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function [flag,endo_simul,err] = solve_perfect_foresight_model(endo_simul,exo_simul,pfm)
% Copyright (C) 2012-2017 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/>.
flag = 0;
err = 0;
stop = 0;
nan_flag = 0;
model_dynamic = pfm.dynamic_model;
Y = endo_simul(:);
if pfm.verbose
disp (['-----------------------------------------------------']) ;
disp (['MODEL SIMULATION :']) ;
fprintf('\n') ;
end
if pfm.use_bytecode
[flag, endo_simul]=bytecode(Y, exo_simul, pfm.params);
return
end
z = Y(find(pfm.lead_lag_incidence'));
[d1,jacobian] = model_dynamic(z,exo_simul,pfm.params,pfm.steady_state,2);
% Initialization of the jacobian of the stacked model.
A = sparse([],[],[],pfm.periods*pfm.ny,pfm.periods*pfm.ny,pfm.periods*nnz(jacobian));
% Initialization of the Newton residuals.
res = zeros(pfm.periods*pfm.ny,1);
h1 = clock;
% Newton loop.
for iter = 1:pfm.maxit_
h2 = clock;
i_rows = 1:pfm.ny;
i_cols = find(pfm.lead_lag_incidence');
i_cols_A = i_cols;
% Fill the jacobian of the stacked model.
for it = 2:(pfm.periods+1)
[d1,jacobian] = model_dynamic(Y(i_cols),exo_simul,pfm.params,pfm.steady_state,it);
if it == 2
A(i_rows,pfm.i_cols_A1) = jacobian(:,pfm.i_cols_1);
elseif it == pfm.periods+1
A(i_rows,i_cols_A(pfm.i_cols_T)) = jacobian(:,pfm.i_cols_T);
else
A(i_rows,i_cols_A) = jacobian(:,pfm.i_cols_j);
end
res(i_rows) = d1;
i_rows = i_rows + pfm.ny;
i_cols = i_cols + pfm.ny;
if it > 2
i_cols_A = i_cols_A + pfm.ny;
end
end
% Stop if Newton residuals are zero.
err = max(abs(res));
if err < pfm.tolerance
stop = 1 ;
if pfm.verbose
fprintf('\n') ;
disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
fprintf('\n') ;
disp([' Convergency obtained.']) ;
fprintf('\n') ;
end
flag = 0;% Convergency obtained.
endo_simul = reshape(Y,pfm.ny,pfm.periods+2);
break
end
% Compute the Newton step.
dy = -A\res;
if any(isnan(dy))
nan_flag = 1;
break
end
% Update the endogenous variables paths.
Y(pfm.i_upd) = Y(pfm.i_upd) + dy;
end
if ~stop
if pfm.verbose
fprintf('\n') ;
disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
fprintf('\n') ;
disp(['WARNING : maximum number of iterations is reached (modify options_.simul.maxit).']) ;
fprintf('\n') ;
end
flag = 1;% more iterations are needed.
endo_simul = 1;
end
if nan_flag
if pfm.verbose
fprintf('\n') ;
disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
fprintf('\n') ;
disp(['WARNING : NaNs!']) ;
fprintf('\n') ;
end
flag = 1;
endo_simul = 1;
end
if pfm.verbose
disp (['-----------------------------------------------------']) ;
end
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