM_SCALAR >*                         inst,
       PRMAttribute< GUM_SCALAR >*                        attr,
       NodeId                                             id,
       std::pair< Idx, std::string >&                     v) {
      if ((*inst).hasRefAttr((*inst).get(v.second).id())) {
        std::vector< std::pair< PRMInstance< GUM_SCALAR >*, std::string > >& refs =
           inst->getRefAttr(inst->get(v.second).id());

        for (auto r = refs.begin(); r != refs.end(); ++r) {
          if (!match.exists(r->first)) {
            data.outputs().insert(id);
            break;
          }
        }
      }

      if (!(data.outputs().size() && (data.outputs().exists(id)))) {
        for (const auto m : data.matches) {
          if (this->hasEvidence(
                 std::make_pair((*m)[v.first], &((*m)[v.first]->get(v.second))))) {
            GUM_ASSERT(inst->type().name() == (*m)[v.first]->type().name());
            GUM_ASSERT(inst->get(v.second).safeName()
                       == (*m)[v.first]->get(v.second).safeName());
            data.obs().insert(id);
            break;
          }
        }

        if (!(data.obs().size() && (data.obs().exists(id))))
          data.inners().insert(id);
      }
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::__buildPatternGraph(
       typename StructuredInference< GUM_SCALAR >::PData& data,
       Set< Potential< GUM_SCALAR >* >&                   pool,
       const Sequence< PRMInstance< GUM_SCALAR >* >&      match) {
      std::pair< Idx, std::string > v;
      Potential< GUM_SCALAR >*      pot = 0;

      for (const auto inst : match) {
        for (const auto& elt : *inst) {
          NodeId id = data.graph.addNode();
          v = std::make_pair(match.pos(inst), elt.second->safeName());
          data.map.insert(id, v);
          data.node2attr.insert(id, __str(inst, elt.second));
          data.mod.insert(id, elt.second->type()->domainSize());
          data.vars.insert(id, &(elt.second->type().variable()));
          pool.insert(
             const_cast< Potential< GUM_SCALAR >* >(&(elt.second->cpf())));
          pot =
             &(const_cast< Potential< GUM_SCALAR >& >(inst->get(v.second).cpf()));

          for (const auto var : pot->variablesSequence()) {
            try {
              if (id != data.vars.first(var))
                data.graph.addEdge(id, data.vars.first(var));
            } catch (DuplicateElement&) {
            } catch (NotFound&) {}
          }

          __insertNodeInElimLists(data, match, inst, elt.second, id, v);

          if (data.inners().exists(id)
              && (inst->type().containerDag().children(elt.second->id()).size()
                  == 0)
              && __allInstanceNoRefAttr(data, v))
            data.barren.insert(id);
        }
      }

      if (!__found_query) {
        for (const auto mat : data.matches) {
          if (mat->exists(
                 const_cast< PRMInstance< GUM_SCALAR >* >(__query.first))) {
            Idx pos =
               mat->pos(const_cast< PRMInstance< GUM_SCALAR >* >(__query.first));
            DiscreteVariable& var =
               match.atPos(pos)->get(__query.second->safeName()).type().variable();
            NodeId id = data.vars.first(&var);
            data.barren.erase(id);
            data.inners().erase(id);
            data.obs().erase(id);
            data.outputs().erase(id);
            data.queries().insert(id);
            __found_query = true;
            __query_data = std::make_pair(pos, __query.second->safeName());
            break;
          }
        }
      }
    }

    template < typename GUM_SCALAR >
    bool StructuredInference< GUM_SCALAR >::__allInstanceNoRefAttr(
       typename StructuredInference< GUM_SCALAR >::PData& data,
       std::pair< Idx, std::string >                      attr) {
      for (const auto mat : data.matches)
        if (mat->atPos(attr.first)
               ->hasRefAttr(mat->atPos(attr.first)->get(attr.second).id()))
          return false;

      return true;
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::__removeBarrenNodes(
       typename StructuredInference< GUM_SCALAR >::PData& data,
       Set< Potential< GUM_SCALAR >* >&                   pool) {
      Sequence< NodeId > candidates;

      for (const auto node : data.barren) {
        for (const auto pot : pool)
          if (pot->contains(*data.vars.second(node))) {
            pool.erase(pot);
            break;
          }

        for (const auto nei : data.graph.neighbours(node))
          if (data.inners().exists(nei)) {
            try {
              candidates.insert(nei);
            } catch (DuplicateElement&) {}
          }
      }

      NodeId                   node;
      Potential< GUM_SCALAR >* my_pot = nullptr;
      short                    count = 0;

      while (candidates.size()) {
        node = candidates.back();
        candidates.erase(node);
        count = 0;

        for (const auto pot : pool) {
          if (pot->contains(*data.vars.second(node))) {
            ++count;
            my_pot = pot;
          }
        }

        if (count == 1) {
          pool.erase(my_pot);
          data.barren.insert(node);

          for (const auto nei : data.graph.neighbours(node)) {
            if (data.inners().exists(nei)) {
              try {
                candidates.insert(nei);
              } catch (DuplicateElement&) {}
            }
          }
        }
      }
    }

    template < typename GUM_SCALAR >
    Set< Potential< GUM_SCALAR >* >*
       StructuredInference< GUM_SCALAR >::__eliminateObservedNodesInSource(
          typename StructuredInference< GUM_SCALAR >::PData& data,
          const Set< Potential< GUM_SCALAR >* >&             pool,
          const Sequence< PRMInstance< GUM_SCALAR >* >&      match,
          const std::vector< NodeId >&                       elim_order) {
      Set< Potential< GUM_SCALAR >* >* my_pool =
         new Set< Potential< GUM_SCALAR >* >(pool);
      std::pair< Idx, std::string > target;
      size_t                        end = data.inners().size() + data.obs().size();

      for (size_t idx = data.inners().size(); idx < end; ++idx) {
        target = data.map[data.vars.first(data.vars.second(elim_order[idx]))];
        eliminateNode(&(match[target.first]->get(target.second).type().variable()),
                      *my_pool,
                      __trash);
      }

      return my_pool;
    }

    template < typename GUM_SCALAR >
    Set< Potential< GUM_SCALAR >* >*
       StructuredInference< GUM_SCALAR >::__eliminateObservedNodes(
          typename StructuredInference< GUM_SCALAR >::PData& data,
          const Set< Potential< GUM_SCALAR >* >&             pool,
          const Sequence< PRMInstance< GUM_SCALAR >* >&      match,
          const std::vector< NodeId >&                       elim_order) {
      Set< Potential< GUM_SCALAR >* >* my_pool =
         __translatePotSet(data, pool, match);
      std::pair< Idx, std::string > target;
      size_t                        end = data.inners().size() + data.obs().size();

      for (size_t idx = data.inners().size(); idx < end; ++idx) {
        target = data.map[data.vars.first(data.vars.second(elim_order[idx]))];
        eliminateNode(&(match[target.first]->get(target.second).type().variable()),
                      *my_pool,
                      __trash);
      }

      return my_pool;
    }

    template < typename GUM_SCALAR >
    Set< Potential< GUM_SCALAR >* >*
       StructuredInference< GUM_SCALAR >::__translatePotSet(
          typename StructuredInference< GUM_SCALAR >::PData& data,
          const Set< Potential< GUM_SCALAR >* >&             pool,
          const Sequence< PRMInstance< GUM_SCALAR >* >&      match) {
#ifdef DEBUG

      for (GSpan< GUM_SCALAR >::MatchedInstances::const_iterator iter =
              data.matches.begin();
           iter != data.matches.end();
           ++iter) {
        GUM_ASSERT((**iter).size() == match.size());

        for (Size idx = 0; idx < match.size(); ++idx) {
          GUM_ASSERT((**iter).atPos(idx)->type() == match.atPos(idx)->type());
        }
      }

#endif
      Set< Potential< GUM_SCALAR >* >* my_pool =
         new Set< Potential< GUM_SCALAR >* >();
      std::pair< Idx, std::string >                                 target;
      Bijection< const DiscreteVariable*, const DiscreteVariable* > bij;
      const Sequence< PRMInstance< GUM_SCALAR >* >&                 source =
         **(data.matches.begin());

      for (Size idx = 0; idx < match.size(); ++idx) {
        __reducedInstances.insert(match[idx]);
        const auto& chains = source[idx]->type().slotChains();

        for (const auto sc : chains) {
#ifdef DEBUG
          GUM_ASSERT(!(sc->isMultiple()));
#endif

          try {
            bij.insert(&(source[idx]
                            ->getInstance(sc->id())
                            .get(sc->lastElt().safeName())
                            .type()
                            .variable()),
                       &(match[idx]
                            ->getInstance(sc->id())
                            .get(sc->lastElt().safeName())
                            .type()
                            .variable()));
          } catch (DuplicateElement&) {
            try {
              if (bij.first(&(match[idx]
                                 ->getInstance(sc->id())
                                 .get(sc->lastElt().safeName())
                                 .type()
                                 .variable()))
                  != &(source[idx]
                          ->getInstance(sc->id())
                          .get(sc->lastElt().safeName())
                          .type()
                          .variable())) {
                delete my_pool;
                GUM_ERROR(OperationNotAllowed, "fake pattern");
              }
            } catch (NotFound&) {
              delete my_pool;
              GUM_ERROR(OperationNotAllowed, "fake pattern");
            }
          }
        }
      }

      for (const auto p : pool) {
        for (const auto v : p->variablesSequence()) {
          try {
            target = data.map[data.vars.first(v)];
            bij.insert(
               v, &(match[target.first]->get(target.second).type().variable()));
          } catch (NotFound&) {
            GUM_ASSERT(bij.existsFirst(v));
          } catch (DuplicateElement&) {}
        }

        try {
          my_pool->insert(copyPotential(bij, *p));
        } catch (Exception&) {
          for (const auto pot : *my_pool)
            delete pot;

          delete my_pool;
          GUM_ERROR(OperationNotAllowed, "fake pattern");
        }
      }

      return my_pool;
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::__reduceAloneInstances(
       typename StructuredInference< GUM_SCALAR >::RGData& rg_data) {
      StructuredInference< GUM_SCALAR >::CData* data = 0;
      Potential< GUM_SCALAR >*                  pot = nullptr;
      PRMInstance< GUM_SCALAR >*                inst = nullptr;

      for (const auto& elt : *this->_sys) {
        inst = elt.second;

        if (!__reducedInstances.exists(inst)) {
          // Checking if its not an empty class
          if (inst->size()) {
            Set< Potential< GUM_SCALAR >* > pool;

            try {
              data = __cdata_map[&(inst->type())];
            } catch (NotFound&) {
              data = new StructuredInference< GUM_SCALAR >::CData(inst->type());
              __cdata_map.insert(&(inst->type()), data);
            }

            data->instances.insert(inst);
            // Filling up the partial ordering
            List< NodeSet > partial_order;

            if (data->inners().size()) partial_order.push_back(data->inners());

            if (data->aggregators().size())
              for (const auto agg : data->aggregators())
                partial_order[0].insert(agg);

            if (data->outputs().size()) partial_order.push_back(data->outputs());

            if (__query.first == inst) {
              // First case, the instance contains the query
              partial_order[0].erase(__query.second->id());

              if (partial_order[0].empty()) partial_order.erase(0);

              if (partial_order.size() > 1) {
                partial_order[1].erase(__query.second->id());

                if (partial_order[1].empty()) partial_order.erase(1);
              }

              NodeSet query_set;
              query_set.insert(__query.second->id());
              partial_order.insert(query_set);

              // Adding the potentials
              for (auto attr = inst->begin(); attr != inst->end(); ++attr)
                pool.insert(&(
                   const_cast< Potential< GUM_SCALAR >& >((*(attr.val())).cpf())));

              // Adding evidences if any
              if (this->hasEvidence(inst))
                for (const auto& elt : this->evidence(inst))
                  pool.insert(const_cast< Potential< GUM_SCALAR >* >(elt.second));

              PartialOrderedTriangulation t(
                 &(data->moral_graph), &(data->mods), &(partial_order));
              const std::vector< NodeId >& v = t.eliminationOrder();

              if (partial_order.size() > 1)
                for (size_t idx = 0; idx < partial_order[0].size(); ++idx)
                  eliminateNode(
                     &(inst->get(v[idx]).type().variable()), pool, __trash);
            } else if (this->hasEvidence(inst)) {
              // Second case, the instance has evidences
              // Adding the potentials
              for (const auto elt : *inst)
                pool.insert(
                   &const_cast< Potential< GUM_SCALAR >& >(elt.second->cpf()));

              // Adding evidences
              for (const auto& elt : this->evidence(inst))
                pool.insert(const_cast< Potential< GUM_SCALAR >* >(elt.second));

              PartialOrderedTriangulation t(
                 &(data->moral_graph), &(data->mods), &(partial_order));

              for (size_t idx = 0; idx < partial_order[0].size(); ++idx)
                eliminateNode(
                   &(inst->get(t.eliminationOrder()[idx]).type().variable()),
                   pool,
                   __trash);
            } else {
              // Last cast, the instance neither contains evidences nor
              // instances
              // We translate the class level potentials into the instance ones
              // and
              // proceed with elimination
              for (const auto srcPot : data->pool) {
                pot = copyPotential(inst->bijection(), *srcPot);
                pool.insert(pot);
                __trash.insert(pot);
              }

              for (const auto agg : data->c.aggregates())
                pool.insert(&(const_cast< Potential< GUM_SCALAR >& >(
                   inst->get(agg->id()).cpf())));

              // We eliminate inner aggregators with their parents if necessary
              // (see
              // CData constructor)
              Size size = data->inners().size() + data->aggregators().size();

              for (size_t idx = data->inners().size(); idx < size; ++idx)
                eliminateNode(
                   &(inst->get(data->elim_order()[idx]).type().variable()),
                   pool,
                   __trash);
            }

            for (const auto pot : pool)
              rg_data.pool.insert(pot);
          }
        }
      }
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::__addEdgesInReducedGraph(
       typename StructuredInference< GUM_SCALAR >::RGData& data) {
      // We first add edges between variables already in pool (i.e. those of the
      // reduced instances)
      NodeId id_1, id_2;

      for (const auto pot : data.pool) {
        const Sequence< const DiscreteVariable* >& vars = pot->variablesSequence();

        for (Size var_1 = 0; var_1 < vars.size(); ++var_1) {
          if (data.var2node.existsFirst(vars.atPos(var_1))) {
            id_1 = data.var2node.second(vars.atPos(var_1));
          } else {
            id_1 = data.reducedGraph.addNode();
            data.var2node.insert(vars.atPos(var_1), id_1);
            data.mods.insert(id_1, vars.atPos(var_1)->domainSize());
            data.outputs().insert(id_1);
          }

          for (Size var_2 = var_1 + 1; var_2 < vars.size(); ++var_2) {
            if (data.var2node.existsFirst(vars.atPos(var_2))) {
              id_2 = data.var2node.second(vars.atPos(var_2));
            } else {
              id_2 = data.reducedGraph.addNode();
              data.var2node.insert(vars.atPos(var_2), id_2);
              data.mods.insert(id_2, vars.atPos(var_2)->domainSize());
              data.outputs().insert(id_2);
            }

            try {
              data.reducedGraph.addEdge(id_1, id_2);
            } catch (DuplicateElement&) {}
          }
        }
      }

      // Adding potentials obtained from reduced patterns
      for (const auto& elt : __elim_map) {
        // We add edges between variables in the same reduced patterns
        for (const auto pot : *elt.second) {
          data.pool.insert(pot);
          const Sequence< const DiscreteVariable* >& vars =
             pot->variablesSequence();

          for (Size var_1 = 0; var_1 < vars.size(); ++var_1) {
            if (data.var2node.existsFirst(vars.atPos(var_1))) {
              id_1 = data.var2node.second(vars.atPos(var_1));
            } else {
              id_1 = data.reducedGraph.addNode();
              data.var2node.insert(vars.atPos(var_1), id_1);
              data.mods.insert(id_1, vars.atPos(var_1)->domainSize());
              data.outputs().insert(id_1);
            }

            for (Size var_2 = var_1 + 1; var_2 < vars.size(); ++var_2) {
              if (data.var2node.existsFirst(vars.atPos(var_2))) {
                id_2 = data.var2node.second(vars.atPos(var_2));
              } else {
                id_2 = data.reducedGraph.addNode();
                data.var2node.insert(vars.atPos(var_2), id_2);
                data.mods.insert(id_2, vars.atPos(var_2)->domainSize());
                data.outputs().insert(id_2);
              }

              try {
                data.reducedGraph.addEdge(id_1, id_2);
              } catch (DuplicateElement&) {}
            }
          }
        }
      }
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::RGData::RGData() {
      GUM_CONSTRUCTOR(StructuredInference< GUM_SCALAR >::RGData);
      partial_order.insert(NodeSet());
      partial_order.insert(NodeSet());
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::PData::PData(
       const gspan::Pattern&                           p,
       typename GSpan< GUM_SCALAR >::MatchedInstances& m) :
        pattern(p),
        matches(m), __real_order(0) {
      GUM_CONSTRUCTOR(StructuredInference< GUM_SCALAR >::PData);

      for (int i = 0; i < 4; ++i)
        __partial_order.push_front(NodeSet());
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::PData::PData(
       const typename StructuredInference< GUM_SCALAR >::PData& source) :
        pattern(source.pattern),
        matches(source.matches), graph(source.graph), mod(source.mod),
        node2attr(source.node2attr), vars(source.vars),
        __partial_order(source.__partial_order), __real_order(0) {
      GUM_CONS_CPY(StructuredInference< GUM_SCALAR >::PData);
    }

    template < typename GUM_SCALAR >
    const List< NodeSet >*
       StructuredInference< GUM_SCALAR >::PData::partial_order() {
      if (!__real_order) {
        __real_order = new List< NodeSet >();

        for (const auto set : __partial_order)
          if (set.size() > 0) __real_order->insert(set);
      }

      return __real_order;
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::CData::CData(
       const PRMClass< GUM_SCALAR >& a_class) :
        c(a_class),
        __elim_order(0) {
      GUM_CONSTRUCTOR(StructuredInference< GUM_SCALAR >::CData);

      // First step we add Attributes and Aggregators
      for (const auto node : c.containerDag().nodes()) {
        switch (c.get(node).elt_type()) {
          case PRMClassElement< GUM_SCALAR >::prm_attribute: {
            pool.insert(
               &(const_cast< Potential< GUM_SCALAR >& >(c.get(node).cpf())));
            // break omited : We want to execute the next block
            // for attributes
          }

          case PRMClassElement< GUM_SCALAR >::prm_aggregate: {
            moral_graph.addNodeWithId(node);
            mods.insert(node, c.get(node).type()->domainSize());
            break;
          }

          default: { /* do nothing */
          }
        }
      }

      // Second, we add edges, moralise the graph and build the partial ordering
      for (const auto node : moral_graph.nodes()) {
        const auto& parents = c.containerDag().parents(node);

        // Adding edges and marrying parents
        for (auto tail = parents.begin(); tail != parents.end(); ++tail) {
          if (PRMClassElement< GUM_SCALAR >::isAttribute(c.get(*tail))
              || PRMClassElement< GUM_SCALAR >::isAggregate(c.get(*tail))) {
            moral_graph.addEdge(*tail, node);
            NodeSet::const_iterator marry = tail;
            ++marry;

            while (marry != parents.end()) {
              if (PRMClassElement< GUM_SCALAR >::isAttribute(c.get(*marry))
                  || PRMClassElement< GUM_SCALAR >::isAggregate(c.get(*marry)))
                moral_graph.addEdge(*tail, *marry);

              ++marry;
            }
          }
        }

        // Adding nodes to the partial ordering
        switch (c.get(node).elt_type()) {
          case PRMClassElement< GUM_SCALAR >::prm_aggregate: {
            if (c.isOutputNode(c.get(node)))
              outputs().insert(node);
            else
              aggregators().insert(node);

            // If the aggregators is not an output and have parents which are
            // not outputs, we must eliminate the parents after adding the
            // aggregator's CPT
            for (const auto par : c.containerDag().parents(node)) {
              const auto& prnt = c.get(par);

              if ((!c.isOutputNode(prnt))
                  && (PRMClassElement< GUM_SCALAR >::isAttribute(prnt)
                      || PRMClassElement< GUM_SCALAR >::isAggregate(prnt))) {
                inners().erase(prnt.id());
                aggregators().insert(prnt.id());
              }
            }

            break;
          }

          case PRMClassElement< GUM_SCALAR >::prm_attribute: {
            pool.insert(
               const_cast< Potential< GUM_SCALAR >* >(&(c.get(node).cpf())));

            if (c.isOutputNode(c.get(node)))
              outputs().insert(node);
            else if (!aggregators().exists(node))
              inners().insert(node);

            break;
          }

          default: { /* Do nothing */
          }
        }
      }

      if (inners().size()) partial_order.insert(inners());

      if (aggregators().size()) partial_order.insert(aggregators());

      if (outputs().size()) partial_order.insert(outputs());

      GUM_ASSERT(partial_order.size());
      PartialOrderedTriangulation t(&moral_graph, &mods, &partial_order);
      __elim_order = t.eliminationOrder();

      for (size_t i = 0; i < inners().size(); ++i)
        eliminateNode(&(c.get(__elim_order[i]).type().variable()), pool, __trash);
    }

    template < typename GUM_SCALAR >
    StructuredInference< GUM_SCALAR >::CData::~CData() {
      GUM_DESTRUCTOR(StructuredInference< GUM_SCALAR >::CData);

      for (const auto pot : __trash)
        delete pot;
    }

    template < typename GUM_SCALAR >
    void StructuredInference< GUM_SCALAR >::searchPatterns() {
      const PRMInstance< GUM_SCALAR >* i = (this->_sys->begin()).val();
      __query = std::make_pair(i, i->begin().val());
      __found_query = false;
      typename StructuredInference< GUM_SCALAR >::RGData data;
      __buildReduceGraph(data);
    }

    template < typename GUM_SCALAR >
    INLINE void StructuredInference< GUM_SCALAR >::setPatternMining(bool b) {
      __mining = b;
    }

    template < typename GUM_SCALAR >
    INLINE std::string StructuredInference< GUM_SCALAR >::__str(
       const PRMInstance< GUM_SCALAR >*  i,
       const PRMAttribute< GUM_SCALAR >* a) const {
      return i->name() + __dot + a->safeName();
    }

    template < typename GUM_SCALAR >
    INLINE std::string StructuredInference< GUM_SCALAR >::__str(
       const PRMInstance< GUM_SCALAR >*  i,
       const PRMAttribute< GUM_SCALAR >& a) const {
      return i->name() + __dot + a.safeName();
    }

    template < typename GUM_SCALAR >
    INLINE std::string StructuredInference< GUM_SCALAR >::__str(
       const PRMInstance< GUM_SCALAR >*  i,
       const PRMSlotChain< GUM_SCALAR >& a) const {
      return i->name() + __dot + a.lastElt().safeName();
    }

    template < typename GUM_SCALAR >
    INLINE StructuredInference< GUM_SCALAR >::RGData::~RGData() {
      GUM_DESTRUCTOR(StructuredInference< GUM_SCALAR >::RGData);
    }

    template < typename GUM_SCALAR >
    INLINE StructuredInference< GUM_SCALAR >::PData::~PData() {
      GUM_DESTRUCTOR(StructuredInference< GUM_SCALAR >::PData);
    }

    template < typename GUM_SCALAR >
    INLINE std::string StructuredInference< GUM_SCALAR >::name() const {
      return "StructuredInference";
    }

    template < typename GUM_SCALAR >
    INLINE GSpan< GUM_SCALAR >& StructuredInference< GUM_SCALAR >::gspan() {
      return *__gspan;
    }

    template < typename GUM_SCALAR >
    INLINE const GSpan< GUM_SCALAR >&
                 StructuredInference< GUM_SCALAR >::gspan() const {
      return *__gspan;
    }

    template < typename GUM_SCALAR >
    INLINE void StructuredInference< GUM_SCALAR >::__removeNode(
       typename StructuredInference< GUM_SCALAR >::PData& data,
       NodeId                                             id,
       Set< Potential< GUM_SCALAR >* >&                   pool) {
      data.graph.eraseNode(id);
      GUM_ASSERT(!data.graph.exists(id));
      data.mod.erase(id);
      GUM_ASSERT(!data.mod.exists(id));
      data.node2attr.eraseFirst(id);
      GUM_ASSERT(!data.node2attr.existsFirst(id));
      data.map.erase(id);
      GUM_ASSERT(!data.map.exists(id));
      data.vars.eraseFirst(id);
      GUM_ASSERT(!data.vars.existsFirst(id));
      data.inners().erase(id);
      GUM_ASSERT(!data.inners().exists(id));
      pool.erase(data.pots[id]);
      GUM_ASSERT(!pool.exists(data.pots[id]));
      data.pots.erase(id);
      GUM_ASSERT(!data.pots.exists(id));
    }

  } /* namespace prm */
} /* namespace gum */