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function [residuals,JJacobian] = perfect_foresight_mcp_problem(y, dynamic_function, Y0, YT, ...
exo_simul, params, steady_state, ...
maximum_lag, T, ny, i_cols, ...
i_cols_J1, i_cols_1, i_cols_T, ...
i_cols_j, i_cols_0,i_cols_J0, eq_index)
% function [residuals,JJacobian] = perfect_foresight_mcp_problem(y, dynamic_function, Y0, YT, ...
% exo_simul, params, steady_state, ...
% maximum_lag, T, ny, i_cols, ...
% i_cols_J1, i_cols_1, i_cols_T, ...
% i_cols_j,eq_index)
% Computes the residuals and the Jacobian matrix for a perfect foresight problem over T periods
% in a mixed complementarity problem context
%
% INPUTS
% y [double] N*1 array, terminal conditions for the endogenous variables
% dynamic_function [handle] function handle to _dynamic-file
% Y0 [double] N*1 array, initial conditions for the endogenous variables
% YT [double] N*1 array, terminal conditions for the endogenous variables
% exo_simul [double] nperiods*M_.exo_nbr matrix of exogenous variables (in declaration order)
% for all simulation periods
% params [double] nparams*1 array, parameter values
% steady_state [double] endo_nbr*1 vector of steady state values
% maximum_lag [scalar] maximum lag present in the model
% T [scalar] number of simulation periods
% ny [scalar] number of endogenous variables
% i_cols [double] indices of variables appearing in M.lead_lag_incidence
% and that need to be passed to _dynamic-file
% i_cols_J1 [double] indices of contemporaneous and forward looking variables
% appearing in M.lead_lag_incidence
% i_cols_1 [double] indices of contemporaneous and forward looking variables in
% M.lead_lag_incidence in dynamic Jacobian (relevant in first period)
% i_cols_T [double] columns of dynamic Jacobian related to contemporaneous and backward-looking
% variables (relevant in last period)
% i_cols_j [double] indices of variables in M.lead_lag_incidence
% in dynamic Jacobian (relevant in intermediate periods)
% eq_index [double] N*1 array, index vector describing residual mapping resulting
% from complementarity setup
% OUTPUTS
% residuals [double] (N*T)*1 array, residuals of the stacked problem
% JJacobian [double] (N*T)*(N*T) array, Jacobian of the stacked problem
% ALGORITHM
% None
%
% SPECIAL REQUIREMENTS
% None.
% Copyright (C) 1996-2020 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/>.
YY = [Y0; y; YT];
residuals = zeros(T*ny,1);
if nargout == 2
iJacobian = cell(T,1);
end
i_rows = 1:ny;
offset = 0;
i_cols_J = i_cols;
for it = maximum_lag+(1:T)
if nargout == 1
res = dynamic_function(YY(i_cols),exo_simul, params, ...
steady_state,it);
residuals(i_rows) = res(eq_index);
elseif nargout == 2
[res,jacobian] = dynamic_function(YY(i_cols),exo_simul, params, steady_state,it);
residuals(i_rows) = res(eq_index);
if T==1 && it==maximum_lag+1
[rows, cols, vals] = find(jacobian(eq_index,i_cols_0));
if size(jacobian, 1) == 1 % find() will return row vectors in this case
rows = rows';
cols = cols';
vals = vals';
end
iJacobian{1} = [rows, i_cols_J0(cols), vals];
elseif it == maximum_lag+1
[rows,cols,vals] = find(jacobian(eq_index,i_cols_1));
if numel(eq_index) == 1 % find() will return row vectors in this case
rows = rows';
cols = cols';
vals = vals';
end
iJacobian{1} = [offset+rows, i_cols_J1(cols), vals];
elseif it == maximum_lag+T
[rows,cols,vals] = find(jacobian(eq_index,i_cols_T));
if numel(eq_index) == 1 % find() will return row vectors in this case
rows = rows';
cols = cols';
vals = vals';
end
iJacobian{T} = [offset+rows, i_cols_J(i_cols_T(cols)), vals];
else
[rows,cols,vals] = find(jacobian(eq_index,i_cols_j));
if numel(eq_index) == 1 % find() will return row vectors in this case
rows = rows';
cols = cols';
vals = vals';
end
iJacobian{it-maximum_lag} = [offset+rows, i_cols_J(cols), vals];
i_cols_J = i_cols_J + ny;
end
offset = offset + ny;
end
i_rows = i_rows + ny;
i_cols = i_cols + ny;
end
if nargout == 2
iJacobian = cat(1,iJacobian{:});
JJacobian = sparse(iJacobian(:,1),iJacobian(:,2),iJacobian(:,3),T*ny,T*ny);
end
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