Add derivatives of static model w.r.t. parameters

The new file is <FILENAME>_static_params_derives.m

Closes: #160

ComputingTasks.cc

@@ -905,7 +905,7 @@ PlannerObjectiveStatement::getPlannerObjective() const
 void
 PlannerObjectiveStatement::computingPass()
 {
-  model_tree->computingPass(eval_context_t(), false, true, false, false);
+  model_tree->computingPass(eval_context_t(), false, true, false, false, false);
 }
 
 void

DynamicModel.cc

@@ -2986,7 +2986,7 @@ DynamicModel::computingPass(bool jacobianExo, bool hessian, bool thirdDerivative
 
   if (paramsDerivatives)
     {
-      cout << " - order 2 (derivatives of Jacobian w.r. to parameters)" << endl;
+      cout << " - derivatives of Jacobian/Hessian w.r. to parameters" << endl;
       computeParamsDerivatives();
 
       if (!no_tmp_terms)
@@ -3715,108 +3715,6 @@ DynamicModel::testTrendDerivativesEqualToZero(const eval_context_t &eval_context
         }
 }
 
-void
-DynamicModel::computeParamsDerivatives()
-{
-  for (deriv_id_table_t::const_iterator it = deriv_id_table.begin();
-       it != deriv_id_table.end(); it++)
-    {
-      if (symbol_table.getType(it->first.first) != eParameter)
-        continue;
-
-      int param = it->second;
-
-      for (int eq = 0; eq < (int) equations.size(); eq++)
-        {
-          expr_t d1 = equations[eq]->getDerivative(param);
-          if (d1 == Zero)
-            continue;
-          residuals_params_derivatives[make_pair(eq, param)] = d1;
-        }
-
-      for (first_derivatives_t::const_iterator it2 = residuals_params_derivatives.begin();
-           it2 != residuals_params_derivatives.end(); it2++)
-        {
-          int eq = it2->first.first;
-          int param1 = it2->first.second;
-          expr_t d1 = it2->second;
-
-          expr_t d2 = d1->getDerivative(param);
-          if (d2 == Zero)
-            continue;
-          residuals_params_second_derivatives[make_pair(eq, make_pair(param1, param))] = d2;
-        }
-
-      for (first_derivatives_t::const_iterator it2 = first_derivatives.begin();
-           it2 != first_derivatives.end(); it2++)
-        {
-          int eq = it2->first.first;
-          int var = it2->first.second;
-          expr_t d1 = it2->second;
-
-          expr_t d2 = d1->getDerivative(param);
-          if (d2 == Zero)
-            continue;
-          jacobian_params_derivatives[make_pair(eq, make_pair(var, param))] = d2;
-        }
-
-      for (second_derivatives_t::const_iterator it2 = jacobian_params_derivatives.begin();
-           it2 != jacobian_params_derivatives.end(); it2++)
-        {
-          int eq = it2->first.first;
-          int var = it2->first.second.first;
-          int param1 = it2->first.second.second;
-          expr_t d1 = it2->second;
-
-          expr_t d2 = d1->getDerivative(param);
-          if (d2 == Zero)
-            continue;
-          jacobian_params_second_derivatives[make_pair(eq, make_pair(var, make_pair(param1, param)))] = d2;
-        }
-
-      for (second_derivatives_t::const_iterator it2 = second_derivatives.begin();
-           it2 != second_derivatives.end(); it2++)
-        {
-          int eq = it2->first.first;
-          int var1 = it2->first.second.first;
-          int var2 = it2->first.second.second;
-          expr_t d1 = it2->second;
-
-          expr_t d2 = d1->getDerivative(param);
-          if (d2 == Zero)
-            continue;
-          hessian_params_derivatives[make_pair(eq, make_pair(var1, make_pair(var2, param)))] = d2;
-        }
-    }
-}
-
-void
-DynamicModel::computeParamsDerivativesTemporaryTerms()
-{
-  map<expr_t, int> reference_count;
-  params_derivs_temporary_terms.clear();
-
-  for (first_derivatives_t::iterator it = residuals_params_derivatives.begin();
-       it != residuals_params_derivatives.end(); it++)
-    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
-
-  for (second_derivatives_t::iterator it = jacobian_params_derivatives.begin();
-       it != jacobian_params_derivatives.end(); it++)
-    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
-
-  for (second_derivatives_t::const_iterator it = residuals_params_second_derivatives.begin();
-       it != residuals_params_second_derivatives.end(); ++it)
-    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
-
-  for (third_derivatives_t::const_iterator it = jacobian_params_second_derivatives.begin();
-       it != jacobian_params_second_derivatives.end(); ++it)
-    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
-
-  for (third_derivatives_t::const_iterator it = hessian_params_derivatives.begin();
-       it != hessian_params_derivatives.end(); ++it)
-    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
-}
-
 void
 DynamicModel::writeParamsDerivativesFile(const string &basename) const
 {

DynamicModel.hh

@@ -57,45 +57,6 @@ private:
   //! Number of columns of dynamic jacobian
   /*! Set by computeDerivID()s and computeDynJacobianCols() */
   int dynJacobianColsNbr;
-
-  //! Derivatives of the residuals w.r. to parameters
-  /*! First index is equation number, second is parameter.
-    Only non-null derivatives are stored in the map.
-    Parameter indices are those of the getDerivID() method.
-  */
-  first_derivatives_t residuals_params_derivatives;
-
-  //! Second derivatives of the residuals w.r. to parameters
-  /*! First index is equation number, second and third indeces are parameters.
-    Only non-null derivatives are stored in the map.
-    Parameter indices are those of the getDerivID() method.
-  */
-  second_derivatives_t residuals_params_second_derivatives;
-
-  //! Derivatives of the jacobian w.r. to parameters
-  /*! First index is equation number, second is endo/exo/exo_det variable, and third is parameter.
-    Only non-null derivatives are stored in the map.
-    Variable and parameter indices are those of the getDerivID() method.
-  */
-  second_derivatives_t jacobian_params_derivatives;
-
-  //! Second derivatives of the jacobian w.r. to parameters
-  /*! First index is equation number, second is endo/exo/exo_det variable, and third and fourth are parameters.
-    Only non-null derivatives are stored in the map.
-    Variable and parameter indices are those of the getDerivID() method.
-  */
-  third_derivatives_t jacobian_params_second_derivatives;
-
-  //! Derivatives of the hessian w.r. to parameters
-  /*! First index is equation number, first and second are endo/exo/exo_det variable, and third is parameter.
-    Only non-null derivatives are stored in the map.
-    Variable and parameter indices are those of the getDerivID() method.
-  */
-  third_derivatives_t hessian_params_derivatives;
-
-  //! Temporary terms for the file containing parameters derivatives
-  temporary_terms_t params_derivs_temporary_terms;
-
   //! Temporary terms for block decomposed models
   vector< vector<temporary_terms_t> > v_temporary_terms;
 
@@ -155,12 +116,8 @@ private:
   virtual int getSymbIDByDerivID(int deriv_id) const throw (UnknownDerivIDException);
   //! Compute the column indices of the dynamic Jacobian
   void computeDynJacobianCols(bool jacobianExo);
-  //! Computes derivatives of the Jacobian w.r. to parameters
-  void computeParamsDerivatives();
   //! Computes derivatives of the Jacobian w.r. to trend vars and tests that they are equal to zero
   void testTrendDerivativesEqualToZero(const eval_context_t &eval_context);
-  //! Computes temporary terms for the file containing parameters derivatives
-  void computeParamsDerivativesTemporaryTerms();
   //! Collect only the first derivatives
   map<pair<int, pair<int, int> >, expr_t> collect_first_order_derivatives_endogenous();
 

ModFile.cc

@@ -380,8 +380,10 @@ ModFile::computingPass(bool no_tmp_terms)
 
           const bool static_hessian = mod_file_struct.identification_present
             || mod_file_struct.estimation_analytic_derivation;
+          const bool paramsDerivatives = mod_file_struct.identification_present
+            || mod_file_struct.estimation_analytic_derivation;
           static_model.computingPass(global_eval_context, no_tmp_terms, static_hessian,
-                                     block, byte_code);
+                                     paramsDerivatives, block, byte_code);
         }
       // Set things to compute for dynamic model
       if (mod_file_struct.simul_present || mod_file_struct.check_present
@@ -640,7 +642,10 @@ ModFile::writeOutputFiles(const string &basename, bool clear_all, bool no_log, b
   if (dynamic_model.equation_number() > 0)
     {
       if (!no_static)
+        {
           static_model.writeStaticFile(basename, block, byte_code, use_dll);
+          static_model.writeParamsDerivativesFile(basename);
+        }
 
       dynamic_model.writeDynamicFile(basename, block, byte_code, use_dll, mod_file_struct.order_option);
       dynamic_model.writeParamsDerivativesFile(basename);

ModelTree.cc

@@ -1460,3 +1460,105 @@ ModelTree::sparseHelper(int order, ostream &output, int row_nb, int col_nb, Expr
     output << row_nb + col_nb * NNZDerivatives[order-1];
   output << RIGHT_ARRAY_SUBSCRIPT(output_type);
 }
+
+void
+ModelTree::computeParamsDerivatives()
+{
+  set<int> deriv_id_set;
+  addAllParamDerivId(deriv_id_set);
+  
+  for (set<int>::const_iterator it = deriv_id_set.begin();
+       it != deriv_id_set.end(); it++)
+    {
+      const int param = *it;
+
+      for (int eq = 0; eq < (int) equations.size(); eq++)
+        {
+          expr_t d1 = equations[eq]->getDerivative(param);
+          if (d1 == Zero)
+            continue;
+          residuals_params_derivatives[make_pair(eq, param)] = d1;
+        }
+
+      for (first_derivatives_t::const_iterator it2 = residuals_params_derivatives.begin();
+           it2 != residuals_params_derivatives.end(); it2++)
+        {
+          int eq = it2->first.first;
+          int param1 = it2->first.second;
+          expr_t d1 = it2->second;
+
+          expr_t d2 = d1->getDerivative(param);
+          if (d2 == Zero)
+            continue;
+          residuals_params_second_derivatives[make_pair(eq, make_pair(param1, param))] = d2;
+        }
+
+      for (first_derivatives_t::const_iterator it2 = first_derivatives.begin();
+           it2 != first_derivatives.end(); it2++)
+        {
+          int eq = it2->first.first;
+          int var = it2->first.second;
+          expr_t d1 = it2->second;
+
+          expr_t d2 = d1->getDerivative(param);
+          if (d2 == Zero)
+            continue;
+          jacobian_params_derivatives[make_pair(eq, make_pair(var, param))] = d2;
+        }
+
+      for (second_derivatives_t::const_iterator it2 = jacobian_params_derivatives.begin();
+           it2 != jacobian_params_derivatives.end(); it2++)
+        {
+          int eq = it2->first.first;
+          int var = it2->first.second.first;
+          int param1 = it2->first.second.second;
+          expr_t d1 = it2->second;
+
+          expr_t d2 = d1->getDerivative(param);
+          if (d2 == Zero)
+            continue;
+          jacobian_params_second_derivatives[make_pair(eq, make_pair(var, make_pair(param1, param)))] = d2;
+        }
+
+      for (second_derivatives_t::const_iterator it2 = second_derivatives.begin();
+           it2 != second_derivatives.end(); it2++)
+        {
+          int eq = it2->first.first;
+          int var1 = it2->first.second.first;
+          int var2 = it2->first.second.second;
+          expr_t d1 = it2->second;
+
+          expr_t d2 = d1->getDerivative(param);
+          if (d2 == Zero)
+            continue;
+          hessian_params_derivatives[make_pair(eq, make_pair(var1, make_pair(var2, param)))] = d2;
+        }
+    }
+}
+
+void
+ModelTree::computeParamsDerivativesTemporaryTerms()
+{
+  map<expr_t, int> reference_count;
+  params_derivs_temporary_terms.clear();
+
+  for (first_derivatives_t::iterator it = residuals_params_derivatives.begin();
+       it != residuals_params_derivatives.end(); it++)
+    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
+
+  for (second_derivatives_t::iterator it = jacobian_params_derivatives.begin();
+       it != jacobian_params_derivatives.end(); it++)
+    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
+
+  for (second_derivatives_t::const_iterator it = residuals_params_second_derivatives.begin();
+       it != residuals_params_second_derivatives.end(); ++it)
+    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
+
+  for (third_derivatives_t::const_iterator it = jacobian_params_second_derivatives.begin();
+       it != jacobian_params_second_derivatives.end(); ++it)
+    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
+
+  for (third_derivatives_t::const_iterator it = hessian_params_derivatives.begin();
+       it != hessian_params_derivatives.end(); ++it)
+    it->second->computeTemporaryTerms(reference_count, params_derivs_temporary_terms, true);
+}

ModelTree.hh

@@ -92,8 +92,49 @@ protected:
   */
   third_derivatives_t third_derivatives;
 
-  //! Temporary terms (those which will be noted Txxxx)
+  //! Derivatives of the residuals w.r. to parameters
+  /*! First index is equation number, second is parameter.
+    Only non-null derivatives are stored in the map.
+    Parameter indices are those of the getDerivID() method.
+  */
+  first_derivatives_t residuals_params_derivatives;
+
+  //! Second derivatives of the residuals w.r. to parameters
+  /*! First index is equation number, second and third indeces are parameters.
+    Only non-null derivatives are stored in the map.
+    Parameter indices are those of the getDerivID() method.
+  */
+  second_derivatives_t residuals_params_second_derivatives;
+
+  //! Derivatives of the jacobian w.r. to parameters
+  /*! First index is equation number, second is endo/exo/exo_det variable, and third is parameter.
+    Only non-null derivatives are stored in the map.
+    Variable and parameter indices are those of the getDerivID() method.
+  */
+  second_derivatives_t jacobian_params_derivatives;
+
+  //! Second derivatives of the jacobian w.r. to parameters
+  /*! First index is equation number, second is endo/exo/exo_det variable, and third and fourth are parameters.
+    Only non-null derivatives are stored in the map.
+    Variable and parameter indices are those of the getDerivID() method.
+  */
+  third_derivatives_t jacobian_params_second_derivatives;
+
+  //! Derivatives of the hessian w.r. to parameters
+  /*! First index is equation number, first and second are endo/exo/exo_det variable, and third is parameter.
+    Only non-null derivatives are stored in the map.
+    Variable and parameter indices are those of the getDerivID() method.
+  */
+  third_derivatives_t hessian_params_derivatives;
+
+
+  //! Temporary terms for the static/dynamic file (those which will be noted Txxxx)
   temporary_terms_t temporary_terms;
+
+  //! Temporary terms for the file containing parameters derivatives
+  temporary_terms_t params_derivs_temporary_terms;
+
+
   //! Trend variables and their growth factors
   trend_symbols_map_t trend_symbols_map;
   //! Nonstationary variables and their deflators
@@ -114,12 +155,16 @@ protected:
   //! Computes 3rd derivatives
   /*! \param vars the derivation IDs w.r. to which derive the 2nd derivatives */
   void computeThirdDerivatives(const set<int> &vars);
+  //! Computes derivatives of the Jacobian and Hessian w.r. to parameters
+  void computeParamsDerivatives();
 
   //! Write derivative of an equation w.r. to a variable
   void writeDerivative(ostream &output, int eq, int symb_id, int lag, ExprNodeOutputType output_type, const temporary_terms_t &temporary_terms) const;
   //! Computes temporary terms (for all equations and derivatives)
   void computeTemporaryTerms(bool is_matlab);
-  //! Writes temporary terms
+  //! Computes temporary terms for the file containing parameters derivatives
+  void computeParamsDerivativesTemporaryTerms();
+//! Writes temporary terms
   void writeTemporaryTerms(const temporary_terms_t &tt, ostream &output, ExprNodeOutputType output_type, deriv_node_temp_terms_t &tef_terms) const;
   //! Compiles temporary terms
   void compileTemporaryTerms(ostream &code_file, unsigned int &instruction_number, const temporary_terms_t &tt, map_idx_t map_idx, bool dynamic, bool steady_dynamic) const;

StaticModel.cc

@@ -1047,7 +1047,7 @@ StaticModel::collect_first_order_derivatives_endogenous()
 }
 
 void
-StaticModel::computingPass(const eval_context_t &eval_context, bool no_tmp_terms, bool hessian, bool block, bool bytecode)
+StaticModel::computingPass(const eval_context_t &eval_context, bool no_tmp_terms, bool hessian, bool paramsDerivatives, bool block, bool bytecode)
 {
   initializeVariablesAndEquations();
 
@@ -1070,6 +1070,15 @@ StaticModel::computingPass(const eval_context_t &eval_context, bool no_tmp_terms
       computeHessian(vars);
     }
 
+if (paramsDerivatives)
+    {
+      cout << " - derivatives of Jacobian/Hessian w.r. to parameters" << endl;
+      computeParamsDerivatives();
+
+      if (!no_tmp_terms)
+        computeParamsDerivativesTemporaryTerms();
+    }
+
   if (block)
     {
       jacob_map_t contemporaneous_jacobian, static_jacobian;
@@ -1542,7 +1551,12 @@ StaticModel::writeOutput(ostream &output, bool block) const
 SymbolType
 StaticModel::getTypeByDerivID(int deriv_id) const throw (UnknownDerivIDException)
 {
-  return symbol_table.getType(getSymbIDByDerivID(deriv_id));
+  if (deriv_id < symbol_table.endo_nbr())
+    return eEndogenous;
+  else if (deriv_id < symbol_table.endo_nbr() + symbol_table.param_nbr())
+    return eParameter;
+  else
+    throw UnknownDerivIDException();
 }
 
 int
@@ -1554,18 +1568,32 @@ StaticModel::getLagByDerivID(int deriv_id) const throw (UnknownDerivIDException)
 int
 StaticModel::getSymbIDByDerivID(int deriv_id) const throw (UnknownDerivIDException)
 {
-  return deriv_id;
+  if (deriv_id < symbol_table.endo_nbr())
+    return symbol_table.getID(eEndogenous, deriv_id);
+  else if (deriv_id < symbol_table.endo_nbr() + symbol_table.param_nbr())
+    return symbol_table.getID(eParameter, deriv_id - symbol_table.endo_nbr());
+  else
+    throw UnknownDerivIDException();
 }
 
 int
 StaticModel::getDerivID(int symb_id, int lag) const throw (UnknownDerivIDException)
 {
   if (symbol_table.getType(symb_id) == eEndogenous)
-    return symb_id;
+    return symbol_table.getTypeSpecificID(symb_id);
+  else if (symbol_table.getType(symb_id) == eParameter)
+    return symbol_table.getTypeSpecificID(symb_id) + symbol_table.endo_nbr();
   else
     return -1;
 }
 
+void
+StaticModel::addAllParamDerivId(set<int> &deriv_id_set)
+{
+  for (int i = 0; i < symbol_table.param_nbr(); i++)
+    deriv_id_set.insert(i + symbol_table.endo_nbr());
+}
+
 map<pair<pair<int, pair<int, int> >, pair<int, int> >, int>
 StaticModel::get_Derivatives(int block)
 {
@@ -1794,3 +1822,159 @@ void StaticModel::writeAuxVarRecursiveDefinitions(const string &basename) const
       output << ";" << endl;
     }
 }
+
+void
+StaticModel::writeParamsDerivativesFile(const string &basename) const
+{
+  if (!residuals_params_derivatives.size()
+      && !residuals_params_second_derivatives.size()
+      && !jacobian_params_derivatives.size()
+      && !jacobian_params_second_derivatives.size()
+      && !hessian_params_derivatives.size())
+    return;
+
+  string filename = basename + "_static_params_derivs.m";
+
+  ofstream paramsDerivsFile;
+  paramsDerivsFile.open(filename.c_str(), ios::out | ios::binary);
+  if (!paramsDerivsFile.is_open())
+    {
+      cerr << "ERROR: Can't open file " << filename << " for writing" << endl;
+      exit(EXIT_FAILURE);
+    }
+  paramsDerivsFile << "function [rp, gp, rpp, gpp, hp] = " << basename << "_static_params_derivs(y, x, params)" << endl
+                   << "%" << endl
+                   << "% Warning : this file is generated automatically by Dynare" << endl
+                   << "%           from model file (.mod)" << endl << endl;
+
+  deriv_node_temp_terms_t tef_terms;
+  writeModelLocalVariables(paramsDerivsFile, oMatlabStaticModel, tef_terms);
+
+  writeTemporaryTerms(params_derivs_temporary_terms, paramsDerivsFile, oMatlabStaticModel, tef_terms);
+
+  // Write parameter derivative
+  paramsDerivsFile << "rp = zeros(" << equation_number() << ", "
+                   << symbol_table.param_nbr() << ");" << endl;
+
+  for (first_derivatives_t::const_iterator it = residuals_params_derivatives.begin();
+       it != residuals_params_derivatives.end(); it++)
+    {
+      int eq = it->first.first;
+      int param = it->first.second;
+      expr_t d1 = it->second;
+
+      int param_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(param)) + 1;
+
+      paramsDerivsFile << "rp(" << eq+1 << ", " << param_col << ") = ";
+      d1->writeOutput(paramsDerivsFile, oMatlabStaticModel, params_derivs_temporary_terms, tef_terms);
+      paramsDerivsFile << ";" << endl;
+    }
+
+  // Write jacobian derivatives
+  paramsDerivsFile << "gp = zeros(" << equation_number() << ", " << symbol_table.endo_nbr() << ", "
+                   << symbol_table.param_nbr() << ");" << endl;
+
+  for (second_derivatives_t::const_iterator it = jacobian_params_derivatives.begin();
+       it != jacobian_params_derivatives.end(); it++)
+    {
+      int eq = it->first.first;
+      int var = it->first.second.first;
+      int param = it->first.second.second;
+      expr_t d2 = it->second;
+
+      int var_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(var)) + 1;
+      int param_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(param)) + 1;
+
+      paramsDerivsFile << "gp(" << eq+1 << ", " << var_col << ", " << param_col << ") = ";
+      d2->writeOutput(paramsDerivsFile, oMatlabStaticModel, params_derivs_temporary_terms, tef_terms);
+      paramsDerivsFile << ";" << endl;
+    }
+
+  // If nargout >= 3...
+  paramsDerivsFile << "if nargout >= 3" << endl;
+
+  // Write parameter second derivatives (only if nargout >= 3)
+  paramsDerivsFile << "rpp = zeros(" << residuals_params_second_derivatives.size()
+                   << ",4);" << endl;
+
+  int i = 1;
+  for (second_derivatives_t::const_iterator it = residuals_params_second_derivatives.begin();
+       it != residuals_params_second_derivatives.end(); ++it, i++)
+    {
+      int eq = it->first.first;
+      int param1 = it->first.second.first;
+      int param2 = it->first.second.second;
+      expr_t d2 = it->second;
+
+      int param1_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(param1)) + 1;
+      int param2_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(param2)) + 1;
+
+      paramsDerivsFile << "rpp(" << i << ",1)=" << eq+1 << ";" << endl
+                       << "rpp(" << i << ",2)=" << param1_col << ";" << endl
+                       << "rpp(" << i << ",3)=" << param2_col << ";" << endl
+                       << "rpp(" << i << ",4)=";
+      d2->writeOutput(paramsDerivsFile, oMatlabStaticModel, params_derivs_temporary_terms, tef_terms);
+      paramsDerivsFile << ";" << endl;
+    }
+
+  // Write jacobian second derivatives  (only if nargout >= 3)
+  paramsDerivsFile << "gpp = zeros(" << jacobian_params_second_derivatives.size()
+                   << ",5);" << endl;
+
+  i = 1;
+  for (third_derivatives_t::const_iterator it = jacobian_params_second_derivatives.begin();
+       it != jacobian_params_second_derivatives.end(); ++it, i++)
+    {
+      int eq = it->first.first;
+      int var = it->first.second.first;
+      int param1 = it->first.second.second.first;
+      int param2 = it->first.second.second.second;
+      expr_t d2 = it->second;
+
+      int var_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(var)) + 1;
+      int param1_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(param1)) + 1;
+      int param2_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(param2)) + 1;
+
+      paramsDerivsFile << "gpp(" << i << ",1)=" << eq+1 << ";" << endl
+                       << "gpp(" << i << ",2)=" << var_col << ";" << endl
+                       << "gpp(" << i << ",3)=" << param1_col << ";" << endl
+                       << "gpp(" << i << ",4)=" << param2_col << ";" << endl
+                       << "gpp(" << i << ",5)=";
+      d2->writeOutput(paramsDerivsFile, oMatlabStaticModel, params_derivs_temporary_terms, tef_terms);
+      paramsDerivsFile << ";" << endl;
+    }
+
+  // If nargout >= 5...
+  paramsDerivsFile << "end" << endl
+                   << "if nargout >= 5" << endl;
+
+  // Write hessian derivatives (only if nargout >= 5)
+  paramsDerivsFile << "hp = zeros(" << hessian_params_derivatives.size() << ",5);" << endl;
+
+  i = 1;
+  for (third_derivatives_t::const_iterator it = hessian_params_derivatives.begin();
+       it != hessian_params_derivatives.end(); ++it, i++)
+    {
+      int eq = it->first.first;
+      int var1 = it->first.second.first;
+      int var2 = it->first.second.second.first;
+      int param = it->first.second.second.second;
+      expr_t d2 = it->second;
+
+      int var1_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(var1)) + 1;
+      int var2_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(var2)) + 1;
+      int param_col = symbol_table.getTypeSpecificID(getSymbIDByDerivID(param)) + 1;
+
+      paramsDerivsFile << "hp(" << i << ",1)=" << eq+1 << ";" << endl
+                       << "hp(" << i << ",2)=" << var1_col << ";" << endl
+                       << "hp(" <<