convert all optional Ordering to function overloads

compiles and passes tests, but some potentially code-breaking changes in:
Marginals.h - order of arguments had to change since `factorization` has a default value
EliminatableFactorGraph.h - marginalMultifrontalBayesNet and marginalMultifrontalBayesTree no longer accept `boost::none` as a placeholder to specify later arguments
Notes:
EliminateableFactorGraph.h - `orderingType` is no longer needed in function overloads that specify ordering, but I left it for the time being to avoid potential code breaking

gtsam/inference/BayesTree-inst.h

@@ -262,7 +262,7 @@ namespace gtsam {
 
     // Now, marginalize out everything that is not variable j
     BayesNetType marginalBN = *cliqueMarginal.marginalMultifrontalBayesNet(
-      Ordering(cref_list_of<1,Key>(j)), boost::none, function);
+      Ordering(cref_list_of<1,Key>(j)), function);
 
     // The Bayes net should contain only one conditional for variable j, so return it
     return marginalBN.front();
@@ -383,7 +383,7 @@ namespace gtsam {
     }
 
     // now, marginalize out everything that is not variable j1 or j2
-    return p_BC1C2.marginalMultifrontalBayesNet(Ordering(cref_list_of<2,Key>(j1)(j2)), boost::none, function);
+    return p_BC1C2.marginalMultifrontalBayesNet(Ordering(cref_list_of<2,Key>(j1)(j2)), function);
   }
 
   /* ************************************************************************* */

gtsam/inference/BayesTreeCliqueBase-inst.h

@@ -171,7 +171,7 @@ namespace gtsam {
 
         // The variables we want to keepSet are exactly the ones in S
         KeyVector indicesS(this->conditional()->beginParents(), this->conditional()->endParents());
-        cachedSeparatorMarginal_ = *p_Cp.marginalMultifrontalBayesNet(Ordering(indicesS), boost::none, function);
+        cachedSeparatorMarginal_ = *p_Cp.marginalMultifrontalBayesNet(Ordering(indicesS), function);
       }
     }
 

gtsam/inference/EliminateableFactorGraph-inst.h

@@ -28,33 +28,19 @@ namespace gtsam {
   template<class FACTORGRAPH>
   boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesNetType>
     EliminateableFactorGraph<FACTORGRAPH>::eliminateSequential(
-    OptionalOrdering ordering, const Eliminate& function,
+    const Eliminate& function, OptionalVariableIndex variableIndex,
-    OptionalVariableIndex variableIndex, OptionalOrderingType orderingType) const
+    OptionalOrderingType orderingType) const {
-  {
+    if(!variableIndex) {
-    if(ordering && variableIndex) {
-      gttic(eliminateSequential);
-      // Do elimination
-      EliminationTreeType etree(asDerived(), *variableIndex, *ordering);
-      boost::shared_ptr<BayesNetType> bayesNet;
-      boost::shared_ptr<FactorGraphType> factorGraph;
-      boost::tie(bayesNet,factorGraph) = etree.eliminate(function);
-      // If any factors are remaining, the ordering was incomplete
-      if(!factorGraph->empty())
-        throw InconsistentEliminationRequested();
-      // Return the Bayes net
-      return bayesNet;
-    }
-    else if(!variableIndex) {
       // If no VariableIndex provided, compute one and call this function again IMPORTANT: we check
       // for no variable index first so that it's always computed if we need to call COLAMD because
-      // no Ordering is provided.
+      // no Ordering is provided.  When removing optional from VariableIndex, create VariableIndex
+      // before creating ordering.
       VariableIndex computedVariableIndex(asDerived());
-      return eliminateSequential(ordering, function, computedVariableIndex, orderingType);
+      return eliminateSequential(function, computedVariableIndex, orderingType);
     }
-    else /*if(!ordering)*/ {
+    else {
-      // If no Ordering provided, compute one and call this function again.  We are guaranteed to
+      // Compute an ordering and call this function again.  We are guaranteed to have a 
-      // have a VariableIndex already here because we computed one if needed in the previous 'else'
+      // VariableIndex already here because we computed one if needed in the previous 'if' block.
-      // block.
       if (orderingType == Ordering::METIS) {
         Ordering computedOrdering = Ordering::Metis(asDerived());
         return eliminateSequential(computedOrdering, function, variableIndex, orderingType);
@@ -67,15 +53,73 @@ namespace gtsam {
 
   /* ************************************************************************* */
   template<class FACTORGRAPH>
-  boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesTreeType>
+  boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesNetType>
-    EliminateableFactorGraph<FACTORGRAPH>::eliminateMultifrontal(
+    EliminateableFactorGraph<FACTORGRAPH>::eliminateSequential(
-    OptionalOrdering ordering, const Eliminate& function,
+    const Ordering& ordering, const Eliminate& function,
     OptionalVariableIndex variableIndex, OptionalOrderingType orderingType) const
   {
-    if(ordering && variableIndex) {
+    if(!variableIndex) {
+      // If no VariableIndex provided, compute one and call this function again
+      VariableIndex computedVariableIndex(asDerived());
+      return eliminateSequential(ordering, function, computedVariableIndex, orderingType);
+    } else {
+      gttic(eliminateSequential);
+      // Do elimination
+      EliminationTreeType etree(asDerived(), *variableIndex, ordering);
+      boost::shared_ptr<BayesNetType> bayesNet;
+      boost::shared_ptr<FactorGraphType> factorGraph;
+      boost::tie(bayesNet,factorGraph) = etree.eliminate(function);
+      // If any factors are remaining, the ordering was incomplete
+      if(!factorGraph->empty())
+        throw InconsistentEliminationRequested();
+      // Return the Bayes net
+      return bayesNet;
+    }
+  }
+
+  /* ************************************************************************* */
+  template<class FACTORGRAPH>
+  boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesTreeType>
+    EliminateableFactorGraph<FACTORGRAPH>::eliminateMultifrontal(
+    const Eliminate& function, OptionalVariableIndex variableIndex,
+    OptionalOrderingType orderingType) const
+  {
+    if(!variableIndex) {
+      // If no VariableIndex provided, compute one and call this function again IMPORTANT: we check
+      // for no variable index first so that it's always computed if we need to call COLAMD because
+      // no Ordering is provided.  When removing optional from VariableIndex, create VariableIndex
+      // before creating ordering.
+      VariableIndex computedVariableIndex(asDerived());
+      return eliminateMultifrontal(function, computedVariableIndex, orderingType);
+    }
+    else {
+      // Compute an ordering and call this function again.  We are guaranteed to have a
+      // VariableIndex already here because we computed one if needed in the previous 'if' block.
+      if (orderingType == Ordering::METIS) {
+        Ordering computedOrdering = Ordering::Metis(asDerived());
+        return eliminateMultifrontal(computedOrdering, function, variableIndex, orderingType);
+      } else {
+        Ordering computedOrdering = Ordering::Colamd(*variableIndex);
+        return eliminateMultifrontal(computedOrdering, function, variableIndex, orderingType);
+      }
+    }
+  }
+
+  /* ************************************************************************* */
+  template<class FACTORGRAPH>
+  boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesTreeType>
+    EliminateableFactorGraph<FACTORGRAPH>::eliminateMultifrontal(
+    const Ordering& ordering, const Eliminate& function,
+    OptionalVariableIndex variableIndex, OptionalOrderingType orderingType) const
+  {
+    if(!variableIndex) {
+      // If no VariableIndex provided, compute one and call this function again
+      VariableIndex computedVariableIndex(asDerived());
+      return eliminateMultifrontal(ordering, function, computedVariableIndex, orderingType);
+    } else {
       gttic(eliminateMultifrontal);
       // Do elimination with given ordering
-      EliminationTreeType etree(asDerived(), *variableIndex, *ordering);
+      EliminationTreeType etree(asDerived(), *variableIndex, ordering);
       JunctionTreeType junctionTree(etree);
       boost::shared_ptr<BayesTreeType> bayesTree;
       boost::shared_ptr<FactorGraphType> factorGraph;
@@ -86,25 +130,6 @@ namespace gtsam {
       // Return the Bayes tree
       return bayesTree;
     }
-    else if(!variableIndex) {
-      // If no VariableIndex provided, compute one and call this function again IMPORTANT: we check
-      // for no variable index first so that it's always computed if we need to call COLAMD because
-      // no Ordering is provided.
-      VariableIndex computedVariableIndex(asDerived());
-      return eliminateMultifrontal(ordering, function, computedVariableIndex, orderingType);
-    }
-    else /*if(!ordering)*/ {
-      // If no Ordering provided, compute one and call this function again.  We are guaranteed to
-      // have a VariableIndex already here because we computed one if needed in the previous 'else'
-      // block.
-      if (orderingType == Ordering::METIS) {
-        Ordering computedOrdering = Ordering::Metis(asDerived());
-        return eliminateMultifrontal(computedOrdering, function, variableIndex, orderingType);
-      } else {
-        Ordering computedOrdering = Ordering::Colamd(*variableIndex);
-        return eliminateMultifrontal(computedOrdering, function, variableIndex, orderingType);
-      }
-    }
   }
 
   /* ************************************************************************* */
@@ -191,57 +216,65 @@ namespace gtsam {
   boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesNetType>
     EliminateableFactorGraph<FACTORGRAPH>::marginalMultifrontalBayesNet(
     boost::variant<const Ordering&, const KeyVector&> variables,
-    OptionalOrdering marginalizedVariableOrdering,
     const Eliminate& function, OptionalVariableIndex variableIndex) const
   {
-    if(variableIndex)
+    if(!variableIndex) {
-    {
+      // If no variable index is provided, compute one and call this function again
-      if(marginalizedVariableOrdering)
+      VariableIndex index(asDerived());
-      {
+      return marginalMultifrontalBayesNet(variables, function, index);
-        gttic(marginalMultifrontalBayesNet);
-        // An ordering was provided for the marginalized variables, so we can first eliminate them
-        // in the order requested.
-        boost::shared_ptr<BayesTreeType> bayesTree;
-        boost::shared_ptr<FactorGraphType> factorGraph;
-        boost::tie(bayesTree,factorGraph) =
-          eliminatePartialMultifrontal(*marginalizedVariableOrdering, function, *variableIndex);
-
-        if(const Ordering* varsAsOrdering = boost::get<const Ordering&>(&variables))
-        {
-          // An ordering was also provided for the unmarginalized variables, so we can also
-          // eliminate them in the order requested.
-          return factorGraph->eliminateSequential(*varsAsOrdering, function);
-        }
-        else
-        {
-          // No ordering was provided for the unmarginalized variables, so order them with COLAMD.
-          return factorGraph->eliminateSequential(boost::none, function);
-        }
-      }
-      else
-      {
-        // No ordering was provided for the marginalized variables, so order them using constrained
-        // COLAMD.
-        bool unmarginalizedAreOrdered = (boost::get<const Ordering&>(&variables) != 0);
-        const KeyVector* variablesOrOrdering =
-          unmarginalizedAreOrdered ?
-          boost::get<const Ordering&>(&variables) : boost::get<const KeyVector&>(&variables);
-
-        Ordering totalOrdering =
-          Ordering::ColamdConstrainedLast(*variableIndex, *variablesOrOrdering, unmarginalizedAreOrdered);
-
-        // Split up ordering
-        const size_t nVars = variablesOrOrdering->size();
-        Ordering marginalizationOrdering(totalOrdering.begin(), totalOrdering.end() - nVars);
-        Ordering marginalVarsOrdering(totalOrdering.end() - nVars, totalOrdering.end());
-
-        // Call this function again with the computed orderings
-        return marginalMultifrontalBayesNet(marginalVarsOrdering, marginalizationOrdering, function, *variableIndex);
-      }
     } else {
+      // No ordering was provided for the marginalized variables, so order them using constrained
+      // COLAMD.
+      bool unmarginalizedAreOrdered = (boost::get<const Ordering&>(&variables) != 0);
+      const KeyVector* variablesOrOrdering =
+        unmarginalizedAreOrdered ?
+        boost::get<const Ordering&>(&variables) : boost::get<const KeyVector&>(&variables);
+
+      Ordering totalOrdering =
+        Ordering::ColamdConstrainedLast(*variableIndex, *variablesOrOrdering, unmarginalizedAreOrdered);
+
+      // Split up ordering
+      const size_t nVars = variablesOrOrdering->size();
+      Ordering marginalizationOrdering(totalOrdering.begin(), totalOrdering.end() - nVars);
+      Ordering marginalVarsOrdering(totalOrdering.end() - nVars, totalOrdering.end());
+
+      // Call this function again with the computed orderings
+      return marginalMultifrontalBayesNet(marginalVarsOrdering, marginalizationOrdering, function, *variableIndex);
+    }
+  }
+
+  /* ************************************************************************* */
+  template<class FACTORGRAPH>
+  boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesNetType>
+    EliminateableFactorGraph<FACTORGRAPH>::marginalMultifrontalBayesNet(
+    boost::variant<const Ordering&, const KeyVector&> variables,
+    const Ordering& marginalizedVariableOrdering,
+    const Eliminate& function, OptionalVariableIndex variableIndex) const
+  {
+    if(!variableIndex) {
       // If no variable index is provided, compute one and call this function again
       VariableIndex index(asDerived());
       return marginalMultifrontalBayesNet(variables, marginalizedVariableOrdering, function, index);
+    } else {
+      gttic(marginalMultifrontalBayesNet);
+      // An ordering was provided for the marginalized variables, so we can first eliminate them
+      // in the order requested.
+      boost::shared_ptr<BayesTreeType> bayesTree;
+      boost::shared_ptr<FactorGraphType> factorGraph;
+      boost::tie(bayesTree,factorGraph) =
+        eliminatePartialMultifrontal(marginalizedVariableOrdering, function, *variableIndex);
+
+      if(const Ordering* varsAsOrdering = boost::get<const Ordering&>(&variables))
+      {
+        // An ordering was also provided for the unmarginalized variables, so we can also
+        // eliminate them in the order requested.
+        return factorGraph->eliminateSequential(*varsAsOrdering, function);
+      }
+      else
+      {
+        // No ordering was provided for the unmarginalized variables, so order them with COLAMD.
+        return factorGraph->eliminateSequential(function);
+      }
     }
   }
 
@@ -250,57 +283,65 @@ namespace gtsam {
   boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesTreeType>
     EliminateableFactorGraph<FACTORGRAPH>::marginalMultifrontalBayesTree(
     boost::variant<const Ordering&, const KeyVector&> variables,
-    OptionalOrdering marginalizedVariableOrdering,
     const Eliminate& function, OptionalVariableIndex variableIndex) const
   {
-    if(variableIndex)
+    if(!variableIndex) {
-    {
+      // If no variable index is provided, compute one and call this function again
-      if(marginalizedVariableOrdering)
+      VariableIndex computedVariableIndex(asDerived());
-      {
+      return marginalMultifrontalBayesTree(variables, function, computedVariableIndex);
-        gttic(marginalMultifrontalBayesTree);
-        // An ordering was provided for the marginalized variables, so we can first eliminate them
-        // in the order requested.
-        boost::shared_ptr<BayesTreeType> bayesTree;
-        boost::shared_ptr<FactorGraphType> factorGraph;
-        boost::tie(bayesTree,factorGraph) =
-          eliminatePartialMultifrontal(*marginalizedVariableOrdering, function, *variableIndex);
-
-        if(const Ordering* varsAsOrdering = boost::get<const Ordering&>(&variables))
-        {
-          // An ordering was also provided for the unmarginalized variables, so we can also
-          // eliminate them in the order requested.
-          return factorGraph->eliminateMultifrontal(*varsAsOrdering, function);
-        }
-        else
-        {
-          // No ordering was provided for the unmarginalized variables, so order them with COLAMD.
-          return factorGraph->eliminateMultifrontal(boost::none, function);
-        }
-      }
-      else
-      {
-        // No ordering was provided for the marginalized variables, so order them using constrained
-        // COLAMD.
-        bool unmarginalizedAreOrdered = (boost::get<const Ordering&>(&variables) != 0);
-        const KeyVector* variablesOrOrdering =
-          unmarginalizedAreOrdered ?
-          boost::get<const Ordering&>(&variables) : boost::get<const KeyVector&>(&variables);
-
-        Ordering totalOrdering =
-          Ordering::ColamdConstrainedLast(*variableIndex, *variablesOrOrdering, unmarginalizedAreOrdered);
-
-        // Split up ordering
-        const size_t nVars = variablesOrOrdering->size();
-        Ordering marginalizationOrdering(totalOrdering.begin(), totalOrdering.end() - nVars);
-        Ordering marginalVarsOrdering(totalOrdering.end() - nVars, totalOrdering.end());
-
-        // Call this function again with the computed orderings
-        return marginalMultifrontalBayesTree(marginalVarsOrdering, marginalizationOrdering, function, *variableIndex);
-      }
     } else {
+      // No ordering was provided for the marginalized variables, so order them using constrained
+      // COLAMD.
+      bool unmarginalizedAreOrdered = (boost::get<const Ordering&>(&variables) != 0);
+      const KeyVector* variablesOrOrdering =
+        unmarginalizedAreOrdered ?
+        boost::get<const Ordering&>(&variables) : boost::get<const KeyVector&>(&variables);
+
+      Ordering totalOrdering =
+        Ordering::ColamdConstrainedLast(*variableIndex, *variablesOrOrdering, unmarginalizedAreOrdered);
+
+      // Split up ordering
+      const size_t nVars = variablesOrOrdering->size();
+      Ordering marginalizationOrdering(totalOrdering.begin(), totalOrdering.end() - nVars);
+      Ordering marginalVarsOrdering(totalOrdering.end() - nVars, totalOrdering.end());
+
+      // Call this function again with the computed orderings
+      return marginalMultifrontalBayesTree(marginalVarsOrdering, marginalizationOrdering, function, *variableIndex);
+    }
+  }
+
+  /* ************************************************************************* */
+  template<class FACTORGRAPH>
+  boost::shared_ptr<typename EliminateableFactorGraph<FACTORGRAPH>::BayesTreeType>
+    EliminateableFactorGraph<FACTORGRAPH>::marginalMultifrontalBayesTree(
+    boost::variant<const Ordering&, const KeyVector&> variables,
+    const Ordering& marginalizedVariableOrdering,
+    const Eliminate& function, OptionalVariableIndex variableIndex) const
+  {
+    if(!variableIndex) {
       // If no variable index is provided, compute one and call this function again
       VariableIndex computedVariableIndex(asDerived());
       return marginalMultifrontalBayesTree(variables, marginalizedVariableOrdering, function, computedVariableIndex);
+    } else {
+      gttic(marginalMultifrontalBayesTree);
+      // An ordering was provided for the marginalized variables, so we can first eliminate them
+      // in the order requested.
+      boost::shared_ptr<BayesTreeType> bayesTree;
+      boost::shared_ptr<FactorGraphType> factorGraph;
+      boost::tie(bayesTree,factorGraph) =
+        eliminatePartialMultifrontal(marginalizedVariableOrdering, function, *variableIndex);
+
+      if(const Ordering* varsAsOrdering = boost::get<const Ordering&>(&variables))
+      {
+        // An ordering was also provided for the unmarginalized variables, so we can also
+        // eliminate them in the order requested.
+        return factorGraph->eliminateMultifrontal(*varsAsOrdering, function);
+      }
+      else
+      {
+        // No ordering was provided for the unmarginalized variables, so order them with COLAMD.
+        return factorGraph->eliminateMultifrontal(function);
+      }
     }
   }
 

gtsam/inference/EliminateableFactorGraph.h

@@ -88,9 +88,6 @@ namespace gtsam {
     /// The function type that does a single dense elimination step on a subgraph.
     typedef boost::function<EliminationResult(const FactorGraphType&, const Ordering&)> Eliminate;
 
-    /// Typedef for an optional ordering as an argument to elimination functions
-    typedef const boost::optional<Ordering>& OptionalOrdering;
-
     /// Typedef for an optional variable index as an argument to elimination functions
     typedef const boost::optional<VariableIndex>& OptionalVariableIndex;
 
@@ -108,25 +105,40 @@ namespace gtsam {
      *  <b> Example - METIS ordering for elimination
      *  \code
      *  boost::shared_ptr<GaussianBayesNet> result = graph.eliminateSequential(OrderingType::METIS);
-     *
-     *  <b> Example - Full QR elimination in specified order:
-     *  \code
-     *  boost::shared_ptr<GaussianBayesNet> result = graph.eliminateSequential(EliminateQR, myOrdering);
      *  \endcode
      *
      *  <b> Example - Reusing an existing VariableIndex to improve performance, and using COLAMD ordering: </b>
      *  \code
      *  VariableIndex varIndex(graph); // Build variable index
      *  Data data = otherFunctionUsingVariableIndex(graph, varIndex); // Other code that uses variable index
-     *  boost::shared_ptr<GaussianBayesNet> result = graph.eliminateSequential(EliminateQR, boost::none, varIndex);
+     *  boost::shared_ptr<GaussianBayesNet> result = graph.eliminateSequential(EliminateQR, varIndex, boost::none);
      *  \endcode
      *  */
     boost::shared_ptr<BayesNetType> eliminateSequential(
-      OptionalOrdering ordering = boost::none,
       const Eliminate& function = EliminationTraitsType::DefaultEliminate,
       OptionalVariableIndex variableIndex = boost::none,
       OptionalOrderingType orderingType = boost::none) const;
 
+    /** Do sequential elimination of all variables to produce a Bayes net.
+     *
+     *  <b> Example - Full QR elimination in specified order:
+     *  \code
+     *  boost::shared_ptr<GaussianBayesNet> result = graph.eliminateSequential(myOrdering, EliminateQR);
+     *  \endcode
+     *
+     *  <b> Example - Reusing an existing VariableIndex to improve performance: </b>
+     *  \code
+     *  VariableIndex varIndex(graph); // Build variable index
+     *  Data data = otherFunctionUsingVariableIndex(graph, varIndex); // Other code that uses variable index
+     *  boost::shared_ptr<GaussianBayesNet> result = graph.eliminateSequential(myOrdering, EliminateQR, varIndex, boost::none);
+     *  \endcode
+     *  */
+    boost::shared_ptr<BayesNetType> eliminateSequential(
+      const Ordering& ordering,
+      const Eliminate& function = EliminationTraitsType::DefaultEliminate,
+      OptionalVariableIndex variableIndex = boost::none,
+      OptionalOrderingType orderingType = boost::none) const; // orderingType is not necessary anymore, kept for backwards compatibility
+
     /** Do multifrontal elimination of all variables to produce a Bayes tree.  If an ordering is not
      *  provided, the ordering will be computed using either COLAMD or METIS, dependeing on
      *  the parameter orderingType (Ordering::COLAMD or Ordering::METIS)
@@ -136,11 +148,6 @@ namespace gtsam {
      *  boost::shared_ptr<GaussianBayesTree> result = graph.eliminateMultifrontal(EliminateCholesky);
      *  \endcode
      *
-     *  <b> Example - Full QR elimination in specified order:
-     *  \code
-     *  boost::shared_ptr<GaussianBayesTree> result = graph.eliminateMultifrontal(EliminateQR, myOrdering);
-     *  \endcode
-     *
      *  <b> Example - Reusing an existing VariableIndex to improve performance, and using COLAMD ordering: </b>
      *  \code
      *  VariableIndex varIndex(graph); // Build variable index
@@ -149,11 +156,25 @@ namespace gtsam {
      *  \endcode
      *  */
     boost::shared_ptr<BayesTreeType> eliminateMultifrontal(
-      OptionalOrdering ordering = boost::none,
       const Eliminate& function = EliminationTraitsType::DefaultEliminate,
       OptionalVariableIndex variableIndex = boost::none,
       OptionalOrderingType orderingType = boost::none) const;
 
+    /** Do multifrontal elimination of all variables to produce a Bayes tree.  If an ordering is not
+     *  provided, the ordering will be computed using either COLAMD or METIS, dependeing on
+     *  the parameter orderingType (Ordering::COLAMD or Ordering::METIS)
+     *
+     *  <b> Example - Full QR elimination in specified order:
+     *  \code
+     *  boost::shared_ptr<GaussianBayesTree> result = graph.eliminateMultifrontal(EliminateQR, myOrdering);
+     *  \endcode
+     *  */
+    boost::shared_ptr<BayesTreeType> eliminateMultifrontal(
+      const Ordering& ordering,
+      const Eliminate& function = EliminationTraitsType::DefaultEliminate,
+      OptionalVariableIndex variableIndex = boost::none,
+      OptionalOrderingType orderingType = boost::none) const; // orderingType no longer needed
+
     /** Do sequential elimination of some variables, in \c ordering provided, to produce a Bayes net
      *  and a remaining factor graph.  This computes the factorization \f$ p(X) = p(A|B) p(B) \f$,
      *  where \f$ A = \f$ \c variables, \f$ X \f$ is all the variables in the factor graph, and \f$
@@ -194,20 +215,47 @@ namespace gtsam {
       const Eliminate& function = EliminationTraitsType::DefaultEliminate,
       OptionalVariableIndex variableIndex = boost::none) const;
 
-    /** Compute the marginal of the requested variables and return the result as a Bayes net.
+    /** Compute the marginal of the requested variables and return the result as a Bayes net.  Uses
+     *  COLAMD marginalization ordering by default
      *  @param variables Determines the variables whose marginal to compute, if provided as an
      *         Ordering they will be ordered in the returned BayesNet as specified, and if provided
      *         as a KeyVector they will be ordered using constrained COLAMD.
-     *  @param marginalizedVariableOrdering Optional ordering for the variables being marginalized
-     *         out, i.e. all variables not in \c variables.  If this is boost::none, the ordering
-     *         will be computed with COLAMD.
      *  @param function Optional dense elimination function, if not provided the default will be
      *         used.
      *  @param variableIndex Optional pre-computed VariableIndex for the factor graph, if not
      *         provided one will be computed. */
     boost::shared_ptr<BayesNetType> marginalMultifrontalBayesNet(
       boost::variant<const Ordering&, const KeyVector&> variables,
-      OptionalOrdering marginalizedVariableOrdering = boost::none,
+      const Eliminate& function = EliminationTraitsType::DefaultEliminate,
+      OptionalVariableIndex variableIndex = boost::none) const;
+
+    /** Compute the marginal of the requested variables and return the result as a Bayes net.
+     *  @param variables Determines the variables whose marginal to compute, if provided as an
+     *         Ordering they will be ordered in the returned BayesNet as specified, and if provided
+     *         as a KeyVector they will be ordered using constrained COLAMD.
+     *  @param marginalizedVariableOrdering Ordering for the variables being marginalized out,
+     *         i.e. all variables not in \c variables.
+     *  @param function Optional dense elimination function, if not provided the default will be
+     *         used.
+     *  @param variableIndex Optional pre-computed VariableIndex for the factor graph, if not
+     *         provided one will be computed. */
+    boost::shared_ptr<BayesNetType> marginalMultifrontalBayesNet(
+      boost::variant<const Ordering&, const KeyVector&> variables,
+      const Ordering& marginalizedVariableOrdering, // this no longer takes boost::none - potentially code breaking
+      const Eliminate& function = EliminationTraitsType::DefaultEliminate,
+      OptionalVariableIndex variableIndex = boost::none) const;
+
+    /** Compute the marginal of the requested variables and return the result as a Bayes tree.  Uses
+     *  COLAMD marginalization order by default
+     *  @param variables Determines the variables whose marginal to compute, if provided as an
+     *         Ordering they will be ordered in the returned BayesNet as specified, and if provided
+     *         as a KeyVector they will be ordered using constrained COLAMD.
+     *  @param function Optional dense elimination function, if not provided the default will be
+     *         used.
+     *  @param variableIndex Optional pre-computed VariableIndex for the factor graph, if not
+     *         provided one will be computed. */
+    boost::shared_ptr<BayesTreeType> marginalMultifrontalBayesTree(
+      boost::variant<const Ordering&, const KeyVector&> variables,
       const Eliminate& function = EliminationTraitsType::DefaultEliminate,
       OptionalVariableIndex variableIndex = boost::none) const;
 
@@ -215,16 +263,15 @@ namespace gtsam {
      *  @param variables Determines the variables whose marginal to compute, if provided as an
      *         Ordering they will be ordered in the returned BayesNet as specified, and if provided
      *         as a KeyVector they will be ordered using constrained COLAMD.
-     *  @param marginalizedVariableOrdering Optional ordering for the variables being marginalized
+     *  @param marginalizedVariableOrdering Ordering for the variables being marginalized out,
-     *         out, i.e. all variables not in \c variables.  If this is boost::none, the ordering
+     *         i.e. all variables not in \c variables.
-     *         will be computed with COLAMD.
      *  @param function Optional dense elimination function, if not provided the default will be
      *         used.
      *  @param variableIndex Optional pre-computed VariableIndex for the factor graph, if not
      *         provided one will be computed. */
     boost::shared_ptr<BayesTreeType> marginalMultifrontalBayesTree(
       boost::variant<const Ordering&, const KeyVector&> variables,
-      OptionalOrdering marginalizedVariableOrdering = boost::none,
+      const Ordering& marginalizedVariableOrdering, // this no longer takes boost::none - potentially code breaking
       const Eliminate& function = EliminationTraitsType::DefaultEliminate,
       OptionalVariableIndex variableIndex = boost::none) const;
 

gtsam/linear/GaussianFactorGraph.cpp

@@ -282,8 +282,13 @@ namespace gtsam {
   }
 
   /* ************************************************************************* */
-  VectorValues GaussianFactorGraph::optimize(OptionalOrdering ordering, const Eliminate& function) const
+  VectorValues GaussianFactorGraph::optimize(const Eliminate& function) const {
-  {
+    gttic(GaussianFactorGraph_optimize);
+    return BaseEliminateable::eliminateMultifrontal(function)->optimize();
+  }
+
+  /* ************************************************************************* */
+  VectorValues GaussianFactorGraph::optimize(const Ordering& ordering, const Eliminate& function) const {
     gttic(GaussianFactorGraph_optimize);
     return BaseEliminateable::eliminateMultifrontal(ordering, function)->optimize();
   }

gtsam/linear/GaussianFactorGraph.h

@@ -282,7 +282,14 @@ namespace gtsam {
      *  the dense elimination function specified in \c function (default EliminatePreferCholesky),
      *  followed by back-substitution in the Bayes tree resulting from elimination.  Is equivalent
      *  to calling graph.eliminateMultifrontal()->optimize(). */
-    VectorValues optimize(OptionalOrdering ordering = boost::none,
+    VectorValues optimize(
+      const Eliminate& function = EliminationTraitsType::DefaultEliminate) const;
+
+    /** Solve the factor graph by performing multifrontal variable elimination in COLAMD order using
+     *  the dense elimination function specified in \c function (default EliminatePreferCholesky),
+     *  followed by back-substitution in the Bayes tree resulting from elimination.  Is equivalent
+     *  to calling graph.eliminateMultifrontal()->optimize(). */
+    VectorValues optimize(const Ordering&,
       const Eliminate& function = EliminationTraitsType::DefaultEliminate) const;
 
     /**

gtsam/linear/IterativeSolver.cpp

@@ -82,29 +82,20 @@ string IterativeOptimizationParameters::verbosityTranslator(
     return "UNKNOWN";
 }
 
+/*****************************************************************************/
+VectorValues IterativeSolver::optimize(const GaussianFactorGraph &gfg,
+    boost::optional<const KeyInfo&> keyInfo,
+    boost::optional<const std::map<Key, Vector>&> lambda) {
+  return optimize(gfg, keyInfo ? *keyInfo : KeyInfo(gfg),
+      lambda ? *lambda : std::map<Key, Vector>());
+}
+
 /*****************************************************************************/
 VectorValues IterativeSolver::optimize(const GaussianFactorGraph &gfg,
     const KeyInfo &keyInfo, const std::map<Key, Vector> &lambda) {
   return optimize(gfg, keyInfo, lambda, keyInfo.x0());
 }
 
-/*****************************************************************************/
-VectorValues IterativeSolver::optimize(const GaussianFactorGraph &gfg,
-    const KeyInfo& keyInfo) {
-  return optimize(gfg, keyInfo, std::map<Key, Vector>());
-}
-
-/*****************************************************************************/
-VectorValues IterativeSolver::optimize(const GaussianFactorGraph &gfg,
-    const std::map<Key, Vector>& lambda) {
-  return optimize(gfg, KeyInfo(gfg), lambda);
-}
-
-/*****************************************************************************/
-VectorValues IterativeSolver::optimize(const GaussianFactorGraph &gfg) {
-  return optimize(gfg, KeyInfo(gfg), std::map<Key, Vector>());
-}
-
 /****************************************************************************/
 KeyInfo::KeyInfo(const GaussianFactorGraph &fg, const Ordering &ordering) :
     ordering_(ordering) {

gtsam/linear/IterativeSolver.h

@@ -91,21 +91,15 @@ public:
   virtual ~IterativeSolver() {
   }
 
+  /* interface to the nonlinear optimizer, without metadata, damping and initial estimate */
+  GTSAM_EXPORT VectorValues optimize(const GaussianFactorGraph &gfg,
+      boost::optional<const KeyInfo&> = boost::none,
+      boost::optional<const std::map<Key, Vector>&> lambda = boost::none);
+
   /* interface to the nonlinear optimizer, without initial estimate */
   GTSAM_EXPORT VectorValues optimize(const GaussianFactorGraph &gfg, const KeyInfo &keyInfo,
       const std::map<Key, Vector> &lambda);
 
-  /* interface to the nonlinear optimizer, without damping and initial estimate */
-  GTSAM_EXPORT VectorValues optimize(const GaussianFactorGraph &gfg,
-      const KeyInfo& keyInfo);
-
-  /* interface to the nonlinear optimizer, without metadata and initial estimate */
-  GTSAM_EXPORT VectorValues optimize(const GaussianFactorGraph &gfg,
-      const std::map<Key, Vector>& lambda);
-
-  /* interface to the nonlinear optimizer, without metadata, damping and initial estimate */
-  GTSAM_EXPORT VectorValues optimize(const GaussianFactorGraph &gfg);
-
   /* interface to the nonlinear optimizer that the subclasses have to implement */
   virtual VectorValues optimize(const GaussianFactorGraph &gfg,
       const KeyInfo &keyInfo, const std::map<Key, Vector> &lambda,

gtsam/linear/Scatter.cpp

@@ -34,17 +34,7 @@ string SlotEntry::toString() const {
 }
 
 /* ************************************************************************* */
-Scatter::Scatter(const GaussianFactorGraph& gfg,
+void Scatter::ScatterHelper(const GaussianFactorGraph& gfg, size_t sortStart) {
-    boost::optional<const Ordering&> ordering) {
-  gttic(Scatter_Constructor);
-
-  // If we have an ordering, pre-fill the ordered variables first
-  if (ordering) {
-    for (Key key : *ordering) {
-      add(key, 0);
-    }
-  }
-
   // Now, find dimensions of variables and/or extend
   for (const auto& factor : gfg) {
     if (!factor)
@@ -68,10 +58,30 @@ Scatter::Scatter(const GaussianFactorGraph& gfg,
 
   // To keep the same behavior as before, sort the keys after the ordering
   iterator first = begin();
-  if (ordering) first += ordering->size();
+  first += sortStart;
   if (first != end()) std::sort(first, end());
 }
 
+/* ************************************************************************* */
+Scatter::Scatter(const GaussianFactorGraph& gfg) {
+  gttic(Scatter_Constructor);
+
+  ScatterHelper(gfg, 0);
+}
+
+/* ************************************************************************* */
+Scatter::Scatter(const GaussianFactorGraph& gfg,
+    const Ordering& ordering) {
+  gttic(Scatter_Constructor);
+
+  // pre-fill the ordered variables first
+  for (Key key : ordering) {
+    add(key, 0);
+  }
+
+  ScatterHelper(gfg, ordering.size());
+}
+
 /* ************************************************************************* */
 void Scatter::add(Key key, size_t dim) {
   emplace_back(SlotEntry(key, dim));

gtsam/linear/Scatter.h

@@ -23,8 +23,6 @@
 #include <gtsam/base/FastMap.h>
 #include <gtsam/dllexport.h>
 
-#include <boost/optional.hpp>
-
 namespace gtsam {
 
 class GaussianFactorGraph;
@@ -53,15 +51,21 @@ class Scatter : public FastVector<SlotEntry> {
   /// Default Constructor
   Scatter() {}
 
-  /// Construct from gaussian factor graph, with optional (partial or complete) ordering
+  /// Construct from gaussian factor graph, without ordering
-  Scatter(const GaussianFactorGraph& gfg,
+  explicit Scatter(const GaussianFactorGraph& gfg);
-          boost::optional<const Ordering&> ordering = boost::none);
+
+  /// Construct from gaussian factor graph, with (partial or complete) ordering
+  explicit Scatter(const GaussianFactorGraph& gfg, const Ordering& ordering);
 
   /// Add a key/dim pair
   void add(Key key, size_t dim);
 
  private:
 
+  /// Helper function for constructors, adds/finds dimensions of variables and
+  //  sorts starting from sortStart
+  void ScatterHelper(const GaussianFactorGraph& gfg, size_t sortStart);
+
   /// Find the SlotEntry with the right key (linear time worst case)
   iterator find(Key key);
 };

gtsam/nonlinear/Marginals.cpp

@@ -26,8 +26,16 @@ using namespace std;
 namespace gtsam {
 
 /* ************************************************************************* */
-Marginals::Marginals(const NonlinearFactorGraph& graph, const Values& solution, Factorization factorization,
+Marginals::Marginals(const NonlinearFactorGraph& graph, const Values& solution, Factorization factorization)
-                     EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering)
+                     : values_(solution), factorization_(factorization) {
+  gttic(MarginalsConstructor);
+  graph_ = *graph.linearize(solution);
+  computeBayesTree();
+}
+
+/* ************************************************************************* */
+Marginals::Marginals(const NonlinearFactorGraph& graph, const Values& solution, const Ordering& ordering,
+                     Factorization factorization)
                      : values_(solution), factorization_(factorization) {
   gttic(MarginalsConstructor);
   graph_ = *graph.linearize(solution);
@@ -35,28 +43,52 @@ Marginals::Marginals(const NonlinearFactorGraph& graph, const Values& solution,
 }
 
 /* ************************************************************************* */
-Marginals::Marginals(const GaussianFactorGraph& graph, const VectorValues& solution, Factorization factorization,
+Marginals::Marginals(const GaussianFactorGraph& graph, const Values& solution, Factorization factorization)
-                     EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering)
+                     : graph_(graph), values_(solution), factorization_(factorization) {
-                     : graph_(graph), factorization_(factorization) {
   gttic(MarginalsConstructor);
-  Values vals;
+  computeBayesTree();
-  for (const auto& keyValue: solution) {
-    vals.insert(keyValue.first, keyValue.second);
-  }
-  values_ = vals;
-  computeBayesTree(ordering);
 }
 
 /* ************************************************************************* */
-Marginals::Marginals(const GaussianFactorGraph& graph, const Values& solution, Factorization factorization,
+Marginals::Marginals(const GaussianFactorGraph& graph, const Values& solution, const Ordering& ordering,
-                     EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering)
+                     Factorization factorization)
                      : graph_(graph), values_(solution), factorization_(factorization) {
   gttic(MarginalsConstructor);
   computeBayesTree(ordering);
 }
 
 /* ************************************************************************* */
-void Marginals::computeBayesTree(EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering) {
+Marginals::Marginals(const GaussianFactorGraph& graph, const VectorValues& solution, Factorization factorization)
+                     : graph_(graph), factorization_(factorization) {
+  gttic(MarginalsConstructor);
+  for (const auto& keyValue: solution) {
+    values_.insert(keyValue.first, keyValue.second);
+  }
+  computeBayesTree();
+}
+
+/* ************************************************************************* */
+Marginals::Marginals(const GaussianFactorGraph& graph, const VectorValues& solution, const Ordering& ordering,
+                     Factorization factorization)
+                     : graph_(graph), factorization_(factorization) {
+  gttic(MarginalsConstructor);
+  for (const auto& keyValue: solution) {
+    values_.insert(keyValue.first, keyValue.second);
+  }
+  computeBayesTree(ordering);
+}
+
+/* ************************************************************************* */
+void Marginals::computeBayesTree() {
+  // Compute BayesTree
+  if(factorization_ == CHOLESKY)
+    bayesTree_ = *graph_.eliminateMultifrontal(EliminatePreferCholesky);
+  else if(factorization_ == QR)
+    bayesTree_ = *graph_.eliminateMultifrontal(EliminateQR);
+}
+
+/* ************************************************************************* */
+void Marginals::computeBayesTree(const Ordering& ordering) {
   // Compute BayesTree
   if(factorization_ == CHOLESKY)
     bayesTree_ = *graph_.eliminateMultifrontal(ordering, EliminatePreferCholesky);
@@ -128,9 +160,9 @@ JointMarginal Marginals::jointMarginalInformation(const KeyVector& variables) co
         jointFG = *bayesTree_.joint(variables[0], variables[1], EliminateQR);
     } else {
       if(factorization_ == CHOLESKY)
-        jointFG = GaussianFactorGraph(*graph_.marginalMultifrontalBayesTree(variables, boost::none, EliminatePreferCholesky));
+        jointFG = GaussianFactorGraph(*graph_.marginalMultifrontalBayesTree(variables, EliminatePreferCholesky));
       else if(factorization_ == QR)
-        jointFG = GaussianFactorGraph(*graph_.marginalMultifrontalBayesTree(variables, boost::none, EliminateQR));
+        jointFG = GaussianFactorGraph(*graph_.marginalMultifrontalBayesTree(variables, EliminateQR));
     }
 
     // Get information matrix

gtsam/nonlinear/Marginals.h

@@ -55,10 +55,33 @@ public:
    * @param graph The factor graph defining the full joint density on all variables.
    * @param solution The linearization point about which to compute Gaussian marginals (usually the MLE as obtained from a NonlinearOptimizer).
    * @param factorization The linear decomposition mode - either Marginals::CHOLESKY (faster and suitable for most problems) or Marginals::QR (slower but more numerically stable for poorly-conditioned problems).
-   * @param ordering An optional variable ordering for elimination.
    */
-  Marginals(const NonlinearFactorGraph& graph, const Values& solution, Factorization factorization = CHOLESKY,
+  Marginals(const NonlinearFactorGraph& graph, const Values& solution, Factorization factorization = CHOLESKY);
-            EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering = boost::none);
+
+  /** Construct a marginals class from a nonlinear factor graph.
+   * @param graph The factor graph defining the full joint density on all variables.
+   * @param solution The linearization point about which to compute Gaussian marginals (usually the MLE as obtained from a NonlinearOptimizer).
+   * @param factorization The linear decomposition mode - either Marginals::CHOLESKY (faster and suitable for most problems) or Marginals::QR (slower but more numerically stable for poorly-conditioned problems).
+   * @param ordering The ordering for elimination.
+   */
+  Marginals(const NonlinearFactorGraph& graph, const Values& solution, const Ordering& ordering, // argument order switch due to default value of factorization, potentially code breaking
+              Factorization factorization = CHOLESKY);
+
+  /** Construct a marginals class from a linear factor graph.
+   * @param graph The factor graph defining the full joint density on all variables.
+   * @param solution The solution point to compute Gaussian marginals.
+   * @param factorization The linear decomposition mode - either Marginals::CHOLESKY (faster and suitable for most problems) or Marginals::QR (slower but more numerically stable for poorly-conditioned problems).
+   */          
+  Marginals(const GaussianFactorGraph& graph, const Values& solution, Factorization factorization = CHOLESKY);
+
+  /** Construct a marginals class from a linear factor graph.
+   * @param graph The factor graph defining the full joint density on all variables.
+   * @param solution The solution point to compute Gaussian marginals.
+   * @param factorization The linear decomposition mode - either Marginals::CHOLESKY (faster and suitable for most problems) or Marginals::QR (slower but more numerically stable for poorly-conditioned problems).
+   * @param ordering The ordering for elimination.
+   */          
+  Marginals(const GaussianFactorGraph& graph, const Values& solution, const Ordering& ordering, // argument order switch due to default value of factorization, potentially code breaking
+              Factorization factorization = CHOLESKY);
 
   /** Construct a marginals class from a linear factor graph.
    * @param graph The factor graph defining the full joint density on all variables.
@@ -66,8 +89,7 @@ public:
    * @param factorization The linear decomposition mode - either Marginals::CHOLESKY (faster and suitable for most problems) or Marginals::QR (slower but more numerically stable for poorly-conditioned problems).
    * @param ordering An optional variable ordering for elimination.
    */          
-  Marginals(const GaussianFactorGraph& graph, const Values& solution, Factorization factorization = CHOLESKY,
+  Marginals(const GaussianFactorGraph& graph, const VectorValues& solution, Factorization factorization = CHOLESKY);
-              EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering = boost::none);
 
   /** Construct a marginals class from a linear factor graph.
    * @param graph The factor graph defining the full joint density on all variables.
@@ -75,8 +97,8 @@ public:
    * @param factorization The linear decomposition mode - either Marginals::CHOLESKY (faster and suitable for most problems) or Marginals::QR (slower but more numerically stable for poorly-conditioned problems).
    * @param ordering An optional variable ordering for elimination.
    */          
-  Marginals(const GaussianFactorGraph& graph, const VectorValues& solution, Factorization factorization = CHOLESKY,
+  Marginals(const GaussianFactorGraph& graph, const VectorValues& solution, const Ordering& ordering, // argument order switch due to default value of factorization, potentially code breaking
-              EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering = boost::none);
+              Factorization factorization = CHOLESKY);
 
   /** print */
   void print(const std::string& str = "Marginals: ", const KeyFormatter& keyFormatter = DefaultKeyFormatter) const;
@@ -103,7 +125,10 @@ public:
 protected:
   
   /** Compute the Bayes Tree as a helper function to the constructor */
-  void computeBayesTree(EliminateableFactorGraph<GaussianFactorGraph>::OptionalOrdering ordering);
+  void computeBayesTree();
+
+  /** Compute the Bayes Tree as a helper function to the constructor */
+  void computeBayesTree(const Ordering& ordering);
 
 };
 

gtsam_unstable/discrete/CSP.cpp

@@ -14,7 +14,14 @@ using namespace std;
 namespace gtsam {
 
   /// Find the best total assignment - can be expensive
-  CSP::sharedValues CSP::optimalAssignment(OptionalOrdering ordering) const {
+  CSP::sharedValues CSP::optimalAssignment() const {
+    DiscreteBayesNet::shared_ptr chordal = this->eliminateSequential();
+    sharedValues mpe = chordal->optimize();
+    return mpe;
+  }
+
+  /// Find the best total assignment - can be expensive
+  CSP::sharedValues CSP::optimalAssignment(const Ordering& ordering) const {
     DiscreteBayesNet::shared_ptr chordal = this->eliminateSequential(ordering);
     sharedValues mpe = chordal->optimize();
     return mpe;

gtsam_unstable/discrete/CSP.h

@@ -60,7 +60,10 @@ namespace gtsam {
 //    }
 
     /// Find the best total assignment - can be expensive
-    sharedValues optimalAssignment(OptionalOrdering ordering = boost::none) const;
+    sharedValues optimalAssignment() const;
+
+    /// Find the best total assignment - can be expensive
+    sharedValues optimalAssignment(const Ordering& ordering) const;
 
 //    /*
 //     * Perform loopy belief propagation

tests/testGaussianFactorGraphB.cpp

@@ -206,7 +206,7 @@ TEST(GaussianFactorGraph, optimize_Cholesky) {
   GaussianFactorGraph fg = createGaussianFactorGraph();
 
   // optimize the graph
-  VectorValues actual = fg.optimize(boost::none, EliminateCholesky);
+  VectorValues actual = fg.optimize(EliminateCholesky);
 
   // verify
   VectorValues expected = createCorrectDelta();
@@ -220,7 +220,7 @@ TEST( GaussianFactorGraph, optimize_QR )
   GaussianFactorGraph fg = createGaussianFactorGraph();
 
   // optimize the graph
-  VectorValues actual = fg.optimize(boost::none, EliminateQR);
+  VectorValues actual = fg.optimize(EliminateQR);
 
   // verify
   VectorValues expected = createCorrectDelta();