129 lines
5.8 KiB
Matlab
129 lines
5.8 KiB
Matlab
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 © 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 <https://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
|