credalNet_tpl.h

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/**
 *
 *   Copyright 2005-2020 Pierre-Henri WUILLEMIN(@LIP6) & Christophe GONZALES(@AMU)
 *   info_at_agrum_dot_org
 *
 *  This library 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.
 *
 *  This library is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this library.  If not, see <http://www.gnu.org/licenses/>.
 *
 */


#include <agrum/agrum.h>

#include <agrum/tools/core/utils_string.h>
#include <agrum/CN/credalNet.h>

namespace gum {
  namespace credal {

    template < typename GUM_SCALAR >
    CredalNet< GUM_SCALAR >::CredalNet() {
      initParams__();

      src_bn__     = BayesNet< GUM_SCALAR >();
      src_bn_min__ = BayesNet< GUM_SCALAR >();
      src_bn_max__ = BayesNet< GUM_SCALAR >();

      GUM_CONSTRUCTOR(CredalNet);
    }

    template < typename GUM_SCALAR >
    NodeId CredalNet< GUM_SCALAR >::addVariable(const std::string& name,
                                                const Size&        card) {
      LabelizedVariable var(name, "node " + name, card);

      NodeId a = src_bn__.add(var);
      NodeId b = src_bn_min__.add(var);
      NodeId c = src_bn_max__.add(var);

      if (a != b || a != c /*|| b != c*/)
        GUM_ERROR(OperationNotAllowed,
                  "addVariable : not the same id over all networks : "
                     << a << ", " << b << ", " << c);

      return a;
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::addArc(const NodeId& tail, const NodeId& head) {
      src_bn__.addArc(tail, head);
      src_bn_min__.addArc(tail, head);
      src_bn_max__.addArc(tail, head);
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::setCPTs(
       const NodeId&                                                  id,
       const std::vector< std::vector< std::vector< GUM_SCALAR > > >& cpt) {
      const Potential< GUM_SCALAR >* const potential(&src_bn__.cpt(id));

      auto var_dSize  = src_bn__.variable(id).domainSize();
      auto entry_size = potential->domainSize() / var_dSize;

      if (cpt.size() != entry_size)
        GUM_ERROR(SizeError,
                  "setCPTs : entry sizes of cpts does not match for node id : "
                     << id << " : " << cpt.size() << " != " << entry_size);

      for (const auto& cset: cpt) {
        if (cset.size() == 0)
          GUM_ERROR(
             SizeError,
             "setCPTs : vertices in credal set does not match for node id : "
                << id << " with 0 vertices");

        for (const auto& vertex: cset) {
          if (vertex.size() != var_dSize)
            GUM_ERROR(SizeError,
                      "setCPTs : variable modalities in cpts does "
                      "not match for node id : "
                         << id << " with vertex " << vertex << " : "
                         << vertex.size() << " != " << var_dSize);

          GUM_SCALAR sum = 0;

          for (const auto& prob: vertex) {
            sum += prob;
          }

          if (std::fabs(sum - 1) > 1e-6)
            GUM_ERROR(CPTNoSumTo1,
                      "setCPTs : a vertex coordinates does not "
                      "sum to one for node id : "
                         << id << " with vertex " << vertex);
        }
      }

      credalNet_src_cpt__.insert(id, cpt);
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::setCPT(
       const NodeId&                                   id,
       Size&                                           entry,
       const std::vector< std::vector< GUM_SCALAR > >& cpt) {
      const Potential< GUM_SCALAR >* const potential(&src_bn__.cpt(id));

      auto var_dSize  = src_bn__.variable(id).domainSize();
      auto entry_size = potential->domainSize() / var_dSize;

      if (entry >= entry_size)
        GUM_ERROR(SizeError,
                  "setCPT : entry is greater or equal than entry size "
                  "(entries start at 0 up to entry_size - 1) : "
                     << entry << " >= " << entry_size);

      if (cpt.size() == 0)
        GUM_ERROR(SizeError, "setCPT : empty credal set for entry : " << entry);

      for (const auto& vertex: cpt) {
        if (vertex.size() != var_dSize)
          GUM_ERROR(SizeError,
                    "setCPT : variable modalities in cpts does not "
                    "match for node id : "
                       << id << " with vertex " << vertex << " at entry " << entry
                       << " : " << vertex.size() << " != " << var_dSize);

        GUM_SCALAR sum = 0;

        for (const auto& prob: vertex) {
          sum += prob;
        }

        if (std::fabs(sum - 1) > 1e-6)
          GUM_ERROR(
             CPTNoSumTo1,
             "setCPT : a vertex coordinates does not sum to one for node id : "
                << id << " at entry " << entry << " with vertex " << vertex);
      }

      // !! auto does NOT use adress (if available) unless explicitly asked !!
      auto& node_cpt = credalNet_src_cpt__.getWithDefault(
         id,
         std::vector< std::vector< std::vector< GUM_SCALAR > > >(entry_size));

      if (node_cpt[entry].size() != 0)
        GUM_ERROR(DuplicateElement,
                  "setCPT : vertices of entry id "
                     << entry << " already set to : " << node_cpt[entry]
                     << ", cannot insert : " << cpt);

      node_cpt[entry] = cpt;

      ///__credalNet_src_cpt.set ( id, node_cpt );
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::setCPT(
       const NodeId&                                   id,
       Instantiation                                   ins,
       const std::vector< std::vector< GUM_SCALAR > >& cpt) {
      const Potential< GUM_SCALAR >* const potential(&src_bn__.cpt(id));

      auto var_dSize  = src_bn__.variable(id).domainSize();
      auto entry_size = potential->domainSize() / var_dSize;

      // to be sure of entry index reorder ins according to the bayes net
      // potentials
      // ( of the credal net )
      // it WONT throw an error if the sequences are not equal not because of
      // order
      // but content, so we double check (before & after order correction)
      // beware of slaves & master
      Instantiation ref(potential);
      ref.forgetMaster();

      ins.forgetMaster();

      const auto& vseq = ref.variablesSequence();

      if (ins.variablesSequence() != vseq) {
        ins.reorder(ref);

        if (ins.variablesSequence() != vseq)
          GUM_ERROR(OperationNotAllowed,
                    "setCPT : instantiation : "
                       << ins << " is not valid for node id " << id
                       << " which accepts instantiations such as (order is not "
                          "important) : "
                       << ref);
      }

      Idx entry = 0, jump = 1;

      for (Idx i = 0, end = ins.nbrDim(); i < end; i++) {
        if (src_bn__.nodeId(ins.variable(i)) == id) continue;

        entry += ins.val(i) * jump;

        jump *= ins.variable(i).domainSize();
      }

      if (entry >= entry_size)
        GUM_ERROR(SizeError,
                  "setCPT : entry is greater or equal than entry size "
                  "(entries start at 0 up to entry_size - 1) : "
                     << entry << " >= " << entry_size);

      if (cpt.size() == 0)
        GUM_ERROR(SizeError, "setCPT : empty credal set for entry : " << entry);

      for (const auto& vertex: cpt) {
        if (vertex.size() != var_dSize)
          GUM_ERROR(SizeError,
                    "setCPT : variable modalities in cpts does not "
                    "match for node id : "
                       << id << " with vertex " << vertex << " at entry " << entry
                       << " : " << vertex.size() << " != " << var_dSize);

        GUM_SCALAR sum = 0;

        for (const auto& prob: vertex) {
          sum += prob;
        }

        if (std::fabs(sum - 1) > 1e-6)
          GUM_ERROR(
             CPTNoSumTo1,
             "setCPT : a vertex coordinates does not sum to one for node id : "
                << id << " at entry " << entry << " with vertex " << vertex);
      }

      auto& node_cpt = credalNet_src_cpt__.getWithDefault(
         id,
         std::vector< std::vector< std::vector< GUM_SCALAR > > >(entry_size));

      if (node_cpt[entry].size() != 0)
        GUM_ERROR(DuplicateElement,
                  "setCPT : vertices of entry : "
                     << ins << " id " << entry << " already set to : "
                     << node_cpt[entry] << ", cannot insert : " << cpt);

      node_cpt[entry] = cpt;

      ///__credalNet_src_cpt.set ( id, node_cpt );
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::fillConstraints(
       const NodeId&                    id,
       const std::vector< GUM_SCALAR >& lower,
       const std::vector< GUM_SCALAR >& upper) {
      try {
        src_bn_min__.cpt(id).fillWith(lower);
        src_bn_max__.cpt(id).fillWith(upper);
      } catch (const SizeError&) {
        GUM_ERROR(
           SizeError,
           "fillConstraints : sizes does not match in fillWith for node id : "
              << id);
      }
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::fillConstraint(
       const NodeId&                    id,
       const Idx&                       entry,
       const std::vector< GUM_SCALAR >& lower,
       const std::vector< GUM_SCALAR >& upper) {
      Potential< GUM_SCALAR >* const potential_min(
         const_cast< Potential< GUM_SCALAR >* const >(&src_bn_min__.cpt(id)));
      Potential< GUM_SCALAR >* const potential_max(
         const_cast< Potential< GUM_SCALAR >* const >(&src_bn_max__.cpt(id)));

      auto var_dSize = src_bn__.variable(id).domainSize();

      if (lower.size() != var_dSize || upper.size() != var_dSize)
        GUM_ERROR(
           SizeError,
           "setCPT : variable modalities in cpts does not match for node id : "
              << id << " with sizes of constraints : ( " << lower.size() << " || "
              << upper.size() << " ) != " << var_dSize);

      auto entry_size = potential_min->domainSize() / var_dSize;

      if (entry >= entry_size)
        GUM_ERROR(SizeError,
                  "setCPT : entry is greater or equal than entry size "
                  "(entries start at 0 up to entry_size - 1) : "
                     << entry << " >= " << entry_size);

      Instantiation min(potential_min);
      Instantiation max(potential_max);
      min.setFirst();
      max.setFirst();

      Idx pos = 0;

      while (pos != entry) {
        ++min;
        ++max;
        ++pos;
      }

      for (Size i = 0; i < var_dSize; i++) {
        potential_min->set(min, lower[i]);
        potential_max->set(max, upper[i]);
        ++min;
        ++max;
      }
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::fillConstraint(
       const NodeId&                    id,
       Instantiation                    ins,
       const std::vector< GUM_SCALAR >& lower,
       const std::vector< GUM_SCALAR >& upper) {
      const Potential< GUM_SCALAR >* const potential(&src_bn__.cpt(id));
      /*
      auto var_dSize = src_bn__.variable ( id ).domainSize();
      auto entry_size = potential->domainSize() / var_dSize;
      */
      // to be sure of entry index reorder ins according to the bayes net
      // potentials
      // ( of the credal net )
      // it WONT throw an error if the sequences are not equal not because of
      // order
      // but content, so we double check (before & after order correction)
      // beware of slaves & master
      Instantiation ref(potential);
      ref.forgetMaster();

      ins.forgetMaster();

      const auto& vseq = ref.variablesSequence();

      if (ins.variablesSequence() != vseq) {
        ins.reorder(ref);

        if (ins.variablesSequence() != vseq)
          GUM_ERROR(OperationNotAllowed,
                    "setCPT : instantiation : "
                       << ins << " is not valid for node id " << id
                       << " which accepts instantiations such as (order is not "
                          "important) : "
                       << ref);
      }

      Idx entry = 0, jump = 1;

      for (Idx i = 0, end = ins.nbrDim(); i < end; i++) {
        if (src_bn__.nodeId(ins.variable(i)) == id) continue;

        entry += ins.val(i) * jump;

        jump *= ins.variable(i).domainSize();
      }

      /*
      if ( entry >= entry_size )
        GUM_ERROR ( SizeError, "setCPT : entry is greater or equal than entry
      size
      (entries start at 0 up to entry_size - 1) : " << entry << " >= " <<
      entry_size
      );

      if ( lower.size() != var_dSize || upper.size() != var_dSize )
        GUM_ERROR ( SizeError, "setCPT : variable modalities in cpts does not
      match
      for node id : " << id << " with sizes of constraints : ( "<< lower.size()
      << "
      || " << upper.size() << " ) != " << var_dSize );
      */
      fillConstraint(id, entry, lower, upper);
    }

    ////////////////////////////////////////////////
    /// bnet accessors / shortcuts

    template < typename GUM_SCALAR >
    INLINE Instantiation CredalNet< GUM_SCALAR >::instantiation(const NodeId& id) {
      return Instantiation(src_bn__.cpt(id));
    }

    template < typename GUM_SCALAR >
    INLINE Size CredalNet< GUM_SCALAR >::domainSize(const NodeId& id) {
      return src_bn__.variable(id).domainSize();
    }

    ///////////////////////////////////////////////

    template < typename GUM_SCALAR >
    CredalNet< GUM_SCALAR >::CredalNet(const std::string& src_min_num,
                                       const std::string& src_max_den) {
      initParams__();
      initCNNets__(src_min_num, src_max_den);

      GUM_CONSTRUCTOR(CredalNet);
    }

    template < typename GUM_SCALAR >
    CredalNet< GUM_SCALAR >::CredalNet(const BayesNet< GUM_SCALAR >& src_min_num,
                                       const BayesNet< GUM_SCALAR >& src_max_den) {
      initParams__();
      initCNNets__(src_min_num, src_max_den);

      GUM_CONSTRUCTOR(CredalNet);
    }

    template < typename GUM_SCALAR >
    CredalNet< GUM_SCALAR >::~CredalNet() {
      if (current_bn__ != nullptr) delete current_bn__;

      if (credalNet_current_cpt__ != nullptr) delete credalNet_current_cpt__;

      if (current_nodeType__ != nullptr) delete current_nodeType__;

      GUM_DESTRUCTOR(CredalNet);
    }

    // from BNs with numerators & denominators or cpts & denominators to credal
    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::bnToCredal(const GUM_SCALAR beta,
                                             const bool       oneNet,
                                             const bool       keepZeroes) {
      GUM_SCALAR epsi_min = 1.;
      GUM_SCALAR epsi_max = 0.;
      GUM_SCALAR epsi_moy = 0.;
      GUM_SCALAR epsi_den = 0.;

      for (auto node: src_bn().nodes()) {
        const Potential< GUM_SCALAR >* const potential(&src_bn__.cpt(node));

        Potential< GUM_SCALAR >* const potential_min(
           const_cast< Potential< GUM_SCALAR >* const >(&src_bn_min__.cpt(node)));
        Potential< GUM_SCALAR >* const potential_max(
           const_cast< Potential< GUM_SCALAR >* const >(&src_bn_max__.cpt(node)));

        Size var_dSize  = src_bn__.variable(node).domainSize();
        Size entry_size = potential->domainSize() / var_dSize;

        Instantiation ins(potential);
        Instantiation ins_min(potential_min);
        Instantiation ins_max(potential_max);

        ins.setFirst();
        ins_min.setFirst();
        ins_max.setFirst();

        std::vector< GUM_SCALAR > vertex(var_dSize);

        for (Size entry = 0; entry < entry_size; entry++) {
          GUM_SCALAR den;

          if (oneNet)
            den = 0;
          else
            den = potential_max->get(ins_max);

          Size nbm = 0;

          for (Size modality = 0; modality < var_dSize; modality++) {
            vertex[modality] = potential->get(ins);

            if (oneNet) {
              den += vertex[modality];

              if (vertex[modality] < 1 && vertex[modality] > 0)
                GUM_ERROR(OperationNotAllowed,
                          "bnToCredal : the BayesNet contains "
                          "probabilities and not event counts "
                          "although user precised oneNet = "
                             << oneNet);
            }

            if (vertex[modality] > 0) nbm++;

            ++ins;
          }

          /// check sum is 1 if not oneNet (we are not using counts)
          if (!oneNet) {
            GUM_SCALAR sum = 0;

            for (auto modality = vertex.cbegin(), theEnd = vertex.cend();
                 modality != theEnd;
                 ++modality) {
              sum += *modality;
            }

            if (std::fabs(1. - sum) > epsRedund__) {
              GUM_ERROR(CPTNoSumTo1,
                        src_bn__.variable(node).name() << "(" << epsRedund__ << ")"
                                                       << " " << entry << std::endl
                                                       << vertex << std::endl
                                                       << ins << std::endl);
            }
          }

          /// end check sum is 1

          GUM_SCALAR epsilon;

          if (beta == 0)
            epsilon = 0;
          else if (den == 0 || beta == 1)
            epsilon = GUM_SCALAR(1.0);
          else
            epsilon = GUM_SCALAR(std::pow(beta, std::log1p(den)));

          epsi_moy += epsilon;
          epsi_den += 1;

          if (epsilon > epsi_max) epsi_max = epsilon;

          if (epsilon < epsi_min) epsi_min = epsilon;

          GUM_SCALAR min, max;

          for (Size modality = 0; modality < var_dSize; modality++) {
            if ((vertex[modality] > 0 && nbm > 1) || !keepZeroes) {
              min = GUM_SCALAR((1. - epsilon) * vertex[modality]);

              if (oneNet) min = GUM_SCALAR(min * 1.0 / den);

              max = GUM_SCALAR(min + epsilon);
            } else {   // if ( ( vertex[modality] == 0 && keepZeroes ) || (
              // vertex[modality] > 0 && nbm <= 1 ) || ( vertex[modality] == 0
              // && nbm <= 1 ) ) {
              min = vertex[modality];

              if (oneNet) min = GUM_SCALAR(min * 1.0 / den);

              max = min;
            }

            potential_min->set(ins_min, min);
            potential_max->set(ins_max, max);

            ++ins_min;
            ++ins_max;
          }   // end of : for each modality

        }   // end of : for each entry

      }   // end of : for each variable

      epsilonMin__ = epsi_min;
      epsilonMax__ = epsi_max;
      epsilonMoy__ = (GUM_SCALAR)epsi_moy / (GUM_SCALAR)epsi_den;

      intervalToCredal__();
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::lagrangeNormalization() {
      for (auto node: src_bn__.nodes()) {
        const Potential< GUM_SCALAR >* const potential(&src_bn__.cpt(node));

        auto var_dSize  = src_bn__.variable(node).domainSize();
        auto entry_size = potential->domainSize() / var_dSize;

        Instantiation ins(potential);

        ins.setFirst();

        std::vector< GUM_SCALAR > vertex(var_dSize);

        for (Size entry = 0; entry < entry_size; entry++) {
          GUM_SCALAR    den      = 0;
          bool          zeroes   = false;
          Instantiation ins_prev = ins;

          for (Size modality = 0; modality < var_dSize; modality++) {
            vertex[modality] = potential->get(ins);

            if (vertex[modality] < 1 && vertex[modality] > 0)
              GUM_ERROR(OperationNotAllowed,
                        "lagrangeNormalization : the BayesNet "
                        "contains probabilities and not event "
                        "counts.");

            den += vertex[modality];

            if (!zeroes && vertex[modality] == 0) { zeroes = true; }

            ++ins;
          }

          if (zeroes) {
            ins = ins_prev;

            for (Size modality = 0; modality < var_dSize; modality++) {
              potential->set(ins, potential->get(ins) + 1);
              ++ins;
            }
          }

        }   // end of : for each entry

      }   // end of : for each variable
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::idmLearning(const Idx s, const bool keepZeroes) {
      for (auto node: src_bn__.nodes()) {
        const Potential< GUM_SCALAR >* const potential(&src_bn__.cpt(node));

        Potential< GUM_SCALAR >* const potential_min(
           const_cast< Potential< GUM_SCALAR >* const >(&src_bn_min__.cpt(node)));
        Potential< GUM_SCALAR >* const potential_max(
           const_cast< Potential< GUM_SCALAR >* const >(&src_bn_max__.cpt(node)));

        Size var_dSize  = src_bn__.variable(node).domainSize();
        Size entry_size = potential->domainSize() / var_dSize;

        Instantiation ins(potential);
        Instantiation ins_min(potential_min);
        Instantiation ins_max(potential_max);

        ins.setFirst();
        ins_min.setFirst();
        ins_max.setFirst();

        std::vector< GUM_SCALAR > vertex(var_dSize);

        for (Size entry = 0; entry < entry_size; entry++) {
          GUM_SCALAR den = 0;
          Size       nbm = 0;

          for (Size modality = 0; modality < var_dSize; modality++) {
            vertex[modality] = potential->get(ins);

            if (vertex[modality] < 1 && vertex[modality] > 0)
              GUM_ERROR(OperationNotAllowed,
                        "idmLearning : the BayesNet contains "
                        "probabilities and not event counts.");

            den += vertex[modality];

            if (vertex[modality] > 0) nbm++;

            ++ins;
          }

          if (nbm > 1 || !keepZeroes) den += s;

          GUM_SCALAR min, max;

          for (Size modality = 0; modality < var_dSize; modality++) {
            min = vertex[modality];
            max = min;

            if ((vertex[modality] > 0 && nbm > 1) || !keepZeroes) { max += s; }

            min = GUM_SCALAR(min * 1.0 / den);
            max = GUM_SCALAR(max * 1.0 / den);

            potential_min->set(ins_min, min);
            potential_max->set(ins_max, max);

            ++ins_min;
            ++ins_max;
          }   // end of : for each modality

        }   // end of : for each entry

      }   // end of : for each variable

      epsilonMin__ = GUM_SCALAR(s);
      epsilonMax__ = GUM_SCALAR(s);
      epsilonMoy__ = GUM_SCALAR(s);
      intervalToCredal__();
    }

    /* no need for lrs : (max ... min ... max) vertices from bnToCredal() */
    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::intervalToCredal__() {
      if (!credalNet_src_cpt__.empty()) credalNet_src_cpt__.clear();

      credalNet_src_cpt__.resize(src_bn__.size());

      for (auto node: src_bn__.nodes()) {
        const Potential< GUM_SCALAR >* const potential_min(
           &src_bn_min__.cpt(node));
        const Potential< GUM_SCALAR >* const potential_max(
           &src_bn_max__.cpt(node));

        Size var_dSize  = src_bn__.variable(node).domainSize();
        Size entry_size = potential_min->domainSize() / var_dSize;

        std::vector< std::vector< std::vector< GUM_SCALAR > > > var_cpt(
           entry_size);

        Instantiation ins_min(potential_min);
        Instantiation ins_max(potential_max);

        ins_min.setFirst();
        ins_max.setFirst();

        std::vector< GUM_SCALAR > lower(var_dSize);
        std::vector< GUM_SCALAR > upper(var_dSize);

        for (Size entry = 0; entry < entry_size; entry++) {
          for (Size modality = 0; modality < var_dSize;
               modality++, ++ins_min, ++ins_max) {
            lower[modality] = potential_min->get(ins_min);
            upper[modality] = potential_max->get(ins_max);
          }

          bool                                     all_equals = true;
          std::vector< std::vector< GUM_SCALAR > > vertices;

          for (Size modality = 0; modality < var_dSize; modality++) {
            if (std::fabs(upper[modality] - lower[modality]) < 1e-6) continue;

            all_equals = false;
            std::vector< GUM_SCALAR > vertex(var_dSize);
            vertex[modality] = upper[modality];

            for (Size mod = 0; mod < var_dSize; mod++) {
              if (modality != mod) vertex[mod] = lower[mod];
            }

            GUM_SCALAR total = 0;

            auto vsize = vertex.size();

            for (Size i = 0; i < vsize; i++)
              total += vertex[i];

            if (std::fabs(total - 1.) > 1e-6)
              GUM_ERROR(CPTNoSumTo1,
                        src_bn__.variable(node).name() << " " << entry << std::endl
                                                       << vertex << std::endl);

            vertices.push_back(vertex);
          }

          if (all_equals) {
            std::vector< GUM_SCALAR > vertex(var_dSize);

            for (Size modality = 0; modality < var_dSize; modality++)
              vertex[modality] = lower[modality];

            GUM_SCALAR total = 0.;

            auto vsize = vertex.size();

            for (Size i = 0; i < vsize; i++)
              total += vertex[i];

            if (std::fabs(total - 1.) > 1e-6)
              GUM_ERROR(CPTNoSumTo1,
                        src_bn__.variable(node).name() << " " << entry << std::endl
                                                       << vertex << std::endl);

            vertices.push_back(vertex);
          }

          var_cpt[entry] = vertices;
        }

        credalNet_src_cpt__.insert(node, var_cpt);

      }   // end of : for each variable (node)

      // get precise/credal/vacuous status of each variable
      sort_varType__();
      separatelySpecified__ = true;
    }

    /* uses lrsWrapper */
    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::intervalToCredal() {
      if (!credalNet_src_cpt__.empty()) credalNet_src_cpt__.clear();

      credalNet_src_cpt__.resize(src_bn__.size());

      LRSWrapper< GUM_SCALAR > lrsWrapper;

      for (auto node: src_bn__.nodes()) {
        const Potential< GUM_SCALAR >* const potential_min(
           &src_bn_min__.cpt(node));
        const Potential< GUM_SCALAR >* const potential_max(
           &src_bn_max__.cpt(node));

        Size var_dSize  = src_bn__.variable(node).domainSize();
        Size entry_size = potential_min->domainSize() / var_dSize;

        std::vector< std::vector< std::vector< GUM_SCALAR > > > var_cpt(
           entry_size);

        Instantiation ins_min(potential_min);
        Instantiation ins_max(potential_max);

        ins_min.setFirst();
        ins_max.setFirst();

        lrsWrapper.setUpH(var_dSize);

        for (Size entry = 0; entry < entry_size; entry++) {
          for (Size modality = 0; modality < var_dSize; modality++) {
            if (potential_min->get(ins_min) > potential_max->get(ins_max)) {
              GUM_ERROR(CPTError,
                        "For variable " << src_bn__.variable(node).name()
                                        << " (at " << ins_min
                                        << "), the min is greater than the max : "
                                        << potential_min->get(ins_min) << ">"
                                        << potential_max->get(ins_max) << ".");
            }
            lrsWrapper.fillH(potential_min->get(ins_min),
                             potential_max->get(ins_max),
                             modality);
            ++ins_min;
            ++ins_max;
          }

          lrsWrapper.H2V();
          var_cpt[entry] = lrsWrapper.getOutput();
          lrsWrapper.nextHInput();
        }

        credalNet_src_cpt__.insert(node, var_cpt);

      }   // end of : for each variable (node)

      // get precise/credal/vacuous status of each variable
      sort_varType__();
      separatelySpecified__ = true;
    }

    /* call lrs */
    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::intervalToCredalWithFiles() {
      if (!credalNet_src_cpt__.empty()) credalNet_src_cpt__.clear();

      credalNet_src_cpt__.resize(src_bn__.size());

      for (auto node: src_bn__.nodes()) {
        const Potential< GUM_SCALAR >* const potential_min(
           &src_bn_min__.cpt(node));
        const Potential< GUM_SCALAR >* const potential_max(
           &src_bn_max__.cpt(node));

        auto var_dSize  = src_bn__.variable(node).domainSize();
        auto entry_size = potential_min->domainSize() / var_dSize;

        std::vector< std::vector< std::vector< GUM_SCALAR > > > var_cpt(
           entry_size);

        Instantiation ins_min(potential_min);
        Instantiation ins_max(potential_max);

        ins_min.setFirst();
        ins_max.setFirst();

        // use iterator
        for (Size entry = 0; entry < entry_size; entry++) {
          std::vector< std::vector< GUM_SCALAR > > vertices;
          std::vector< GUM_SCALAR > vertex(var_dSize);   // if not interval

          std::vector< std::vector< GUM_SCALAR > > inequalities(
             var_dSize * 2,
             std::vector< GUM_SCALAR >(var_dSize + 1, 0));

          std::vector< GUM_SCALAR > sum_ineq1(var_dSize + 1, -1);
          std::vector< GUM_SCALAR > sum_ineq2(var_dSize + 1, 1);
          sum_ineq1[0] = 1;
          sum_ineq2[0] = -1;

          bool isInterval = false;

          for (Size modality = 0; modality < var_dSize; modality++) {
            inequalities[modality * 2][0]     = -potential_min->get(ins_min);
            inequalities[modality * 2 + 1][0] = potential_max->get(ins_max);
            inequalities[modality * 2][modality + 1]     = 1;
            inequalities[modality * 2 + 1][modality + 1] = -1;

            vertex[modality] = inequalities[modality * 2 + 1][0];

            if (!isInterval
                && (-inequalities[modality * 2][0]
                    != inequalities[modality * 2 + 1][0]))
              isInterval = true;

            ++ins_min;
            ++ins_max;
          }

          inequalities.push_back(sum_ineq1);
          inequalities.push_back(sum_ineq2);

          if (!isInterval) {
            vertices.push_back(vertex);
          } else {
            try {
              H2Vlrs__(inequalities, vertices);
              //__H2Vcdd ( inequalities, vertices );
            } catch (const std::exception& err) {
              std::cout << err.what() << std::endl;
              throw;
            }

          }   // end of : is interval

          if (entry == 0 && vertices.size() >= 2) {
            auto tmp    = vertices[0];
            vertices[0] = vertices[1];
            vertices[1] = tmp;
          }

          var_cpt[entry] = vertices;

        }   // end of : for each entry

        credalNet_src_cpt__.insert(node, var_cpt);
        // std::cout << src_bn__.variable(node_idIt).name() << std::endl;
        // std::cout << var_cpt << std::endl;

      }   // end of : for each variable (node)

      // get precise/credal/vacuous status of each variable
      sort_varType__();
      separatelySpecified__ = true;
    }

    /**
     * to call after bnToCredal( GUM_SCALAR beta )
     * save a BN with lower probabilities and a BN with upper ones
     */
    template < typename GUM_SCALAR >
    void
       CredalNet< GUM_SCALAR >::saveBNsMinMax(const std::string& min_path,
                                              const std::string& max_path) const {
      BIFWriter< GUM_SCALAR > writer;

      std::string   minfilename = min_path;   //"min.bif";
      std::string   maxfilename = max_path;   //"max.bif";
      std::ofstream min_file(minfilename.c_str(), std::ios::out | std::ios::trunc);
      std::ofstream max_file(maxfilename.c_str(), std::ios::out | std::ios::trunc);

      if (!min_file.good())
        GUM_ERROR(
           IOError,
           "bnToCredal() : could not open stream : min_file : " << minfilename);

      if (!max_file.good()) {
        min_file.close();
        GUM_ERROR(
           IOError,
           "bnToCredal() : could not open stream : min_file : " << maxfilename);
      }

      try {
        writer.write(min_file, src_bn_min__);
        writer.write(max_file, src_bn_max__);
      } catch (Exception& err) {
        GUM_SHOWERROR(err);
        min_file.close();
        max_file.close();
        throw(err);
      }

      min_file.close();
      max_file.close();
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::approximatedBinarization() {
      // don't forget to delete the old one (current__), if necessary at the end
      auto bin_bn = new BayesNet< GUM_SCALAR >();

      //__bnCopy ( *bin_bn__ );
      // delete old one too
      auto credalNet_bin_cpt = new NodeProperty<
         std::vector< std::vector< std::vector< GUM_SCALAR > > > >();

      // delete old one too
      auto bin_nodeType = new NodeProperty< NodeType >();

      const BayesNet< GUM_SCALAR >* current_bn;
      // const NodeProperty< nodeType > *current_nodeType__;
      const NodeProperty<
         std::vector< std::vector< std::vector< GUM_SCALAR > > > >*
         credalNet_current_cpt;

      if (this->current_bn__ == nullptr)
        current_bn = &this->src_bn__;
      else
        current_bn = this->current_bn__;

      if (this->credalNet_current_cpt__ == nullptr)
        credalNet_current_cpt = &this->credalNet_src_cpt__;
      else
        credalNet_current_cpt = this->credalNet_current_cpt__;

      /*if ( this->current_nodeType__ == nullptr )
        current_nodeType__ = & this->nodeType__;
      else
        current_nodeType__ = this->current_nodeType__;*/

      if (!var_bits__.empty()) var_bits__.clear();

      bin_bn->beginTopologyTransformation();

      for (auto node: current_bn->nodes()) {
        auto var_dSize = current_bn->variable(node).domainSize();

        if (var_dSize != 2) {
          unsigned long b, c;
          superiorPow((unsigned long)var_dSize, b, c);
          Size nb_bits{Size(b)};

          std::string           bit_name;
          std::vector< NodeId > bits(nb_bits);

          for (Size bit = 0; bit < nb_bits; bit++) {
            bit_name = current_bn->variable(node).name() + "-b";
            std::stringstream ss;
            ss << bit;
            bit_name += ss.str();

            LabelizedVariable var_bit(bit_name, "node " + bit_name, 2);
            NodeId            iD = bin_bn->add(var_bit);

            bits[bit] = iD;
          }   // end of : for each bit

          var_bits__.insert(node, bits);

        }   // end of : if variable is not binary
        else {
          std::string       bit_name = current_bn->variable(node).name();
          LabelizedVariable var_bit(bit_name, "node " + bit_name, 2);
          NodeId            iD = bin_bn->add(var_bit);

          var_bits__.insert(node, std::vector< NodeId >(1, iD));
        }

      }   // end of : for each original variable

      for (auto node: current_bn->nodes()) {
        NodeSet parents = current_bn->parents(node);

        if (!parents.empty()) {
          for (auto par: current_bn->parents(node)) {
            for (Size parent_bit = 0, spbits = Size(var_bits__[par].size());
                 parent_bit < spbits;
                 parent_bit++)
              for (Size var_bit = 0, mbits = Size(var_bits__[node].size());
                   var_bit < mbits;
                   var_bit++)
                bin_bn->addArc(var_bits__[par][parent_bit],
                               var_bits__[node][var_bit]);
          }
        }

        // arcs with one's bits
        auto bitsize = var_bits__[node].size();

        for (Size bit_c = 1; bit_c < bitsize; bit_c++)
          for (Size bit_p = 0; bit_p < bit_c; bit_p++)
            bin_bn->addArc(var_bits__[node][bit_p], var_bits__[node][bit_c]);

      }   // end of : for each original variable

      bin_bn->endTopologyTransformation();

      // binarization of cpts

      auto varsize = current_bn->size();

      for (Size var = 0; var < varsize; var++) {
        auto bitsize = var_bits__[var].size();

        for (Size i = 0; i < bitsize; i++) {
          Potential< GUM_SCALAR > const* potential(
             &bin_bn->cpt(var_bits__[var][i]));
          Instantiation ins(potential);
          ins.setFirst();

          auto entry_size = potential->domainSize() / 2;
          std::vector< std::vector< std::vector< GUM_SCALAR > > > var_cpt(
             entry_size);

          Size old_conf = 0;

          for (Size conf = 0; conf < entry_size; conf++) {
            std::vector< std::vector< GUM_SCALAR > > pvar_cpt;
            auto verticessize = (*credalNet_current_cpt)[var][old_conf].size();

            for (Size old_distri = 0; old_distri < verticessize; old_distri++) {
              const std::vector< GUM_SCALAR >& vertex
                 = (*credalNet_current_cpt)[var][old_conf][old_distri];
              auto vertexsize = vertex.size();

              std::vector< Idx > incc(vertexsize, 0);

              for (Size preced = 0; preced < i; preced++) {
                auto bit_pos = ins.pos(bin_bn->variable(var_bits__[var][preced]));
                auto val     = ins.val(bit_pos);

                Size pas = Size(int2Pow((unsigned long)preced));
                Size elem;

                if (val == 0)
                  elem = 0;
                else
                  elem = pas;

                while (elem < vertexsize) {
                  incc[elem]++;
                  elem++;

                  if (elem % pas == 0) elem += pas;
                }
              }

              Size pas = Size(int2Pow((unsigned long)i));

              std::vector< GUM_SCALAR > distri(2, 0);
              int                       pos = 1;

              for (Size elem = 0; elem < vertexsize; elem++) {
                if (elem % pas == 0) pos = -pos;

                if (incc[elem] == i)
                  (pos < 0) ? (distri[0] += vertex[elem])
                            : (distri[1] += vertex[elem]);
              }

              if (i > 0) {
                GUM_SCALAR den = distri[0] + distri[1];

                if (den == 0) {
                  distri[0] = 0;
                  distri[1] = 0;
                } else {
                  distri[0] /= den;
                  distri[1] /= den;
                }
              }

              pvar_cpt.push_back(distri);

            }   // end of old distris

            // get min/max approx, 2 vertices
            std::vector< std::vector< GUM_SCALAR > > vertices(
               2,
               std::vector< GUM_SCALAR >(2, 1));
            vertices[1][1] = 0;

            auto new_verticessize = pvar_cpt.size();

            for (Size v = 0; v < new_verticessize; v++) {
              if (pvar_cpt[v][1] < vertices[0][1]) vertices[0][1] = pvar_cpt[v][1];

              if (pvar_cpt[v][1] > vertices[1][1]) vertices[1][1] = pvar_cpt[v][1];
            }

            vertices[0][0] = 1 - vertices[0][1];
            vertices[1][0] = 1 - vertices[1][1];

            pvar_cpt = vertices;

            var_cpt[conf] = pvar_cpt;

            ++ins;
            ++ins;

            old_conf++;

            if (old_conf == (*credalNet_current_cpt)[var].size()) old_conf = 0;

          }   // end of new parent conf

          credalNet_bin_cpt->insert(var_bits__[var][i], var_cpt);

        }   // end of bit i

      }   // end of old variable

      bin_bn->beginTopologyTransformation();

      /* indicatrices variables */
      auto old_varsize = var_bits__.size();

      for (Size i = 0; i < old_varsize; i++) {
        auto bitsize = var_bits__[i].size();

        // binary variable
        if (bitsize == 1) continue;

        auto old_card = src_bn__.variable(i).domainSize();

        for (Size mod = 0; mod < old_card; mod++) {
          std::stringstream ss;
          ss << src_bn__.variable(i).name();
          ss << "-v";
          ss << mod;

          LabelizedVariable var(ss.str(), "node " + ss.str(), 2);
          const NodeId      indic = bin_bn->add(var);

          // arcs from one's bits
          for (Size bit = 0; bit < bitsize; bit++)
            bin_bn->addArc(var_bits__[i][bit], indic);

          // cpt
          Size num = Size(int2Pow(long(bitsize)));

          std::vector< std::vector< std::vector< GUM_SCALAR > > > icpt(num);

          for (Size entry = 0; entry < num; entry++) {
            std::vector< std::vector< GUM_SCALAR > > vertices(
               1,
               std::vector< GUM_SCALAR >(2, 0));

            if (mod == entry)
              vertices[0][1] = 1;
            else
              vertices[0][0] = 1;

            icpt[entry] = vertices;
          }

          credalNet_bin_cpt->insert(indic, icpt);

          bin_nodeType->insert(indic, NodeType::Indic);
        }   // end of each modality, i.e. as many indicatrice
      }

      bin_bn->endTopologyTransformation();

      if (this->current_bn__ != nullptr) delete this->current_bn__;

      this->current_bn__ = bin_bn;

      if (this->credalNet_current_cpt__ != nullptr)
        delete this->credalNet_current_cpt__;

      this->credalNet_current_cpt__ = credalNet_bin_cpt;

      if (this->current_nodeType__ != nullptr) delete this->current_nodeType__;

      this->current_nodeType__ = bin_nodeType;

      sort_varType__();   // will fill bin_nodeType__ except for NodeType::Indic
                          // variables

      computeBinaryCPTMinMax();
    }

    template < typename GUM_SCALAR >
    const NodeProperty< std::vector< std::vector< std::vector< GUM_SCALAR > > > >&
       CredalNet< GUM_SCALAR >::credalNet_currentCpt() const {
      if (credalNet_current_cpt__ != nullptr) return *credalNet_current_cpt__;

      return credalNet_src_cpt__;
    }

    template < typename GUM_SCALAR >
    const NodeProperty< std::vector< std::vector< std::vector< GUM_SCALAR > > > >&
       CredalNet< GUM_SCALAR >::credalNet_srcCpt() const {
      return credalNet_src_cpt__;
    }

    template < typename GUM_SCALAR >
    typename CredalNet< GUM_SCALAR >::NodeType
       CredalNet< GUM_SCALAR >::currentNodeType(const NodeId& id) const {
      if (current_nodeType__ != nullptr) return (*(current_nodeType__))[id];

      return original_nodeType__[id];
    }

    template < typename GUM_SCALAR >
    typename CredalNet< GUM_SCALAR >::NodeType
       CredalNet< GUM_SCALAR >::nodeType(const NodeId& id) const {
      return original_nodeType__[id];
    }

    template < typename GUM_SCALAR >
    const bool CredalNet< GUM_SCALAR >::isSeparatelySpecified() const {
      return separatelySpecified__;
    }

    template < typename GUM_SCALAR >
    const bool CredalNet< GUM_SCALAR >::hasComputedBinaryCPTMinMax() const {
      return hasComputedBinaryCPTMinMax__;
    }

    // only if CN is binary !!
    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::computeBinaryCPTMinMax() {
      binCptMin__.resize(current_bn().size());
      binCptMax__.resize(current_bn().size());

      for (auto node: current_bn().nodes()) {
        auto                      pConf = credalNet_currentCpt()[node].size();
        std::vector< GUM_SCALAR > min(pConf);
        std::vector< GUM_SCALAR > max(pConf);

        for (Size pconf = 0; pconf < pConf; pconf++) {
          GUM_SCALAR v1, v2;
          v1 = credalNet_currentCpt()[node][pconf][0][1];

          if (credalNet_currentCpt()[node][pconf].size() > 1)
            v2 = credalNet_currentCpt()[node][pconf][1][1];
          else
            v2 = v1;

          GUM_SCALAR delta = v1 - v2;
          min[pconf]       = (delta >= 0) ? v2 : v1;
          max[pconf]       = (delta >= 0) ? v1 : v2;
        }

        binCptMin__[node] = min;
        binCptMax__[node] = max;
      }

      hasComputedBinaryCPTMinMax__ = true;
    }

    template < typename GUM_SCALAR >
    const std::vector< std::vector< GUM_SCALAR > >&
       CredalNet< GUM_SCALAR >::get_binaryCPT_min() const {
      return binCptMin__;
    }

    template < typename GUM_SCALAR >
    const std::vector< std::vector< GUM_SCALAR > >&
       CredalNet< GUM_SCALAR >::get_binaryCPT_max() const {
      return binCptMax__;
    }

    template < typename GUM_SCALAR >
    const GUM_SCALAR& CredalNet< GUM_SCALAR >::epsilonMin() const {
      return epsilonMin__;
    }

    template < typename GUM_SCALAR >
    const GUM_SCALAR& CredalNet< GUM_SCALAR >::epsilonMax() const {
      return epsilonMax__;
    }

    template < typename GUM_SCALAR >
    const GUM_SCALAR& CredalNet< GUM_SCALAR >::epsilonMean() const {
      return epsilonMoy__;
    }

    template < typename GUM_SCALAR >
    std::string CredalNet< GUM_SCALAR >::toString() const {
      std::stringstream             output;
      const BayesNet< GUM_SCALAR >* current_bn__;
      const NodeProperty<
         std::vector< std::vector< std::vector< GUM_SCALAR > > > >*
         credalNet_current_cpt__;

      if (this->current_bn__ == nullptr)
        current_bn__ = &this->src_bn__;
      else
        current_bn__ = this->current_bn__;

      if (this->credalNet_current_cpt__ == nullptr)
        credalNet_current_cpt__ = &this->credalNet_src_cpt__;
      else
        credalNet_current_cpt__ = this->credalNet_current_cpt__;

      for (auto node: current_bn__->nodes()) {
        const Potential< GUM_SCALAR >* potential(&current_bn__->cpt(node));
        auto                           pconfs
           = potential->domainSize() / current_bn__->variable(node).domainSize();

        output << "\n" << current_bn__->variable(node) << "\n";

        Instantiation ins(potential);
        ins.forgetMaster();
        ins.erase(current_bn__->variable(node));
        ins.setFirst();

        for (Size pconf = 0; pconf < pconfs; pconf++) {
          output << ins << " : ";
          output << (*credalNet_current_cpt__)[node][pconf] << "\n";

          if (pconf < pconfs - 1) ++ins;
        }
      }

      output << "\n";

      return output.str();
    }

    template < typename GUM_SCALAR >
    const BayesNet< GUM_SCALAR >& CredalNet< GUM_SCALAR >::current_bn() const {
      if (current_bn__ != nullptr) return *current_bn__;

      return src_bn__;
    }

    template < typename GUM_SCALAR >
    const BayesNet< GUM_SCALAR >& CredalNet< GUM_SCALAR >::src_bn() const {
      return src_bn__;
    }

    /////////// protected stuff //////////

    /////////// private stuff ////////////

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::initParams__() {
      epsilonMin__ = 0;
      epsilonMax__ = 0;
      epsilonMoy__ = 0;

      epsRedund__ = GUM_SCALAR(1e-6);

      // farey algorithm
      epsF__   = GUM_SCALAR(1e-6);
      denMax__ = GUM_SCALAR(1e6);   // beware LRSWrapper

      // continued fractions, beware LRSWrapper
      // decimal paces (epsC__ * precisionC__ == 1)
      precisionC__ = GUM_SCALAR(1e6);
      deltaC__     = 5;

      // old custom algorithm
      precision__ = GUM_SCALAR(1e6);   // beware LRSWrapper

      current_bn__            = nullptr;
      credalNet_current_cpt__ = nullptr;
      current_nodeType__      = nullptr;

      hasComputedBinaryCPTMinMax__ = false;
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::initCNNets__(const std::string& src_min_num,
                                               const std::string& src_max_den) {
      BIFReader< GUM_SCALAR > reader(&src_bn__, src_min_num);
      std::string             other;

      if (src_max_den.compare("") != 0)
        other = src_max_den;
      else
        other = src_min_num;

      BIFReader< GUM_SCALAR > reader_min(&src_bn_min__, src_min_num);
      BIFReader< GUM_SCALAR > reader_max(&src_bn_max__, other);

      reader.proceed();
      reader_min.proceed();
      reader_max.proceed();
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::initCNNets__(
       const BayesNet< GUM_SCALAR >& src_min_num,
       const BayesNet< GUM_SCALAR >& src_max_den) {
      src_bn__     = src_min_num;
      src_bn_min__ = src_min_num;

      if (src_max_den.size() > 0)
        src_bn_max__ = src_max_den;
      else
        src_bn_max__ = src_min_num;
    }

    template < typename GUM_SCALAR >
    int CredalNet< GUM_SCALAR >::find_dNode_card__(
       const std::vector< std::vector< std::vector< GUM_SCALAR > > >& var_cpt)
       const {
      Size vertices_size = 0;

      for (auto entry = var_cpt.cbegin(), theEnd = var_cpt.cend(); entry != theEnd;
           ++entry) {
        if (entry->size() > vertices_size) vertices_size = Size(entry->size());
      }

      return int(vertices_size);
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::bnCopy__(BayesNet< GUM_SCALAR >& dest) {
      const BayesNet< GUM_SCALAR >* current_bn__;

      if (this->current_bn__ == nullptr)
        current_bn__ = &this->src_bn__;
      else
        current_bn__ = this->current_bn__;

      for (auto node: current_bn__->nodes())
        dest.add(current_bn__->variable(node));

      dest.beginTopologyTransformation();

      for (auto node: current_bn__->nodes()) {
        for (auto parent_idIt: current_bn__->cpt(node).variablesSequence()) {
          if (current_bn__->nodeId(*parent_idIt) != node)
            dest.addArc(current_bn__->nodeId(*parent_idIt), node);
        }   // end of : for each parent in order of appearence
      }     // end of : for each variable

      dest.endTopologyTransformation();
    }

    /*
      // cdd can use real values, not just rationals / integers
      template< typename GUM_SCALAR >
      void CredalNet< GUM_SCALAR >::H2Vcdd__ ( const std::vector< std::vector<
      GUM_SCALAR > > & h_rep, std::vector< std::vector< GUM_SCALAR > > & v_rep )
      const {
        dd_set_global_constants();

        dd_MatrixPtr M, G;
        dd_PolyhedraPtr poly;
        dd_ErrorType err;

        unsigned int rows = h_rep.size();
        unsigned int cols = 0;
        if( h_rep.size() > 0 )
          cols = h_rep[0].size();

        M = dd_CreateMatrix( rows, cols);

        for ( unsigned int row = 0; row < rows; row++ )
          for ( unsigned int col = 0; col < cols; col++ )
            dd_set_d( M->matrix[row][col], h_rep[row][col] );

        M->representation = dd_Inequality;

        poly = dd_DDMatrix2Poly(M, &err);
        G = dd_CopyGenerators(poly);

        rows = G->rowsize;
        cols = G->colsize;

        v_rep.clear();
        for ( unsigned int row = 0; row < rows; row++ ) {
          std::vector< GUM_SCALAR > aRow(cols - 1);

          if ( *G->matrix[row][0] != 1 )
            GUM_ERROR(OperationNotAllowed, "__H2Vcdd : not reading a vertex");

          for ( unsigned int col = 0; col < cols - 1; col++ )
            aRow[col] = *G->matrix[row][ col + 1 ];

          v_rep.push_back(aRow);
        }

        dd_FreeMatrix(M);
        dd_FreeMatrix(G);
        dd_FreePolyhedra(poly);

        dd_free_global_constants();
      }
    */

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::H2Vlrs__(
       const std::vector< std::vector< GUM_SCALAR > >& h_rep,
       std::vector< std::vector< GUM_SCALAR > >&       v_rep) const {
      // write H rep file
      int64_t num, den;

      std::string sinefile
         = getUniqueFileName();   // generate unique file name, we
      // need to add .ine or .ext for lrs
      // to know which input it is (Hrep
      // to Vrep or Vrep to Hrep)
      sinefile += ".ine";

      std::ofstream h_file(sinefile.c_str(), std::ios::out | std::ios::trunc);

      if (!h_file.good())
        GUM_ERROR(IOError,
                  "__H2Vlrs : could not open lrs input file : " << sinefile);

      h_file << "H - representation\n";
      h_file << "begin\n";
      h_file << h_rep.size() << ' ' << h_rep[0].size() << " rational\n";

      for (auto it = h_rep.cbegin(), theEnd = h_rep.cend(); it != theEnd; ++it) {
        for (auto it2 = it->cbegin(), theEnd2 = it->cend(); it2 != theEnd2;
             ++it2) {
          // get integer fraction from decimal value
          // smallest numerator & denominator is farley, also
          // best precision
          Rational< GUM_SCALAR >::farey(num,
                                        den,
                                        ((*it2 > 0) ? *it2 : -*it2),
                                        int64_t(denMax__),
                                        epsF__);

          h_file << ((*it2 > 0) ? num : -num) << '/' << den << ' ';
        }

        h_file << '\n';
      }

      h_file << "end\n";
      h_file.close();

      // call lrs
      // lrs arguments
      char* args[3];

      std::string soft_name = "lrs";
      std::string extfile(sinefile);
      extfile += ".ext";

      args[0] = new char[soft_name.size()];
      args[1] = new char[sinefile.size()];
      args[2] = new char[extfile.size()];

      strcpy(args[0], soft_name.c_str());
      strcpy(args[1], sinefile.c_str());
      strcpy(args[2], extfile.c_str());

      // standard cout to null (avoid lrs flooding)
      int old_cout, new_cout;
      fflush(stdout);
      old_cout = dup(1);

      new_cout = open("/dev/null", O_WRONLY);
      dup2(new_cout, 1);
      close(new_cout);

      lrs_main(3, args);

      // restore standard cout
      fflush(stdout);
      dup2(old_cout, 1);
      close(old_cout);

      delete[] args[2];
      delete[] args[1];
      delete[] args[0];

      // read V rep file
      std::ifstream v_file(extfile.c_str() /*extfilename.c_str()*/, std::ios::in);

      if (!v_file.good())
        GUM_ERROR(IOError, "__H2Vlrs : could not open lrs ouput file : ");

      std::string line, tmp;
      char *      cstr, *p;
      GUM_SCALAR  probability;

      std::string::size_type pos;
      bool                   keep_going = true;
      // int vertices;

      std::vector< GUM_SCALAR > vertex;

      v_file.ignore(256, 'l');

      while (v_file.good() && keep_going) {
        getline(v_file, line);

        if (line.size() == 0)
          continue;
        else if (line.compare("end") == 0) {
          keep_going = false;
          // this is to get vertices number :
          /*getline ( v_file, line );
          std::string::size_type pos, end_pos;
          pos = line.find ( "vertices = " );
          end_pos = line.find ( "rays", pos + 9 );
          vertices = atoi ( line.substr ( pos + 9, end_pos - pos - 9 ).c_str()
          );*/
          break;
        } else if (line[1] != '1') {
          GUM_ERROR(IOError,
                    "__H2Vlrs : reading something other than a vertex from "
                    "lrs output file : ");
        }

        line = line.substr(2);
        cstr = new char[line.size() + 1];
        strcpy(cstr, line.c_str());

        p = strtok(cstr, " ");

        while (p != nullptr) {
          tmp = p;

          if (tmp.compare("1") == 0 || tmp.compare("0") == 0)
            probability = GUM_SCALAR(atof(tmp.c_str()));
          else {
            pos = tmp.find("/");
            probability
               = GUM_SCALAR(atof(tmp.substr(0, pos).c_str())
                            / atof(tmp.substr(pos + 1, tmp.size()).c_str()));
          }

          vertex.push_back(probability);
          p = strtok(nullptr, " ");
        }   // end of : for all tokens

        delete[] p;
        delete[] cstr;

        bool is_redund = false;

#pragma omp parallel
        {
          int this_thread = getThreadNumber();
          int num_threads = getNumberOfRunningThreads();

          auto begin_pos = (this_thread + 0) * v_rep.size() / num_threads;
          auto end_pos   = (this_thread + 1) * v_rep.size() / num_threads;

          for (auto p = begin_pos; p < end_pos; p++) {
#pragma omp flush(is_redund)

            if (is_redund) break;

            bool thread_redund = true;

            auto vsize = vertex.size();

            for (Size modality = 0; modality < vsize; modality++) {
              if (std::fabs(vertex[modality] - v_rep[p][modality]) > epsRedund__) {
                thread_redund = false;
                break;
              }
            }

            if (thread_redund) {
              is_redund = true;
#pragma omp flush(is_redund)
            }
          }   // end of : each thread for
        }     // end of : parallel

        if (!is_redund) v_rep.push_back(vertex);

        vertex.clear();

      }   // end of : file

      v_file.close();

      if (std::remove(sinefile.c_str()) != 0)
        GUM_ERROR(IOError, "error removing : " + sinefile);

      if (std::remove(extfile.c_str()) != 0)
        GUM_ERROR(IOError, "error removing : " + extfile);
    }

    template < typename GUM_SCALAR >
    void CredalNet< GUM_SCALAR >::sort_varType__() {
      NodeProperty< NodeType >* current_nodeType__;
      const NodeProperty<
         std::vector< std::vector< std::vector< GUM_SCALAR > > > >*
         credalNet_current_cpt__;

      const BayesNet< GUM_SCALAR >* current_bn__;

      if (this->current_bn__ == nullptr)
        current_bn__ = &src_bn__;
      else
        current_bn__ = this->current_bn__;

      if (this->credalNet_current_cpt__ == nullptr)
        credalNet_current_cpt__ = &credalNet_src_cpt__;
      else
        credalNet_current_cpt__ = this->credalNet_current_cpt__;

      if (this->current_nodeType__ == nullptr)
        current_nodeType__ = &original_nodeType__;
      else
        current_nodeType__ = this->current_nodeType__;

      /*if ( ! current_nodeType__->empty() )
        current_nodeType__->clear();*/

      for (auto node: current_bn__->nodes()) {
        // indicatrices are already present
        if (current_nodeType__->exists(node)) continue;

        bool precise = true, vacuous = true;

        for (auto entry   = (*credalNet_current_cpt__)[node].cbegin(),
                  theEnd2 = (*credalNet_current_cpt__)[node].cend();
             entry != theEnd2;
             ++entry) {
          auto vertices  = entry->size();
          auto var_dSize = (*entry)[0].size();

          if (precise && vertices > 1) precise = false;

          if (vacuous && vertices == var_dSize) {
            std::vector< bool > elem(var_dSize, false);

            for (auto vertex = entry->cbegin(), vEnd = entry->cend();
                 vertex != vEnd;
                 ++vertex) {
              for (auto probability = vertex->cbegin(), pEnd = vertex->cend();
                   probability != pEnd;
                   ++probability) {
                if (*probability == 1) {
                  elem[probability - vertex->begin()] = true;
                  break;
                }
              }   // end of : for each modality

              break;   // not vacuous
            }          // end of : for each vertex

            for (auto /*std::vector< bool >::const_iterator*/ probability
                 = elem.cbegin();
                 probability != elem.cend();
                 ++probability)
              if (*probability == false) vacuous = false;

          }   // end of : if vertices == dSize
          else
            vacuous = false;

          if (vacuous == false && precise == false) {
            current_nodeType__->insert(node, NodeType::Credal);
            break;
          }

        }   // end of : for each parents entry

        if (vacuous)
          current_nodeType__->insert(node, NodeType::Vacuous);
        else if (precise)
          current_nodeType__->insert(node, NodeType::Precise);

      }   // end of : for each variable
    }

  }   // namespace credal
}   // namespace gum