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function [forcs, e]= mcforecast3(cL,H,mcValue,shocks,forcs,T,R,mv,mu)
% [forcs, e] = mcforecast3(cL,H,mcValue,shocks,forcs,T,R,mv,mu)
% Computes the shock values for constrained forecasts necessary to keep
% endogenous variables at their constrained paths
%
% INPUTS
% o cL [scalar] number of controlled periods
% o H [scalar] number of forecast periods
% o mcValue [n_controlled_vars by cL double] paths for constrained variables
% o shocks [nexo by H double] shock values draws (with zeros for controlled_varexo)
% o forcs [n_endovars by H+1 double] matrix of endogenous variables storing the inital condition
% o T [n_endovars by n_endovars double] transition matrix of the state equation.
% o R [n_endovars by n_exo double] matrix relating the endogenous variables to the innovations in the state equation.
% o mv [n_controlled_exo by n_endovars boolean] indicator vector selecting constrained endogenous variables
% o mu [n_controlled_vars by nexo boolean] indicator vector selecting controlled exogenous variables
% OUTPUTS
% o forcs [n_endovars by H+1 double] matrix of forecasted endogenous variables
% o e [nexo by H double] matrix of exogenous variables
%
% Algorithm:
% Relies on state-space form:
% y_t=T*y_{t-1}+R*shocks(:,t)
% Shocks are split up into shocks_uncontrolled and shockscontrolled while
% the endogenous variables are also split up into controlled and
% uncontrolled ones to get:
% y_t(controlled_vars_index)=T*y_{t-1}(controlled_vars_index)+R(controlled_vars_index,uncontrolled_shocks_index)*shocks_uncontrolled_t
% + R(controlled_vars_index,controlled_shocks_index)*shocks_controlled_t
%
% This is then solved to get:
% shocks_controlled_t=(y_t(controlled_vars_index)-(T*y_{t-1}(controlled_vars_index)+R(controlled_vars_index,uncontrolled_shocks_index)*shocks_uncontrolled_t)/R(controlled_vars_index,controlled_shocks_index)
%
% Variable number of controlled vars are allowed in different
% periods. Missing control information are indicated by NaN in
% y_t(controlled_vars_index).
%
% After obtaining the shocks, and for uncontrolled periods, the state-space representation
% y_t=T*y_{t-1}+R*shocks(:,t)
% is used for forecasting
%
% Copyright (C) 2006-2017 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 <https://www.gnu.org/licenses/>.
if cL
e = zeros(size(mcValue,1),cL);
for t = 1:cL
% missing conditional values are indicated by NaN
k = find(isfinite(mcValue(:,t)));
e(k,t) = inv(mv(k,:)*R*mu(:,k))*(mcValue(k,t)-mv(k,:)*T*forcs(:,t)-mv(k,:)*R*shocks(:,t));
forcs(:,t+1) = T*forcs(:,t)+R*(mu(:,k)*e(k,t)+shocks(:,t));
end
end
for t = cL+1:H
forcs(:,t+1) = T*forcs(:,t)+R*shocks(:,t);
end
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