function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK,T,R,P,PK,decomp] = DsgeSmoother(xparam1,gend,Y,data_index,missing_value)
% Estimation of the smoothed variables and innovations. 
% 
% INPUTS 
%   o xparam1       [double]   (p*1) vector of (estimated) parameters. 
%   o gend          [integer]  scalar specifying the number of observations ==> varargin{1}.
%   o data          [double]   (T*n) matrix of data.
%   o data_index    [cell]      1*smpl cell of column vectors of indices.
%   o missing_value 1 if missing values, 0 otherwise
%  
% OUTPUTS 
%   o alphahat      [double]  (m*T) matrix, smoothed endogenous variables.
%   o etahat        [double]  (r*T) matrix, smoothed structural shocks (r>n is the umber of shocks).
%   o epsilonhat    [double]  (n*T) matrix, smoothed measurement errors.
%   o ahat          [double]  (m*T) matrix, one step ahead filtered (endogenous) variables.
%   o SteadyState   [double]  (m*1) vector specifying the steady state level of each endogenous variable.
%   o trend_coeff   [double]  (n*1) vector, parameters specifying the slope of the trend associated to each observed variable.
%   o aK            [double]  (K,n,T+K) array, k (k=1,...,K) steps ahead filtered (endogenous) variables.
%   o T and R       [double]  Matrices defining the state equation (T is the (m*m) transition matrix).
%    P:             3D array of one-step ahead forecast error variance
%                   matrices
%    PK:            4D array of k-step ahead forecast error variance
%                   matrices (meaningless for periods 1:d)
%    
% ALGORITHM 
%   Diffuse Kalman filter (Durbin and Koopman)       
%
% SPECIAL REQUIREMENTS
%   None

% Copyright (C) 2006-2010 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/>.

global bayestopt_ M_ oo_ estim_params_ options_

alphahat        = [];
etahat  = [];
epsilonhat      = [];
ahat          = [];
SteadyState   = [];
trend_coeff   = [];
aK            = [];
T             = [];
R             = [];
P             = [];
PK            = [];
decomp        = [];
nobs            = size(options_.varobs,1);
smpl          = size(Y,2);

set_all_parameters(xparam1);

%------------------------------------------------------------------------------
% 2. call model setup & reduction program
%------------------------------------------------------------------------------
[T,R,SteadyState] = dynare_resolve(bayestopt_.smoother_var_list,...
                                        bayestopt_.smoother_restrict_columns,[]);
bayestopt_.mf = bayestopt_.smoother_mf;
if options_.noconstant
    constant = zeros(nobs,1);
else
    if options_.loglinear == 1
        constant = log(SteadyState(bayestopt_.mfys));
    else
        constant = SteadyState(bayestopt_.mfys);
    end
end
trend_coeff = zeros(nobs,1);
if bayestopt_.with_trend == 1
    trend_coeff = zeros(nobs,1);
    t = options_.trend_coeffs;
    for i=1:length(t)
        if ~isempty(t{i})
            trend_coeff(i) = evalin('base',t{i});
        end
    end
    trend = constant*ones(1,gend)+trend_coeff*(1:gend);
else
    trend = constant*ones(1,gend);
end
start = options_.presample+1;
np    = size(T,1);
mf    = bayestopt_.smoother_mf;
% ------------------------------------------------------------------------------
%  3. Initial condition of the Kalman filter
% ------------------------------------------------------------------------------
% 
%  C'est ici qu'il faut déterminer Pinf et Pstar. Si le modèle est stationnaire,
%  alors il suffit de poser Pstar comme la solution de l'éuation de Lyapounov et
%  Pinf=[].
%
Q = M_.Sigma_e;
H = M_.H;

kalman_algo = options_.kalman_algo;
if options_.lik_init == 1               % Kalman filter
    if kalman_algo ~= 2
        kalman_algo = 1;
    end
    Pstar = lyapunov_symm(T,R*Q*transpose(R),options_.qz_criterium,options_.lyapunov_complex_threshold);
    Pinf        = [];
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
    if kalman_algo ~= 2
        kalman_algo = 1;
    end
    Pstar = options_.Harvey_scale_factor*eye(np);
    Pinf        = [];
elseif options_.lik_init == 3 % Diffuse Kalman filter
    if kalman_algo ~= 4
        kalman_algo = 3;
    end
    [QT,ST] = schur(T);
    e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
    [QT,ST] = ordschur(QT,ST,e1);
    k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
    nk = length(k);
    nk1 = nk+1;
    Pinf = zeros(np,np);
    Pinf(1:nk,1:nk) = eye(nk);
    Pstar = zeros(np,np);
    B = QT'*R*Q*R'*QT;
    for i=np:-1:nk+2
        if ST(i,i-1) == 0
            if i == np
                c = zeros(np-nk,1);
            else
                c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
                    ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
            end
            q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
            Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
            Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
        else
            if i == np
                c = zeros(np-nk,1);
                c1 = zeros(np-nk,1);
            else
                c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
                    ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
                    ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
                c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
                     ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
                     ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
            end
            q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
                 -ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
            z =  q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
            Pstar(nk1:i,i) = z(1:(i-nk));
            Pstar(nk1:i,i-1) = z(i-nk+1:end);
            Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
            Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
            i = i - 1;
        end
    end
    if i == nk+2
        c = ST(nk+1,:)*(Pstar(:,nk+2:end)*ST(nk1,nk+2:end)')+ST(nk1,nk1)*ST(nk1,nk+2:end)*Pstar(nk+2:end,nk1);
        Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
    end
    
    Z = QT(mf,:);
    R1 = QT'*R;
    [QQ,RR,EE] = qr(Z*ST(:,1:nk),0);
    k = find(abs(diag([RR; zeros(nk-size(Z,1),size(RR,2))])) < 1e-8);
    if length(k) > 0
        k1 = EE(:,k);
        dd =ones(nk,1);
        dd(k1) = zeros(length(k1),1);
        Pinf(1:nk,1:nk) = diag(dd);
    end
end
kalman_tol = options_.kalman_tol;
riccati_tol = options_.riccati_tol;
data1 = Y-trend;
% -----------------------------------------------------------------------------
%  4. Kalman smoother
% -----------------------------------------------------------------------------
if any(any(H ~= 0))   % should be replaced by a flag
    if kalman_algo == 1
        [alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp] = ...
            kalman_smoother(T,R,Q,H,Pstar,data1,start,mf,kalman_tol,riccati_tol);
        if all(alphahat(:)==0)
            kalman_algo = 2;
            if ~estim_params_.ncn
                [alphahat,epsilonhat,etahat,ahat,aK] = ...
                    DiffuseKalmanSmootherH3(T,R,Q,H,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
            else
                [alphahat,epsilonhat,etahat,ahat,aK] = ...
                    DiffuseKalmanSmootherH3corr(T,R,Q,H,Pinf,Pstar,Y,trend, ...
                                                nobs,np,smpl,mf);
            end
        end
    elseif kalman_algo == 2
        if ~estim_params_.ncn
            [alphahat,epsilonhat,etahat,ahat,aK] = ...
                DiffuseKalmanSmootherH3(T,R,Q,H,Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
        else
            [alphahat,epsilonhat,etahat,ahat,aK] = ...
                DiffuseKalmanSmootherH3corr(T,R,Q,H,Pinf,Pstar,Y,trend, ...
                                            nobs,np,smpl,mf);
        end
    elseif kalman_algo == 3 | kalman_algo == 4
        data1 = Y - trend;
        if kalman_algo == 3
            [alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
                DiffuseKalmanSmootherH1_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1,nobs,np,smpl);
            if all(alphahat(:)==0)
                kalman_algo = 4;
                if ~estim_params_.ncn
                    [alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
                        DiffuseKalmanSmootherH3_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1,nobs,np,smpl);
                else
                    [alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
                        DiffuseKalmanSmootherH3corr_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
                                                      nobs,np,smpl);
                end
            end
        else
            if ~estim_params_.ncn
                [alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
                    DiffuseKalmanSmootherH3_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
                                              nobs,np,smpl);
            else
                [alphahat,epsilonhat,etahat,ahat,P,aK,PK,d,decomp] = ...
                    DiffuseKalmanSmootherH3corr_Z(ST,Z,R1,Q,H,Pinf,Pstar,data1, ...
                                                  nobs,np,smpl);
            end
        end
        alphahat = QT*alphahat;
        ahat = QT*ahat;
        nk = options_.nk;
        for jnk=1:nk
            aK(jnk,:,:) = QT*squeeze(aK(jnk,:,:));
            for i=1:size(PK,4)
                PK(jnk,:,:,i) = QT*squeeze(PK(jnk,:,:,i))*QT';
            end
            for i=1:size(decomp,4)
                decomp(jnk,:,:,i) = QT*squeeze(decomp(jnk,:,:,i));
            end
        end
        for i=1:size(P,4)
            P(:,:,i) = QT*squeeze(P(:,:,i))*QT';
        end
    end
else
    H = 0;
    if kalman_algo == 1
        if missing_value
            [alphahat,etahat,ahat,aK] = missing_DiffuseKalmanSmoother1(T,R,Q, ...
                                                              Pinf,Pstar,Y,trend,nobs,np,smpl,mf,data_index);
        else
            [alphahat,epsilonhat,etahat,ahat,P,aK,PK,decomp] = ...
                kalman_smoother(T,R,Q,H,Pstar,data1,start,mf,kalman_tol,riccati_tol);
        end
        if all(alphahat(:)==0)
            kalman_algo = 2;
        end
    end
    if kalman_algo == 2
        if missing_value
            [alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother3(T,R,Q, ...
                                                              Pinf,Pstar,Y,trend,nobs,np,smpl,mf,data_index);
        else
            [alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother3(T,R,Q, ...
                                                              Pinf,Pstar,Y,trend,nobs,np,smpl,mf);
        end
    end
    if kalman_algo == 3
        data1 = Y - trend;
        if missing_value
            [alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother1_Z(ST, ...
                                                              Z,R1,Q,Pinf,Pstar,data1,nobs,np,smpl,data_index);
        else
            [alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother1_Z(ST, ...
                                                              Z,R1,Q,Pinf,Pstar, ...
                                                              data1,nobs,np,smpl);
        end
        if all(alphahat(:)==0)
            kalman_algo = 4;
        end
    end
    if kalman_algo == 4
        data1 = Y - trend;
        if missing_value
            [alphahat,etahat,ahat,P,aK,PK,d,decomp] = missing_DiffuseKalmanSmoother3_Z(ST, ...
                                                              Z,R1,Q,Pinf,Pstar,data1,nobs,np,smpl,data_index);
        else
            [alphahat,etahat,ahat,P,aK,PK,d,decomp] = DiffuseKalmanSmoother3_Z(ST, ...
                                                              Z,R1,Q,Pinf,Pstar, ...
                                                              data1,nobs,np,smpl);
        end
    end
    if kalman_algo == 3 | kalman_algo == 4
        alphahat = QT*alphahat;
        ahat = QT*ahat;
        nk = options_.nk;
% $$$           if M_.exo_nbr<2 % Fix the crash of Dynare when the estimated model has only one structural shock (problem with 
% $$$                           % the squeeze function, that does not affect 2D arrays).
% $$$               size_decomp = 0;
% $$$           else
% $$$               size_decomp = size(decomp,4);
% $$$           end
        for jnk=1:nk
            aK(jnk,:,:) = QT*squeeze(aK(jnk,:,:));
            for i=1:size(PK,4)
                PK(jnk,:,:,i) = QT*dynare_squeeze(PK(jnk,:,:,i))*QT';
            end
            for i=1:size(decomp,4)
                decomp(jnk,:,:,i) = QT*dynare_squeeze(decomp(jnk,:,:,i));
            end
        end
        for i=1:size(P,4)
            P(:,:,i) = QT*dynare_squeeze(P(:,:,i))*QT';
        end
    end
end