preprocessor/src/StaticModel.cc

/*
 * Copyright © 2003-2023 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.at(it)->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));

  cutoff = m.cutoff;
  mfs = m.mfs;

  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::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(),
                            u_count_int,
                            symbol_table.endo_nbr()};

  writeBytecodeHelper<false>(code_file);
}

void
StaticModel::writeStaticBlockBytecode(const string &basename) const
{
  BytecodeWriter code_file {basename + "/model/bytecode/block/static.cod"};

  const filesystem::path bin_filename {basename + "/model/bytecode/block/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.string() << 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(),
                                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, bool use_dll)
{
  initializeVariablesAndEquations();

  /* 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 derivatives matrix of the " << modelClassName() << " 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 " << modelClassName() << " derivatives (order " << derivsOrder << ")." << endl;

  computeDerivatives(derivsOrder, vars);

  if (paramsDerivsOrder > 0)
    {
      cout << "Computing " << modelClassName() << " derivatives w.r.t. parameters (order " << paramsDerivsOrder << ")." << endl;
      computeParamsDerivatives(paramsDerivsOrder);
    }

  computeTemporaryTerms(!use_dll, no_tmp_terms);

  if (paramsDerivsOrder > 0 && !no_tmp_terms)
    computeParamsDerivativesTemporaryTerms();

  computingPassBlock(eval_context, no_tmp_terms);
  if (!block_decomposed && 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);
    }
}

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_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_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_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";

  filesystem::path filename {packageDir(basename) / (name + ".m")};
  ofstream output{filename, ios::out | ios::binary};
  if (!output.is_open())
    {
      cerr << "ERROR: Can't open file " << filename.string() << " 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
{
  filesystem::path filename {packageDir(basename) / (name_tt + ".m")};
  ofstream output{filename, ios::out | ios::binary};
  if (!output.is_open())
    {
      cerr << "ERROR: Can't open file " << filename.string() << " 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.string() << " 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
{
  filesystem::path filename {packageDir(basename) / "static.m"};
  ofstream output{filename, ios::out | ios::binary};
  if (!output.is_open())
    {
      cerr << "ERROR: Can't open file " << filename.string() << " for writing" << endl;
      exit(EXIT_FAILURE);
    }
  int ntt { static_cast<int>(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::writeStaticFile(const string &basename, bool use_dll, const string &mexext, const filesystem::path &matlabroot, bool julia) const
{
  filesystem::path model_dir{basename};
  model_dir /= "model";
  if (use_dll)
    {
      create_directories(model_dir / "src" / "sparse");
      if (block_decomposed)
        create_directories(model_dir / "src" / "sparse" / "block");
    }
  if (julia)
    create_directories(model_dir / "julia");
  else
    {
      auto plusfolder {packageDir(basename)};
      /* The following is not a duplicate of the same call from
         ModFile::writeMOutput(), because of planner_objective which needs its
         +objective subdirectory */
      create_directories(plusfolder);

      auto sparsefolder {plusfolder / "+sparse"};
      create_directories(sparsefolder);
      if (block_decomposed)
        create_directories(sparsefolder / "+block");

      create_directories(plusfolder / "+debug");
    }
  create_directories(model_dir / "bytecode" / "block");

  // Legacy representation
  if (use_dll)
    writeModelCFile<false>(basename, mexext, matlabroot);
  else if (!julia) // M-files
    writeStaticMFile(basename);
  // The legacy representation is no longer produced for Julia

  writeStaticBytecode(basename);
  if (block_decomposed)
    writeStaticBlockBytecode(basename);

  // Sparse representation
  if (use_dll)
    writeSparseModelCFiles<false>(basename, mexext, matlabroot);
  else if (julia)
    writeSparseModelJuliaFiles<false>(basename);
  else // MATLAB/Octave
    writeSparseModelMFiles<false>(basename);

  writeSetAuxiliaryVariablesFile<false>(basename, julia);

  // Support for model debugging
  if (!julia)
    writeDebugModelMFiles<false>(basename);
}

bool
StaticModel::exoPresentInEqs() const
{
  for (auto equation : equations)
    if (equation->hasExogenous())
      return true;
  return false;
}

void
StaticModel::writeDriverOutput(ostream &output) const
{
  output << "M_.static_tmp_nbr = [";
  for (const auto &temporary_terms_derivative : temporary_terms_derivatives)
    output << temporary_terms_derivative.size() << "; ";
  output << "];" << endl;

  if (block_decomposed)
    writeBlockDriverOutput(output);

  writeDriverSparseIndicesHelper<false>(output);
}

void
StaticModel::writeBlockDriverOutput(ostream &output) const
{
  for (int blk = 0; blk < static_cast<int>(blocks.size()); blk++)
    {
      output << "M_.block_structure_stat.block(" << blk+1 << ").Simulation_Type = " << static_cast<int>(blocks[blk].simulation_type) << ";" << endl
             << "M_.block_structure_stat.block(" << blk+1 << ").endo_nbr = " << blocks[blk].size << ";" << endl
             << "M_.block_structure_stat.block(" << blk+1 << ").mfs = " << blocks[blk].mfs_size << ";" << endl
             << "M_.block_structure_stat.block(" << blk+1 << ").equation = [";
      for (int eq = 0; eq < blocks[blk].size; eq++)
        output << " " << getBlockEquationID(blk, eq)+1;
      output << "];" << endl
             << "M_.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.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;

  writeBlockDriverSparseIndicesHelper<false>(output);
}

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);
  blocks_jacobian_sparse_column_major_order.resize(nb_blocks);
  blocks_jacobian_sparse_colptr.resize(nb_blocks);

  for (int blk = 0; blk < nb_blocks; blk++)
    {
      int nb_recursives = blocks[blk].getRecursiveSize();
      BlockSimulationType simulation_type { blocks[blk].simulation_type };

      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(simulation_type != BlockSimulationType::solveTwoBoundariesSimple
             && simulation_type != BlockSimulationType::solveTwoBoundariesComplete);

      int size = blocks[blk].size;
      map<expr_t, set<int>> non_null_chain_rule_derivatives;
      map<pair<expr_t, int>, expr_t> chain_rule_deriv_cache;
      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, non_null_chain_rule_derivatives, chain_rule_deriv_cache);
              if (d1 != Zero)
                blocks_derivatives[blk][{ eq, var, 0 }] = d1;
            }
        }

      // Compute the sparse representation of the Jacobian
      if (simulation_type != BlockSimulationType::evaluateForward
          && simulation_type != BlockSimulationType::evaluateBackward)
        {
          for (const auto &[indices, d1] : blocks_derivatives[blk])
            {
              auto &[eq, var, lag] { indices };
              assert(lag == 0);
              if (eq >= nb_recursives && var >= nb_recursives)
                blocks_jacobian_sparse_column_major_order[blk].try_emplace({eq-nb_recursives, var-nb_recursives}, d1);
            }
          blocks_jacobian_sparse_colptr[blk] = computeCSCColPtr(blocks_jacobian_sparse_column_major_order[blk], blocks[blk].mfs_size);
        }
    }
}

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::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)->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": ")";
      aux_equation->arg2->writeJsonOutput(output, temporary_terms, tef_terms, false);
      output << R"("})";
    }
}

void
StaticModel::writeJsonOutput(ostream &output) const
{
  output << R"("static_tmp_nbr": [)";
  for (bool printed_something {false};
       const auto &tts : temporary_terms_derivatives)
    {
      if (exchange(printed_something, true))
        output << ", ";
      output << tts.size();
    }
  output << "], ";
  writeJsonSparseIndicesHelper<false>(output);
}

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()
         << "}";
}

void
StaticModel::computeRamseyMultipliersDerivatives(int ramsey_orig_endo_nbr, bool is_matlab,
                                                 bool no_tmp_terms)
{
  // Compute derivation IDs of Lagrange multipliers
  set<int> mult_symb_ids { symbol_table.getLagrangeMultipliers() };
  vector<int> mult_deriv_ids;
  for (int symb_id : mult_symb_ids)
    mult_deriv_ids.push_back(getDerivID(symb_id, 0));

  // Compute the list of aux vars for which to apply the chain rule derivation
  map<int, BinaryOpNode *> recursive_variables;
  for (auto aux_eq : aux_equations)
    {
      auto varexpr { dynamic_cast<VariableNode *>(aux_eq->arg1) };
      assert(varexpr && symbol_table.isAuxiliaryVariable(varexpr->symb_id));
      /* Determine whether the auxiliary variable has been added after the last
         Lagrange multiplier. We use the guarantee given by SymbolTable that
         symbol IDs are increasing. */
      if (varexpr->symb_id > *mult_symb_ids.crbegin())
        recursive_variables.emplace(getDerivID(varexpr->symb_id, 0), aux_eq);
    }

  // Compute the chain rule derivatives w.r.t. multipliers
  map<expr_t, set<int>> non_null_chain_rule_derivatives;
  map<pair<expr_t, int>, expr_t> cache;
  for (int eq {0}; eq < ramsey_orig_endo_nbr; eq++)
    for (int mult {0}; mult < static_cast<int>(mult_deriv_ids.size()); mult++)
      if (expr_t d { equations[eq]->getChainRuleDerivative(mult_deriv_ids[mult], recursive_variables,
                                                           non_null_chain_rule_derivatives, cache) };
          d != Zero)
        ramsey_multipliers_derivatives.try_emplace({ eq, mult }, d);

  // Compute the temporary terms
  map<pair<int, int>, temporary_terms_t> temp_terms_map;
  map<expr_t, pair<int, pair<int, int>>> reference_count;
  for (const auto &[row_col, d] : ramsey_multipliers_derivatives)
    d->computeTemporaryTerms({ 1, 0 }, temp_terms_map, reference_count, is_matlab);
  /* If the user has specified the notmpterms option, clear all temporary
     terms, except those that correspond to external functions (since they are
     not optional) */
  if (no_tmp_terms)
    for (auto &it : temp_terms_map)
      erase_if(it.second,
               [](expr_t e) { return !dynamic_cast<AbstractExternalFunctionNode *>(e); });
  ramsey_multipliers_derivatives_temporary_terms = move(temp_terms_map[{ 1, 0 }]);
  for (int idx {0};
       auto it : ramsey_multipliers_derivatives_temporary_terms)
    ramsey_multipliers_derivatives_temporary_terms_idxs[it] = idx++;

  // Compute the CSC format
  ramsey_multipliers_derivatives_sparse_colptr = computeCSCColPtr(ramsey_multipliers_derivatives,
                                                                  mult_deriv_ids.size());
}

void
StaticModel::writeDriverRamseyMultipliersDerivativesSparseIndices(ostream &output) const
{
  output << "M_.ramsey_multipliers_static_g1_sparse_rowval = int32([";
  for (auto &[row_col, d] : ramsey_multipliers_derivatives)
    output << row_col.first+1 << ' ';
  output << "]);" << endl
         << "M_.ramsey_multipliers_static_g1_sparse_colval = int32([";
  for (auto &[row_col, d] : ramsey_multipliers_derivatives)
    output << row_col.second+1 << ' ';
  output << "]);" << endl
         << "M_.ramsey_multipliers_static_g1_sparse_colptr = int32([";
  for (int it : ramsey_multipliers_derivatives_sparse_colptr)
    output << it+1 << ' ';
  output << "]);" << endl;
}

void
StaticModel::writeRamseyMultipliersDerivativesMFile(const string &basename, int ramsey_orig_endo_nbr) const
{
  constexpr auto output_type { ExprNodeOutputType::matlabStaticModel };
  filesystem::path filename {packageDir(basename) / "ramsey_multipliers_static_g1.m"};
  ofstream output_file{filename, ios::out | ios::binary};
  if (!output_file.is_open())
    {
      cerr << "ERROR: Can't open file " << filename.string() << " for writing" << endl;
      exit(EXIT_FAILURE);
    }

  output_file << "function g1m = ramsey_multipliers_static_g1(y, x, params, sparse_rowval, sparse_colval, sparse_colptr)" << endl
              << "g1m_v=NaN(" << ramsey_multipliers_derivatives.size() << ",1);" << endl;

  writeRamseyMultipliersDerivativesHelper<output_type>(output_file);

  // On MATLAB < R2020a, sparse() does not accept int32 indices
  output_file << "if ~isoctave && matlab_ver_less_than('9.8')" << endl
              << "    sparse_rowval = double(sparse_rowval);" << endl
              << "    sparse_colval = double(sparse_colval);" << endl
              << "end" << endl
              << "g1m = sparse(sparse_rowval, sparse_colval, g1m_v, " << ramsey_orig_endo_nbr << ", " << symbol_table.getLagrangeMultipliers().size() << ");" << endl
              << "end" << endl;
  output_file.close();
}

void
StaticModel::writeRamseyMultipliersDerivativesCFile(const string &basename, const string &mexext, const filesystem::path &matlabroot, int ramsey_orig_endo_nbr) const
{
  constexpr auto output_type { ExprNodeOutputType::CStaticModel };
  const filesystem::path model_src_dir {filesystem::path{basename} / "model" / "src"};

  const int xlen { symbol_table.exo_nbr()+symbol_table.exo_det_nbr() };
  const int nzval { static_cast<int>(ramsey_multipliers_derivatives.size()) };
  const int ncols { static_cast<int>(symbol_table.getLagrangeMultipliers().size()) };

  const filesystem::path p {model_src_dir / "ramsey_multipliers_static_g1.c"};
  ofstream output{p, ios::out | ios::binary};
  if (!output.is_open())
    {
      cerr << "ERROR: Can't open file " << p.string() << " for writing" << endl;
      exit(EXIT_FAILURE);
    }

  output << "#include <math.h>" << endl << endl
         << R"(#include "mex.h")" << endl // Needed for calls to external functions
         << endl;
  writePowerDeriv(output);
  output << endl
         << "void ramsey_multipliers_static_g1(const double *restrict y, const double *restrict x, const double *restrict params, double *restrict T, double *restrict g1m_v)" << endl
         << "{" << endl;
  writeRamseyMultipliersDerivativesHelper<output_type>(output);
  output << "}" << endl
         << endl
         << "void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])" << endl
         << "{" << endl
         << "  if (nrhs != 6)" << endl
         << R"(    mexErrMsgTxt("Accepts exactly 6 input arguments");)" << endl
         << "  if (nlhs != 1)" << endl
         << R"(    mexErrMsgTxt("Accepts exactly 1 output argument");)" << endl
         << "  if (!(mxIsDouble(prhs[0]) && !mxIsComplex(prhs[0]) && !mxIsSparse(prhs[0]) && mxGetNumberOfElements(prhs[0]) == " << symbol_table.endo_nbr() << "))" << endl
           << R"(    mexErrMsgTxt("y must be a real dense numeric array with )" << symbol_table.endo_nbr() << R"( elements");)" << endl
         << "  const double *restrict y = mxGetPr(prhs[0]);" << endl
         << "  if (!(mxIsDouble(prhs[1]) && !mxIsComplex(prhs[1]) && !mxIsSparse(prhs[1]) && mxGetNumberOfElements(prhs[1]) == " << xlen << "))" << endl
         << R"(    mexErrMsgTxt("x must be a real dense numeric array with )" << xlen << R"( elements");)" << endl
         << "  const double *restrict x = mxGetPr(prhs[1]);" << endl
         << "  if (!(mxIsDouble(prhs[2]) && !mxIsComplex(prhs[2]) && !mxIsSparse(prhs[2]) && mxGetNumberOfElements(prhs[2]) == " << symbol_table.param_nbr() << "))" << endl
         << R"(    mexErrMsgTxt("params must be a real dense numeric array with )" << symbol_table.param_nbr() << R"( elements");)" << endl
         << "  const double *restrict params = mxGetPr(prhs[2]);" << endl
         << "  if (!(mxIsInt32(prhs[3]) && mxGetNumberOfElements(prhs[3]) == " << nzval << "))" << endl
         << R"(    mexErrMsgTxt("sparse_rowval must be an int32 array with )" << nzval << R"( elements");)" << endl
         << "  if (!(mxIsInt32(prhs[5]) && mxGetNumberOfElements(prhs[5]) == " << ncols+1 << "))" << endl
         << R"(    mexErrMsgTxt("sparse_colptr must be an int32 array with )" << ncols+1 << R"( elements");)" << endl
         << "#if MX_HAS_INTERLEAVED_COMPLEX" << endl
         << "  const int32_T *restrict sparse_rowval = mxGetInt32s(prhs[3]);" << endl
         << "  const int32_T *restrict sparse_colptr = mxGetInt32s(prhs[5]);" << endl
         << "#else" << endl
         << "  const int32_T *restrict sparse_rowval = (int32_T *) mxGetData(prhs[3]);" << endl
         << "  const int32_T *restrict sparse_colptr = (int32_T *) mxGetData(prhs[5]);" << endl
         << "#endif" << endl
         << "  plhs[0] = mxCreateSparse(" << ramsey_orig_endo_nbr << ", " << ncols << ", " << nzval << ", mxREAL);" << endl
         << "  mwIndex *restrict ir = mxGetIr(plhs[0]), *restrict jc = mxGetJc(plhs[0]);" << endl
         << "  for (mwSize i = 0; i < " << nzval << "; i++)" << endl
         << "    *ir++ = *sparse_rowval++ - 1;" << endl
         << "  for (mwSize i = 0; i < " << ncols+1 << "; i++)" << endl
         << "    *jc++ = *sparse_colptr++ - 1;" << endl
         << "  mxArray *T_mx = mxCreateDoubleMatrix(" << ramsey_multipliers_derivatives_temporary_terms.size() << ", 1, mxREAL);" << endl
         << "  ramsey_multipliers_static_g1(y, x, params, mxGetPr(T_mx), mxGetPr(plhs[0]));" << endl
         << "  mxDestroyArray(T_mx);" << endl
         << "}" << endl;

  output.close();

  compileMEX(packageDir(basename), "ramsey_multipliers_static_g1", mexext, { p }, matlabroot);
}