function [dr,info,M_,options_,oo_] = dr1(dr,task,M_,options_,oo_)
% Computes the reduced form solution of a rational expectation model (first or second order
% approximation of the stochastic model around the deterministic steady state). 
%
% INPUTS
%   dr         [matlab structure] Decision rules for stochastic simulations.
%   task       [integer]          if task = 0 then dr1 computes decision rules.
%                                 if task = 1 then dr1 computes eigenvalues.
%   M_         [matlab structure] Definition of the model.           
%   options_   [matlab structure] Global options.
%   oo_        [matlab structure] Results 
%    
% OUTPUTS
%   dr         [matlab structure] Decision rules for stochastic simulations.
%   info       [integer]          info=1: the model doesn't define current variables uniquely
%                                 info=2: problem in mjdgges.dll info(2) contains error code. 
%                                 info=3: BK order condition not satisfied info(2) contains "distance"
%                                         absence of stable trajectory.
%                                 info=4: BK order condition not satisfied info(2) contains "distance"
%                                         indeterminacy.
%                                 info=5: BK rank condition not satisfied.
%   M_         [matlab structure]            
%   options_   [matlab structure]
%   oo_        [matlab structure]
%  
% ALGORITHM
%   ...
%    
% SPECIAL REQUIREMENTS
%   none.
%  

% Copyright (C) 1996-2008 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/>.

    info = 0;
  
    options_ = set_default_option(options_,'loglinear',0);
    options_ = set_default_option(options_,'noprint',0);
    options_ = set_default_option(options_,'olr',0);
    options_ = set_default_option(options_,'olr_beta',1);
    options_ = set_default_option(options_,'qz_criterium',1.000001);
    
    xlen = M_.maximum_endo_lead + M_.maximum_endo_lag + 1;
    klen = M_.maximum_endo_lag + M_.maximum_endo_lead + 1;
    iyv = M_.lead_lag_incidence';
    iyv = iyv(:);
    iyr0 = find(iyv) ;
    it_ = M_.maximum_lag + 1 ;
    
    if M_.exo_nbr == 0
        oo_.exo_steady_state = [] ;
    end
    
    % expanding system for Optimal Linear Regulator
    if options_.ramsey_policy
        if isfield(M_,'orig_model')
            orig_model = M_.orig_model;
            M_.endo_nbr = orig_model.endo_nbr;
            M_.endo_names = orig_model.endo_names;
            M_.lead_lag_incidence = orig_model.lead_lag_incidence;
            M_.maximum_lead = orig_model.maximum_lead;
            M_.maximum_endo_lead = orig_model.maximum_endo_lead;
            M_.maximum_lag = orig_model.maximum_lag;
            M_.maximum_endo_lag = orig_model.maximum_endo_lag;
        end
        old_solve_algo = options_.solve_algo;
        %  options_.solve_algo = 1;
        oo_.steady_state = dynare_solve('dyn_ramsey_static_',oo_.steady_state,0,M_,options_,oo_,it_);
        options_.solve_algo = old_solve_algo;
        [junk,junk,multbar] = dyn_ramsey_static_(oo_.steady_state,M_,options_,oo_,it_);
        [jacobia_,M_] = dyn_ramsey_dynamic_(oo_.steady_state,multbar,M_,options_,oo_,it_);
        klen = M_.maximum_lag + M_.maximum_lead + 1;
        dr.ys = [oo_.steady_state;zeros(M_.exo_nbr,1);multbar];
% $$$         if options_.ramsey_policy == 2
% $$$             mask = M_.orig_model.lead_lag_incidence ~= 0;
% $$$             incidence_submatrix = M_.lead_lag_incidence(M_.orig_model.maximum_lead+(1:size(mask,1)),1:M_.orig_model.endo_nbr); 
% $$$             k = nonzeros((incidence_submatrix.*mask)');
% $$$             nl = nnz(M_.lead_lag_incidence);
% $$$             k = [k; nl+(1:M_.exo_nbr)'];
% $$$             kk = reshape(1:(nl+M_.exo_nbr)^2,nl+M_.exo_nbr,nl+M_.exo_nbr);
% $$$             kk2 = kk(k,k);
% $$$             
% $$$             k1 = find(M_.orig_model.lead_lag_incidence');
% $$$             y = repmat(oo_.dr.ys(1:M_.orig_model.endo_nbr),1,M_.orig_model.maximum_lag+M_.orig_model.maximum_lead+1);
% $$$             [f,fJ,fh] = feval([M_.fname '_dynamic'],y(k1),zeros(1,M_.exo_nbr), M_.params, it_);
% $$$             
% $$$             % looking for dynamic variables that are both in the original model
% $$$             % and in the optimal policy model
% $$$             k1 = k1+nnz(M_.lead_lag_incidence(1:M_.orig_model.maximum_lead,1:M_.orig_model.endo_nbr));
% $$$             hessian = sparse([],[],[],size(jacobia_,1),(nl+M_.exo_nbr)^2,nnz(fh));
% $$$             hessian(M_.orig_model.endo_nbr+(1:size(fh,1)),kk2) = fh;
% $$$             options_.order = 2;
% $$$         elseif options_.ramsey_policy == 3
% $$$             maxlag1 = M_.orig_model.maximum_lag;
% $$$             maxlead1 = M_.orig_model.maximum_lead;
% $$$             endo_nbr1 = M_.orig_model.endo_nbr;
% $$$             lead_lag_incidence1 = M_.orig_model.lead_lag_incidence;
% $$$             y = repmat(oo_.dr.ys(1:M_.orig_model.endo_nbr),1,M_.orig_model.maximum_lag+M_.orig_model.maximum_lead+1);
% $$$             k1 = find(M_.orig_model.lead_lag_incidence');
% $$$             [f,fj,fh] = feval([M_.fname '_dynamic'],y(k1),zeros(1,M_.exo_nbr), M_.params, it_);
% $$$             nrj = size(fj,1); 
% $$$             
% $$$             iy = M_.lead_lag_incidence;
% $$$             kstate = oo_.dr.kstate;
% $$$             inv_order_var = oo_.dr.inv_order_var;
% $$$             offset = 0;
% $$$             i3 = zeros(0,1);
% $$$             i4 = find(kstate(:,2) <= M_.maximum_lag+1);
% $$$             kstate1 = kstate(i4,:);
% $$$             kk2 = zeros(0,1);
% $$$             % lagged variables
% $$$             for i=2:M_.maximum_lag + 1
% $$$                 i1 = find(kstate(:,2) == i);
% $$$                 k1 = kstate(i1,:);
% $$$                 i2 = find(oo_.dr.order_var(k1(:,1)) <= M_.orig_model.endo_nbr);
% $$$                 i3 = [i3; i2+offset]; 
% $$$                 offset = offset + size(k1,1);
% $$$                 i4 = find(kstate1(:,2) == i);
% $$$                 kk2 = [kk2; i4];
% $$$             end
% $$$             i2 = find(oo_.dr.order_var(k1(:,1)) > M_.orig_model.endo_nbr);
% $$$             j2 = k1(i2,1);
% $$$             nj2 = length(j2);
% $$$             k2 = offset+(1:nj2)';
% $$$             offset = offset + length(i2);
% $$$             i3 = [i3; ...
% $$$                   find(M_.orig_model.lead_lag_incidence(M_.orig_model.maximum_lag+1:end,:)')+offset];
% $$$             i3 = [i3; (1:M_.exo_nbr)'+length(i3)];
% $$$             ni3 = length(i3);
% $$$             nrfj = size(fj,1);
% $$$             jacobia_ = zeros(nrfj+length(j2),ni3);
% $$$             jacobia_(1:nrfj,i3) = fj;
% $$$             jacobia_(nrfj+(1:nj2),1:size(oo_.dr.ghx,2)) = oo_.dr.ghx(j2,:);
% $$$             jacobia_(nrfj+(1:nj2),k2) = eye(nj2);
% $$$             kk1 = reshape(1:ni3^2,ni3,ni3);
% $$$             hessian =  zeros(nrfj+length(j2),ni3^2);
% $$$             hessian(1:nrfj,kk1(i3,i3)) = fh;
% $$$             
% $$$             k = find(any(M_.lead_lag_incidence(1:M_.maximum_lag, ...
% $$$                                                M_.orig_model.endo_nbr+1:end)));
% $$$             if maxlead1 > maxlag1
% $$$                 M_.lead_lag_incidence = [ [zeros(maxlead1-maxlag1,endo_nbr1); ...
% $$$                                     lead_lag_incidence1] ...
% $$$                                     [M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
% $$$                                                            k); zeros(maxlead1,length(k))]];
% $$$             elseif maxlag1 > maxlead1
% $$$                 M_.lead_lag_incidence = [ [lead_lag_incidence1; zeros(maxlag1- ...
% $$$                                                                   maxlead1,endo_nbr1);] ...
% $$$                                     [M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
% $$$                                                            k); zeros(maxlead1,length(k))]];
% $$$             else % maxlag1 == maxlead1
% $$$                 M_.lead_lag_incidence = [ lead_lag_incidence1
% $$$                                     [M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
% $$$                                                            k); zeros(maxlead1,length(k))]];
% $$$             end
% $$$             M_.maximum_lag = max(maxlead1,maxlag1);
% $$$             M_.maximum_endo_lag = M_.maximum_lag;
% $$$             M_.maximum_lead = M_.maximum_lag;
% $$$             M_.maximum_endo_lead = M_.maximum_lag;
% $$$             
% $$$             M_.endo_names = strvcat(M_.orig_model.endo_names, M_.endo_names(endo_nbr1+k,:));
% $$$             M_.endo_nbr = endo_nbr1+length(k);  
% $$$         end
    else
        klen = M_.maximum_lag + M_.maximum_lead + 1;
        iyv = M_.lead_lag_incidence';
        iyv = iyv(:);
        iyr0 = find(iyv) ;
        it_ = M_.maximum_lag + 1 ;
        
        if M_.exo_nbr == 0
            oo_.exo_steady_state = [] ;
        end
        
        it_ = M_.maximum_lag + 1;
        z = repmat(dr.ys,1,klen);
        z = z(iyr0) ;
        if options_.order == 1
            [junk,jacobia_] = feval([M_.fname '_dynamic'],z,[oo_.exo_simul ...
                                oo_.exo_det_simul], M_.params, it_);
        elseif options_.order == 2
            [junk,jacobia_,hessian] = feval([M_.fname '_dynamic'],z,...
                                            [oo_.exo_simul ...
                                oo_.exo_det_simul], M_.params, it_);
        end
    end
    
    if options_.debug
        save([M_.fname '_debug.mat'],'jacobia_')
    end
    
    if ~isreal(jacobia_)
        if max(max(abs(imag(jacobia_)))) < 1e-15
            jacobia_ = real(jacobia_);
        else
            info(1) = 6;
            info(2) = sum(sum(imag(jacobia_).^2));
            return
        end
    end

    dr=set_state_space(dr,M_);
    kstate = dr.kstate;
    kad = dr.kad;
    kae = dr.kae;
    nstatic = dr.nstatic;
    nfwrd = dr.nfwrd;
    npred = dr.npred;
    nboth = dr.nboth;
    order_var = dr.order_var;
    nd = size(kstate,1);
    nz = nnz(M_.lead_lag_incidence);
    
    sdyn = M_.endo_nbr - nstatic;
    
    k0 = M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var);
    b = jacobia_(:,k0);
    
    if M_.maximum_endo_lead == 0;  % backward models
        % If required, try Gary Anderson and G Moore AIM solver if not
        % check only and if 1st order (added by GP July'08)
        if (options_.useAIM == 1) && (task == 0) && (options_.order == 1) 
            try
                [dr,aimcode]=dynAIMsolver1(jacobia_,M_,dr);
                if aimcode ~=1
                    info(1) = aimcode;
                    info(2) = 1.0e+8;
                    return
                end
            catch
                %warning('Problem with using AIM solver - Using Dynare solver instead');
                disp('Problem with using AIM solver - Using Dynare solver instead');
                options_.useAIM = 0; % and try mjdgges instead
            end
        end % end if useAIM and...
        %else use original Dynare solver
        if ~((options_.useAIM == 1) && (task == 0) && (options_.order == 1))
            [k1,junk,k2] = find(kstate(:,4));
            dr.ghx(:,k1) = -b\jacobia_(:,k2); 
            if M_.exo_nbr
                dr.ghu = -b\jacobia_(:,nz+1:end);
            end
        end % if not use AIM or not...
        dr.eigval = eig(transition_matrix(dr));
        dr.rank = 0;
        if any(abs(dr.eigval) > options_.qz_criterium)
            temp = sort(abs(dr.eigval));
            nba = nnz(abs(dr.eigval) > options_.qz_criterium);
            temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
            info(1) = 3;
            info(2) = temp'*temp;
        end
        return;
    end
    
    %forward--looking models
    if nstatic > 0
        [Q,R] = qr(b(:,1:nstatic));
        aa = Q'*jacobia_;
    else
        aa = jacobia_;
    end

    % If required, try Gary Anderson and G Moore AIM solver, that is, if not check
    % only and if 1st order (added by GP July'08)
    if (options_.useAIM == 1) && (task == 0) && (options_.order == 1) 
        try
            [dr,aimcode]=dynAIMsolver1(aa,M_,dr);

            % reuse some of the bypassed code and tests that may be needed 
            
            if aimcode ~=1
                info(1) = aimcode;
                info(2) = 1.0e+8;
                return
            end
            [A,B] =transition_matrix(dr);
            dr.eigval = eig(A);
%            if any(abs(dr.eigval) > options_.qz_criterium)
%                temp = sort(abs(dr.eigval));
%                nba = nnz(abs(dr.eigval) > options_.qz_criterium);
%                temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
%                info(1) = 3;
%                info(2) = temp'*temp;
%                return
%            end
            sdim = sum( abs(dr.eigval) < options_.qz_criterium );
            nba = nd-sdim;

            nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
            if nba ~= nyf
                temp = sort(abs(dr.eigval));
                if nba > nyf
                    temp = temp(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
                    info(1) = 3;
                elseif nba < nyf;
                    temp = temp(nd-nyf+1:nd-nba)-1-options_.qz_criterium;
                    info(1) = 4;
                end
                info(2) = temp'*temp;
                return
            end
        catch
            %warning('Problem with using AIM solver - Using Dynare solver instead');
            disp('Problem with using AIM solver - Using Dynare solver instead');
            options_.useAIM = 0; % and then try mjdgges instead
        end
    end % end if useAIM and...
    %else  % use original Dynare solver
    if  ~((options_.useAIM == 1)&& (task == 0) && (options_.order == 1)) % || isempty(options_.useAIM)  
        k1 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_endo_lag+1),:);
        a = aa(:,nonzeros(k1'));
        b = aa(:,k0);
        b10 = b(1:nstatic,1:nstatic);
        b11 = b(1:nstatic,nstatic+1:end);
        b2 = b(nstatic+1:end,nstatic+1:end);
        if any(isinf(a(:)))
            info = 1;
            return
        end

        % buildind D and E
        d = zeros(nd,nd) ;
        e = d ;

        k = find(kstate(:,2) >= M_.maximum_endo_lag+2 & kstate(:,3));
        d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
        k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
        e(1:sdyn,k1) =  -b2(:,kstate(k1,1)-nstatic);
        k = find(kstate(:,2) <= M_.maximum_endo_lag+1 & kstate(:,4));
        e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
        k2 = find(kstate(:,2) == M_.maximum_endo_lag+1);
        k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
        d(1:sdyn,k2) = b2(:,kstate(k2,1)-nstatic);

        if ~isempty(kad)
            for j = 1:size(kad,1)
                d(sdyn+j,kad(j)) = 1 ;
                e(sdyn+j,kae(j)) = 1 ;
            end
        end

        % 1) if mjdgges.dll (or .mexw32 or ....) doesn't exit, 
        % matlab/qz is added to the path. There exists now qz/mjdgges.m that 
        % contains the calls to the old Sims code 
        % 2) In  global_initialization.m, if mjdgges.m is visible exist(...)==2, 
        % this means that the DLL isn't avaiable and use_qzdiv is set to 1

        [ss,tt,w,sdim,dr.eigval,info1] = mjdgges(e,d,options_.qz_criterium);

        if info1
            info(1) = 2;
            info(2) = info1;
            return
        end

        nba = nd-sdim;

        nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);

        if task == 1
            dr.rank = rank(w(1:nyf,nd-nyf+1:end));
            % Under Octave, eig(A,B) doesn't exist, and
            % lambda = qz(A,B) won't return infinite eigenvalues
            if ~exist('OCTAVE_VERSION')
                dr.eigval = eig(e,d);
            end
            return
        end

        if nba ~= nyf
            temp = sort(abs(dr.eigval));
            if nba > nyf
                temp = temp(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
                info(1) = 3;
            elseif nba < nyf;
                temp = temp(nd-nyf+1:nd-nba)-1-options_.qz_criterium;
                info(1) = 4;
            end
            info(2) = temp'*temp;
            return
        end

        np = nd - nyf;
        n2 = np + 1;
        n3 = nyf;
        n4 = n3 + 1;
        % derivatives with respect to dynamic state variables
        % forward variables
        w1 =w(1:n3,n2:nd);
        if condest(w1) > 1e9;
            info(1) = 5;
            info(2) = condest(w1);
            return;
        else
            gx = -w1'\w(n4:nd,n2:nd)';
        end  

        % predetermined variables
        hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
        hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);

        k1 = find(kstate(n4:nd,2) == M_.maximum_endo_lag+1);
        k2 = find(kstate(1:n3,2) == M_.maximum_endo_lag+2);
        dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];

        %lead variables actually present in the model
        j3 = nonzeros(kstate(:,3));
        j4  = find(kstate(:,3));
        % derivatives with respect to exogenous variables
        if M_.exo_nbr
            fu = aa(:,nz+(1:M_.exo_nbr));
            a1 = b;
            aa1 = [];
            if nstatic > 0
                aa1 = a1(:,1:nstatic);
            end
            dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
                                                     npred) a1(:,nstatic+npred+1:end)]\fu;
        else
            dr.ghu = [];
        end

        % static variables
        if nstatic > 0
            temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
            j5 = find(kstate(n4:nd,4));
            temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
            temp = b10\(temp-b11*dr.ghx);
            dr.ghx = [temp; dr.ghx];
            temp = [];
        end
    end % if not use AIM and ....
    % End of if... and if not... main AIM Blocks, continue as per usual...
    
    if options_.loglinear == 1
        k = find(dr.kstate(:,2) <= M_.maximum_endo_lag+1);
        klag = dr.kstate(k,[1 2]);
        k1 = dr.order_var;
        
        dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
                 repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
        dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
    end
    
    if  ~((options_.useAIM == 1) && (options_.order == 1)) % if not use AIM ...
        %% Necessary when using Sims' routines for QZ
        if options_.use_qzdiv
            gx = real(gx);
            hx = real(hx);
            dr.ghx = real(dr.ghx);
            dr.ghu = real(dr.ghu);
        end
    end % if not use AIM 
    
    %exogenous deterministic variables
    if M_.exo_det_nbr > 0
        f1 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+2:end,order_var))));
        f0 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var))));
        fudet = sparse(jacobia_(:,nz+M_.exo_nbr+1:end));
        M1 = inv(f0+[zeros(M_.endo_nbr,nstatic) f1*gx zeros(M_.endo_nbr,nyf-nboth)]);
        M2 = M1*f1;
        dr.ghud = cell(M_.exo_det_length,1);
        dr.ghud{1} = -M1*fudet;
        for i = 2:M_.exo_det_length
            dr.ghud{i} = -M2*dr.ghud{i-1}(end-nyf+1:end,:);
        end
    end
    
    if options_.order == 1
        return
    end
    
    % Second order
    %tempex = oo_.exo_simul ;
    
    %hessian = real(hessext('ff1_',[z; oo_.exo_steady_state]))' ;
    kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
    if M_.maximum_endo_lag > 0
        kk = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); kk];
    end
    kk = kk';
    kk = find(kk(:));
    nk = size(kk,1) + M_.exo_nbr + M_.exo_det_nbr;
    k1 = M_.lead_lag_incidence(:,order_var);
    k1 = k1';
    k1 = k1(:);
    k1 = k1(kk);
    k2 = find(k1);
    kk1(k1(k2)) = k2;
    kk1 = [kk1 length(k1)+1:length(k1)+M_.exo_nbr+M_.exo_det_nbr];
    kk = reshape([1:nk^2],nk,nk);
    kk1 = kk(kk1,kk1);
    %[junk,junk,hessian] = feval([M_.fname '_dynamic'],z, oo_.exo_steady_state);
    hessian(:,kk1(:)) = hessian;
    
    %oo_.exo_simul = tempex ;
    %clear tempex
    
    n1 = 0;
    n2 = np;
    zx = zeros(np,np);
    zu=zeros(np,M_.exo_nbr);
    for i=2:M_.maximum_endo_lag+1
        k1 = sum(kstate(:,2) == i);
        zx(n1+1:n1+k1,n2-k1+1:n2)=eye(k1);
        n1 = n1+k1;
        n2 = n2-k1;
    end
    kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
    k0 = [1:M_.endo_nbr];
    gx1 = dr.ghx;
    hu = dr.ghu(nstatic+[1:npred],:);
    zx = [zx; gx1];
    zu = [zu; dr.ghu];
    for i=1:M_.maximum_endo_lead
        k1 = find(kk(i+1,k0) > 0);
        zu = [zu; gx1(k1,1:npred)*hu];
        gx1 = gx1(k1,:)*hx;
        zx = [zx; gx1];
        kk = kk(:,k0);
        k0 = k1;
    end
    zx=[zx; zeros(M_.exo_nbr,np);zeros(M_.exo_det_nbr,np)];
    zu=[zu; eye(M_.exo_nbr);zeros(M_.exo_det_nbr,M_.exo_nbr)];
    [nrzx,nczx] = size(zx);
    
    % Workaround for USE_DLL option: at this time, it returns a full hessian
    hessian = sparse(hessian);
    
    rhs = -sparse_hessian_times_B_kronecker_C(hessian,zx);
    
    %lhs
    n = M_.endo_nbr+sum(kstate(:,2) > M_.maximum_endo_lag+1 & kstate(:,2) < M_.maximum_endo_lag+M_.maximum_endo_lead+1);
    A = zeros(n,n);
    B = zeros(n,n);
    A(1:M_.endo_nbr,1:M_.endo_nbr) = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
    % variables with the highest lead
    k1 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead+1);
    if M_.maximum_endo_lead > 1
        k2 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead);
        [junk,junk,k3] = intersect(kstate(k1,1),kstate(k2,1));
    else
        k2 = [1:M_.endo_nbr];
        k3 = kstate(k1,1);
    end
    % Jacobian with respect to the variables with the highest lead
    B(1:M_.endo_nbr,end-length(k2)+k3) = jacobia_(:,kstate(k1,3)+M_.endo_nbr);
    offset = M_.endo_nbr;
    k0 = [1:M_.endo_nbr];
    gx1 = dr.ghx;
    for i=1:M_.maximum_endo_lead-1
        k1 = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
        [k2,junk,k3] = find(kstate(k1,3));
        A(1:M_.endo_nbr,offset+k2) = jacobia_(:,k3+M_.endo_nbr);
        n1 = length(k1);
        A(offset+[1:n1],nstatic+[1:npred]) = -gx1(kstate(k1,1),1:npred);
        gx1 = gx1*hx;
        A(offset+[1:n1],offset+[1:n1]) = eye(n1);
        n0 = length(k0);
        E = eye(n0);
        if i == 1
            [junk,junk,k4]=intersect(kstate(k1,1),[1:M_.endo_nbr]);
        else
            [junk,junk,k4]=intersect(kstate(k1,1),kstate(k0,1));
        end
        i1 = offset-n0+n1;
        B(offset+[1:n1],offset-n0+[1:n0]) = -E(k4,:);
        k0 = k1;
        offset = offset + n1;
    end
    [junk,k1,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+M_.maximum_endo_lead+1,order_var));
    A(1:M_.endo_nbr,nstatic+1:nstatic+npred)=...
        A(1:M_.endo_nbr,nstatic+[1:npred])+jacobia_(:,k2)*gx1(k1,1:npred);
    C = hx;
    D = [rhs; zeros(n-M_.endo_nbr,size(rhs,2))];
    
    
    dr.ghxx = gensylv(2,A,B,C,D);
    
    %ghxu
    %rhs
    hu = dr.ghu(nstatic+1:nstatic+npred,:);
    %kk = reshape([1:np*np],np,np);
    %kk = kk(1:npred,1:npred);
    %rhs = -hessian*kron(zx,zu)-f1*dr.ghxx(end-nyf+1:end,kk(:))*kron(hx(1:npred,:),hu(1:npred,:));
    
    rhs = sparse_hessian_times_B_kronecker_C(hessian,zx,zu);
    
    nyf1 = sum(kstate(:,2) == M_.maximum_endo_lag+2);
    hu1 = [hu;zeros(np-npred,M_.exo_nbr)];
    %B1 = [B(1:M_.endo_nbr,:);zeros(size(A,1)-M_.endo_nbr,size(B,2))];
    [nrhx,nchx] = size(hx);
    [nrhu1,nchu1] = size(hu1);
    
    B1 = B*A_times_B_kronecker_C(dr.ghxx,hx,hu1);
    rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
    
    
    %lhs
    dr.ghxu = A\rhs;
    
    %ghuu
    %rhs
    kk = reshape([1:np*np],np,np);
    kk = kk(1:npred,1:npred);
    
    rhs = sparse_hessian_times_B_kronecker_C(hessian,zu);
    
    
    B1 = A_times_B_kronecker_C(B*dr.ghxx,hu1);
    rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
    
    %lhs
    dr.ghuu = A\rhs;
    
    dr.ghxx = dr.ghxx(1:M_.endo_nbr,:);
    dr.ghxu = dr.ghxu(1:M_.endo_nbr,:);
    dr.ghuu = dr.ghuu(1:M_.endo_nbr,:);
    
    
    % dr.ghs2
    % derivatives of F with respect to forward variables
    % reordering predetermined variables in diminishing lag order
    O1 = zeros(M_.endo_nbr,nstatic);
    O2 = zeros(M_.endo_nbr,M_.endo_nbr-nstatic-npred);
    LHS = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
    RHS = zeros(M_.endo_nbr,M_.exo_nbr^2);
    kk = find(kstate(:,2) == M_.maximum_endo_lag+2);
    gu = dr.ghu; 
    guu = dr.ghuu; 
    Gu = [dr.ghu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr)];
    Guu = [dr.ghuu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr*M_.exo_nbr)];
    E = eye(M_.endo_nbr);
    M_.lead_lag_incidenceordered = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
    if M_.maximum_endo_lag > 0
        M_.lead_lag_incidenceordered = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); M_.lead_lag_incidenceordered];
    end
    M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered';
    M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered(:);
    k1 = find(M_.lead_lag_incidenceordered);
    M_.lead_lag_incidenceordered(k1) = [1:length(k1)]';
    M_.lead_lag_incidenceordered =reshape(M_.lead_lag_incidenceordered,M_.endo_nbr,M_.maximum_endo_lag+M_.maximum_endo_lead+1)';
    kh = reshape([1:nk^2],nk,nk);
    kp = sum(kstate(:,2) <= M_.maximum_endo_lag+1);
    E1 = [eye(npred); zeros(kp-npred,npred)];
    H = E1;
    hxx = dr.ghxx(nstatic+[1:npred],:);
    for i=1:M_.maximum_endo_lead
        for j=i:M_.maximum_endo_lead
            [junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+j+1,order_var));
            [junk,k3a,k3] = ...
                find(M_.lead_lag_incidenceordered(M_.maximum_endo_lag+j+1,:));
            nk3a = length(k3a);
            B1 = sparse_hessian_times_B_kronecker_C(hessian(:,kh(k3,k3)),gu(k3a,:));
            RHS = RHS + jacobia_(:,k2)*guu(k2a,:)+B1;
        end
        % LHS
        [junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+i+1,order_var));
        LHS = LHS + jacobia_(:,k2)*(E(k2a,:)+[O1(k2a,:) dr.ghx(k2a,:)*H O2(k2a,:)]);
        
        if i == M_.maximum_endo_lead 
            break
        end
        
        kk = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
        gu = dr.ghx*Gu;
        [nrGu,ncGu] = size(Gu);
        G1 = A_times_B_kronecker_C(dr.ghxx,Gu);
        G2 = A_times_B_kronecker_C(hxx,Gu);
        guu = dr.ghx*Guu+G1;
        Gu = hx*Gu;
        Guu = hx*Guu;
        Guu(end-npred+1:end,:) = Guu(end-npred+1:end,:) + G2;
        H = E1 + hx*H;
    end
    RHS = RHS*M_.Sigma_e(:);
    dr.fuu = RHS;
    %RHS = -RHS-dr.fbias;
    RHS = -RHS;
    dr.ghs2 = LHS\RHS;
    
    % deterministic exogenous variables
    if M_.exo_det_nbr > 0
        hud = dr.ghud{1}(nstatic+1:nstatic+npred,:);
        zud=[zeros(np,M_.exo_det_nbr);dr.ghud{1};gx(:,1:npred)*hud;zeros(M_.exo_nbr,M_.exo_det_nbr);eye(M_.exo_det_nbr)];
        R1 = hessian*kron(zx,zud);
        dr.ghxud = cell(M_.exo_det_length,1);
        kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
        kp = nstatic+[1:npred];
        dr.ghxud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{1}(kp,:)));
        Eud = eye(M_.exo_det_nbr);
        for i = 2:M_.exo_det_length
            hudi = dr.ghud{i}(kp,:);
            zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
            R2 = hessian*kron(zx,zudi);
            dr.ghxud{i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hx,Eud)+dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{i}(kp,:)))-M1*R2;
        end
        R1 = hessian*kron(zu,zud);
        dr.ghudud = cell(M_.exo_det_length,1);
        kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
        
        dr.ghuud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghu(kp,:),dr.ghud{1}(kp,:)));
        Eud = eye(M_.exo_det_nbr);
        for i = 2:M_.exo_det_length
            hudi = dr.ghud{i}(kp,:);
            zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
            R2 = hessian*kron(zu,zudi);
            dr.ghuud{i} = -M2*dr.ghxud{i-1}(kf,:)*kron(hu,Eud)-M1*R2;
        end
        R1 = hessian*kron(zud,zud);
        dr.ghudud = cell(M_.exo_det_length,M_.exo_det_length);
        dr.ghudud{1,1} = -M1*R1-M2*dr.ghxx(kf,:)*kron(hud,hud);
        for i = 2:M_.exo_det_length
            hudi = dr.ghud{i}(nstatic+1:nstatic+npred,:);
            zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi+dr.ghud{i-1}(kf,:);zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
            R2 = hessian*kron(zudi,zudi);
            dr.ghudud{i,i} = -M2*(dr.ghudud{i-1,i-1}(kf,:)+...
                                  2*dr.ghxud{i-1}(kf,:)*kron(hudi,Eud) ...
                                  +dr.ghxx(kf,:)*kron(hudi,hudi))-M1*R2;
            R2 = hessian*kron(zud,zudi);
            dr.ghudud{1,i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hud,Eud)+...
                                  dr.ghxx(kf,:)*kron(hud,hudi))...
                -M1*R2;
            for j=2:i-1
                hudj = dr.ghud{j}(kp,:);
                zudj=[zeros(np,M_.exo_det_nbr);dr.ghud{j};gx(:,1:npred)*hudj;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
                R2 = hessian*kron(zudj,zudi);
                dr.ghudud{j,i} = -M2*(dr.ghudud{j-1,i-1}(kf,:)+dr.ghxud{j-1}(kf,:)* ...
                                      kron(hudi,Eud)+dr.ghxud{i-1}(kf,:)* ...
                                      kron(hudj,Eud)+dr.ghxx(kf,:)*kron(hudj,hudi))-M1*R2;
            end
            
        end
    end