influenceDiagram_tpl.h

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/****************************************************************************
 *   This file is part of the aGrUM/pyAgrum library.                        *
 *                                                                          *
 *   Copyright (c) 2005-2026 by                                             *
 *       - Pierre-Henri WUILLEMIN(_at_LIP6)                                 *
 *       - Christophe GONZALES(_at_AMU)                                     *
 *                                                                          *
 *   The aGrUM/pyAgrum library is free software; you can redistribute it    *
 *   and/or modify it under the terms of either :                           *
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 *      the Free Software Foundation, either version 3 of the License,      *
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 *    - the MIT license (MIT),                                              *
 *    - or both in dual license, as here.                                   *
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 *   (see https://agrum.gitlab.io/articles/dual-licenses-lgplv3mit.html)    *
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 *   See LICENCES for more details.                                         *
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 *   SPDX-FileCopyrightText: Copyright 2005-2026                            *
 *       - Pierre-Henri WUILLEMIN(_at_LIP6)                                 *
 *       - Christophe GONZALES(_at_AMU)                                     *
 *   SPDX-License-Identifier: LGPL-3.0-or-later OR MIT                      *
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 *   Contact  : info_at_agrum_dot_org                                       *
 *   homepage : http://agrum.gitlab.io                                      *
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 ****************************************************************************/
 
#pragma once
 

 
#include <algorithm>
#include <cstdio>
#include <iostream>
 
#include <agrum/base/graphs/fastGraph.h>
#include <agrum/base/variables/allDiscreteVariables.h>
#include <agrum/ID/influenceDiagram.h>
 
namespace gum {
  template < GUM_Numeric GUM_SCALAR >
  NodeId build_node_for_ID(gum::InfluenceDiagram< GUM_SCALAR >& infdiag,
                           std::string                          node,
                           std::string_view                     domain) {
    bool        isUtil  = false;
    bool        isDeci  = false;
    bool        isChanc = false;
    std::string ds(domain);
    switch (*(node.begin())) {
      case '*' :
        isDeci = true;
        node.erase(0, 1);
        break;
      case '$' :
        isUtil = true;
        ds     = "[1]";
        node.erase(0, 1);
        break;
      default : isChanc = true;
    }
    auto v = fastVariable< GUM_SCALAR >(node, ds);
 
    NodeId res;
    if (infdiag.exists(v->name())) {
      res = infdiag.idFromName(v->name());
    } else {
      if (isChanc) res = infdiag.addChanceNode(*v);
      else if (isDeci) res = infdiag.addDecisionNode(*v);
      else if (isUtil) res = infdiag.addUtilityNode(*v);
      else
        GUM_ERROR(FatalError,
                  "No type (chance, decision or utility) for the node '" << node << "'.")
    }
 
    return res;
  }
 
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >
      InfluenceDiagram< GUM_SCALAR >::fastPrototype(std::string_view dotlike, Size domainSize) {
    return fastPrototype(dotlike, "[" + std::to_string(domainSize) + "]");
  }
 
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >
      InfluenceDiagram< GUM_SCALAR >::fastPrototype(std::string_view dotlike,
                                                    std::string_view domain) {
    gum::InfluenceDiagram< GUM_SCALAR > infdiag;
 
    auto resolve
        = [&](const std::string& node) { return build_node_for_ID(infdiag, node, domain); };
    auto addArc = [&](NodeId tail, NodeId head, const std::string&) { infdiag.addArc(tail, head); };
    auto addEdge = [&](NodeId, NodeId, const std::string& token) {
      GUM_ERROR(InvalidEdge,
                "fastPrototype: '" << token << "' is preceded by '-' but an InfluenceDiagram "
                                   << "does not support edges")
    };
 
    for (const auto& chaine: split(remove_newline(dotlike), ";")) {
      using namespace detail;
      fastGraphWalkTokens(fastGraphTokenize(chaine), dotlike, resolve, addArc, addEdge);
    }
 
    for (const auto n: infdiag.nodes()) {
      if (infdiag.isChanceNode(n)) infdiag.cpt(n).randomCPT();
      else if (infdiag.isUtilityNode(n)) { infdiag.utility(n).random().scale(50).translate(-10); }
    }
 
    infdiag.setProperty("name", "anonymousID");
    return infdiag;
  }
 
  // ===========================================================================
  // Constructors / Destructors
  // ===========================================================================
 
  /*
   * Default constructor.
   */
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >::InfluenceDiagram() : DAGmodel() {
    GUM_CONSTRUCTOR(InfluenceDiagram)
  }
 
  /*
   * Destructor.
   */
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >::~InfluenceDiagram() {
    GUM_DESTRUCTOR(InfluenceDiagram)
    removeTables_();
  }
 
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >::InfluenceDiagram(InfluenceDiagram< GUM_SCALAR >&& source) noexcept
      :
      DAGmodel(std::move(source)), _tensorMap_(std::move(source._tensorMap_)),
      _utilityMap_(std::move(source._utilityMap_)),
      _temporalOrder_(std::move(source._temporalOrder_)) {
    GUM_CONS_MOV(InfluenceDiagram)
  }
 
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >&
      InfluenceDiagram< GUM_SCALAR >::operator=(InfluenceDiagram< GUM_SCALAR >&& source) noexcept {
    if (this != &source) {
      removeTables_();
      DAGmodel::operator=(std::move(source));
      _tensorMap_     = std::move(source._tensorMap_);
      _utilityMap_    = std::move(source._utilityMap_);
      _temporalOrder_ = std::move(source._temporalOrder_);
      GUM_OP_MOV(InfluenceDiagram)
    }
    return *this;
  }
 
  /*
   * Copy Constructor
   */
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >::InfluenceDiagram(const InfluenceDiagram< GUM_SCALAR >& source) {
    GUM_CONS_CPY(InfluenceDiagram)
    copyStructureAndTables_(source);
  }
 
  /*
   * Copy Operator
   */
  template < GUM_Numeric GUM_SCALAR >
  InfluenceDiagram< GUM_SCALAR >&
      InfluenceDiagram< GUM_SCALAR >::operator=(const InfluenceDiagram< GUM_SCALAR >& source) {
    if (this != &source) {
      clear();
      // Copying tables and structure
      copyStructureAndTables_(source);
    }
 
    return *this;
  }
 
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::InfluenceDiagram::clear() {
    // Removing previous tensors
    removeTables_();
    this->varMap_.clear();
    dag_.clear();
    _tensorMap_.clear();
    _utilityMap_.clear();
  }
 
  /*
   * Removing ancient table
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::removeTables_() {
    for (const auto& [node, tensor]: _tensorMap_)
      delete tensor;
    for (const auto& [node, tensor]: _utilityMap_)
      delete tensor;
  }
 
  /*
   * Copying tables from another influence diagram
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::copyStructureAndTables_(
      const InfluenceDiagram< GUM_SCALAR >& IDsource) {
    for (auto node: IDsource.nodes()) {
      if (IDsource.isChanceNode(node)) addChanceNode(IDsource.variable(node), node);
      else if (IDsource.isUtilityNode(node)) addUtilityNode(IDsource.variable(node), node);
      else   // decision node
        addDecisionNode(IDsource.variable(node), node);
    }
    // we add arc in the same order of the tensors
    for (auto node: IDsource.nodes()) {
      const auto& s = IDsource.variable(node).name();
      if (IDsource.isChanceNode(node)) {
        for (Idx par = 1; par <= IDsource.parents(node).size(); par++)
          addArc(IDsource.cpt(node).variable(par).name(), s);
      } else if (IDsource.isUtilityNode(node)) {
        for (Idx par = 1; par <= IDsource.parents(node).size(); par++)
          addArc(IDsource.utility(node).variable(par).name(), s);
      } else {   // decision node
        // here the order does not depend on a Tensor
        for (NodeId par: IDsource.parents(node))
          addArc(par, node);
      }
    }
 
    // Copying tensors
    for (auto node: IDsource.nodes()) {
      const auto& s = IDsource.variable(node).name();
      if (IDsource.isChanceNode(node)) {
        cpt(node).fillWith(IDsource.cpt(s));
      } else if (IDsource.isUtilityNode(node)) {
        utility(node).fillWith(IDsource.utility(s));
      }
    }
  }
 
  template < GUM_Numeric GUM_SCALAR >
  std::string InfluenceDiagram< GUM_SCALAR >::toDot() const {
    std::stringstream output;
    std::stringstream decisionNode;
    std::stringstream utilityNode;
    std::stringstream chanceNode;
    std::stringstream arcstream;
 
    output << std::format("digraph \"{}\" {{\n", this->propertyWithDefault("name", "no_name"));
 
    output << "  node [bgcolor=\"#AAAAAA\", style=filled, height=0];" << std::endl;
 
    decisionNode << "node [shape = box];" << std::endl;
 
    utilityNode << "node [shape =  hexagon, margin=0];" << std::endl;
    chanceNode << "node [shape = ellipse];" << std::endl;
    std::string tab = "  ";
 
    for (const auto node: dag_.nodes()) {
      if (isChanceNode(node))
        chanceNode << std::format("  \"{}-{}\";", node, variable(node).name());
      else if (isUtilityNode(node))
        utilityNode << std::format("  \"{}-{}\";", node, variable(node).name());
      else decisionNode << std::format("  \"{}-{}\";", node, variable(node).name());
 
      if (dag_.children(node).size() > 0)
        for (const auto chi: dag_.children(node)) {
          arcstream << std::format("\"{}-{}\" -> \"{}-{}\"",
                                   node,
                                   variable(node).name(),
                                   chi,
                                   variable(chi).name());
          if (isDecisionNode(chi)) { arcstream << " [style=\"tapered, bold\"]"; }
          arcstream << ";\n";
        }
    }
 
    output << decisionNode.str() << std::endl
           << utilityNode.str() << std::endl
           << chanceNode.str() << std::endl
           << std::endl
           << arcstream.str() << std::endl
           << "}" << std::endl;
 
    return output.str();
  }
 
  template < GUM_Numeric GUM_SCALAR >
  std::string InfluenceDiagram< GUM_SCALAR >::toString() const {
    std::stringstream output;
 
    output << "Influence Diagram{" << std::endl;
    output << std::format("  chance: {},\n", chanceNodeSize());
    output << std::format("  utility: {},\n", utilityNodeSize());
    output << std::format("  decision: {},\n", decisionNodeSize());
    output << std::format("  arcs: {},\n", dag().sizeArcs());
 
    if (double dSize = log10DomainSize(); dSize > 6)
      output << std::format("  domainSize: 10^{}", dSize);
    else output << std::format("  domainSize: {}", std::round(std::pow(10.0, dSize)));
 
    output << std::endl << "}";
 
    return output.str();
  }
 
  // ===========================================================================
  // Variable manipulation methods.
  // ===========================================================================
 
  /*
   * Returns the CPT of a chance variable.
   */
  template < GUM_Numeric GUM_SCALAR >
  const Tensor< GUM_SCALAR >& InfluenceDiagram< GUM_SCALAR >::cpt(NodeId varId) const {
    return *(_tensorMap_[varId]);
  }
 
  /*
   * Returns the utility table of a utility node.
   */
  template < GUM_Numeric GUM_SCALAR >
  const Tensor< GUM_SCALAR >& InfluenceDiagram< GUM_SCALAR >::utility(NodeId varId) const {
    return *(_utilityMap_[varId]);
  }
 
  /*
   * Return true if node is a utility one
   */
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::isUtilityNode(NodeId varId) const {
    return _utilityMap_.exists(varId);
  }
 
  /*
   * Return true if node is a utility one
   */
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::isDecisionNode(NodeId varId) const {
    bool ret = true;
 
    if (isUtilityNode(varId) || isChanceNode(varId)) ret = false;
 
    return ret;
  }
 
  /*
   * Return true if node is a chance one
   */
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::isChanceNode(NodeId varId) const {
    return _tensorMap_.exists(varId);
  }
 
  /*
   * Returns the number of utility nodes
   */
  template < GUM_Numeric GUM_SCALAR >
  Size InfluenceDiagram< GUM_SCALAR >::utilityNodeSize() const {
    return _utilityMap_.size();
  }
 
  /*
   * Returns the number of chance nodes
   */
  template < GUM_Numeric GUM_SCALAR >
  Size InfluenceDiagram< GUM_SCALAR >::chanceNodeSize() const {
    return _tensorMap_.size();
  }
 
  /*
   * Returns the number of decision nodes
   */
  template < GUM_Numeric GUM_SCALAR >
  Size InfluenceDiagram< GUM_SCALAR >::decisionNodeSize() const {
    return (size() - _utilityMap_.size() - _tensorMap_.size());
  }
 
  /*
   * Add a chance variable, it's associate node and it's CPT. The id of the new
   * variable is automatically generated.
   */
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::add(const DiscreteVariable& var, NodeId varId) {
    return addChanceNode(var, varId);
  }
 
  /*
   * Add a utility variable, it's associate node and it's UT. The id of the new
   * variable is automatically generated.
   * @Throws : Gum::InvalidArgument if var has more than one state
   */
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::addUtilityNode(const DiscreteVariable& var, NodeId varId) {
    auto   newMultiDim = new MultiDimArray< GUM_SCALAR >();
    NodeId res;
 
    try {
      res = addUtilityNode(var, newMultiDim, varId);
    } catch (Exception const&) {
      if (newMultiDim != nullptr) delete newMultiDim;
      throw;
    }
 
    return res;
  }
 
  /*
   * Add a decision variable. The id of the new
   * variable is automatically generated.
   */
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::addDecisionNode(const DiscreteVariable& var,
                                                         NodeId                  varId) {
    return addNode_(var, varId);
  }
 
  /*
   * Add a chance variable, it's associate node and it's CPT. The id of the new
   * variable is automatically generated.
   */
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::addChanceNode(const DiscreteVariable& var, NodeId varId) {
    auto   newMultiDim = new MultiDimArray< GUM_SCALAR >();
    NodeId res;
 
    try {
      res = addChanceNode(var, newMultiDim, varId);
    } catch (Exception const&) {
      delete newMultiDim;
      throw;
    }
 
    return res;
  }
 
  /*
   * Add a chance variable, it's associate node and it's CPT. The id of the new
   * variable is automatically generated.
   */
  template < GUM_Numeric GUM_SCALAR >
  NodeId
      InfluenceDiagram< GUM_SCALAR >::addChanceNode(const DiscreteVariable&               var,
                                                    MultiDimImplementation< GUM_SCALAR >* aContent,
                                                    NodeId DesiredId) {
    NodeId proposedId = addNode_(var, DesiredId);
 
    auto varcpt = new Tensor< GUM_SCALAR >(aContent);
    (*varcpt) << variable(proposedId);
    _tensorMap_.insert(proposedId, varcpt);
 
    return proposedId;
  }
 
  /*
   * Add a utility variable, it's associate node and it's UT. The id of the new
   * variable is automatically generated.
   * @Throws : Gum::InvalidArgument if var has more than one state
   */
  template < GUM_Numeric GUM_SCALAR >
  NodeId
      InfluenceDiagram< GUM_SCALAR >::addUtilityNode(const DiscreteVariable&               var,
                                                     MultiDimImplementation< GUM_SCALAR >* aContent,
                                                     NodeId DesiredId) {
    if (var.domainSize() != 1) {
      GUM_ERROR(InvalidArgument,
                "Utility var have no state ( which implicates a "
                "single label for data output reasons ).")
    }
 
    NodeId proposedId = addNode_(var, DesiredId);
 
    auto varut = new Tensor< GUM_SCALAR >(aContent);
 
    (*varut) << variable(proposedId);
 
    _utilityMap_.insert(proposedId, varut);
 
    return proposedId;
  }
 
  /*
   * Add a node
   */
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::addNode_(const DiscreteVariable& variableType,
                                                  NodeId                  DesiredId) {
    // None thread safe code!
    NodeId proposedId;
 
    if (DesiredId == 0) proposedId = dag_.nextNodeId();
    else proposedId = DesiredId;
 
    this->varMap_.insert(proposedId, variableType);
 
    dag_.addNodeWithId(proposedId);
 
    // end critical section
    return proposedId;
  }
 
  /*
   * Erase a Variable from the network and remove the variable from
   * all children of id.
   * If no variable matches the id, then nothing is done.
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::erase(NodeId varId) {
    if (this->varMap_.exists(varId)) {
      // Reduce the variable child's CPT or Utility Table if necessary
      for (const auto chi: dag_.children(varId))
        if (isChanceNode(chi)) _tensorMap_[chi]->erase(variable(varId));
        else if (isUtilityNode(chi)) _utilityMap_[chi]->erase(variable(varId));
 
      if (isChanceNode(varId)) {
        delete _tensorMap_[varId];
        _tensorMap_.erase(varId);
      } else if (isUtilityNode(varId)) {
        delete _utilityMap_[varId];
        _utilityMap_.erase(varId);
      }
 
      this->varMap_.erase(varId);
      dag_.eraseNode(varId);
    }
  }
 
  /*
   * Erase a Variable from the network and remove the variable from
   * all children of var.
   * If no variable matches, then nothing is done.
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::erase(const DiscreteVariable& var) {
    erase(this->varMap_.get(var));
  }
 
  /* we allow the user to change the name of a variable
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::changeVariableName(NodeId id, std::string_view new_name) {
    this->varMap_.changeName(id, new_name);
  }
 
  // ===========================================================================
  // @name Arc manipulation methods.
  // ===========================================================================
  /*
   * Add an arc in the ID, and update diagram's chance nodes cpt if necessary.
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::addArc(NodeId tail, NodeId head) {
    if (isUtilityNode(tail)) { GUM_ERROR(InvalidArc, "Tail cannot be a utility node") }
 
    dag_.addArc(tail, head);
 
    if (isChanceNode(head))
      // Add parent in the child's CPT
      (*(_tensorMap_[head])) << variable(tail);
    else if (isUtilityNode(head)) {
      // Add parent in the child's UT
      (*(_utilityMap_[head])) << variable(tail);
    }
  }
 
  /*
   * Removes an arc in the ID, and update diagram chance nodes cpt if necessary.
   *
   * If (tail, head) doesn't exist, the nothing happens.
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::eraseArc(const Arc& arc) {
    if (dag_.existsArc(arc)) {
      NodeId head = arc.head();
      NodeId tail = arc.tail();
      dag_.eraseArc(arc);
 
      if (isChanceNode(head))
        // Removes parent in the child's CPT
        (*(_tensorMap_[head])) >> variable(tail);
      else if (isUtilityNode(head))
        // Removes parent in the child's UT
        (*(_utilityMap_[head])) >> variable(tail);
    }
  }
 
  /*
   * Removes an arc in the ID, and update diagram chance nodes cpt if necessary.
   *
   * If (tail, head) doesn't exist, the nothing happens.
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::eraseArc(NodeId tail, NodeId head) {
    eraseArc(Arc(tail, head));
  }
 
  // ===========================================================================
  // Graphical methods
  // ===========================================================================
 
  /*
   * The node's id are coherent with the variables and nodes of the topology.
   */
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::moralGraph_(UndiGraph& graph) const {
    for (const auto node: dag_.nodes())
      if (!isUtilityNode(node)) graph.addNodeWithId(node);
 
    for (const auto node: dag_.nodes()) {
      if (!isDecisionNode(node))
        for (const auto par: dag_.parents(node)) {
          if (isChanceNode(node)) graph.addEdge(node, par);
 
          for (const auto par2: dag_.parents(node))
            if (par != par2) graph.addEdge(par, par2);
        }
    }
  }
 
  /*
   * True if a directed path exist with all decision nodes
   */
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::decisionOrderExists() const {
    const Sequence< NodeId > order = topologicalOrder();
 
    // Finding first decision node
    Sequence< NodeId >::const_iterator orderIter = order.begin();
 
    while ((orderIter != order.end()) && (!isDecisionNode(*orderIter)))
      ++orderIter;
 
    if (orderIter == order.end()) return true;
 
    NodeId parentDecision = (*orderIter);
    ++orderIter;
 
    // Checking path between decisions nodes
    while (orderIter != order.end()) {
      if (isDecisionNode(*orderIter)) {
        if (!existsPathBetween(parentDecision, *orderIter)) return false;
 
        parentDecision = *orderIter;
      }
 
      ++orderIter;
    }
 
    return true;
  }
 
  /*
   * Returns true if a path exists between source and destination
   */
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::existsPathBetween(NodeId src, NodeId dest) const {
    List< NodeId > nodeFIFO;
    // mark[node] contains 0 if not visited
    // mark[node] = predecessor if visited
    NodeProperty< int > mark = dag_.nodesPropertyFromVal(-1);
    NodeId              current;
 
    mark[src] = (int)src;
    nodeFIFO.pushBack(src);
 
    while (!nodeFIFO.empty()) {
      current = nodeFIFO.front();
      nodeFIFO.popFront();
 
      for (const auto new_one: dag_.children(current)) {
        if (mark[new_one] != -1) continue;   // if this node is already marked, continue
 
        mark[new_one] = (int)current;
 
        if (new_one == dest) break;   // if we reach *orderIter, stop.
 
        nodeFIFO.pushBack(new_one);
      }
    }
 
    if (mark[dest] == -1) return false;
 
    return true;
  }
 
  /*
   * Returns the decision graph
   */
  template < GUM_Numeric GUM_SCALAR >
  gum::DAG InfluenceDiagram< GUM_SCALAR >::getDecisionGraph() const {
    gum::DAG temporalGraph;
 
    for (const auto node: dag_.nodes()) {
      if (isDecisionNode(node)) {
        if (!temporalGraph.existsNode(node)) temporalGraph.addNodeWithId(node);
 
        for (const auto chi: getChildrenDecision_(node)) {
          if (!temporalGraph.existsNode(chi)) temporalGraph.addNodeWithId(chi);
 
          temporalGraph.addArc(node, chi);
        }
      }
    }
 
    return temporalGraph;
  }
 
  /*
   * Returns the list of children decision for a given nodeId
   */
  template < GUM_Numeric GUM_SCALAR >
  Sequence< NodeId >
      InfluenceDiagram< GUM_SCALAR >::getChildrenDecision_(NodeId parentDecision) const {
    Sequence< NodeId > childrenSeq;
 
    List< NodeId > nodeFIFO;
    NodeId         current;
 
    // mark[node] contains false if not visited
    // mark[node] contains true if visited
    NodeProperty< bool > mark = dag_.nodesPropertyFromVal(false);
 
    mark[parentDecision] = true;
 
    nodeFIFO.pushBack(parentDecision);
 
    while (!nodeFIFO.empty()) {
      current = nodeFIFO.front();
      nodeFIFO.popFront();
 
      for (const auto new_one: dag_.children(current)) {
        if (mark[new_one]) continue;   // if this node is already marked, continue
 
        mark[new_one] = true;
 
        if (!isDecisionNode(new_one)) nodeFIFO.pushBack(new_one);
        else childrenSeq.insert(new_one);
      }
    }
 
    return childrenSeq;
  }
 
  /*
   * Returns the sequence of decision nodes
   * @throw NotFound if such a sequence does not exist
   */
  template < GUM_Numeric GUM_SCALAR >
  std::vector< NodeId > InfluenceDiagram< GUM_SCALAR >::decisionOrder() const {
    if (!decisionOrderExists()) { GUM_ERROR(NotFound, "No decision path exists") }
 
    std::vector< NodeId > decisionSequence;
 
    for (const auto elt: topologicalOrder())
      if (isDecisionNode(elt)) decisionSequence.push_back(elt);
 
    return decisionSequence;
  }
 
  /*
   * Returns partial temporal ordering
   * @throw NotFound if such a sequence does not exist
   */
  template < GUM_Numeric GUM_SCALAR >
  const List< NodeSet >& InfluenceDiagram< GUM_SCALAR >::getPartialTemporalOrder(bool clear) const {
    if (clear) {
      _temporalOrder_.clear();
 
      std::vector< NodeId > order    = decisionOrder();
      NodeSet               nodeList = dag_.asNodeSet();
 
      for (auto i: order) {
        NodeSet partialOrderedSet;
 
        for (const auto par: dag_.parents(i)) {
          if (nodeList.contains(par) && isChanceNode(par)) {
            partialOrderedSet.insert(par);
            nodeList.erase(par);
          }
        }
 
        if (!partialOrderedSet.empty()) _temporalOrder_.pushFront(partialOrderedSet);
 
        NodeSet decisionSet;
 
        decisionSet.insert(i);
 
        _temporalOrder_.pushFront(decisionSet);
      }
 
      NodeSet lastSet;   //= new gum::NodeSet();
 
      for (const auto node: nodeList)
        if (isChanceNode(node)) lastSet.insert(node);
 
      if (!lastSet.empty()) _temporalOrder_.pushFront(lastSet);
    }
 
    return _temporalOrder_;
  }
 
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::addChanceNode(std::string_view fast_description,
                                                       unsigned int     default_nbrmod) {
    auto v = fastVariable< GUM_SCALAR >(std::string(fast_description), default_nbrmod);
    if (v->domainSize() < 2) GUM_ERROR(OperationNotAllowed, v->name() << " has a domain size <2")
    return addChanceNode(*v);
  }
 
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::addUtilityNode(std::string_view fast_description) {
    auto v = fastVariable< GUM_SCALAR >(std::string(fast_description), 1);
    if (v->domainSize() >= 2)
      GUM_ERROR(OperationNotAllowed,
                v->name() << " has a domain size >= 2 which is impossible for a utility node")
    return addUtilityNode(*v);
  }
 
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::addDecisionNode(std::string_view fast_description,
                                                         unsigned int     default_nbrmod) {
    auto v = fastVariable< GUM_SCALAR >(std::string(fast_description), default_nbrmod);
    if (v->domainSize() < 2) GUM_ERROR(OperationNotAllowed, v->name() << " has a domain size <2")
    return addDecisionNode(*v);
  }
 
  template < GUM_Numeric GUM_SCALAR >
  NodeId InfluenceDiagram< GUM_SCALAR >::add(std::string_view fast_description,
                                             unsigned int     default_nbrmod) {
    std::string node(fast_description);
    switch (*(node.begin())) {
      case '*' : node.erase(0, 1); return addDecisionNode(node, default_nbrmod);
      case '$' : node.erase(0, 1); return addUtilityNode(node);
      default : return addChanceNode(fast_description, default_nbrmod);
    }
  }

  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::beginTopologyTransformation() {
    for (const auto node: nodes())
      if (isChanceNode(node)) _tensorMap_[node]->beginMultipleChanges();
      else if (this->isUtilityNode(node)) _utilityMap_[node]->beginMultipleChanges();
  }

  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::endTopologyTransformation() {
    for (const auto node: nodes())
      if (isChanceNode(node)) _tensorMap_[node]->endMultipleChanges();
      else if (isUtilityNode(node)) _utilityMap_[node]->endMultipleChanges();
  }
 
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::operator==(const InfluenceDiagram& from) const {
    if (size() != from.size()) { return false; }
 
    if (sizeArcs() != from.sizeArcs()) { return false; }
 
    // alignment of variables between the 2 BNs
    Bijection< const DiscreteVariable*, const DiscreteVariable* > alignment;
 
    for (auto node: nodes()) {
      const auto& v1 = variable(node);
      if (!from.exists(v1.name())) return false;
      const auto& v2 = from.variableFromName(v1.name());
      if (v1 != v2) { return false; }
 
      if (isChanceNode(v1.name()) && !from.isChanceNode(v2.name())) { return false; }
      if (isUtilityNode(v1.name()) && !from.isUtilityNode(v2.name())) { return false; }
      if (isDecisionNode(v1.name()) && !from.isDecisionNode(v2.name())) { return false; }
 
      alignment.insert(&variable(node), &from.variableFromName(v1.name()));
    }
 
    auto check_pot
        = [&](const gum::Tensor< GUM_SCALAR >& p1, const gum::Tensor< GUM_SCALAR >& p2) -> bool {
      if (p1.nbrDim() != p2.nbrDim()) { return false; }
 
      if (p1.domainSize() != p2.domainSize()) { return false; }
 
      Instantiation i(p1);
      Instantiation j(p2);
 
      for (i.setFirst(); !i.end(); i.inc()) {
        for (Idx indice = 0; indice < p1.nbrDim(); ++indice) {
          const DiscreteVariable* p = &(i.variable(indice));
          j.chgVal(*(alignment.second(p)), i.val(*p));
        }
 
        if (std::pow(p1.get(i) - p2.get(j), (GUM_SCALAR)2) > (GUM_SCALAR)1e-6) { return false; }
      }
      return true;
    };
    for (auto node: nodes()) {
      NodeId fromnode = from.idFromName(variable(node).name());
      if (isChanceNode(node)) {
        if (!check_pot(cpt(node), from.cpt(fromnode))) { return false; }
      } else if (isUtilityNode(node)) {
        if (!check_pot(utility(node), from.utility(fromnode))) { return false; }
      }
    }
 
    return true;
  }
 
  template < GUM_Numeric GUM_SCALAR >
  const Tensor< GUM_SCALAR >& InfluenceDiagram< GUM_SCALAR >::cpt(std::string_view name) const {
    return cpt(idFromName(name));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  const Tensor< GUM_SCALAR >& InfluenceDiagram< GUM_SCALAR >::utility(std::string_view name) const {
    return utility(idFromName(name));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::isUtilityNode(std::string_view name) const {
    return isUtilityNode(idFromName(name));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::isDecisionNode(std::string_view name) const {
    return isDecisionNode(idFromName(name));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::isChanceNode(std::string_view name) const {
    return isChanceNode(idFromName(name));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  const DiscreteVariable& InfluenceDiagram< GUM_SCALAR >::variable(std::string_view name) const {
    return variable(idFromName(name));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::erase(std::string_view name) {
    erase(idFromName(name));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::changeVariableName(std::string_view name,
                                                          std::string_view new_name) {
    changeVariableName(idFromName(name), new_name);
  }
 
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::addArc(std::string_view tail, std::string_view head) {
    addArc(idFromName(tail), idFromName(head));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  void InfluenceDiagram< GUM_SCALAR >::eraseArc(std::string_view tail, std::string_view head) {
    eraseArc(idFromName(tail), idFromName(head));
  }
 
  template < GUM_Numeric GUM_SCALAR >
  bool InfluenceDiagram< GUM_SCALAR >::existsPathBetween(std::string_view src,
                                                         std::string_view dest) const {
    return existsPathBetween(idFromName(src), idFromName(dest));
  }
 
}   // namespace gum