function [fval,cost_flag,ys,trend_coeff,info] = dsge_posterior_kernel(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
% function [fval,cost_flag,ys,trend_coeff,info] = dsge_posterior_kernel(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
% Evaluates the posterior kernel of a dsge model. 
% 
% INPUTS 
%   xparam1                        [double]   vector of model parameters.
%   gend                           [integer]  scalar specifying the number of observations.
%   data                           [double]   matrix of data
%   data_index                     [cell]     cell of column vectors
%   number_of_observations         [integer]
%   no_more_missing_observations   [integer] 
% OUTPUTS 
%   fval        :     value of the posterior kernel at xparam1.
%   cost_flag   :     zero if the function returns a penalty, one otherwise.
%   ys          :     steady state of original endogenous variables
%   trend_coeff :
%   info        :     vector of informations about the penalty:
%                     41: one (many) parameter(s) do(es) not satisfied the lower bound
%                     42: one (many) parameter(s) do(es) not satisfied the upper bound
%               
% SPECIAL REQUIREMENTS
%

% Copyright (C) 2004-2011 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_ estim_params_ options_ trend_coeff_ M_ oo_
fval            = [];
ys              = [];
trend_coeff     = [];
cost_flag       = 1;
nobs            = size(options_.varobs,1);
%------------------------------------------------------------------------------
% 1. Get the structural parameters & define penalties
%------------------------------------------------------------------------------
if ~isequal(options_.mode_compute,1) && any(xparam1 < bayestopt_.lb)
    k = find(xparam1 < bayestopt_.lb);
    fval = bayestopt_.penalty+sum((bayestopt_.lb(k)-xparam1(k)).^2);
    cost_flag = 0;
    info = 41;
    return;
end
if ~isequal(options_.mode_compute,1) && any(xparam1 > bayestopt_.ub)
    k = find(xparam1 > bayestopt_.ub);
    fval = bayestopt_.penalty+sum((xparam1(k)-bayestopt_.ub(k)).^2);
    cost_flag = 0;
    info = 42;
    return;
end
Q = M_.Sigma_e;
H = M_.H;
for i=1:estim_params_.nvx
    k =estim_params_.var_exo(i,1);
    Q(k,k) = xparam1(i)*xparam1(i);
end
offset = estim_params_.nvx;
if estim_params_.nvn
    for i=1:estim_params_.nvn
        k = estim_params_.var_endo(i,1);
        H(k,k) = xparam1(i+offset)*xparam1(i+offset);
    end
    offset = offset+estim_params_.nvn;
end     
if estim_params_.ncx
    for i=1:estim_params_.ncx
        k1 =estim_params_.corrx(i,1);
        k2 =estim_params_.corrx(i,2);
        Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
        Q(k2,k1) = Q(k1,k2);
    end
    [CholQ,testQ] = chol(Q);
    if testQ    %% The variance-covariance matrix of the structural innovations is not definite positive.
        %% We have to compute the eigenvalues of this matrix in order to build the penalty.
        a = diag(eig(Q));
        k = find(a < 0);
        if k > 0
            fval = bayestopt_.penalty+sum(-a(k));
            cost_flag = 0;
            info = 43;
            return
        end
    end
    offset = offset+estim_params_.ncx;
end
if estim_params_.ncn 
    for i=1:estim_params_.ncn
        k1 = options_.lgyidx2varobs(estim_params_.corrn(i,1));
        k2 = options_.lgyidx2varobs(estim_params_.corrn(i,2));
        H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
        H(k2,k1) = H(k1,k2);
    end
    [CholH,testH] = chol(H);
    if testH
        a = diag(eig(H));
        k = find(a < 0);
        if k > 0
            fval = bayestopt_.penalty+sum(-a(k));
            cost_flag = 0;
            info = 44;
            return
        end
    end
    offset = offset+estim_params_.ncn;
end
if estim_params_.np > 0
    M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
end
M_.Sigma_e = Q;
M_.H = H;
%------------------------------------------------------------------------------
% 2. call model setup & reduction program
%------------------------------------------------------------------------------
[T,R,SteadyState,info,M_,options_,oo_] = dynare_resolve(M_,options_,oo_);
if info(1) == 1 || info(1) == 2 || info(1) == 5
    fval = bayestopt_.penalty+1;
    cost_flag = 0;
    return
elseif info(1) == 3 || info(1) == 4 || info(1) == 20
    fval = bayestopt_.penalty+info(2);%^2; % penalty power raised in DR1.m and resol already. GP July'08
    cost_flag = 0;
    return
end
bayestopt_.mf = bayestopt_.mf1;
if ~options_.noconstant
    if options_.loglinear == 1
        constant = log(SteadyState(bayestopt_.mfys));
    else
        constant = SteadyState(bayestopt_.mfys);
    end
else
    constant = zeros(nobs,1);
end
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 = repmat(constant,1,gend)+trend_coeff*[1:gend];
else
    trend = repmat(constant,1,gend);
end
start = options_.presample+1;
np    = size(T,1);
mf    = bayestopt_.mf;
no_missing_data_flag = (number_of_observations==gend*nobs);
%------------------------------------------------------------------------------
% 3. Initial condition of the Kalman filter
%------------------------------------------------------------------------------
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*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 = 10*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)) < 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
if kalman_algo == 2
    no_correlation_flag = 1;
    if length(H)==1
        H = zeros(nobs,1);
    else
        if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
            H = diag(H);
        else
            no_correlation_flag = 0;
        end
    end
end
kalman_tol = options_.kalman_tol;
riccati_tol = options_.riccati_tol;
mf = bayestopt_.mf1;
Y   = data-trend;
%------------------------------------------------------------------------------
% 4. Likelihood evaluation
%------------------------------------------------------------------------------
if (kalman_algo==1)% Multivariate Kalman Filter
    if no_missing_data_flag
        LIK = kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol); 
    else
        LIK = ...
            missing_observations_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol, ...
                                               data_index,number_of_observations,no_more_missing_observations);
    end
    if isinf(LIK)
        kalman_algo = 2;
    end
end
if (kalman_algo==2)% Univariate Kalman Filter
    if no_correlation_flag
        LIK = univariate_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
    else
        LIK = univariate_kalman_filter_corr(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
    end
end
if (kalman_algo==3)% Multivariate Diffuse Kalman Filter
    if no_missing_data_flag
        LIK = diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol);
    else
        LIK = missing_observations_diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol,...
                                                         data_index,number_of_observations,no_more_missing_observations);
    end
    if isinf(LIK)
        kalman_algo = 4;
    end
end
if (kalman_algo==4)% Univariate Diffuse Kalman Filter
    if no_correlation_flag
        LIK = univariate_diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol,...
                                               data_index,number_of_observations,no_more_missing_observations);
    else
        LIK = univariate_diffuse_kalman_filter_corr(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol,riccati_tol,...
                                                    data_index,number_of_observations,no_more_missing_observations);
    end
end
if imag(LIK) ~= 0
    likelihood = bayestopt_.penalty;
else
    likelihood = LIK;
end
% ------------------------------------------------------------------------------
% Adds prior if necessary
% ------------------------------------------------------------------------------
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
fval    = (likelihood-lnprior);
options_.kalman_algo = kalman_algo;
