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StaticModel.cc

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  • Forked from Dynare / preprocessor
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    StaticModel.cc 62.16 KiB
    /*
     * Copyright © 2003-2022 Dynare Team
     *
     * This file is part of Dynare.
     *
     * Dynare is free software: you can redistribute it and/or modify
     * it under the terms of the GNU General Public License as published by
     * the Free Software Foundation, either version 3 of the License, or
     * (at your option) any later version.
     *
     * Dynare is distributed in the hope that it will be useful,
     * but WITHOUT ANY WARRANTY; without even the implied warranty of
     * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     * GNU General Public License for more details.
     *
     * You should have received a copy of the GNU General Public License
     * along with Dynare.  If not, see <https://www.gnu.org/licenses/>.
     */
    
    #include <iostream>
    #include <cmath>
    #include <cstdlib>
    #include <cassert>
    #include <algorithm>
    #include <sstream>
    #include <numeric>
    
    #include "StaticModel.hh"
    #include "DynamicModel.hh"
    
    StaticModel::StaticModel(SymbolTable &symbol_table_arg,
                             NumericalConstants &num_constants_arg,
                             ExternalFunctionsTable &external_functions_table_arg) :
      ModelTree{symbol_table_arg, num_constants_arg, external_functions_table_arg}
    {
    }
    
    StaticModel::StaticModel(const StaticModel &m) :
      ModelTree{m}
    {
    }
    
    StaticModel &
    StaticModel::operator=(const StaticModel &m)
    {
      ModelTree::operator=(m);
    
      return *this;
    }
    
    StaticModel::StaticModel(const DynamicModel &m) :
      ModelTree{m.symbol_table, m.num_constants, m.external_functions_table}
    {
      // Convert model local variables (need to be done first)
      for (int it : m.local_variables_vector)
        AddLocalVariable(it, m.local_variables_table.find(it)->second->toStatic(*this));
    
      // Convert equations
      int static_only_index = 0;
      set<int> dynamic_equations = m.equation_tags.getDynamicEqns();
      for (int i = 0; i < static_cast<int>(m.equations.size()); i++)
        try
          {
            // If equation is dynamic, replace it by an equation marked [static]
            if (dynamic_equations.contains(i))
              {
                auto [static_only_equations,
                      static_only_equations_lineno,
                      static_only_equations_equation_tags] = m.getStaticOnlyEquationsInfo();
    
                addEquation(static_only_equations[static_only_index]->toStatic(*this),
                            static_only_equations_lineno[static_only_index],
                            static_only_equations_equation_tags.getTagsByEqn(static_only_index));
                static_only_index++;
              }
            else
              addEquation(m.equations[i]->toStatic(*this),
                          m.equations_lineno[i],
                          m.equation_tags.getTagsByEqn(i));
          }
        catch (DataTree::DivisionByZeroException)
          {
            cerr << "...division by zero error encountered when converting equation " << i << " to static" << endl;
            exit(EXIT_FAILURE);
          }
    
      // Convert auxiliary equations
      for (auto aux_eq : m.aux_equations)
        addAuxEquation(aux_eq->toStatic(*this));
    
      user_set_add_flags = m.user_set_add_flags;
      user_set_subst_flags = m.user_set_subst_flags;
      user_set_add_libs = m.user_set_add_libs;
      user_set_subst_libs = m.user_set_subst_libs;
      user_set_compiler = m.user_set_compiler;
    }
    
    void
    StaticModel::writeStaticPerBlockMFiles(const string &basename) const
    {
      temporary_terms_t temporary_terms; // Temp terms written so far
    
      for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
        {
          BlockSimulationType simulation_type = blocks[blk].simulation_type;
    
          string filename = packageDir(basename + ".block") + "/static_" + to_string(blk+1) + ".m";
          ofstream output{filename, ios::out | ios::binary};
          if (!output.is_open())
            {
              cerr << "ERROR: Can't open file " << filename << " for writing" << endl;
              exit(EXIT_FAILURE);
            }
          output << "%" << endl
                 << "% " << filename << " : Computes static version of one block" << endl
                 << "%" << endl
                 << "% Warning : this file is generated automatically by Dynare" << endl
                 << "%           from model file (.mod)" << endl << endl
                 << "%" << endl;
          if (simulation_type == BlockSimulationType::evaluateBackward
              || simulation_type == BlockSimulationType::evaluateForward)
            output << "function [y, T] = static_" << blk+1 << "(y, x, params, T)" << endl;
          else
            output << "function [residual, y, T, g1] = static_" << blk+1 << "(y, x, params, T)" << endl;
    
          output << "  % ////////////////////////////////////////////////////////////////////////" << endl
                 << "  % //" << "                     Block "s.substr(static_cast<int>(log10(blk + 1))) << blk+1
                 << "                                        //" << endl
                 << "  % //                     Simulation type "
                 << BlockSim(simulation_type) << "  //" << endl
                 << "  % ////////////////////////////////////////////////////////////////////////" << endl;
    
          if (simulation_type != BlockSimulationType::evaluateBackward
              && simulation_type != BlockSimulationType::evaluateForward)
            output << "  residual=zeros(" << blocks[blk].mfs_size << ",1);" << endl
                   << "  g1_i=zeros(" << blocks_derivatives[blk].size() << ",1);" << endl
                   << "  g1_j=zeros(" << blocks_derivatives[blk].size() << ",1);" << endl
                   << "  g1_v=zeros(" << blocks_derivatives[blk].size() << ",1);" << endl
                   << endl;
    
          writeStaticPerBlockHelper<ExprNodeOutputType::matlabStaticModel>(blk, output, temporary_terms);
    
          if (simulation_type != BlockSimulationType::evaluateBackward
              && simulation_type != BlockSimulationType::evaluateForward)
            output << endl
                   << "  g1=sparse(g1_i, g1_j, g1_v, "  << blocks[blk].mfs_size << "," << blocks[blk].mfs_size << ");" << endl;
    
          output << "end" << endl;
          output.close();
        }
    }
    
    void
    StaticModel::writeStaticPerBlockCFiles(const string &basename) const
    {
      temporary_terms_t temporary_terms; // Temp terms written so far
    
      for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
        {
          BlockSimulationType simulation_type = blocks[blk].simulation_type;
    
          string filename = basename + "/model/src/static_" + to_string(blk+1) + ".c";
          ofstream output{filename, ios::out | ios::binary};
          if (!output.is_open())
            {
              cerr << "ERROR: Can't open file " << filename << " for writing" << endl;
              exit(EXIT_FAILURE);
            }
          output << "/* Block " << blk+1 << endl
                 << "   " << BlockSim(simulation_type) << " */" << endl
                 << endl
                 << "#include <math.h>" << endl
                 << "#include <stdlib.h>" << endl
                 << R"(#include "mex.h")" << endl
                 << endl;
    
          // Write function definition if BinaryOpcode::powerDeriv is used
          writePowerDerivHeader(output);
    
          output << endl;
    
          if (simulation_type == BlockSimulationType::evaluateBackward
              || simulation_type == BlockSimulationType::evaluateForward)
            output << "void static_" << blk+1 << "(double *restrict y, const double *restrict x, const double *restrict params, double *restrict T)" << endl;
          else
            output << "void static_" << blk+1 << "(double *restrict y, const double *restrict x, const double *restrict params, double *restrict T, double *restrict residual, double *restrict g1_i, double *restrict g1_j, double *restrict g1_v)" << endl;
          output << '{' << endl;
    
          writeStaticPerBlockHelper<ExprNodeOutputType::CStaticModel>(blk, output, temporary_terms);
    
          output << '}' << endl
                 << endl;
    
          ostringstream header;
          if (simulation_type == BlockSimulationType::evaluateBackward
              || simulation_type == BlockSimulationType::evaluateForward)
            {
              header << "void static_" << blk+1 << "_mx(mxArray *y, const mxArray *x, const mxArray *params, mxArray *T)";
              output << header.str() << endl
                     << '{' << endl
                     << "  static_" << blk+1 << "(mxGetPr(y), mxGetPr(x), mxGetPr(params), mxGetPr(T));" << endl
                     << '}' << endl;
            }
          else
            {
              header << "void static_" << blk+1 << "_mx(mxArray *y, const mxArray *x, const mxArray *params, mxArray *T, mxArray **residual, mxArray **g1)";
              output << header.str() << endl
                     << '{' << endl
                     << "  *residual = mxCreateDoubleMatrix(" << blocks[blk].mfs_size << ",1,mxREAL);" << endl
                     << "  mxArray *g1_i = mxCreateDoubleMatrix(" << blocks_derivatives[blk].size() << ",1,mxREAL);" << endl
                     << "  mxArray *g1_j = mxCreateDoubleMatrix(" << blocks_derivatives[blk].size() << ",1,mxREAL);" << endl
                     << "  mxArray *g1_v = mxCreateDoubleMatrix(" << blocks_derivatives[blk].size() << ",1,mxREAL);" << endl
                     << "  static_" << blk+1 << "(mxGetPr(y), mxGetPr(x), mxGetPr(params), mxGetPr(T), mxGetPr(*residual), mxGetPr(g1_i), mxGetPr(g1_j), mxGetPr(g1_v));" << endl
                     << "  mxArray *plhs[1];" << endl
                     << "  mxArray *m = mxCreateDoubleScalar(" << blocks[blk].mfs_size << ");" << endl
                     << "  mxArray *n = mxCreateDoubleScalar(" << blocks[blk].mfs_size << ");" << endl
                     << "  mxArray *prhs[5] = { g1_i, g1_j, g1_v, m, n };" << endl
                     << R"(  mexCallMATLAB(1, plhs, 5, prhs, "sparse");)" << endl
                     << "  *g1 = plhs[0];" << endl
                     << "  mxDestroyArray(g1_i);" << endl
                     << "  mxDestroyArray(g1_j);" << endl
                     << "  mxDestroyArray(g1_v);" << endl
                     << "  mxDestroyArray(m);" << endl
                     << "  mxDestroyArray(n);" << endl
                     << '}' << endl;
            }
    
          output.close();
    
          filename = basename + "/model/src/static_" + to_string(blk+1) + ".h";
          ofstream header_output{filename, ios::out | ios::binary};
          if (!header_output.is_open())
            {
              cerr << "ERROR: Can't open file " << filename << " for writing" << endl;
              exit(EXIT_FAILURE);
            }
          header_output << header.str() << ';' << endl;
          header_output.close();
        }
    }
    
    void
    StaticModel::writeStaticBytecode(const string &basename) const
    {
      // First write the .bin file
      int u_count_int { writeBytecodeBinFile(basename + "/model/bytecode/static.bin", false) };
    
      BytecodeWriter code_file {basename + "/model/bytecode/static.cod"};
      vector<int> eq_idx(equations.size());
      iota(eq_idx.begin(), eq_idx.end(), 0);
      vector<int> endo_idx(symbol_table.endo_nbr());
      iota(endo_idx.begin(), endo_idx.end(), 0);
    
      // Declare temporary terms and the (single) block
      code_file << FDIMST_{static_cast<int>(temporary_terms_derivatives[0].size()
                                            + temporary_terms_derivatives[1].size())}
                << FBEGINBLOCK_{symbol_table.endo_nbr(),
                                BlockSimulationType::solveForwardComplete,
                                0,
                                symbol_table.endo_nbr(),
                                endo_idx,
                                eq_idx,
                                false,
                                symbol_table.endo_nbr(),
                                0,
                                0,
                                u_count_int,
                                symbol_table.endo_nbr()};
    
      writeBytecodeHelper<false>(code_file);
    }
    
    void
    StaticModel::writeStaticBlockBytecode(const string &basename) const
    {
      BytecodeWriter code_file {basename + "/model/bytecode/static.cod"};
    
      const string bin_filename {basename + "/model/bytecode/static.bin"};
      ofstream bin_file {bin_filename, ios::out | ios::binary};
      if (!bin_file.is_open())
        {
          cerr << R"(Error : Can't open file ")" << bin_filename << R"(" for writing)" << endl;
          exit(EXIT_FAILURE);
        }
    
      // Temporary variables declaration
      code_file << FDIMST_{static_cast<int>(blocks_temporary_terms_idxs.size())};
    
      for (int block {0}; block < static_cast<int>(blocks.size()); block++)
        {
          const BlockSimulationType simulation_type {blocks[block].simulation_type};
          const int block_size {blocks[block].size};
    
          const int u_count {simulation_type == BlockSimulationType::solveBackwardComplete
                             || simulation_type == BlockSimulationType::solveForwardComplete
                             ? writeBlockBytecodeBinFile(bin_file, block)
                             : 0};
    
          code_file << FBEGINBLOCK_{blocks[block].mfs_size,
                                    simulation_type,
                                    blocks[block].first_equation,
                                    block_size,
                                    endo_idx_block2orig,
                                    eq_idx_block2orig,
                                    blocks[block].linear,
                                    symbol_table.endo_nbr(),
                                    0,
                                    0,
                                    u_count,
                                    block_size};
    
          writeBlockBytecodeHelper<false>(code_file, block);
        }
      code_file << FEND_{};
    }
    
    void
    StaticModel::computingPass(int derivsOrder, int paramsDerivsOrder, const eval_context_t &eval_context, bool no_tmp_terms, bool block)
    {
      initializeVariablesAndEquations();
    
      vector<BinaryOpNode *> neweqs;
      for (int eq = 0; eq < static_cast<int>(equations.size() - aux_equations.size()); eq++)
        {
          expr_t eq_tmp = equations[eq]->substituteStaticAuxiliaryVariable();
          neweqs.push_back(dynamic_cast<BinaryOpNode *>(eq_tmp->toStatic(*this)));
        }
    
      for (auto &aux_equation : aux_equations)
        {
          expr_t eq_tmp = aux_equation->substituteStaticAuxiliaryDefinition();
          neweqs.push_back(dynamic_cast<BinaryOpNode *>(eq_tmp->toStatic(*this)));
        }
    
      equations.clear();
      copy(neweqs.begin(), neweqs.end(), back_inserter(equations));
    
      /* In both MATLAB and Julia, tensors for higher-order derivatives are stored
         in matrices whose columns correspond to variable multi-indices. Since we
         currently are limited to 32-bit signed integers (hence 31 bits) for matrix
         indices, check that we will not overflow (see #89). Note that such a check
         is not needed for parameter derivatives, since tensors for those are not
         stored as matrices. This check is implemented at this place for symmetry
         with DynamicModel::computingPass(). */
      if (log2(symbol_table.endo_nbr())*derivsOrder >= numeric_limits<int>::digits)
        {
          cerr << "ERROR: The static derivatives matrix is too large. Please decrease the approximation order." << endl;
          exit(EXIT_FAILURE);
        }
    
      // Compute derivatives w.r. to all endogenous
      set<int> vars;
      for (int i = 0; i < symbol_table.endo_nbr(); i++)
        {
          int id = symbol_table.getID(SymbolType::endogenous, i);
          vars.insert(getDerivID(id, 0));
        }
    
      // Launch computations
      cout << "Computing static model derivatives (order " << derivsOrder << ")." << endl;
    
      computeDerivatives(derivsOrder, vars);
    
      if (paramsDerivsOrder > 0)
        {
          cout << "Computing static model derivatives w.r.t. parameters (order " << paramsDerivsOrder << ")." << endl;
          computeParamsDerivatives(paramsDerivsOrder);
        }
    
      computeTemporaryTerms(true, no_tmp_terms);
    
      /* Must be called after computeTemporaryTerms(), because it depends on
         temporary_terms_mlv to be filled */
      if (paramsDerivsOrder > 0 && !no_tmp_terms)
        computeParamsDerivativesTemporaryTerms();
    
      if (!computingPassBlock(eval_context, no_tmp_terms) && block)
        {
          cerr << "ERROR: Block decomposition requested but failed. If your model does not have a steady state, you may want to try the 'no_static' option of the 'model' block." << endl;
          exit(EXIT_FAILURE);
        }
    }
    
    bool
    StaticModel::computingPassBlock(const eval_context_t &eval_context, bool no_tmp_terms)
    {
      auto contemporaneous_jacobian = evaluateAndReduceJacobian(eval_context);
      if (!computeNonSingularNormalization(contemporaneous_jacobian, false))
        return false;
      auto [prologue, epilogue] = computePrologueAndEpilogue();
      auto first_order_endo_derivatives = collectFirstOrderDerivativesEndogenous();
      equationTypeDetermination(first_order_endo_derivatives, mfs);
      cout << "Finding the optimal block decomposition of the static model..." << endl;
      computeBlockDecomposition(prologue, epilogue);
      reduceBlockDecomposition();
      printBlockDecomposition();
      computeChainRuleJacobian();
      determineLinearBlocks();
      if (!no_tmp_terms)
        computeBlockTemporaryTerms();
      return true;
    }
    
    void
    StaticModel::writeStaticMFile(const string &basename) const
    {
      auto [d_output, tt_output] = writeModelFileHelper<ExprNodeOutputType::matlabStaticModel>();
    
      ostringstream init_output, end_output;
      init_output << "residual = zeros(" << equations.size() << ", 1);";
      end_output << "if ~isreal(residual)" << endl
                 << "  residual = real(residual)+imag(residual).^2;" << endl
                 << "end";
      writeStaticMFileHelper(basename, "static_resid", "residual", "static_resid_tt",
                             temporary_terms_mlv.size() + temporary_terms_derivatives[0].size(),
                             "", init_output, end_output,
                             d_output[0], tt_output[0]);
    
      init_output.str("");
      end_output.str("");
      init_output << "g1 = zeros(" << equations.size() << ", " << symbol_table.endo_nbr() << ");";
      end_output << "if ~isreal(g1)" << endl
                 << "    g1 = real(g1)+2*imag(g1);" << endl
                 << "end";
      writeStaticMFileHelper(basename, "static_g1", "g1", "static_g1_tt",
                             temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() + temporary_terms_derivatives[1].size(),
                             "static_resid_tt",
                             init_output, end_output,
                             d_output[1], tt_output[1]);
      writeStaticMWrapperFunction(basename, "g1");
    
      // For order ≥ 2
      int ncols{symbol_table.endo_nbr()};
      int ntt{static_cast<int>(temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() + temporary_terms_derivatives[1].size())};
      for (size_t i{2}; i < derivatives.size(); i++)
        {
          ncols *= symbol_table.endo_nbr();
          ntt += temporary_terms_derivatives[i].size();
          string gname{"g" + to_string(i)};
          string gprevname{"g" + to_string(i-1)};
    
          init_output.str("");
          end_output.str("");
          if (derivatives[i].size())
            {
              init_output << gname << "_i = zeros(" << NNZDerivatives[i] << ",1);" << endl
                          << gname << "_j = zeros(" << NNZDerivatives[i] << ",1);" << endl
                          << gname << "_v = zeros(" << NNZDerivatives[i] << ",1);" << endl;
              end_output << gname << " = sparse("
                         << gname << "_i," << gname << "_j," << gname << "_v,"
                         << equations.size() << "," << ncols << ");";
            }
          else
            init_output << gname << " = sparse([],[],[]," << equations.size() << "," << ncols << ");";
          writeStaticMFileHelper(basename, "static_" + gname, gname,
                                 "static_" + gname + "_tt",
                                 ntt,
                                 "static_" + gprevname + "_tt",
                                 init_output, end_output,
                                 d_output[i], tt_output[i]);
          if (i <= 3)
            writeStaticMWrapperFunction(basename, gname);
        }
    
      writeStaticMCompatFile(basename);
    }
    
    void
    StaticModel::writeStaticMWrapperFunction(const string &basename, const string &ending) const
    {
      string name;
      if (ending == "g1")
        name = "static_resid_g1";
      else if (ending == "g2")
        name = "static_resid_g1_g2";
      else if (ending == "g3")
        name = "static_resid_g1_g2_g3";
    
      string filename = packageDir(basename) + "/" + name + ".m";
      ofstream output{filename, ios::out | ios::binary};
      if (!output.is_open())
        {
          cerr << "Error: Can't open file " << filename << " for writing" << endl;
          exit(EXIT_FAILURE);
        }
    
      if (ending == "g1")
        output << "function [residual, g1] = " << name << "(T, y, x, params, T_flag)" << endl
               << "% function [residual, g1] = " << name << "(T, y, x, params, T_flag)" << endl;
      else if (ending == "g2")
        output << "function [residual, g1, g2] = " << name << "(T, y, x, params, T_flag)" << endl
               << "% function [residual, g1, g2] = " << name << "(T, y, x, params, T_flag)" << endl;
      else if (ending == "g3")
        output << "function [residual, g1, g2, g3] = " << name << "(T, y, x, params, T_flag)" << endl
               << "% function [residual, g1, g2, g3] = " << name << "(T, y, x, params, T_flag)" << endl;
    
      output << "%" << endl
             << "% Wrapper function automatically created by Dynare" << endl
             << "%" << endl
             << endl
             << "    if T_flag" << endl
             << "        T = " << basename << ".static_" << ending << "_tt(T, y, x, params);" << endl
             << "    end" << endl;
    
      if (ending == "g1")
        output << "    residual = " << basename << ".static_resid(T, y, x, params, false);" << endl
               << "    g1       = " << basename << ".static_g1(T, y, x, params, false);" << endl;
      else if (ending == "g2")
        output << "    [residual, g1] = " << basename << ".static_resid_g1(T, y, x, params, false);" << endl
               << "    g2       = " << basename << ".static_g2(T, y, x, params, false);" << endl;
      else if (ending == "g3")
        output << "    [residual, g1, g2] = " << basename << ".static_resid_g1_g2(T, y, x, params, false);" << endl
               << "    g3       = " << basename << ".static_g3(T, y, x, params, false);" << endl;
    
      output << endl << "end" << endl;
      output.close();
    }
    
    void
    StaticModel::writeStaticMFileHelper(const string &basename,
                                        const string &name, const string &retvalname,
                                        const string &name_tt, size_t ttlen,
                                        const string &previous_tt_name,
                                        const ostringstream &init_s, const ostringstream &end_s,
                                        const ostringstream &s, const ostringstream &s_tt) const
    {
      string filename = packageDir(basename) + "/" + name_tt + ".m";
      ofstream output{filename, ios::out | ios::binary};
      if (!output.is_open())
        {
          cerr << "Error: Can't open file " << filename << " for writing" << endl;
          exit(EXIT_FAILURE);
        }
    
      output << "function T = " << name_tt << "(T, y, x, params)" << endl
             << "% function T = " << name_tt << "(T, y, x, params)" << endl
             << "%" << endl
             << "% File created by Dynare Preprocessor from .mod file" << endl
             << "%" << endl
             << "% Inputs:" << endl
             << "%   T         [#temp variables by 1]  double   vector of temporary terms to be filled by function" << endl
             << "%   y         [M_.endo_nbr by 1]      double   vector of endogenous variables in declaration order" << endl
             << "%   x         [M_.exo_nbr by 1]       double   vector of exogenous variables in declaration order" << endl
             << "%   params    [M_.param_nbr by 1]     double   vector of parameter values in declaration order" << endl
             << "%" << endl
             << "% Output:" << endl
             << "%   T         [#temp variables by 1]  double   vector of temporary terms" << endl
             << "%" << endl << endl
             << "assert(length(T) >= " << ttlen << ");" << endl
             << endl;
    
      if (!previous_tt_name.empty())
        output << "T = " << basename << "." << previous_tt_name << "(T, y, x, params);" << endl << endl;
    
      output << s_tt.str() << endl
             << "end" << endl;
      output.close();
    
      filename = packageDir(basename) + "/" + name + ".m";
      output.open(filename, ios::out | ios::binary);
      if (!output.is_open())
        {
          cerr << "Error: Can't open file " << filename << " for writing" << endl;
          exit(EXIT_FAILURE);
        }
    
      output << "function " << retvalname << " = " << name << "(T, y, x, params, T_flag)" << endl
             << "% function " << retvalname << " = " << name << "(T, y, x, params, T_flag)" << endl
             << "%" << endl
             << "% File created by Dynare Preprocessor from .mod file" << endl
             << "%" << endl
             << "% Inputs:" << endl
             << "%   T         [#temp variables by 1]  double   vector of temporary terms to be filled by function" << endl
             << "%   y         [M_.endo_nbr by 1]      double   vector of endogenous variables in declaration order" << endl
             << "%   x         [M_.exo_nbr by 1]       double   vector of exogenous variables in declaration order" << endl
             << "%   params    [M_.param_nbr by 1]     double   vector of parameter values in declaration order" << endl
             << "%                                              to evaluate the model" << endl
             << "%   T_flag    boolean                 boolean  flag saying whether or not to calculate temporary terms" << endl
             << "%" << endl
             << "% Output:" << endl
             << "%   " << retvalname << endl
             << "%" << endl << endl;
    
      if (!name_tt.empty())
        output << "if T_flag" << endl
               << "    T = " << basename << "."  << name_tt << "(T, y, x, params);" << endl
               << "end" << endl;
    
      output << init_s.str() << endl
             << s.str()
             << end_s.str() << endl
             << "end" << endl;
      output.close();
    }
    
    void
    StaticModel::writeStaticMCompatFile(const string &basename) const
    {
      string filename = packageDir(basename) + "/static.m";
      ofstream output{filename, ios::out | ios::binary};
      if (!output.is_open())
        {
          cerr << "Error: Can't open file " << filename << " for writing" << endl;
          exit(EXIT_FAILURE);
        }
      int ntt = temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() + temporary_terms_derivatives[1].size() + temporary_terms_derivatives[2].size() + temporary_terms_derivatives[3].size();
    
      output << "function [residual, g1, g2, g3] = static(y, x, params)" << endl
             << "    T = NaN(" << ntt << ", 1);" << endl
             << "    if nargout <= 1" << endl
             << "        residual = " << basename << ".static_resid(T, y, x, params, true);" << endl
             << "    elseif nargout == 2" << endl
             << "        [residual, g1] = " << basename << ".static_resid_g1(T, y, x, params, true);" << endl
             << "    elseif nargout == 3" << endl
             << "        [residual, g1, g2] = " << basename << ".static_resid_g1_g2(T, y, x, params, true);" << endl
             << "    else" << endl
             << "        [residual, g1, g2, g3] = " << basename << ".static_resid_g1_g2_g3(T, y, x, params, true);" << endl
             << "    end" << endl
             << "end" << endl;
    
      output.close();
    }
    
    void
    StaticModel::writeStaticCFile(const string &basename) const
    {
      // Writing comments and function definition command
      string filename{basename + "/model/src/static.c"};
    
      int ntt{static_cast<int>(temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() + temporary_terms_derivatives[1].size() + temporary_terms_derivatives[2].size() + temporary_terms_derivatives[3].size())};
    
      ofstream output{filename, ios::out | ios::binary};
      if (!output.is_open())
        {
          cerr << "ERROR: Can't open file " << filename << " for writing" << endl;
          exit(EXIT_FAILURE);
        }
    
      output << "/*" << endl
             << " * " << filename << " : Computes static model for Dynare" << endl
             << " *" << endl
             << " * Warning : this file is generated automatically by Dynare" << endl
             << " *           from model file (.mod)" << endl << endl
             << " */" << endl
             << endl
             << "#include <math.h>" << endl
             << "#include <stdlib.h>" << endl
             << R"(#include "mex.h")" << endl
             << endl;
    
      // Write function definition if BinaryOpcode::powerDeriv is used
      writePowerDeriv(output);
    
      output << endl;
    
      auto [d_output, tt_output] = writeModelFileHelper<ExprNodeOutputType::CStaticModel>();
    
      for (size_t i = 0; i < d_output.size(); i++)
        {
          string funcname{i == 0 ? "resid" : "g" + to_string(i)};
          output << "void static_" << funcname << "_tt(const double *restrict y, const double *restrict x, const double *restrict params, double *restrict T)" << endl
                 << "{" << endl
                 << tt_output[i].str()
                 << "}" << endl
                 << endl
                 << "void static_" << funcname << "(const double *restrict y, const double *restrict x, const double *restrict params, const double *restrict T, ";
          if (i == 0)
            output << "double *restrict residual";
          else if (i == 1)
            output << "double *restrict g1";
          else
            output << "double *restrict " << funcname << "_i, double *restrict " << funcname << "_j, double *restrict " << funcname << "_v";
          output << ")" << endl
                       << "{" << endl;
          if (i == 0)
            output << "  double lhs, rhs;" << endl;
          output << d_output[i].str()
                 << "}" << endl
                 << endl;
        }
    
      output << "void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])" << endl
             << "{" << endl
             << "  if (nrhs > 3)" << endl
             << R"(    mexErrMsgTxt("Accepts at most 3 output arguments");)" << endl
             << "  if (nrhs != 3)" << endl
             << R"(    mexErrMsgTxt("Requires exactly 3 input arguments");)" << endl
             << "  double *y = mxGetPr(prhs[0]);" << endl
             << "  double *x = mxGetPr(prhs[1]);" << endl
             << "  double *params = mxGetPr(prhs[2]);" << endl
             << endl
             << "  double *T = (double *) malloc(sizeof(double)*" << ntt << ");" << endl
             << endl
             << "  if (nlhs >= 1)" << endl
             << "    {" << endl
             << "      plhs[0] = mxCreateDoubleMatrix(" << equations.size() << ",1, mxREAL);" << endl
             << "      double *residual = mxGetPr(plhs[0]);" << endl
             << "      static_resid_tt(y, x, params, T);" << endl
             << "      static_resid(y, x, params, T, residual);" << endl
             << "    }" << endl
             << endl
             << "  if (nlhs >= 2)" << endl
             << "    {" << endl
             << "      plhs[1] = mxCreateDoubleMatrix(" << equations.size() << ", " << symbol_table.endo_nbr() << ", mxREAL);" << endl
             << "      double *g1 = mxGetPr(plhs[1]);" << endl
             << "      static_g1_tt(y, x, params, T);" << endl
             << "      static_g1(y, x, params, T, g1);" << endl
             << "    }" << endl
             << endl
             << "  if (nlhs >= 3)" << endl
             << "    {" << endl
             << "      mxArray *g2_i = mxCreateDoubleMatrix(" << NNZDerivatives[2] << ", " << 1 << ", mxREAL);" << endl
             << "      mxArray *g2_j = mxCreateDoubleMatrix(" << NNZDerivatives[2] << ", " << 1 << ", mxREAL);" << endl
             << "      mxArray *g2_v = mxCreateDoubleMatrix(" << NNZDerivatives[2] << ", " << 1 << ", mxREAL);" << endl
             << "      static_g2_tt(y, x, params, T);" << endl
             << "      static_g2(y, x, params, T, mxGetPr(g2_i), mxGetPr(g2_j), mxGetPr(g2_v));" << endl
             << "      mxArray *m = mxCreateDoubleScalar(" << equations.size() << ");" << endl
             << "      mxArray *n = mxCreateDoubleScalar(" << symbol_table.endo_nbr()*symbol_table.endo_nbr() << ");" << endl
             << "      mxArray *plhs_sparse[1], *prhs_sparse[5] = { g2_i, g2_j, g2_v, m, n };" << endl
             << R"(      mexCallMATLAB(1, plhs_sparse, 5, prhs_sparse, "sparse");)" << endl
             << "      plhs[2] = plhs_sparse[0];" << endl
             << "      mxDestroyArray(g2_i);" << endl
             << "      mxDestroyArray(g2_j);" << endl
             << "      mxDestroyArray(g2_v);" << endl
             << "      mxDestroyArray(m);" << endl
             << "      mxDestroyArray(n);" << endl
             << "    }" << endl
             << endl
             << "  free(T);" << endl
             << "}" << endl;
    
      output.close();
    }
    
    void
    StaticModel::writeStaticJuliaFile(const string &basename) const
    {
      auto [d_output, tt_output] = writeModelFileHelper<ExprNodeOutputType::juliaStaticModel>();
    
      stringstream output;
      output << "module " << basename << "Static" << endl
             << "#" << endl
             << "# NB: this file was automatically generated by Dynare" << endl
             << "#     from " << basename << ".mod" << endl
             << "#" << endl
             << "using StatsFuns" << endl << endl
             << "export tmp_nbr, static!, staticResid!, staticG1!, staticG2!, staticG3!" << endl << endl
             << "#=" << endl
             << "# The comments below apply to all functions contained in this module #" << endl
             << "  NB: The arguments contained on the first line of the function" << endl
             << "      definition are those that are modified in place" << endl << endl
             << "## Exported Functions ##" << endl
             << "  static!      : Wrapper function; computes residuals, Jacobian, Hessian," << endl
             << "                 and third order derivatives matroces depending on the arguments provided" << endl
             << "  staticResid! : Computes the static model residuals" << endl
             << "  staticG1!    : Computes the static model Jacobian" << endl
             << "  staticG2!    : Computes the static model Hessian" << endl
             << "  staticG3!    : Computes the static model third derivatives" << endl << endl
             << "## Exported Variables ##" << endl
             << "  tmp_nbr      : Vector{Int}(4) respectively the number of temporary variables" << endl
             << "                 for the residuals, g1, g2 and g3." << endl << endl
             << "## Local Functions ##" << endl
             << "  staticResidTT! : Computes the static model temporary terms for the residuals" << endl
             << "  staticG1TT!    : Computes the static model temporary terms for the Jacobian" << endl
             << "  staticG2TT!    : Computes the static model temporary terms for the Hessian" << endl
             << "  staticG3TT!    : Computes the static model temporary terms for the third derivatives" << endl << endl
             << "## Function Arguments ##" << endl
             << "  T        : Vector{<: Real}(num_temp_terms) temporary terms" << endl
             << "  y        : Vector{<: Real}(model_.endo_nbr) endogenous variables in declaration order" << endl
             << "  x        : Vector{<: Real}(model_.exo_nbr) exogenous variables in declaration order" << endl
             << "  params   : Vector{<: Real}(model_.param) parameter values in declaration order" << endl
             << "  residual : Vector{<: Real}(model_.eq_nbr) residuals of the static model equations" << endl
             << "             in order of declaration of the equations. Dynare may prepend auxiliary equations," << endl
             << "             see model.aux_vars" << endl
             << "  g1       : Matrix{<: Real}(model.eq_nbr,model_.endo_nbr) Jacobian matrix of the static model equations" << endl
             << "             The columns and rows respectively correspond to the variables in declaration order and the" << endl
             << "             equations in order of declaration" << endl
             << "  g2       : spzeros(model.eq_nbr, model_.endo^2) Hessian matrix of the static model equations" << endl
             << "             The columns and rows respectively correspond to the variables in declaration order and the" << endl
             << "             equations in order of declaration" << endl
             << "  g3       : spzeros(model.eq_nbr, model_.endo^3) Third order derivatives matrix of the static model equations" << endl
             << "             The columns and rows respectively correspond to the variables in declaration order and the" << endl
             << "             equations in order of declaration" << endl << endl
             << "## Remarks ##" << endl
             << "  [1] The size of `T`, ie the value of `num_temp_terms`, depends on the version of the static model called. The number of temporary variables" << endl
             << "      used for the different returned objects (residuals, jacobian, hessian or third order derivatives) is given by the elements in `tmp_nbr`" << endl
             << "      exported vector. The first element is the number of temporaries used for the computation of the residuals, the second element is the" << endl
             << "      number of temporaries used for the evaluation of the jacobian matrix, etc. If one calls the version of the static model computing the" << endl
             << "      residuals, and the jacobian and hessian matrices, then `T` must have at least `sum(tmp_nbr[1:3])` elements." << endl
             << "=#" << endl << endl;
    
      // Write the number of temporary terms
      output << "tmp_nbr = zeros(Int,4)" << endl
             << "tmp_nbr[1] = " << temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() << "# Number of temporary terms for the residuals" << endl
             << "tmp_nbr[2] = " << temporary_terms_derivatives[1].size() << "# Number of temporary terms for g1 (jacobian)" << endl
             << "tmp_nbr[3] = " << temporary_terms_derivatives[2].size() << "# Number of temporary terms for g2 (hessian)" << endl
             << "tmp_nbr[4] = " << temporary_terms_derivatives[3].size() << "# Number of temporary terms for g3 (third order derivates)" << endl << endl;
    
      // staticResidTT!
      output << "function staticResidTT!(T::Vector{<: Real}," << endl
             << "                        y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real})" << endl
             << "    @assert length(T) >= " << temporary_terms_mlv.size() + temporary_terms_derivatives[0].size()  << endl
             << "    @inbounds begin" << endl
             << tt_output[0].str()
    	 << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // static!
      output << "function staticResid!(T::Vector{<: Real}, residual::Vector{<: Real}," << endl
             << "                      y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real}, T0_flag::Bool)" << endl
             << "    @assert length(y) == " << symbol_table.endo_nbr() << endl
             << "    @assert length(x) == " << symbol_table.exo_nbr() << endl
             << "    @assert length(params) == " << symbol_table.param_nbr() << endl
             << "    @assert length(residual) == " << equations.size() << endl
             << "    if T0_flag" << endl
             << "        staticResidTT!(T, y, x, params)" << endl
             << "    end" << endl
             << "    @inbounds begin" << endl
             << d_output[0].str()
    	 << "    end" << endl
             << "    if ~isreal(residual)" << endl
             << "        residual = real(residual)+imag(residual).^2;" << endl
             << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // staticG1TT!
      output << "function staticG1TT!(T::Vector{<: Real}," << endl
             << "                     y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real}, T0_flag::Bool)" << endl
             << "    if T0_flag" << endl
             << "        staticResidTT!(T, y, x, params)" << endl
             << "    end" << endl
             << "    @inbounds begin" << endl
             << tt_output[1].str()
    	 << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // staticG1!
      output << "function staticG1!(T::Vector{<: Real}, g1::Matrix{<: Real}," << endl
             << "                   y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real}, T1_flag::Bool, T0_flag::Bool)" << endl
             << "    @assert length(T) >= "
             << temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() + temporary_terms_derivatives[1].size() << endl
             << "    @assert size(g1) == (" << equations.size() << ", " << symbol_table.endo_nbr() << ")" << endl
             << "    @assert length(y) == " << symbol_table.endo_nbr() << endl
             << "    @assert length(x) == " << symbol_table.exo_nbr() << endl
             << "    @assert length(params) == " << symbol_table.param_nbr() << endl
             << "    if T1_flag" << endl
             << "        staticG1TT!(T, y, x, params, T0_flag)" << endl
             << "    end" << endl
             << "    fill!(g1, 0.0)" << endl
             << "     @inbounds begin" << endl
             << d_output[1].str()
    	 << "    end" << endl
             << "    if ~isreal(g1)" << endl
             << "        g1 = real(g1)+2*imag(g1);" << endl
             << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // staticG2TT!
      output << "function staticG2TT!(T::Vector{<: Real}," << endl
             << "                     y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real}, T1_flag::Bool, T0_flag::Bool)" << endl
             << "    if T1_flag" << endl
             << "        staticG1TT!(T, y, x, params, TO_flag)" << endl
             << "    end" << endl
             << "    @inbounds begin" << endl
             << tt_output[2].str()
    	 << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // staticG2!
      int hessianColsNbr{symbol_table.endo_nbr() * symbol_table.endo_nbr()};
      output << "function staticG2!(T::Vector{<: Real}, g2::Matrix{<: Real}," << endl
             << "                   y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real}, T2_flag::Bool, T1_flag::Bool, T0_flag::Bool)" << endl
             << "    @assert length(T) >= "
             << temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() + temporary_terms_derivatives[1].size() + temporary_terms_derivatives[2].size() << endl
             << "    @assert size(g2) == (" << equations.size() << ", " << hessianColsNbr << ")" << endl
             << "    @assert length(y) == " << symbol_table.endo_nbr() << endl
             << "    @assert length(x) == " << symbol_table.exo_nbr() << endl
             << "    @assert length(params) == " << symbol_table.param_nbr() << endl
             << "    if T2_flag" << endl
             << "        staticG2TT!(T, y, x, params, T1_flag, T0_flag)" << endl
             << "    end" << endl
             << "    fill!(g2, 0.0)" << endl
             << "    @inbounds begin" << endl
             << d_output[2].str()
    	 << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // staticG3TT!
      output << "function staticG3TT!(T::Vector{<: Real}," << endl
             << "                     y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real}, T2_flag::Bool, T1_flag::Bool, T0_flag::Bool)" << endl
             << "    if T2_flag" << endl
             << "        staticG2TT!(T, y, x, params, T1_flag, T0_flag)" << endl
             << "    end" << endl
             << "    @inbounds begin" << endl
             << tt_output[3].str()
    	 << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // staticG3!
      int ncols{hessianColsNbr * symbol_table.endo_nbr()};
      output << "function staticG3!(T::Vector{<: Real}, g3::Matrix{<: Real}," << endl
             << "                   y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real}, T3_flag::Bool, T2_flag::Bool, T1_flag::Bool, T0_flag::Bool)" << endl
             << "    @assert length(T) >= "
             << temporary_terms_mlv.size() + temporary_terms_derivatives[0].size() + temporary_terms_derivatives[1].size() + temporary_terms_derivatives[2].size() + temporary_terms_derivatives[3].size() << endl
             << "    @assert size(g3) == (" << equations.size() << ", " << ncols << ")" << endl
             << "    @assert length(y) == " << symbol_table.endo_nbr() << endl
             << "    @assert length(x) == " << symbol_table.exo_nbr() << endl
             << "    @assert length(params) == " << symbol_table.param_nbr() << endl
             << "    if T3_flag" << endl
             << "        staticG3TT!(T, y, x, params, T2_flag, T1_flag, T0_flag)" << endl
             << "    end" << endl
             << "    fill!(g3, 0.0)" << endl
             << "    @inbounds begin" << endl
             << d_output[3].str()
    	 << "    end" << endl
             << "    return nothing" << endl
             << "end" << endl << endl;
    
      // static!
      output << "function static!(T::Vector{<: Real}, residual::Vector{<: Real}," << endl
             << "                  y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real})" << endl
             << "    staticResid!(T, residual, y, x, params, true)" << endl
             << "    return nothing" << endl
             << "end" << endl
             << endl
             << "function static!(T::Vector{<: Real}, residual::Vector{<: Real}, g1::Matrix{<: Real}," << endl
             << "                 y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real})" << endl
             << "    staticG1!(T, g1, y, x, params, true, true)" << endl
             << "    staticResid!(T, residual, y, x, params, false)" << endl
             << "    return nothing" << endl
             << "end" << endl
             << endl
             << "function static!(T::Vector{<: Real}, g1::Matrix{<: Real}," << endl
             << "                 y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real})" << endl
             << "    staticG1!(T, g1, y, x, params, true, false)" << endl
             << "    return nothing" << endl
             << "end" << endl
             << endl
             << "function static!(T::Vector{<: Real}, residual::Vector{<: Real}, g1::Matrix{<: Real}, g2::Matrix{<: Real}," << endl
             << "                 y::Vector{<: Real}, x::Vector{<: Real}, params::Vector{<: Real})" << endl
             << "    staticG2!(T, g2, y, x, params, true, true, true)" << endl
             << "    staticG1!(T, g1, y, x, params, false, false)" << endl
             << "    staticResid!(T, residual, y, x, params, false)" << endl
             << "    return nothing" << endl
             << "end" << endl
             << endl;
    
      // Write function definition if BinaryOpcode::powerDeriv is used
      writePowerDerivJulia(output);
    
      output << "end" << endl;
    
      writeToFileIfModified(output, basename + "Static.jl");
    }
    
    void
    StaticModel::writeStaticFile(const string &basename, bool block, bool use_dll, const string &mexext, const filesystem::path &matlabroot, const filesystem::path &dynareroot, bool julia) const
    {
      filesystem::path model_dir{basename};
      model_dir /= "model";
      if (use_dll)
        filesystem::create_directories(model_dir / "src");
      filesystem::create_directories(model_dir / "bytecode");
    
      if (block)
        {
          writeStaticBlockBytecode(basename);
    
          if (use_dll)
            {
              writeStaticPerBlockCFiles(basename);
              writeStaticBlockCFile(basename);
              vector<filesystem::path> src_files(blocks.size() + 1);
              for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
                src_files[blk] = model_dir / "src" / ("static_" + to_string(blk+1) + ".c");
              src_files[blocks.size()] = model_dir / "src" / "static.c";
              compileMEX(basename, "static", mexext, src_files, matlabroot, dynareroot);
            }
          else if (julia)
            {
              cerr << "'block' option is not available with Julia" << endl;
              exit(EXIT_FAILURE);
            }
          else // M-files
            {
              writeStaticPerBlockMFiles(basename);
              writeStaticBlockMFile(basename);
            }
        }
      else
        {
          writeStaticBytecode(basename);
    
          if (use_dll)
            {
              writeStaticCFile(basename);
              compileMEX(basename, "static", mexext, { model_dir / "src" / "static.c" },
                         matlabroot, dynareroot);
            }
          else if (julia)
            writeStaticJuliaFile(basename);
          else // M-files
            writeStaticMFile(basename);
        }
    
      writeSetAuxiliaryVariables(basename, julia);
    }
    
    bool
    StaticModel::exoPresentInEqs() const
    {
      for (auto equation : equations)
        if (equation->hasExogenous())
          return true;
      return false;
    }
    
    void
    StaticModel::writeStaticBlockMFile(const string &basename) const
    {
      string filename = packageDir(basename) + "/static.m";
    
      ofstream output{filename, ios::out | ios::binary};
      if (!output.is_open())
        {
          cerr << "ERROR: Can't open file " << filename << " for writing" << endl;
          exit(EXIT_FAILURE);
        }
    
      output << "function [residual, y, T, g1] = static(nblock, y, x, params, T)" << endl
             << "  switch nblock" << endl;
    
      for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
        {
          output << "    case " << blk+1 << endl;
    
          BlockSimulationType simulation_type = blocks[blk].simulation_type;
    
          if (simulation_type == BlockSimulationType::evaluateBackward
              || simulation_type == BlockSimulationType::evaluateForward)
            output << "      [y, T] = " << basename << ".block.static_" << blk+1 << "(y, x, params, T);" << endl
                   << "      residual = [];" << endl
                   << "      g1 = [];" << endl;
          else
            output << "      [residual, y, T, g1] = " << basename << ".block.static_" << blk+1 << "(y, x, params, T);" << endl;
    
        }
      output << "  end" << endl
             << "end" << endl;
      output.close();
    }
    
    void
    StaticModel::writeStaticBlockCFile(const string &basename) const
    {
      string filename = basename + "/model/src/static.c";
    
      ofstream output{filename, ios::out | ios::binary};
      if (!output.is_open())
        {
          cerr << "ERROR: Can't open file " << filename << " for writing" << endl;
          exit(EXIT_FAILURE);
        }
    
      output << "#include <math.h>" << endl
             << R"(#include "mex.h")" << endl;
    
      for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
        output << R"(#include "static_)" << blk+1 << R"(.h")" << endl;
    
      output << endl;
      writePowerDeriv(output);
    
      output << endl
             << "void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])" << endl
             << "{" << endl
             << "  if (nrhs != 5)" << endl
             << R"(    mexErrMsgTxt("Requires exactly 5 input arguments");)" << endl
             << "  if (nlhs > 4)" << endl
             << R"(    mexErrMsgTxt("Accepts at most 4 output arguments");)" << endl
             << "  int nblock = (int) mxGetScalar(prhs[0]);" << endl
             << "  const mxArray *y = prhs[1], *x = prhs[2], *params = prhs[3], *T = prhs[4];" << endl
             << "  mxArray *T_new = mxDuplicateArray(T);" << endl
             << "  mxArray *y_new = mxDuplicateArray(y);" << endl
             << "  mxArray *residual, *g1;" << endl
             << "  switch (nblock)" << endl
             << "    {" << endl;
    
      for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
        {
          output << "    case " << blk+1 << ':' << endl;
    
          BlockSimulationType simulation_type = blocks[blk].simulation_type;
    
          if (simulation_type == BlockSimulationType::evaluateBackward
              || simulation_type == BlockSimulationType::evaluateForward)
            output << "      static_" << blk+1 << "_mx(y_new, x, params, T_new);" << endl
                   << "      residual = mxCreateDoubleMatrix(0,0,mxREAL);" << endl
                   << "      g1 = mxCreateDoubleMatrix(0,0,mxREAL);" << endl;
          else
            output << "      static_" << blk+1 << "_mx(y_new, x, params, T_new, &residual, &g1);" << endl;
          output << "      break;" << endl;
        }
      output << "    }" << endl
             << endl
             << "  if (nlhs >= 1)" << endl
             << "    plhs[0] = residual;" << endl
             << "  else" << endl
             << "    mxDestroyArray(residual);" << endl
             << "  if (nlhs >= 2)" << endl
             << "    plhs[1] = y_new;" << endl
             << "  else" << endl
             << "    mxDestroyArray(y_new);" << endl
             << "  if (nlhs >= 3)" << endl
             << "    plhs[2] = T_new;" << endl
             << "  else" << endl
             << "    mxDestroyArray(T_new);" << endl
             << "  if (nlhs >= 4)" << endl
             << "    plhs[3] = g1;" << endl
             << "  else" << endl
             << "    mxDestroyArray(g1);" << endl
             << "}" << endl;
      output.close();
    }
    
    void
    StaticModel::writeDriverOutput(ostream &output, bool block) const
    {
      output << "M_.static_tmp_nbr = [";
      for (const auto &temporary_terms_derivative : temporary_terms_derivatives)
        output << temporary_terms_derivative.size() << "; ";
      output << "];" << endl;
    
      /* Write mapping between model local variables and indices in the temporary
         terms vector (dynare#1722) */
      output << "M_.model_local_variables_static_tt_idxs = {" << endl;
      for (auto [mlv, value] : temporary_terms_mlv)
        output << "  '" << symbol_table.getName(mlv->symb_id) << "', "
               << temporary_terms_idxs.at(mlv)+1 << ';' << endl;
      output << "};" << endl;
    
      if (!block)
        return;
    
      for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
        {
          output << "block_structure_stat.block(" << blk+1 << ").Simulation_Type = " << static_cast<int>(blocks[blk].simulation_type) << ";" << endl
                 << "block_structure_stat.block(" << blk+1 << ").endo_nbr = " << blocks[blk].size << ";" << endl
                 << "block_structure_stat.block(" << blk+1 << ").mfs = " << blocks[blk].mfs_size << ";" << endl
                 << "block_structure_stat.block(" << blk+1 << ").equation = [";
          for (int eq = 0; eq < blocks[blk].size; eq++)
            output << " " << getBlockEquationID(blk, eq)+1;
          output << "];" << endl
                 << "block_structure_stat.block(" << blk+1 << ").variable = [";
          for (int var = 0; var < blocks[blk].size; var++)
            output << " " << getBlockVariableID(blk, var)+1;
          output << "];" << endl;
        }
      output << "M_.block_structure_stat.block = block_structure_stat.block;" << endl
             << "M_.block_structure_stat.variable_reordered = [";
      for (int i = 0; i < symbol_table.endo_nbr(); i++)
        output << " " << endo_idx_block2orig[i]+1;
      output << "];" << endl
             << "M_.block_structure_stat.equation_reordered = [";
      for (int i = 0; i < symbol_table.endo_nbr(); i++)
        output << " " << eq_idx_block2orig[i]+1;
      output << "];" << endl;
    
      set<pair<int, int>> row_incidence;
      for (const auto &[indices, d1] : derivatives[1])
        if (int deriv_id = indices[1];
            getTypeByDerivID(deriv_id) == SymbolType::endogenous)
          {
            int eq = indices[0];
            int var { getTypeSpecificIDByDerivID(deriv_id) };
            row_incidence.emplace(eq, var);
          }
      output << "M_.block_structure_stat.incidence.sparse_IM = [" << endl;
      for (auto [eq, var] : row_incidence)
        output << " " << eq+1 << " " << var+1 << ";" << endl;
      output << "];" << endl
             << "M_.block_structure_stat.tmp_nbr = " << blocks_temporary_terms_idxs.size()
             << ";" << endl;
    }
    
    SymbolType
    StaticModel::getTypeByDerivID(int deriv_id) const noexcept(false)
    {
      if (deriv_id < symbol_table.endo_nbr())
        return SymbolType::endogenous;
      else if (deriv_id < symbol_table.endo_nbr() + symbol_table.param_nbr())
        return SymbolType::parameter;
      else
        throw UnknownDerivIDException();
    }
    
    int
    StaticModel::getLagByDerivID([[maybe_unused]] int deriv_id) const noexcept(false)
    {
      return 0;
    }
    
    int
    StaticModel::getSymbIDByDerivID(int deriv_id) const noexcept(false)
    {
      if (deriv_id < symbol_table.endo_nbr())
        return symbol_table.getID(SymbolType::endogenous, deriv_id);
      else if (deriv_id < symbol_table.endo_nbr() + symbol_table.param_nbr())
        return symbol_table.getID(SymbolType::parameter, deriv_id - symbol_table.endo_nbr());
      else
        throw UnknownDerivIDException();
    }
    
    int
    StaticModel::getTypeSpecificIDByDerivID(int deriv_id) const
    {
      if (deriv_id < symbol_table.endo_nbr())
        return deriv_id;
      else if (deriv_id < symbol_table.endo_nbr() + symbol_table.param_nbr())
        return deriv_id - symbol_table.endo_nbr();
      else
        throw UnknownDerivIDException();
    }
    
    int
    StaticModel::getDerivID(int symb_id, [[maybe_unused]] int lag) const noexcept(false)
    {
      if (symbol_table.getType(symb_id) == SymbolType::endogenous)
        return symbol_table.getTypeSpecificID(symb_id);
      else if (symbol_table.getType(symb_id) == SymbolType::parameter)
        return symbol_table.getTypeSpecificID(symb_id) + symbol_table.endo_nbr();
      else
        /* See the special treatment in VariableNode::prepareForDerivation(),
           VariableNode::computeDerivative() and VariableNode::getChainRuleDerivative() */
        throw UnknownDerivIDException{};
    }
    
    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());
    }
    
    void
    StaticModel::computeChainRuleJacobian()
    {
      int nb_blocks = blocks.size();
      blocks_derivatives.resize(nb_blocks);
      for (int blk = 0; blk < nb_blocks; blk++)
        {
          int nb_recursives = blocks[blk].getRecursiveSize();
    
          map<int, BinaryOpNode *> recursive_vars;
          for (int i = 0; i < nb_recursives; i++)
            {
              int deriv_id = getDerivID(symbol_table.getID(SymbolType::endogenous, getBlockVariableID(blk, i)), 0);
              if (getBlockEquationType(blk, i) == EquationType::evaluateRenormalized)
                recursive_vars[deriv_id] = getBlockEquationRenormalizedExpr(blk, i);
              else
                recursive_vars[deriv_id] = getBlockEquationExpr(blk, i);
            }
    
          assert(blocks[blk].simulation_type != BlockSimulationType::solveTwoBoundariesSimple
                 && blocks[blk].simulation_type != BlockSimulationType::solveTwoBoundariesComplete);
    
          int size = blocks[blk].size;
    
          for (int eq = nb_recursives; eq < size; eq++)
            {
              int eq_orig = getBlockEquationID(blk, eq);
              for (int var = nb_recursives; var < size; var++)
                {
                  int var_orig = getBlockVariableID(blk, var);
                  expr_t d1 = equations[eq_orig]->getChainRuleDerivative(getDerivID(symbol_table.getID(SymbolType::endogenous, var_orig), 0), recursive_vars);
                  if (d1 != Zero)
                    blocks_derivatives[blk][{ eq, var, 0 }] = d1;
                }
            }
        }
    }
    
    void
    StaticModel::writeLatexFile(const string &basename, bool write_equation_tags) const
    {
      writeLatexModelFile(basename, "static", ExprNodeOutputType::latexStaticModel, write_equation_tags);
    }
    
    void
    StaticModel::writeAuxVarInitval(ostream &output, ExprNodeOutputType output_type) const
    {
      for (auto aux_equation : aux_equations)
        {
          dynamic_cast<ExprNode *>(aux_equation)->writeOutput(output, output_type);
          output << ";" << endl;
        }
    }
    
    void
    StaticModel::writeSetAuxiliaryVariables(const string &basename, bool julia) const
    {
      ostringstream output_func_body;
      ExprNodeOutputType output_type = julia ? ExprNodeOutputType::juliaStaticModel : ExprNodeOutputType::matlabStaticModel;
      writeAuxVarRecursiveDefinitions(output_func_body, output_type);
    
      if (output_func_body.str().empty())
        return;
    
      string func_name = julia ? "set_auxiliary_variables!" : "set_auxiliary_variables";
      string comment = julia ? "#" : "%";
    
      stringstream output;
      if (julia)
        output << "module " << basename << "SetAuxiliaryVariables" << endl
               << "export " << func_name << endl;
      output << "function ";
      if (!julia)
        output << "y = ";
      output << func_name << "(y, x, params)" << endl
             << comment << endl
             << comment << " Status : Computes static model for Dynare" << endl
             << comment << endl
             << comment << " Warning : this file is generated automatically by Dynare" << endl
             << comment << "           from model file (.mod)" << endl << endl;
      if (julia)
        output << "@inbounds begin" << endl;
      output << output_func_body.str()
             << "end" << endl;
      if (julia)
        output << "end" << endl
               << "end" << endl;
    
      writeToFileIfModified(output, julia ? basename + "SetAuxiliaryVariables.jl" : packageDir(basename) + "/" + func_name + ".m");
    }
    
    void
    StaticModel::writeAuxVarRecursiveDefinitions(ostream &output, ExprNodeOutputType output_type) const
    {
      deriv_node_temp_terms_t tef_terms;
      for (auto aux_equation : aux_equations)
        if (dynamic_cast<ExprNode *>(aux_equation)->containsExternalFunction())
          dynamic_cast<ExprNode *>(aux_equation)->writeExternalFunctionOutput(output, ExprNodeOutputType::matlabStaticModel, {}, {}, tef_terms);
      for (auto aux_equation : aux_equations)
        {
          dynamic_cast<ExprNode *>(aux_equation->substituteStaticAuxiliaryDefinition())->writeOutput(output, output_type);
          output << ";" << endl;
        }
    }
    
    void
    StaticModel::writeLatexAuxVarRecursiveDefinitions(ostream &output) const
    {
      deriv_node_temp_terms_t tef_terms;
      temporary_terms_t temporary_terms;
      temporary_terms_idxs_t temporary_terms_idxs;
      for (auto aux_equation : aux_equations)
        if (dynamic_cast<ExprNode *>(aux_equation)->containsExternalFunction())
          dynamic_cast<ExprNode *>(aux_equation)->writeExternalFunctionOutput(output, ExprNodeOutputType::latexStaticModel,
                                                                              temporary_terms, temporary_terms_idxs, tef_terms);
      for (auto aux_equation : aux_equations)
        {
          output << R"(\begin{dmath})" << endl;
          dynamic_cast<ExprNode *>(aux_equation->substituteStaticAuxiliaryDefinition())->writeOutput(output, ExprNodeOutputType::latexStaticModel);
          output << endl << R"(\end{dmath})" << endl;
        }
    }
    
    void
    StaticModel::writeJsonAuxVarRecursiveDefinitions(ostream &output) const
    {
      deriv_node_temp_terms_t tef_terms;
      temporary_terms_t temporary_terms;
    
      for (auto aux_equation : aux_equations)
        if (dynamic_cast<ExprNode *>(aux_equation)->containsExternalFunction())
          {
            vector<string> efout;
            dynamic_cast<ExprNode *>(aux_equation)->writeJsonExternalFunctionOutput(efout,
                                                                                    temporary_terms,
                                                                                    tef_terms,
                                                                                    false);
            for (bool printed_something{false};
                 const auto &it : efout)
              {
                if (exchange(printed_something, true))
                  output << ", ";
                output << it;
              }
          }
    
      for (auto aux_equation : aux_equations)
        {
          output << R"(, {"lhs": ")";
          aux_equation->arg1->writeJsonOutput(output, temporary_terms, tef_terms, false);
          output << R"(", "rhs": ")";
          dynamic_cast<BinaryOpNode *>(aux_equation->substituteStaticAuxiliaryDefinition())->arg2->writeJsonOutput(output, temporary_terms, tef_terms, false);
          output << R"("})";
        }
    }
    
    void
    StaticModel::writeJsonOutput(ostream &output) const
    {
      deriv_node_temp_terms_t tef_terms;
      writeJsonModelLocalVariables(output, false, tef_terms);
      output << ", ";
      writeJsonModelEquations(output, false);
    }
    
    void
    StaticModel::writeJsonComputingPassOutput(ostream &output, bool writeDetails) const
    {
      auto [mlv_output, d_output] { writeJsonComputingPassOutputHelper<false>(writeDetails) };
    
      if (writeDetails)
        output << R"("static_model": {)";
      else
        output << R"("static_model_simple": {)";
      output << mlv_output.str();
      for (const auto &it : d_output)
        output << ", " << it.str();
      output << "}";
    }
    
    void
    StaticModel::writeJsonParamsDerivatives(ostream &output, bool writeDetails) const
    {
      if (!params_derivatives.size())
        return;
    
      auto [mlv_output, tt_output, rp_output, gp_output, rpp_output, gpp_output, hp_output, g3p_output]
        { writeJsonParamsDerivativesHelper<false>(writeDetails) };
      // g3p_output is ignored
    
      if (writeDetails)
        output << R"("static_model_params_derivative": {)";
      else
        output << R"("static_model_params_derivatives_simple": {)";
      output << mlv_output.str()
             << ", " << tt_output.str()
             << ", " << rp_output.str()
             << ", " << gp_output.str()
             << ", " << rpp_output.str()
             << ", " << gpp_output.str()
             << ", " << hp_output.str()
             << "}";
    }