function PackedConditionalVarianceDecomposition = conditional_variance_decomposition(StateSpaceModel, Steps, SubsetOfVariables,sigma_e_is_diagonal)
% This function computes the conditional variance decomposition of a given state space model
% for a subset of endogenous variables.
% 
% INPUTS 
%   StateSpaceModel     [structure]   Specification of the state space model.
%   Steps               [integer]     1*h vector of dates.
%   SubsetOfVariables   [integer]     1*q vector of indices.
%    
% OUTPUTS 
%   PackedConditionalVarianceDecomposition  [double] n(n+1)/2*p matrix, where p is the number of state innovations and
%                                                    n is equal to length(SubsetOfVariables).    
%
% SPECIAL REQUIREMENTS
%
% [1] In this version, absence of measurement errors is assumed...

% Copyright (C) 2009 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/>.
number_of_state_innovations = ...
    StateSpaceModel.number_of_state_innovations;
transition_matrix = StateSpaceModel.transition_matrix;
number_of_state_equations = ...
    StateSpaceModel.number_of_state_equations;
nSteps = length(Steps);

ConditionalVariance = zeros(number_of_state_equations,number_of_state_equations);
ConditionalVariance = repmat(ConditionalVariance,[1 1 nSteps ...
                    number_of_state_innovations]);

if StateSpaceModel.sigma_e_is_diagonal
    B = StateSpaceModel.impulse_matrix.* ...
        repmat(sqrt(diag(StateSpaceModel.state_innovations_covariance_matrix)'),...
               number_of_state_equations,1);
else
    B = StateSpaceModel.impulse_matrix*chol(StateSpaceModel.state_innovations_covariance_matrix)';
end

for i=1:number_of_state_innovations
    BB = B(:,i)*B(:,i)';
    V = zeros(number_of_state_equations,number_of_state_equations);
    m = 1;
    for h = 1:max(Steps)
        V = transition_matrix*V*transition_matrix'+BB;
        if h == Steps(m)
            ConditionalVariance(:,:,m,i) = V;
            m = m+1;
        end
    end
end

ConditionalVariance = ConditionalVariance(SubsetOfVariables,SubsetOfVariables,:,:);
NumberOfVariables = length(SubsetOfVariables);
PackedConditionalVarianceDecomposition = zeros(NumberOfVariables*(NumberOfVariables+1)/2,length(Steps),StateSpaceModel.number_of_state_innovations); 
for i=1:number_of_state_innovations
    for h = 1:length(Steps)
        PackedConditionalVarianceDecomposition(:,h,i) = vech(ConditionalVariance(:,:,h,i));
    end
end