dynare%2B%2B/kord/decision_rule.cc

/*
 * Copyright © 2004 Ondra Kamenik
 * Copyright © 2019 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 <http://www.gnu.org/licenses/>.
 */

#include "kord_exception.hh"
#include "decision_rule.hh"
#include "dynamic_model.hh"
#include "seed_generator.hh"

#include "SymSchurDecomp.hh"

#include <dynlapack.h>

#include <limits>
#include <utility>
#include <memory>

// FoldDecisionRule conversion from UnfoldDecisionRule
FoldDecisionRule::FoldDecisionRule(const UnfoldDecisionRule &udr)
  : DecisionRuleImpl<Storage::fold>(ctraits<Storage::fold>::Tpol(udr.nrows(), udr.nvars()),
                                    udr.ypart, udr.nu, udr.ysteady)
{
  for (const auto &it : udr)
    insert(std::make_unique<ctraits<Storage::fold>::Ttensym>(*(it.second)));
}

// UnfoldDecisionRule conversion from FoldDecisionRule
UnfoldDecisionRule::UnfoldDecisionRule(const FoldDecisionRule &fdr)
  : DecisionRuleImpl<Storage::unfold>(ctraits<Storage::unfold>::Tpol(fdr.nrows(), fdr.nvars()),
                                      fdr.ypart, fdr.nu, fdr.ysteady)
{
  for (const auto &it : fdr)
    insert(std::make_unique<ctraits<Storage::unfold>::Ttensym>(*(it.second)));
}

/* This runs simulations with an output to journal file. Note that we
   report how many simulations had to be thrown out due to Nan or Inf. */

void
SimResults::simulate(int num_sim, const DecisionRule &dr, const Vector &start,
                     const TwoDMatrix &vcov, Journal &journal)
{
  JournalRecordPair paa(journal);
  paa << "Performing " << num_sim << " stochastic simulations for "
      << num_per << " periods burning " << num_burn << " initial periods"  << endrec;
  simulate(num_sim, dr, start, vcov);
  int thrown = num_sim - data.size();
  if (thrown > 0)
    {
      JournalRecord rec(journal);
      rec << "I had to throw " << thrown << " simulations away due to Nan or Inf" << endrec;
    }
}

/* This runs a given number of simulations by creating
   SimulationWorker for each simulation and inserting them to the
   thread group. */

void
SimResults::simulate(int num_sim, const DecisionRule &dr, const Vector &start,
                     const TwoDMatrix &vcov)
{
  std::vector<RandomShockRealization> rsrs;
  rsrs.reserve(num_sim);

  sthread::detach_thread_group gr;
  for (int i = 0; i < num_sim; i++)
    {
      RandomShockRealization sr(vcov, seed_generator::get_new_seed());
      rsrs.push_back(sr);
      gr.insert(std::make_unique<SimulationWorker>(*this, dr, DecisionRule::emethod::horner,
                                                   num_per+num_burn, start, rsrs.back()));
    }
  gr.run();
}

/* This adds the data with the realized shocks. It takes only periods
   which are not to be burnt. If the data is not finite, the both data
   and shocks are thrown away. */

bool
SimResults::addDataSet(const TwoDMatrix &d, const ExplicitShockRealization &sr, const ConstVector &st)
{
  KORD_RAISE_IF(d.nrows() != num_y,
                "Incompatible number of rows for SimResults::addDataSets");
  KORD_RAISE_IF(d.ncols() != num_per+num_burn,
                "Incompatible number of cols for SimResults::addDataSets");
  bool ret = false;
  if (d.isFinite())
    {
      data.emplace_back(d, num_burn, num_per);
      shocks.emplace_back(ConstTwoDMatrix(sr.getShocks(), num_burn, num_per));
      if (num_burn == 0)
        start.emplace_back(st);
      else
        start.emplace_back(d.getCol(num_burn-1));
      ret = true;
    }

  return ret;
}

void
SimResults::writeMat(const std::string &base, const std::string &lname) const
{
  std::string matfile_name = base + ".mat";
  mat_t *matfd = Mat_Create(matfile_name.c_str(), nullptr);
  if (matfd)
    {
      writeMat(matfd, lname);
      Mat_Close(matfd);
    }
}

/* This save the results as matrices with given prefix and with index
   appended. If there is only one matrix, the index is not appended. */

void
SimResults::writeMat(mat_t *fd, const std::string &lname) const
{
  for (int i = 0; i < getNumSets(); i++)
    {
      std::string tmp = lname + "_data";
      if (getNumSets() > 1)
        tmp += std::to_string(i+1);
      data[i].writeMat(fd, tmp);
    }
}

void
SimResultsStats::simulate(int num_sim, const DecisionRule &dr,
                          const Vector &start,
                          const TwoDMatrix &vcov, Journal &journal)
{
  SimResults::simulate(num_sim, dr, start, vcov, journal);
  {
    JournalRecordPair paa(journal);
    paa << "Calculating means from the simulations." << endrec;
    calcMean();
  }
  {
    JournalRecordPair paa(journal);
    paa << "Calculating covariances from the simulations." << endrec;
    calcVcov();
  }
}

/* Here we do not save the data itself, we save only mean and vcov. */
void
SimResultsStats::writeMat(mat_t *fd, const std::string &lname) const
{
  ConstTwoDMatrix(num_y, 1, mean).writeMat(fd, lname + "_mean");;
  vcov.writeMat(fd, lname + "_vcov");
}

void
SimResultsStats::calcMean()
{
  mean.zeros();
  if (data.size()*num_per > 0)
    {
      double mult = 1.0/data.size()/num_per;
      for (const auto &i : data)
        {
          for (int j = 0; j < num_per; j++)
            {
              ConstVector col{i.getCol(j)};
              mean.add(mult, col);
            }
        }
    }
}

void
SimResultsStats::calcVcov()
{
  if (data.size()*num_per > 1)
    {
      vcov.zeros();
      double mult = 1.0/(data.size()*num_per - 1);
      for (const auto &d : data)
        for (int j = 0; j < num_per; j++)
          for (int m = 0; m < num_y; m++)
            for (int n = m; n < num_y; n++)
              {
                double s = (d.get(m, j)-mean[m])*(d.get(n, j)-mean[n]);
                vcov.get(m, n) += mult*s;
                if (m != n)
                  vcov.get(n, m) += mult*s;
              }
    }
  else
    vcov.infs();
}

void
SimResultsDynamicStats::simulate(int num_sim, const DecisionRule &dr,
                                 const Vector &start,
                                 const TwoDMatrix &vcov, Journal &journal)
{
  SimResults::simulate(num_sim, dr, start, vcov, journal);
  {
    JournalRecordPair paa(journal);
    paa << "Calculating means of the conditional simulations." << endrec;
    calcMean();
  }
  {
    JournalRecordPair paa(journal);
    paa << "Calculating variances of the conditional simulations." << endrec;
    calcVariance();
  }
}

void
SimResultsDynamicStats::writeMat(mat_t *fd, const std::string &lname) const
{
  mean.writeMat(fd, lname + "_cond_mean");
  variance.writeMat(fd, lname + "_cond_variance");
}

void
SimResultsDynamicStats::calcMean()
{
  mean.zeros();
  if (data.size() > 0)
    {
      double mult = 1.0/data.size();
      for (int j = 0; j < num_per; j++)
        {
          Vector meanj{mean.getCol(j)};
          for (const auto &i : data)
            {
              ConstVector col{i.getCol(j)};
              meanj.add(mult, col);
            }
        }
    }
}

void
SimResultsDynamicStats::calcVariance()
{
  if (data.size() > 1)
    {
      variance.zeros();
      double mult = 1.0/(data.size()-1);
      for (int j = 0; j < num_per; j++)
        {
          ConstVector meanj{mean.getCol(j)};
          Vector varj{variance.getCol(j)};
          for (const auto &i : data)
            {
              Vector col{i.getCol(j)};
              col.add(-1.0, meanj);
              for (int k = 0; k < col.length(); k++)
                col[k] = col[k]*col[k];
              varj.add(mult, col);
            }
        }
    }
  else
    variance.infs();
}

void
SimResultsIRF::simulate(const DecisionRule &dr, Journal &journal)
{
  JournalRecordPair paa(journal);
  paa << "Performing " << control.getNumSets() << " IRF simulations for "
      << num_per << " periods; shock=" << ishock << ", impulse=" << imp << endrec;
  simulate(dr);
  int thrown = control.getNumSets() - data.size();
  if (thrown > 0)
    {
      JournalRecord rec(journal);
      rec << "I had to throw " << thrown
          << " simulations away due to Nan or Inf" << endrec;
    }
  calcMeans();
  calcVariances();
}

void
SimResultsIRF::simulate(const DecisionRule &dr)
{
  sthread::detach_thread_group gr;
  for (int idata = 0; idata < control.getNumSets(); idata++)
    gr.insert(std::make_unique<SimulationIRFWorker>(*this, dr, DecisionRule::emethod::horner,
                                                    num_per, idata, ishock, imp));
  gr.run();
}

void
SimResultsIRF::calcMeans()
{
  means.zeros();
  if (data.size() > 0)
    {
      for (const auto &i : data)
        means.add(1.0, i);
      means.mult(1.0/data.size());
    }
}

void
SimResultsIRF::calcVariances()
{
  if (data.size() > 1)
    {
      variances.zeros();
      for (const auto &i : data)
        {
          TwoDMatrix d(i);
          d.add(-1.0, means);
          for (int j = 0; j < d.nrows(); j++)
            for (int k = 0; k < d.ncols(); k++)
              variances.get(j, k) += d.get(j, k)*d.get(j, k);
          d.mult(1.0/(data.size()-1));
        }
    }
  else
    variances.infs();
}

void
SimResultsIRF::writeMat(mat_t *fd, const std::string &lname) const
{
  means.writeMat(fd, lname + "_mean");
  variances.writeMat(fd, lname + "_var");
}

void
RTSimResultsStats::simulate(int num_sim, const DecisionRule &dr, const Vector &start,
                            const TwoDMatrix &v, Journal &journal)
{
  JournalRecordPair paa(journal);
  paa << "Performing " << num_sim << " real-time stochastic simulations for "
      << num_per << " periods" << endrec;
  simulate(num_sim, dr, start, v);
  mean = nc.getMean();
  mean.add(1.0, dr.getSteady());
  nc.getVariance(vcov);
  if (thrown_periods > 0)
    {
      JournalRecord rec(journal);
      rec << "I had to throw " << thrown_periods << " periods away due to Nan or Inf" << endrec;
      JournalRecord rec1(journal);
      rec1 << "This affected " << incomplete_simulations << " out of "
           << num_sim << " simulations" << endrec;
    }
}

void
RTSimResultsStats::simulate(int num_sim, const DecisionRule &dr, const Vector &start,
                            const TwoDMatrix &vcov)
{
  std::vector<RandomShockRealization> rsrs;
  rsrs.reserve(num_sim);

  sthread::detach_thread_group gr;
  for (int i = 0; i < num_sim; i++)
    {
      RandomShockRealization sr(vcov, seed_generator::get_new_seed());
      rsrs.push_back(sr);
      gr.insert(std::make_unique<RTSimulationWorker>(*this, dr, DecisionRule::emethod::horner,
                                                     num_per, start, rsrs.back()));
    }
  gr.run();
}

void
RTSimResultsStats::writeMat(mat_t *fd, const std::string &lname)
{
  ConstTwoDMatrix(nc.getDim(), 1, mean).writeMat(fd, lname + "_rt_mean");
  vcov.writeMat(fd, lname + "_rt_vcov");
}

IRFResults::IRFResults(const DynamicModel &mod, const DecisionRule &dr,
                       const SimResults &control, std::vector<int> ili,
                       Journal &journal)
  : model(mod), irf_list_ind(std::move(ili))
{
  int num_per = control.getNumPer();
  JournalRecordPair pa(journal);
  pa << "Calculating IRFs against control for " << static_cast<int>(irf_list_ind.size()) << " shocks and for "
     << num_per << " periods" << endrec;
  const TwoDMatrix &vcov = mod.getVcov();
  for (int ishock : irf_list_ind)
    {
      double stderror = sqrt(vcov.get(ishock, ishock));
      irf_res.emplace_back(control, model.numeq(), num_per,
                           ishock, stderror);
      irf_res.emplace_back(control, model.numeq(), num_per,
                           ishock, -stderror);
    }

  for (unsigned int ii = 0; ii < irf_list_ind.size(); ii++)
    {
      irf_res[2*ii].simulate(dr, journal);
      irf_res[2*ii+1].simulate(dr, journal);
    }
}

void
IRFResults::writeMat(mat_t *fd, const std::string &prefix) const
{
  for (unsigned int i = 0; i < irf_list_ind.size(); i++)
    {
      int ishock = irf_list_ind[i];
      auto shockname = model.getExogNames().getName(ishock);
      irf_res[2*i].writeMat(fd, prefix + "_irfp_" + shockname);
      irf_res[2*i+1].writeMat(fd, prefix + "_irfm_" + shockname);
    }
}

void
SimulationWorker::operator()(std::mutex &mut)
{
  ExplicitShockRealization esr(sr, np);
  TwoDMatrix m{dr.simulate(em, np, st, esr)};
  {
    std::unique_lock<std::mutex> lk{mut};
    res.addDataSet(m, esr, st);
  }
}

/* Here we create a new instance of ExplicitShockRealization of the
   corresponding control, add the impulse, and simulate. */

void
SimulationIRFWorker::operator()(std::mutex &mut)
{
  ExplicitShockRealization esr(res.control.getShocks(idata));
  esr.addToShock(ishock, 0, imp);
  TwoDMatrix m{dr.simulate(em, np, res.control.getStart(idata), esr)};
  m.add(-1.0, res.control.getData(idata));
  {
    std::unique_lock<std::mutex> lk{mut};
    res.addDataSet(m, esr, res.control.getStart(idata));
  }
}

void
RTSimulationWorker::operator()(std::mutex &mut)
{
  NormalConj nc(res.nc.getDim());
  const PartitionY &ypart = dr.getYPart();
  int nu = dr.nexog();
  const Vector &ysteady = dr.getSteady();

  // initialize vectors and subvectors for simulation
  Vector dyu(ypart.nys()+nu);
  ConstVector ystart_pred(ystart, ypart.nstat, ypart.nys());
  ConstVector ysteady_pred(ysteady, ypart.nstat, ypart.nys());
  Vector dy(dyu, 0, ypart.nys());
  Vector u(dyu, ypart.nys(), nu);
  Vector y(nc.getDim());
  ConstVector ypred(y, ypart.nstat, ypart.nys());

  // simulate the first real-time period
  int ip = 0;
  dy = ystart_pred;
  dy.add(-1.0, ysteady_pred);
  sr.get(ip, u);
  dr.eval(em, y, dyu);
  if (ip >= res.num_burn)
    nc.update(y);

  // simulate other real-time periods
  while (y.isFinite() && ip < res.num_burn + res.num_per)
    {
      ip++;
      dy = ypred;
      sr.get(ip, u);
      dr.eval(em, y, dyu);
      if (ip >= res.num_burn)
        nc.update(y);
    }
  {
    std::unique_lock<std::mutex> lk{mut};
    res.nc.update(nc);
    if (res.num_per-ip > 0)
      {
        res.incomplete_simulations++;
        res.thrown_periods += res.num_per-ip;
      }
  }
}

/* This calculates factorization FFᵀ=V in the Cholesky way. It does
   not work for semidefinite matrices. */

void
RandomShockRealization::choleskyFactor(const ConstTwoDMatrix &v)
{
  factor = v;
  lapack_int rows = factor.nrows(), lda = factor.getLD();
  for (int i = 0; i < rows; i++)
    for (int j = i+1; j < rows; j++)
      factor.get(i, j) = 0.0;
  lapack_int info;

  dpotrf("L", &rows, factor.base(), &lda, &info);
  KORD_RAISE_IF(info != 0,
                "Info!=0 in RandomShockRealization::choleskyFactor");
}

/* This calculates FFᵀ=V factorization by symmetric Schur
   decomposition. It works for semidefinite matrices. */

void
RandomShockRealization::schurFactor(const ConstTwoDMatrix &v)
{
  SymSchurDecomp(v).getFactor(factor);
}

void
RandomShockRealization::get(int n, Vector &out)
{
  KORD_RAISE_IF(out.length() != numShocks(),
                "Wrong length of out vector in RandomShockRealization::get");
  Vector d(out.length());
  for (int i = 0; i < d.length(); i++)
    d[i] = dis(mtwister);
  out.zeros();
  factor.multaVec(out, ConstVector(d));
}

ExplicitShockRealization::ExplicitShockRealization(ShockRealization &sr,
                                                   int num_per)
  : shocks(sr.numShocks(), num_per)
{
  for (int j = 0; j < num_per; j++)
    {
      Vector jcol{shocks.getCol(j)};
      sr.get(j, jcol);
    }
}

void
ExplicitShockRealization::get(int n, Vector &out)
{
  KORD_RAISE_IF(out.length() != numShocks(),
                "Wrong length of out vector in ExplicitShockRealization::get");
  int i = n % shocks.ncols();
  ConstVector icol{shocks.getCol(i)};
  out = icol;
}

void
ExplicitShockRealization::addToShock(int ishock, int iper, double val)
{
  KORD_RAISE_IF(ishock < 0 || ishock > numShocks(),
                "Wrong index of shock in ExplicitShockRealization::addToShock");
  int j = iper % shocks.ncols();
  shocks.get(ishock, j) += val;
}

void
GenShockRealization::get(int n, Vector &out)
{
  KORD_RAISE_IF(out.length() != numShocks(),
                "Wrong length of out vector in GenShockRealization::get");
  ExplicitShockRealization::get(n, out);
  Vector r(numShocks());
  RandomShockRealization::get(n, r);
  for (int j = 0; j < numShocks(); j++)
    if (!std::isfinite(out[j]))
      out[j] = r[j];
}