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function y = irf(M_, options_, dr, e1, long, drop, replic, iorder)
% function y = irf(M_, options_, dr, e1, long, drop, replic, iorder)
% Computes impulse response functions
%
% INPUTS
% M_: structure representing the model
% options_: structure representing options for commands
% dr: structure of decisions rules for stochastic simulations
% e1: exogenous variables value in time 1 after one shock
% long: number of periods of simulation
% drop: truncation (in order 2)
% replic: number of replications (in order 2)
% iorder: first or second order approximation
%
% OUTPUTS
% y: impulse response matrix
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2003-2019 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/>.
if M_.maximum_lag >= 1
temps = repmat(dr.ys,1,M_.maximum_lag);
else
temps = zeros(M_.endo_nbr, 1); % Dummy values for purely forward models
end
y = 0;
local_order = iorder;
if local_order~=1 && M_.hessian_eq_zero
local_order = 1;
end
if local_order == 1
y1 = repmat(dr.ys,1,long);
ex2 = zeros(long,M_.exo_nbr);
ex2(1,:) = e1';
y2 = simult_(M_,options_,temps,dr,ex2,local_order);
y = y2(:,M_.maximum_lag+1:end)-y1;
else
% eliminate shocks with 0 variance
i_exo_var = setdiff([1:M_.exo_nbr],find(diag(M_.Sigma_e) == 0 ));
nxs = length(i_exo_var);
ex1 = zeros(long+drop,M_.exo_nbr);
chol_S = chol(M_.Sigma_e(i_exo_var,i_exo_var));
for j = 1: replic
ex1(:,i_exo_var) = randn(long+drop,nxs)*chol_S;
ex2 = ex1;
ex2(drop+1,:) = ex2(drop+1,:)+e1';
y1 = simult_(M_,options_,temps,dr,ex1,local_order);
y2 = simult_(M_,options_,temps,dr,ex2,local_order);
y = y+(y2(:,M_.maximum_lag+drop+1:end)-y1(:,M_.maximum_lag+drop+1:end));
end
y=y/replic;
end
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