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preprocessor/BlockTriangular.cc

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/*
* Copyright (C) 2007-2009 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 <iostream>
#include <sstream>
#include <fstream>
#include <ctime>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <functional>
#include "MinimumFeedbackSet.hh"
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/max_cardinality_matching.hpp>
#include <boost/graph/strong_components.hpp>
//------------------------------------------------------------------------------
#include "BlockTriangular.hh"
//------------------------------------------------------------------------------
using namespace std;
using namespace boost;
using namespace MFS;
BlockTriangular::BlockTriangular(SymbolTable &symbol_table_arg, NumericalConstants &num_const_arg)
: symbol_table(symbol_table_arg),
//normalization(symbol_table_arg),
incidencematrix(symbol_table_arg),
num_const(num_const_arg)
{
bt_verbose = 0;
ModelBlock = NULL;
periods = 0;
Normalized_Equation = new DataTree(symbol_table, num_const);
}
BlockTriangular::~BlockTriangular()
{
delete Normalized_Equation;
}
//------------------------------------------------------------------------------
// Find the prologue and the epilogue of the model
void
BlockTriangular::Prologue_Epilogue(bool *IM, int &prologue, int &epilogue, int n, vector<int> &Index_Var_IM, vector<int> &Index_Equ_IM, bool *IM0)
{
bool modifie = 1;
int i, j, k, l = 0;
/*Looking for a prologue */
prologue = 0;
while (modifie)
{
modifie = 0;
for (i = prologue; i < n; i++)
{
k = 0;
for (j = prologue; j < n; j++)
{
if (IM[i*n + j])
{
k++;
l = j;
}
}
if ((k == 1) && IM0[Index_Equ_IM[i]*n + Index_Var_IM[l]])
{
modifie = 1;
incidencematrix.swap_IM_c(IM, prologue, i, l, Index_Var_IM, Index_Equ_IM, n);
prologue++;
}
}
}
epilogue = 0;
modifie = 1;
while (modifie)
{
modifie = 0;
for (i = prologue; i < n - epilogue; i++)
{
k = 0;
for (j = prologue; j < n - epilogue; j++)
{
if (IM[j*n + i])
{
k++;
l = j;
}
}
if ((k == 1) && IM0[Index_Equ_IM[l]*n + Index_Var_IM[i]])
{
modifie = 1;
incidencematrix.swap_IM_c(IM, n - (1 + epilogue), l, i, Index_Var_IM, Index_Equ_IM, n);
epilogue++;
}
}
}
}
//------------------------------------------------------------------------------
// Find a matching between equations and endogenous variables
bool
BlockTriangular::Compute_Normalization(bool *IM, int equation_number, int prologue, int epilogue, bool verbose, bool *IM0, vector<int> &Index_Equ_IM) const
{
int n = equation_number - prologue - epilogue;
typedef adjacency_list<vecS, vecS, undirectedS> BipartiteGraph;
/*
Vertices 0 to n-1 are for endogenous (using type specific ID)
Vertices n to 2*n-1 are for equations (using equation no.)
*/
BipartiteGraph g(2 * n);
// Fill in the graph
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (IM0[(i+prologue) * equation_number+j+prologue])
add_edge(i + n, j, g);
// Compute maximum cardinality matching
typedef vector<graph_traits<BipartiteGraph>::vertex_descriptor> mate_map_t;
mate_map_t mate_map(2*n);
bool check = checked_edmonds_maximum_cardinality_matching(g, &mate_map[0]);
//cout << "check = " << check << "\n";
if (check)
{
// Check if all variables are normalized
mate_map_t::const_iterator it = find(mate_map.begin(), mate_map.begin() + n, graph_traits<BipartiteGraph>::null_vertex());
if (it != mate_map.begin() + n)
{
if (verbose)
{
cerr << "ERROR: Could not normalize dynamic model. Variable "
<< symbol_table.getName(symbol_table.getID(eEndogenous, it - mate_map.begin()))
<< " is not in the maximum cardinality matching." << endl;
exit(EXIT_FAILURE);
}
return false;
}
vector<int> Index_Equ_IM_tmp(Index_Equ_IM);
bool *SIM;
SIM = (bool *) malloc(equation_number*equation_number*sizeof(bool));
memcpy(SIM, IM, equation_number*equation_number*sizeof(bool));
for (int i = 0; i < n; i++)
{
Index_Equ_IM[i + prologue] = Index_Equ_IM_tmp[mate_map[i] - n + prologue];
for (int k = 0; k < n; k++)
IM[(i+prologue)*equation_number+k +prologue] = SIM[(mate_map[i]-n+prologue)*equation_number+k +prologue];
}
free(SIM);
}
return check;
}
t_vtype
BlockTriangular::Get_Variable_LeadLag_By_Block(vector<int > &components_set, int nb_blck_sim, int prologue, int epilogue) const
{
int nb_endo = symbol_table.endo_nbr();
vector<int> variable_blck(nb_endo), equation_blck(nb_endo);
t_vtype Variable_Type(nb_endo);
for (int i = 0; i < nb_endo; i++)
{
if (i < prologue)
{
variable_blck[Index_Var_IM[i]] = i;
equation_blck[Index_Equ_IM[i]] = i;
}
else if (i < components_set.size() + prologue)
{
variable_blck[Index_Var_IM[i]] = components_set[i-prologue] + prologue;
equation_blck[Index_Equ_IM[i]] = components_set[i-prologue] + prologue;
}
else
{
variable_blck[Index_Var_IM[i]] = i- (nb_endo - nb_blck_sim - prologue - epilogue);
equation_blck[Index_Equ_IM[i]] = i- (nb_endo - nb_blck_sim - prologue - epilogue);
}
//cout << "equation_blck[" << Index_Equ_IM[i] << "]=" << equation_blck[Index_Equ_IM[i]] << " variable_blck[" << Index_Var_IM[i] << "] = " << variable_blck[Index_Var_IM[i]] << "\n";
Variable_Type[i] = make_pair(0, 0);
}
for (int k = -incidencematrix.Model_Max_Lag_Endo; k <= incidencematrix.Model_Max_Lead_Endo; k++)
{
bool *Cur_IM = incidencematrix.Get_IM(k, eEndogenous);
if (Cur_IM)
{
for (int i = 0; i < nb_endo; i++)
{
int i_1 = Index_Var_IM[i];
for (int j = 0; j < nb_endo; j++)
{
if (Cur_IM[i_1 + Index_Equ_IM[ j] * nb_endo] and variable_blck[i_1] == equation_blck[Index_Equ_IM[ j]])
{
if (k > Variable_Type[i_1].second)
Variable_Type[i_1] = make_pair(Variable_Type[i_1].first, k);
if (k < -Variable_Type[i_1].first)
Variable_Type[i_1] = make_pair(-k, Variable_Type[i_1].second);
}
}
}
}
}
/*for(int i = 0; i < nb_endo; i++)
cout << "Variable_Type[" << Index_Equ_IM[i] << "].first = " << Variable_Type[Index_Equ_IM[i]].first << " Variable_Type[" << Index_Equ_IM[i] << "].second=" << Variable_Type[Index_Equ_IM[i]].second << "\n";*/
return (Variable_Type);
}
void
BlockTriangular::Compute_Block_Decomposition_and_Feedback_Variables_For_Each_Block(bool *IM, int nb_var, int prologue, int epilogue, vector<int> &Index_Equ_IM, vector<int> &Index_Var_IM, vector<pair<int, int> > &blocks, t_etype &Equation_Type, bool verbose_) const
{
t_vtype V_Variable_Type;
int n = nb_var - prologue - epilogue;
bool *AMp;
AMp = (bool *) malloc(n*n*sizeof(bool));
//transforms the incidence matrix of the complet model into an adjancent matrix of the non-recursive part of the model
for (int i = prologue; i < nb_var - epilogue; i++)
for (int j = prologue; j < nb_var - epilogue; j++)
if (j != i)
AMp[(i-prologue)*n+j-prologue] = IM[i*nb_var + j];
else
AMp[(i-prologue)*n+j-prologue] = 0;
//In a first step we compute the strong components of the graph representation of the static model.
// This insures that block are dynamically recursives.
GraphvizDigraph G2 = AM_2_GraphvizDigraph(AMp, n);
vector<int> component(num_vertices(G2)), discover_time(num_vertices(G2));
int num = strong_components(G2, &component[0]);
blocks = vector<pair<int, int> >(num, make_pair(0, 0));
//This vector contains for each block:
// - first set = equations belonging to the block,
// - second set = the feeback variables,
// - third vector = the reordered non-feedback variables.
vector<pair<set<int>, pair<set<int>, vector<int> > > > components_set(num);
for (unsigned int i = 0; i < component.size(); i++)
{
blocks[component[i]].first++;
components_set[component[i]].first.insert(i);
}
V_Variable_Type = Get_Variable_LeadLag_By_Block(component, num, prologue, epilogue);
vector<int> tmp_Index_Equ_IM(Index_Equ_IM), tmp_Index_Var_IM(Index_Var_IM);
int order = prologue;
bool *SIM;
SIM = (bool *) malloc(nb_var*nb_var*sizeof(bool));
memcpy(SIM, IM, nb_var*nb_var*sizeof(bool));
//Add a loop on vertices which could not be normalized or vertices related to lead variables => force those vertices to belong to the feedback set
for (int i = 0; i < n; i++)
if (Equation_Type[Index_Equ_IM[i+prologue]].first == E_SOLVE or V_Variable_Type[Index_Var_IM[i+prologue]].second >= 0 or V_Variable_Type[Index_Var_IM[i+prologue]].first > 0)
add_edge(i, i, G2);
//For each block, the minimum set of feedback variable is computed
// and the non-feedback variables are reordered to get
// a sub-recursive block without feedback variables
for (int i = 0; i < num; i++)
{
AdjacencyList_type G = GraphvizDigraph_2_AdjacencyList(G2, components_set[i].first);
set<int> feed_back_vertices;
//Print(G);
AdjacencyList_type G1 = Minimal_set_of_feedback_vertex(feed_back_vertices, G);
property_map<AdjacencyList_type, vertex_index_t>::type v_index = get(vertex_index, G);
components_set[i].second.first = feed_back_vertices;
blocks[i].second = feed_back_vertices.size();
vector<int> Reordered_Vertice;
Reordered_Vertice = Reorder_the_recursive_variables(G, feed_back_vertices);
//First we have the recursive equations conditional on feedback variables
for (vector<int>::iterator its = Reordered_Vertice.begin(); its != Reordered_Vertice.end(); its++)
{
Index_Equ_IM[order] = tmp_Index_Equ_IM[*its+prologue];
Index_Var_IM[order] = tmp_Index_Var_IM[*its+prologue];
order++;
}
components_set[i].second.second = Reordered_Vertice;
//Second we have the equations related to the feedback variables
for (set<int>::iterator its = feed_back_vertices.begin(); its != feed_back_vertices.end(); its++)
{
Index_Equ_IM[order] = tmp_Index_Equ_IM[v_index[vertex(*its, G)]+prologue];
Index_Var_IM[order] = tmp_Index_Var_IM[v_index[vertex(*its, G)]+prologue];
order++;
}
}
free(AMp);
free(SIM);
}
void
BlockTriangular::Allocate_Block(int size, int *count_Equ, int count_Block, BlockType type, BlockSimulationType SimType, Model_Block *ModelBlock, t_etype &Equation_Type, int recurs_Size)
{
int i, j, k, l, ls, m, i_1, Lead, Lag, first_count_equ, i1, li;
int *tmp_size, *tmp_size_other_endo, *tmp_size_exo, *tmp_var, *tmp_endo, *tmp_other_endo, *tmp_exo, tmp_nb_other_endo, tmp_nb_exo, nb_lead_lag_endo;
bool *tmp_variable_evaluated;
bool *Cur_IM;
bool *IM, OK;
int Lag_Endo, Lead_Endo, Lag_Exo, Lead_Exo, Lag_Other_Endo, Lead_Other_Endo;
ModelBlock->Periods = periods;
ModelBlock->Block_List[count_Block].is_linear = true;
ModelBlock->Block_List[count_Block].Size = size;
ModelBlock->Block_List[count_Block].Type = type;
ModelBlock->Block_List[count_Block].Nb_Recursives = recurs_Size;
ModelBlock->Block_List[count_Block].Temporary_InUse = new temporary_terms_inuse_type();
ModelBlock->Block_List[count_Block].Temporary_InUse->clear();
ModelBlock->Block_List[count_Block].Simulation_Type = SimType;
ModelBlock->Block_List[count_Block].Equation = (int *) malloc(ModelBlock->Block_List[count_Block].Size * sizeof(int));
ModelBlock->Block_List[count_Block].Equation_Type = (EquationType *) malloc(ModelBlock->Block_List[count_Block].Size * sizeof(EquationType));
ModelBlock->Block_List[count_Block].Equation_Normalized = (NodeID *) malloc(ModelBlock->Block_List[count_Block].Size * sizeof(NodeID));
ModelBlock->Block_List[count_Block].Variable = (int *) malloc(ModelBlock->Block_List[count_Block].Size * sizeof(int));
ModelBlock->Block_List[count_Block].Temporary_Terms_in_Equation = (temporary_terms_type **) malloc(ModelBlock->Block_List[count_Block].Size * sizeof(temporary_terms_type));
ModelBlock->Block_List[count_Block].Own_Derivative = (int *) malloc(ModelBlock->Block_List[count_Block].Size * sizeof(int));
Lead = Lag = 0;
first_count_equ = *count_Equ;
tmp_var = (int *) malloc(size * sizeof(int));
tmp_endo = (int *) malloc((incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1) * sizeof(int));
tmp_other_endo = (int *) malloc(symbol_table.endo_nbr() * sizeof(int));
tmp_size = (int *) malloc((incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1) * sizeof(int));
tmp_size_other_endo = (int *) malloc((incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1) * sizeof(int));
tmp_size_exo = (int *) malloc((incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1) * sizeof(int));
memset(tmp_size_exo, 0, (incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1)*sizeof(int));
memset(tmp_size_other_endo, 0, (incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1)*sizeof(int));
memset(tmp_size, 0, (incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1)*sizeof(int));
memset(tmp_endo, 0, (incidencematrix.Model_Max_Lead + incidencematrix.Model_Max_Lag + 1)*sizeof(int));
memset(tmp_other_endo, 0, symbol_table.endo_nbr()*sizeof(int));
nb_lead_lag_endo = 0;
Lag_Endo = Lead_Endo = Lag_Other_Endo = Lead_Other_Endo = Lag_Exo = Lead_Exo = 0;
//Variable by variable looking for all leads and lags its occurence in each equation of the block
tmp_variable_evaluated = (bool *) malloc(symbol_table.endo_nbr()*sizeof(bool));
memset(tmp_variable_evaluated, 0, symbol_table.endo_nbr()*sizeof(bool));
for (i = 0; i < size; i++)
{
ModelBlock->Block_List[count_Block].Temporary_Terms_in_Equation[i] = new temporary_terms_type();
ModelBlock->Block_List[count_Block].Temporary_Terms_in_Equation[i]->clear();
ModelBlock->Block_List[count_Block].Equation[i] = Index_Equ_IM[*count_Equ];
ModelBlock->Block_List[count_Block].Variable[i] = Index_Var_IM[*count_Equ];
ModelBlock->Block_List[count_Block].Equation_Type[i] = Equation_Type[Index_Equ_IM[*count_Equ]].first;
ModelBlock->Block_List[count_Block].Equation_Normalized[i] = Equation_Type[Index_Equ_IM[*count_Equ]].second;
/*if(Equation_Type[Index_Equ_IM[*count_Equ]].second)
{
temporary_terms_type temporary_terms;
cout << "Equation_Type[Index_Equ_IM[*count_Equ]].second->get_op_code()=" << Equation_Type[Index_Equ_IM[*count_Equ]].second->get_op_code() << "\n";
cout << "ModelBlock->Block_List[" << count_Block << "].Equation_Normalized[" << i << "]->get_op_code()=" << ModelBlock->Block_List[count_Block].Equation_Normalized[i]->get_op_code() << "\n";
ModelBlock->Block_List[count_Block].Equation_Normalized[i]->writeOutput(cout, oMatlabDynamicModelSparse, temporary_terms);
}*/
i_1 = Index_Var_IM[*count_Equ];
for (k = -incidencematrix.Model_Max_Lag_Endo; k <= incidencematrix.Model_Max_Lead_Endo; k++)
{
Cur_IM = incidencematrix.Get_IM(k, eEndogenous);
if (Cur_IM)
{
OK = false;
if (k >= 0)
{
for (j = 0; j < size; j++)
{
if (Cur_IM[i_1 + Index_Equ_IM[first_count_equ + j]*symbol_table.endo_nbr()])
{
tmp_variable_evaluated[i_1] = true;
tmp_size[incidencematrix.Model_Max_Lag_Endo + k]++;
if (!OK)
{
tmp_endo[incidencematrix.Model_Max_Lag + k]++;
nb_lead_lag_endo++;
OK = true;
}
if (k > Lead)
Lead = k;
}
}
}
else
{
for (j = 0; j < size; j++)
{
if (Cur_IM[i_1 + Index_Equ_IM[first_count_equ + j]*symbol_table.endo_nbr()])
{
tmp_variable_evaluated[i_1] = true;
tmp_size[incidencematrix.Model_Max_Lag_Endo + k]++;
if (!OK)
{
tmp_variable_evaluated[i_1] = true;
tmp_endo[incidencematrix.Model_Max_Lag + k]++;
nb_lead_lag_endo++;
OK = true;
}
if (-k > Lag)
Lag = -k;
}
}
}
}
}
(*count_Equ)++;
}
Lag_Endo = Lag;
Lead_Endo = Lead;
tmp_nb_other_endo = 0;
for (i = 0; i < size; i++)
{
for (k = -incidencematrix.Model_Max_Lag_Endo; k <= incidencematrix.Model_Max_Lead_Endo; k++)
{
Cur_IM = incidencematrix.Get_IM(k, eEndogenous);
if (Cur_IM)
{
i_1 = Index_Equ_IM[first_count_equ+i] * symbol_table.endo_nbr();
for (j = 0; j < symbol_table.endo_nbr(); j++)
if (Cur_IM[i_1 + j])
{
if (!tmp_variable_evaluated[j])
{
tmp_other_endo[j] = 1;
tmp_nb_other_endo++;
}
if (k > 0 && k > Lead_Other_Endo)
Lead_Other_Endo = k;
else if (k < 0 && (-k) > Lag_Other_Endo)
Lag_Other_Endo = -k;
if (k > 0 && k > Lead)
Lead = k;
else if (k < 0 && (-k) > Lag)
Lag = -k;
tmp_size_other_endo[k+incidencematrix.Model_Max_Lag_Endo]++;
}
}
}
}
ModelBlock->Block_List[count_Block].nb_other_endo = tmp_nb_other_endo;
ModelBlock->Block_List[count_Block].Other_Endogenous = (int *) malloc(tmp_nb_other_endo * sizeof(int));
tmp_exo = (int *) malloc(symbol_table.exo_nbr() * sizeof(int));
memset(tmp_exo, 0, symbol_table.exo_nbr() * sizeof(int));
tmp_nb_exo = 0;
for (i = 0; i < size; i++)
{
for (k = -incidencematrix.Model_Max_Lag_Exo; k <= incidencematrix.Model_Max_Lead_Exo; k++)
{
Cur_IM = incidencematrix.Get_IM(k, eExogenous);
if (Cur_IM)
{
i_1 = Index_Equ_IM[first_count_equ+i] * symbol_table.exo_nbr();
for (j = 0; j < symbol_table.exo_nbr(); j++)
if (Cur_IM[i_1 + j])
{
if (!tmp_exo[j])
{
tmp_exo[j] = 1;
tmp_nb_exo++;
}
if (k > 0 && k > Lead_Exo)
Lead_Exo = k;
else if (k < 0 && (-k) > Lag_Exo)
Lag_Exo = -k;
if (k > 0 && k > Lead)
Lead = k;
else if (k < 0 && (-k) > Lag)
Lag = -k;
tmp_size_exo[k+incidencematrix.Model_Max_Lag_Exo]++;
}
}
}
}
ModelBlock->Block_List[count_Block].nb_exo = tmp_nb_exo;
ModelBlock->Block_List[count_Block].Exogenous = (int *) malloc(tmp_nb_exo * sizeof(int));
k = 0;
for (j = 0; j < symbol_table.exo_nbr(); j++)
if (tmp_exo[j])
{
ModelBlock->Block_List[count_Block].Exogenous[k] = j;
k++;
}
ModelBlock->Block_List[count_Block].nb_exo_det = 0;
ModelBlock->Block_List[count_Block].Max_Lag = Lag;
ModelBlock->Block_List[count_Block].Max_Lead = Lead;
ModelBlock->Block_List[count_Block].Max_Lag_Endo = Lag_Endo;
ModelBlock->Block_List[count_Block].Max_Lead_Endo = Lead_Endo;
ModelBlock->Block_List[count_Block].Max_Lag_Other_Endo = Lag_Other_Endo;
ModelBlock->Block_List[count_Block].Max_Lead_Other_Endo = Lead_Other_Endo;
ModelBlock->Block_List[count_Block].Max_Lag_Exo = Lag_Exo;
ModelBlock->Block_List[count_Block].Max_Lead_Exo = Lead_Exo;
ModelBlock->Block_List[count_Block].IM_lead_lag = (IM_compact *) malloc((Lead + Lag + 1) * sizeof(IM_compact));
ls = l = li = size;
i1 = 0;
ModelBlock->Block_List[count_Block].Nb_Lead_Lag_Endo = nb_lead_lag_endo;
for (i = 0; i < Lead + Lag + 1; i++)
{
if (incidencematrix.Model_Max_Lag_Endo-Lag+i >= 0)
{
ModelBlock->Block_List[count_Block].IM_lead_lag[i].size = tmp_size[incidencematrix.Model_Max_Lag_Endo - Lag + i];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].nb_endo = tmp_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].u = (int *) malloc(tmp_size[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].us = (int *) malloc(tmp_size[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var = (int *) malloc(tmp_size[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ = (int *) malloc(tmp_size[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var_Index = (int *) malloc(tmp_size[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_Index = (int *) malloc(tmp_size[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].size_other_endo = tmp_size_other_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].nb_other_endo = tmp_other_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].u_other_endo = (int *) malloc(tmp_size_other_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var_other_endo = (int *) malloc(tmp_size_other_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_other_endo = (int *) malloc(tmp_size_other_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var_Index_other_endo = (int *) malloc(tmp_size_other_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_Index_other_endo = (int *) malloc(tmp_size_other_endo[incidencematrix.Model_Max_Lag_Endo - Lag + i] * sizeof(int));
}
else
ModelBlock->Block_List[count_Block].IM_lead_lag[i].size = 0;
/*if (incidencematrix.Model_Max_Lag_Exo-Lag+i>=0)
{
ModelBlock->Block_List[count_Block].IM_lead_lag[i].size_exo = tmp_size_exo[incidencematrix.Model_Max_Lag_Exo - Lag + i];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Exogenous = (int*)malloc(tmp_size_exo[incidencematrix.Model_Max_Lag_Exo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Exogenous_Index = (int*)malloc(tmp_size_exo[incidencematrix.Model_Max_Lag_Exo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_X = (int*)malloc(tmp_size_exo[incidencematrix.Model_Max_Lag_Exo - Lag + i] * sizeof(int));
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_X_Index = (int*)malloc(tmp_size_exo[incidencematrix.Model_Max_Lag_Exo - Lag + i] * sizeof(int));
}
else
ModelBlock->Block_List[count_Block].IM_lead_lag[i].size_exo = 0;*/
ModelBlock->Block_List[count_Block].IM_lead_lag[i].u_init = l;
memset(tmp_variable_evaluated, 0, symbol_table.endo_nbr()*sizeof(bool));
IM = incidencematrix.Get_IM(i - Lag, eEndogenous);
if (IM)
{
for (j = first_count_equ; j < size + first_count_equ; j++)
{
i_1 = Index_Var_IM[j];
m = 0;
for (k = first_count_equ; k < size + first_count_equ; k++)
if (IM[i_1 + Index_Equ_IM[k] * symbol_table.endo_nbr()])
m++;
if (m > 0)
{
tmp_var[j - first_count_equ] = i1;
i1++;
}
}
m = 0;
for (j = first_count_equ; j < size + first_count_equ; j++)
{
i_1 = Index_Equ_IM[j] * symbol_table.endo_nbr();
for (k = first_count_equ; k < size + first_count_equ; k++)
if (IM[Index_Var_IM[k] + i_1])
{
if (i == Lag)
{
ModelBlock->Block_List[count_Block].IM_lead_lag[i].us[m] = ls;
ls++;
}
ModelBlock->Block_List[count_Block].IM_lead_lag[i].u[m] = li;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ[m] = j - first_count_equ;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var[m] = k - first_count_equ;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_Index[m] = Index_Equ_IM[j];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var_Index[m] = Index_Var_IM[k];
tmp_variable_evaluated[Index_Var_IM[k]] = true;
l++;
m++;
li++;
}
}
ModelBlock->Block_List[count_Block].IM_lead_lag[i].u_finish = li - 1;
m = 0;
for (j = first_count_equ; j < size + first_count_equ; j++)
{
i_1 = Index_Equ_IM[j] * symbol_table.endo_nbr();
for (k = 0; k < symbol_table.endo_nbr(); k++)
if ((!tmp_variable_evaluated[Index_Var_IM[k]]) && IM[Index_Var_IM[k] + i_1])
{
ModelBlock->Block_List[count_Block].IM_lead_lag[i].u_other_endo[m] = l;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_other_endo[m] = j - first_count_equ;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var_other_endo[m] = k;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_Index_other_endo[m] = Index_Equ_IM[j];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Var_Index_other_endo[m] = Index_Var_IM[k];
l++;
m++;
}
}
ModelBlock->Block_List[count_Block].IM_lead_lag[i].size_other_endo = m;
}
/*IM = incidencematrix.Get_IM(i - Lag, eExogenous);
if (IM)
{
m = 0;
for (j = first_count_equ;j < size + first_count_equ;j++)
{
i_1 = Index_Equ_IM[j] * symbol_table.exo_nbr();
for (k = 0; k<tmp_nb_exo; k++)
{
if (IM[ModelBlock->Block_List[count_Block].Exogenous[k]+i_1])
{
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Exogenous[m] = k;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Exogenous_Index[m] = ModelBlock->Block_List[count_Block].Exogenous[k];
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_X[m] = j - first_count_equ;
ModelBlock->Block_List[count_Block].IM_lead_lag[i].Equ_X_Index[m] = Index_Equ_IM[j];
m++;
}
}
}
}*/
}
free(tmp_size);
free(tmp_size_other_endo);
free(tmp_size_exo);
free(tmp_endo);
free(tmp_other_endo);
free(tmp_exo);
free(tmp_var);
free(tmp_variable_evaluated);
}
void
BlockTriangular::Free_Block(Model_Block *ModelBlock) const
{
int blk, i;
for (blk = 0; blk < ModelBlock->Size; blk++)
{
free(ModelBlock->Block_List[blk].Equation);
free(ModelBlock->Block_List[blk].Variable);
free(ModelBlock->Block_List[blk].Exogenous);
free(ModelBlock->Block_List[blk].Own_Derivative);
free(ModelBlock->Block_List[blk].Other_Endogenous);
free(ModelBlock->Block_List[blk].Equation_Type);
free(ModelBlock->Block_List[blk].Equation_Normalized);
for (i = 0; i < ModelBlock->Block_List[blk].Max_Lag + ModelBlock->Block_List[blk].Max_Lead + 1; i++)
{
if (incidencematrix.Model_Max_Lag_Endo-ModelBlock->Block_List[blk].Max_Lag+i >= 0 /*&& ModelBlock->Block_List[blk].IM_lead_lag[i].size*/)
{
free(ModelBlock->Block_List[blk].IM_lead_lag[i].u);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].us);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Equ);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Var);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Equ_Index);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Var_Index);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].u_other_endo);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Var_other_endo);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Equ_other_endo);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Var_Index_other_endo);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Equ_Index_other_endo);
}
/*if (incidencematrix.Model_Max_Lag_Exo-ModelBlock->Block_List[blk].Max_Lag+i>=0 )
{
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Exogenous);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Exogenous_Index);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Equ_X_Index);
free(ModelBlock->Block_List[blk].IM_lead_lag[i].Equ_X);
}*/
}
free(ModelBlock->Block_List[blk].IM_lead_lag);
for (i = 0; i < ModelBlock->Block_List[blk].Size; i++)
delete ModelBlock->Block_List[blk].Temporary_Terms_in_Equation[i];
free(ModelBlock->Block_List[blk].Temporary_Terms_in_Equation);
delete (ModelBlock->Block_List[blk].Temporary_InUse);
}
free(ModelBlock->Block_List);
free(ModelBlock);
}
t_etype
BlockTriangular::Equation_Type_determination(vector<BinaryOpNode *> &equations, map<pair<int, int >, NodeID> &first_cur_endo_derivatives, vector<int> &Index_Var_IM, vector<int> &Index_Equ_IM)
{
NodeID lhs, rhs;
ostringstream tmp_output;
BinaryOpNode *eq_node;
ostringstream tmp_s;
temporary_terms_type temporary_terms;
EquationType Equation_Simulation_Type;
t_etype V_Equation_Simulation_Type(equations.size());
for (unsigned int i = 0; i < equations.size(); i++)
{
temporary_terms.clear();
int eq = Index_Equ_IM[i];
int var = Index_Var_IM[i];
eq_node = equations[eq];
lhs = eq_node->get_arg1();
rhs = eq_node->get_arg2();
Equation_Simulation_Type = E_SOLVE;
tmp_s.str("");
tmp_output.str("");
lhs->writeOutput(tmp_output, oMatlabDynamicModelSparse, temporary_terms);
tmp_s << "y(it_, " << Index_Var_IM[i]+1 << ")";
map<pair<int, int>, NodeID>::iterator derivative = first_cur_endo_derivatives.find(make_pair(eq, var));
/*cout << "eq=" << eq << " var=" << var << "=";
first_cur_endo_derivatives[make_pair(eq, var)]->writeOutput(cout, oMatlabDynamicModelSparse, temporary_terms);
cout << "\n";
cout << "equation : ";
eq_node->writeOutput(cout, oMatlabDynamicModelSparse, temporary_terms);
cout << "\n";*/
set<pair<int, int> > result;
pair<bool, NodeID> res;
derivative->second->collectEndogenous(result);
/*for(set<pair<int, int> >::const_iterator iitt = result.begin(); iitt!=result.end(); iitt++)
cout << "result = " << iitt->first << ", " << iitt->second << "\n";*/
set<pair<int, int> >::const_iterator d_endo_variable = result.find(make_pair(var, 0));
//Determine whether the equation could be evaluated rather than to be solved
if (tmp_output.str() == tmp_s.str() and d_endo_variable == result.end())
{
Equation_Simulation_Type = E_EVALUATE;
}
else
{
//the equation could be normalized by a permutation of the rhs and the lhs
if (d_endo_variable == result.end()) //the equation is linear in the endogenous and could be normalized using the derivative
{
Equation_Simulation_Type = E_EVALUATE_S;
//cout << " gone normalized : ";
res = equations[eq]->normalizeLinearInEndoEquation(var, derivative->second);
/*res.second->writeOutput(cout, oMatlabDynamicModelSparse, temporary_terms);
cout << " done\n";*/
}
}
V_Equation_Simulation_Type[eq] = make_pair(Equation_Simulation_Type, dynamic_cast<BinaryOpNode *>(res.second));
}
return (V_Equation_Simulation_Type);
}
t_type
BlockTriangular::Reduce_Blocks_and_type_determination(int prologue, int epilogue, vector<pair<int, int> > &blocks, vector<BinaryOpNode *> &equations, t_etype &Equation_Type)
{
int i = 0;
int count_equ = 0, blck_count_simult = 0;
int Blck_Size, Recurs_Size;
int Lead, Lag;
t_type Type;
bool *Cur_IM;
BlockSimulationType Simulation_Type, prev_Type = UNKNOWN;
int eq = 0;
for (i = 0; i < prologue+(int) blocks.size()+epilogue; i++)
{
int first_count_equ = count_equ;
if (i < prologue)
{
Blck_Size = 1;
Recurs_Size = 0;
}
else if (i < prologue+(int) blocks.size())
{
Blck_Size = blocks[blck_count_simult].first;
Recurs_Size = Blck_Size - blocks[blck_count_simult].second;
blck_count_simult++;
}
else if (i < prologue+(int) blocks.size()+epilogue)
{
Blck_Size = 1;
Recurs_Size = 0;
}
Lag = Lead = 0;
for (count_equ = first_count_equ; count_equ < Blck_Size+first_count_equ; count_equ++)
{
int i_1 = Index_Var_IM[count_equ];
for (int k = -incidencematrix.Model_Max_Lag_Endo; k <= incidencematrix.Model_Max_Lead_Endo; k++)
{
Cur_IM = incidencematrix.Get_IM(k, eEndogenous);
if (Cur_IM)
{
for (int j = 0; j < Blck_Size; j++)
{
if (Cur_IM[i_1 + Index_Equ_IM[first_count_equ + j] * symbol_table.endo_nbr()])
{
if (k > Lead)
Lead = k;
else if (-k > Lag)
Lag = -k;
}
}
}
}
}
if ((Lag > 0) && (Lead > 0))
{
if (Blck_Size == 1)
Simulation_Type = SOLVE_TWO_BOUNDARIES_SIMPLE;
else
Simulation_Type = SOLVE_TWO_BOUNDARIES_COMPLETE;
}
else if (Blck_Size > 1)
{
if (Lead > 0)
Simulation_Type = SOLVE_BACKWARD_COMPLETE;
else
Simulation_Type = SOLVE_FORWARD_COMPLETE;
}
else
{
if (Lead > 0)
Simulation_Type = SOLVE_BACKWARD_SIMPLE;
else
Simulation_Type = SOLVE_FORWARD_SIMPLE;
}
if (Blck_Size == 1)
{
if (Equation_Type[Index_Equ_IM[eq]].first == E_EVALUATE /*or Equation_Type[Index_Equ_IM[eq]].first==E_EVALUATE_R*/ or Equation_Type[Index_Equ_IM[eq]].first == E_EVALUATE_S)
{
if (Simulation_Type == SOLVE_BACKWARD_SIMPLE)
Simulation_Type = EVALUATE_BACKWARD;
else if (Simulation_Type == SOLVE_FORWARD_SIMPLE)
Simulation_Type = EVALUATE_FORWARD;
}
if (i > 0)
{
if ((prev_Type == EVALUATE_FORWARD and Simulation_Type == EVALUATE_FORWARD)
or (prev_Type == EVALUATE_BACKWARD and Simulation_Type == EVALUATE_BACKWARD))
{
BlockSimulationType c_Type = (Type[Type.size()-1]).first;
int c_Size = (Type[Type.size()-1]).second.first;
Type[Type.size()-1] = make_pair(c_Type, make_pair(++c_Size, Type[Type.size()-1].second.second));
}
else
Type.push_back(make_pair(Simulation_Type, make_pair(Blck_Size, Recurs_Size)));
}
else
Type.push_back(make_pair(Simulation_Type, make_pair(Blck_Size, Recurs_Size)));
}
else
{
Type.push_back(make_pair(Simulation_Type, make_pair(Blck_Size, Recurs_Size)));
}
prev_Type = Simulation_Type;
eq += Blck_Size;
}
return (Type);
}
void
BlockTriangular::Normalize_and_BlockDecompose(bool *IM, Model_Block *ModelBlock, int n, int &prologue, int &epilogue, vector<int> &Index_Var_IM, vector<int> &Index_Equ_IM, bool *IM_0, jacob_map &j_m, vector<BinaryOpNode *> &equations, t_etype &V_Equation_Type, map<pair<int, int >, NodeID> &first_cur_endo_derivatives)
{
int i, j, Nb_TotalBlocks, Nb_RecursBlocks, Nb_SimulBlocks;
BlockType Btype;
int count_Block, count_Equ;
bool *SIM0, *SIM00;
SIM0 = (bool *) malloc(n * n * sizeof(bool));
memcpy(SIM0, IM_0, n*n*sizeof(bool));
Prologue_Epilogue(IM, prologue, epilogue, n, Index_Var_IM, Index_Equ_IM, SIM0);
free(SIM0);
int counted = 0;
if (prologue+epilogue < n)
{
cout << "Normalizing the model ...\n";
double *max_val = (double *) malloc(n*sizeof(double));
memset(max_val, 0, n*sizeof(double));
for (map< pair< int, int >, double >::iterator iter = j_m.begin(); iter != j_m.end(); iter++)
{
if (fabs(iter->second) > max_val[iter->first.first])
max_val[iter->first.first] = fabs(iter->second);
}
for (map< pair< int, int >, double >::iterator iter = j_m.begin(); iter != j_m.end(); iter++)
iter->second /= max_val[iter->first.first];
free(max_val);
bool OK = false;
double bi = 0.99999999;
//double bi=1e-13;
int suppressed = 0;
vector<int> Index_Equ_IM_save(Index_Equ_IM);
while (!OK && bi > 1e-14)
{
int suppress = 0;
Index_Equ_IM = Index_Equ_IM_save;
SIM0 = (bool *) malloc(n * n * sizeof(bool));
memset(SIM0, 0, n*n*sizeof(bool));
SIM00 = (bool *) malloc(n * n * sizeof(bool));
memset(SIM00, 0, n*n*sizeof(bool));
for (map< pair< int, int >, double >::iterator iter = j_m.begin(); iter != j_m.end(); iter++)
{
if (fabs(iter->second) > bi)
{
SIM0[iter->first.first*n+iter->first.second] = 1;
if (!IM_0[iter->first.first*n+iter->first.second])
{
cout << "Error nothing at IM_0[" << iter->first.first << ", " << iter->first.second << "]=" << IM_0[iter->first.first*n+iter->first.second] << " " << iter->second << "\n";
}
}
else
suppress++;
}
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
{
SIM00[i*n + j] = SIM0[Index_Equ_IM[i] * n + Index_Var_IM[j]];
}
free(SIM0);
if (suppress != suppressed)
OK = Compute_Normalization(IM, n, prologue, epilogue, false, SIM00, Index_Equ_IM);
suppressed = suppress;
if (!OK)
//bi/=1.07;
bi /= 2;
counted++;
if (bi > 1e-14)
free(SIM00);
}
if (!OK)
Compute_Normalization(IM, n, prologue, epilogue, true, SIM00, Index_Equ_IM);
}
V_Equation_Type = Equation_Type_determination(equations, first_cur_endo_derivatives, Index_Var_IM, Index_Equ_IM);
cout << "Finding the optimal block decomposition of the model ...\n";
vector<pair<int, int> > blocks;
if (prologue+epilogue < n)
Compute_Block_Decomposition_and_Feedback_Variables_For_Each_Block(IM, n, prologue, epilogue, Index_Equ_IM, Index_Var_IM, blocks, V_Equation_Type, false);
t_type Type = Reduce_Blocks_and_type_determination(prologue, epilogue, blocks, equations, V_Equation_Type);
i = 0;
j = 0;
Nb_SimulBlocks = 0;
int Nb_fv = 0;
for (t_type::const_iterator it = Type.begin(); it != Type.end(); it++)
{
if (it->first == SOLVE_FORWARD_COMPLETE || it->first == SOLVE_BACKWARD_COMPLETE || it->first == SOLVE_TWO_BOUNDARIES_COMPLETE)
{
Nb_SimulBlocks++;
if (it->second.first > j)
{
j = it->second.first;
Nb_fv = blocks[Nb_SimulBlocks-1].second;
}
}
}
Nb_TotalBlocks = Type.size();
Nb_RecursBlocks = Nb_TotalBlocks - Nb_SimulBlocks;
cout << Nb_TotalBlocks << " block(s) found:\n";
cout << " " << Nb_RecursBlocks << " recursive block(s) and " << blocks.size() << " simultaneous block(s). \n";
cout << " the largest simultaneous block has " << j << " equation(s)\n"
<<" and " << Nb_fv << " feedback variable(s).\n";
ModelBlock->Size = Nb_TotalBlocks;
ModelBlock->Periods = periods;
ModelBlock->Block_List = (Block *) malloc(sizeof(ModelBlock->Block_List[0]) * Nb_TotalBlocks);
count_Equ = count_Block = 0;
for (t_type::const_iterator it = Type.begin(); it != Type.end(); it++)
{
if (count_Equ < prologue)
Btype = PROLOGUE;
else if (count_Equ < n-epilogue)
if (it->second.first == 1)
Btype = PROLOGUE;
else
Btype = SIMULTANS;
else
Btype = EPILOGUE;
Allocate_Block(it->second.first, &count_Equ, count_Block++, Btype, it->first, ModelBlock, V_Equation_Type, it->second.second);
}
}
//------------------------------------------------------------------------------
// normalize each equation of the dynamic model
// and find the optimal block triangular decomposition of the static model
void
BlockTriangular::Normalize_and_BlockDecompose_Static_0_Model(jacob_map &j_m, vector<BinaryOpNode *> &equations, t_etype &equation_simulation_type, map<pair<int, int >, NodeID> &first_cur_endo_derivatives)
{
bool *SIM, *SIM_0;
bool *Cur_IM;
int i, k, size;
//First create a static model incidence matrix
size = symbol_table.endo_nbr() * symbol_table.endo_nbr() * sizeof(*SIM);
SIM = (bool *) malloc(size);
for (i = 0; i < symbol_table.endo_nbr() * symbol_table.endo_nbr(); i++) SIM[i] = 0;
for (k = -incidencematrix.Model_Max_Lag_Endo; k <= incidencematrix.Model_Max_Lead_Endo; k++)
{
Cur_IM = incidencematrix.Get_IM(k, eEndogenous);
if (Cur_IM)
{
for (i = 0; i < symbol_table.endo_nbr()*symbol_table.endo_nbr(); i++)
{
SIM[i] = (SIM[i]) || (Cur_IM[i]);
}
}
}
if (bt_verbose)
{
cout << "incidence matrix for the static model (unsorted) \n";
incidencematrix.Print_SIM(SIM, eEndogenous);
}
Index_Equ_IM = vector<int>(symbol_table.endo_nbr());
for (i = 0; i < symbol_table.endo_nbr(); i++)
{
Index_Equ_IM[i] = i;
}
Index_Var_IM = vector<int>(symbol_table.endo_nbr());
for (i = 0; i < symbol_table.endo_nbr(); i++)
{
Index_Var_IM[i] = i;
}
if (ModelBlock != NULL)
Free_Block(ModelBlock);
ModelBlock = (Model_Block *) malloc(sizeof(*ModelBlock));
Cur_IM = incidencematrix.Get_IM(0, eEndogenous);
SIM_0 = (bool *) malloc(symbol_table.endo_nbr() * symbol_table.endo_nbr() * sizeof(*SIM_0));
for (i = 0; i < symbol_table.endo_nbr()*symbol_table.endo_nbr(); i++)
SIM_0[i] = Cur_IM[i];
Normalize_and_BlockDecompose(SIM, ModelBlock, symbol_table.endo_nbr(), prologue, epilogue, Index_Var_IM, Index_Equ_IM, SIM_0, j_m, equations, equation_simulation_type, first_cur_endo_derivatives);
free(SIM_0);
free(SIM);
}
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