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function [endogenousvariables, success, err, iter] = sim1_lbj(endogenousvariables, exogenousvariables, steadystate, M_, options_)
% Performs deterministic simulations with lead or lag on one period using the historical LBJ algorithm
%
% INPUTS
% ...
%
% OUTPUTS
% endogenousvariables [matrix] All endogenous variables of the model
% success [logical] Whether a solution was found
% err [double] ∞-norm of Δendogenousvariables
% iter [integer] Number of iterations
%
% ALGORITHM
% Laffargue, Boucekkine, Juillard (LBJ)
% see Juillard (1996) Dynare: A program for the resolution and
% simulation of dynamic models with forward variables through the use
% of a relaxation algorithm. CEPREMAP. Couverture Orange. 9602.
%
% SPECIAL REQUIREMENTS
% None.
% Copyright © 1996-2023 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/>.
lead_lag_incidence = M_.lead_lag_incidence;
ny = size(endogenousvariables,1);
nyp = nnz(lead_lag_incidence(1,:));
nyf = nnz(lead_lag_incidence(3,:));
nrs = ny+nyp+nyf+1;
nrc = nyf+1;
iyf = find(lead_lag_incidence(3,:)>0);
iyp = find(lead_lag_incidence(1,:)>0);
isp = 1:nyp;
is = nyp+1:ny+nyp;
isf = iyf+nyp;
isf1 = nyp+ny+1:nyf+nyp+ny+1;
success = false;
iz = 1:ny+nyp+nyf;
function [r, g1] = bytecode_wrapper(y, xpath, params, ys, it_)
ypath = NaN(ny, 3);
ypath(find(lead_lag_incidence')) = y;
[r, s] = bytecode('dynamic', 'evaluate', M_, options_, ypath, xpath(it_+(-1:1), :), params, ys, 1);
g1 = s.g1;
end
if options_.bytecode
dynamicmodel = @bytecode_wrapper;
else
dynamicmodel = str2func(sprintf('%s.dynamic', M_.fname));
end
verbose = options_.verbosity;
if verbose
printline(56)
fprintf('MODEL SIMULATION :\n')
end
h1 = clock;
for iter = 1:options_.simul.maxit
h2 = clock;
c = zeros(ny*options_.periods, nrc);
it_ = M_.maximum_lag+1;
z = [endogenousvariables(iyp,it_-1) ; endogenousvariables(:,it_) ; endogenousvariables(iyf,it_+1)];
[d1, jacobian] = dynamicmodel(z, exogenousvariables, M_.params, steadystate, it_);
jacobian = [jacobian(:,iz), -d1];
ic = 1:ny;
icp = iyp;
c (ic,:) = jacobian(:,is)\jacobian(:,isf1);
for it_ = M_.maximum_lag+(2:options_.periods)
z = [endogenousvariables(iyp,it_-1) ; endogenousvariables(:,it_) ; endogenousvariables(iyf,it_+1)];
[d1, jacobian] = dynamicmodel(z, exogenousvariables, M_.params, steadystate, it_);
jacobian = [jacobian(:,iz), -d1];
jacobian(:,[isf nrs]) = jacobian(:,[isf nrs])-jacobian(:,isp)*c(icp,:);
ic = ic + ny;
icp = icp + ny;
c (ic,:) = jacobian(:,is)\jacobian(:,isf1);
end
c = back_subst_lbj(c, ny, iyf, options_.periods);
endogenousvariables(:,M_.maximum_lag+(1:options_.periods)) = endogenousvariables(:,M_.maximum_lag+(1:options_.periods))+c;
err = max(max(abs(c)));
if verbose
fprintf('Iter: %s,\t err. = %s, \t time = %s\n', num2str(iter), num2str(err), num2str(etime(clock, h2)));
end
if err < options_.dynatol.x
success = true; % Convergency obtained.
break
end
end
if verbose
fprintf('\nTotal time of simulation: %s\n', num2str(etime(clock,h1)))
if success
printline(56)
else
disp('Maximum number of iterations is reached (modify option maxit).')
printline(62)
end
skipline()
end
end
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