function [dr,info,M_,options_,oo_] = dr1_PI(dr,task,M_,options_,oo_)
% function [dr,info,M_,options_,oo_] = dr1_PI(dr,task,M_,options_,oo_)
% Computes the reduced form solution of a rational expectation model first
% order
% approximation of the Partial Information stochastic model solver around the deterministic steady state).
% Prepares System as
%        A0*E_t[y(t+1])+A1*y(t)=A2*y(t-1)+c+psi*eps(t)
% with z an exogenous variable process.
% and calls PI_Gensys.m solver
% based on Pearlman et al 1986 paper and derived from
% C.Sims' gensys linear solver.
% to return solution in format
%       [s(t)' x(t)' E_t x(t+1)']'=G1pi [s(t-1)' x(t-1)' x(t)]'+C+impact*eps(t),
%
% 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) 1996-2018 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/>.

global lq_instruments;
info = 0;

options_ = set_default_option(options_,'qz_criterium',1.000001);

xlen = M_.maximum_endo_lead + M_.maximum_endo_lag + 1;

if options_.aim_solver
    options_.aim_solver = false;
    warning('You can not use AIM with Part Info solver. AIM ignored');
end
if (options_.order > 1)
    warning('You can not use order higher than 1 with Part Info solver. Order 1 assumed');
    options_.order =1;
end

% expanding system for Optimal Linear Regulator
if options_.ramsey_policy && ~options_.ACES_solver
    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;
    opt = options_;
    opt.jacobian_flag = false;
    oo_.steady_state = dynare_solve('ramsey_static',oo_.steady_state,opt,M_,options_,oo_,it_);
    options_.solve_algo = old_solve_algo;
    [~,~,multbar] = ramsey_static(oo_.steady_state,M_,options_,oo_,it_);
    [jacobia_,M_] = 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];
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


    if options_.ACES_solver
        sim_ruleids=[];
        tct_ruleids=[];
        if  size(M_.equations_tags,1)>0  % there are tagged equations, check if they are aceslq rules
            for teq=1:size(M_.equations_tags,1)
                if strcmp(M_.equations_tags(teq,3),'aceslq_sim_rule')
                    sim_ruleids=[sim_ruleids cell2mat(M_.equations_tags(teq,1))]
                end
                if strcmp(M_.equations_tags(teq,3),'aceslq_tct_rule')
                    tct_ruleids=[tct_ruleids cell2mat(M_.equations_tags(teq,1))]
                end
            end
        end
        lq_instruments.sim_ruleids=sim_ruleids;
        lq_instruments.tct_ruleids=tct_ruleids;
        %if isfield(lq_instruments,'xsopt_SS') %% changed by BY
        [~, lq_instruments.xsopt_SS,lq_instruments.lmopt_SS,s2,check] = opt_steady_get;%% changed by BY
        [qc, DYN_Q] = QPsolve(lq_instruments, s2, check); %% added by BY
        z = repmat(lq_instruments.xsopt_SS,1,klen);
    else
        z = repmat(dr.ys,1,klen);
    end
    z = z(iyr0) ;
    [~,jacobia_] = feval([M_.fname '.dynamic'],z,[oo_.exo_simul ...
                        oo_.exo_det_simul], M_.params, dr.ys, it_);

    if options_.ACES_solver && (length(sim_ruleids)>0 || length(tct_ruleids)>0 )
        if length(sim_ruleids)>0
            sim_rule=jacobia_(sim_ruleids,:);
            % uses the subdirectory - BY
            save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_sim_rule.txt'], 'sim_rule', '-ascii', '-double', '-tabs');
        end
        if length(tct_ruleids)>0
            tct_rule=jacobia_(tct_ruleids,:);
            % uses the subdirectory - BY
            save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_tct_rule.txt'], 'tct_rule', '-ascii', '-double', '-tabs');
        end
        aces_ruleids=union(tct_ruleids,sim_ruleids);
        j_size=size(jacobia_,1);
        j_rows=1:j_size;
        j_rows = setxor(j_rows,aces_ruleids);
        jacobia_=jacobia_(j_rows ,:);
    end

end

if options_.debug
    save([M_.dname filesep 'Output' filesep M_.fname '_debug.mat'],'jacobia_')
end

dr=set_state_space(dr,M_,options_);
kstate = dr.kstate;
nstatic = M_.nstatic;
nfwrd = M_.nfwrd;
nspred = M_.nspred;
nboth = M_.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);
k1 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_endo_lag+1),:);

if options_.aim_solver
    error('Anderson and Moore AIM solver is not compatible with Partial Information models');
end % end if useAIM and...

% If required, try PCL86 solver, that is, if not the check being
% performed only and if it is 1st order
% create sparse, extended jacobia AA:
nendo=M_.endo_nbr; % = size(aa,1)


if(options_.ACES_solver)
    %if ~isfield(lq_instruments,'names')
    if isfield(options_,'instruments')
        lq_instruments.names=options_.instruments;
    end
    %end
    if isfield(lq_instruments,'names')
        num_inst=size(lq_instruments.names,1);
        if ~isfield(lq_instruments,'inst_var_indices') && num_inst>0
            for i=1:num_inst
                i_tmp = strmatch(deblank(lq_instruments.names(i,:)), M_.endo_names,'exact');
                if isempty(i_tmp)
                    error (['One of the specified instrument variables does not exist']) ;
                else
                    i_var(i) = i_tmp;
                end
            end
            lq_instruments.inst_var_indices=i_var;
        elseif size(lq_instruments.inst_var_indices)>0
            i_var=lq_instruments.inst_var_indices;
            if ~num_inst
                num_inst=size(lq_instruments.inst_var_indices);
            end
        else
            i_var=[];
            num_inst=0;
        end
        if size(i_var,2)>0 && size(i_var,2)==num_inst
            m_var=zeros(nendo,1);
            for i=1:nendo
                if isempty(find(i_var==i))
                    m_var(i)=i;
                end
            end
            m_var=nonzeros(m_var);
            lq_instruments.m_var=m_var;
        else
            error('WARNING: There are no instrumnets for ACES!');
        end
    else %if(options_.ACES_solver==1)
        error('WARNING: There are no instrumnets for ACES!');
    end
end

% find size xlen of the state vector Y and of A0, A1 and A2 transition matrices:
% it is the sum the all i variables's lag/lead representations,
% for each variable i representation being defined as:
% Max (i_lags-1,0)+ Max (i_leads-1,0)+1
% so that if variable x appears with 2 lags and 1 lead, and z
% with 2 lags and 3 leads, the size of the state space is:
% 1+0+1   +   1+2+1   =6
% e.g. E_t Y(t+1)=
%     E_t x(t)
%     E_t x(t+1)
%     E_t z(t)
%     E_t z(t+1)
%     E_t z(t+2)
%     E_t z(t+3)

% partition jacobian:
jlen=M_.nspred+M_.nsfwrd+M_.endo_nbr+M_.exo_nbr; % length of jacobian
PSI=-jacobia_(:, jlen-M_.exo_nbr+1:end); % exog
                                         % first transpose M_.lead_lag_incidence';
lead_lag=M_.lead_lag_incidence';
max_lead_lag=zeros(nendo,2); % lead/lag representation in Y for each endogenous variable i
if ( M_.maximum_lag <= 1) && (M_.maximum_lead <= 1)
    xlen=size(jacobia_,1);%nendo;
    AA0=zeros(xlen,xlen);  % empty A0
    AA2=AA0; % empty A2 and A3
    AA3=AA0;
    if xlen==nendo % && M_.maximum_lag <=1 && M_.maximum_lead <=1 % apply a shortcut
        AA1=jacobia_(:,nspred+1:nspred+nendo);
        if M_.maximum_lead ==1
            fnd = find(lead_lag(:,M_.maximum_lag+2));
            AA0(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,M_.maximum_lag+2))); %forwd jacobian
        end
        if nspred>0 && M_.maximum_lag ==1
            fnd = find(lead_lag(:,1));
            AA2(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,1))); %backward
        end
    elseif options_.ACES_solver % more endo vars than equations in jacobia_
    if nendo-xlen==num_inst
        PSI=[PSI;zeros(num_inst, M_.exo_nbr)];
        % AA1 contemporary
        AA_all=jacobia_(:,nspred+1:nspred+nendo);
        AA1=AA_all(:,lq_instruments.m_var); % endo without instruments
        lq_instruments.ij1=AA_all(:,lq_instruments.inst_var_indices); %  instruments only
        lq_instruments.B1=-[lq_instruments.ij1; eye(num_inst)];
        AA1=[AA1, zeros(xlen,num_inst); zeros(num_inst,xlen), eye(num_inst)];
        %PSI=[PSI; zeros(num_inst,M_.exo_nbr)];
        if M_.maximum_lead ==1 % AA0 forward looking
            AA_all(:,:)=0.0;
            fnd = find(lead_lag(:,M_.maximum_lag+2));
            AA_all(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,M_.maximum_lag+2))); %forwd jacobian
            AA0=AA_all(:,lq_instruments.m_var);
            lq_instruments.ij0=AA_all(:,lq_instruments.inst_var_indices); %  instruments only
            lq_instruments.B0=[lq_instruments.ij0; eye(num_inst)];
            AA0=[AA0, zeros(xlen,num_inst); zeros(num_inst,xlen+num_inst)];
        end
        if nspred>0 && M_.maximum_lag ==1
            AA_all(:,:)=0.0;
            fnd = find(lead_lag(:,1));
            AA_all(:, fnd)= jacobia_(:,nonzeros(lead_lag(:,1))); %backward
            AA2=AA_all(:,lq_instruments.m_var);
            lq_instruments.ij2=AA_all(:,lq_instruments.inst_var_indices); %  instruments only
            lq_instruments.B2=[lq_instruments.ij2; eye(num_inst)];
            AA2=[AA2, lq_instruments.ij2 ; zeros(num_inst,xlen+num_inst)];
        end
    else
        error('ACES number of instruments does match');
    end
    else
        error('More than one lead or lag in the jabian');
    end
    if M_.orig_endo_nbr<nendo
        % findif there are any expecatations at time t
        exp_0= strmatch('AUX_EXPECT_LEAD_0_', M_.endo_names);
        num_exp_0=size(exp_0,1);
        if num_exp_0>0
            AA3(:,exp_0)=AA1(:,exp_0);
            XX0=zeros(nendo,num_exp_0);
            AA1(:,exp_0)=XX0(:,[1:num_exp_0])
        end
    end
end
PSI=-[[zeros(xlen-nendo,M_.exo_nbr)];[jacobia_(:, jlen-M_.exo_nbr+1:end)]]; % exog
cc=0;
NX=M_.exo_nbr; % no of exogenous varexo shock variables.
NETA=nfwrd+nboth; % total no of exp. errors  set to no of forward looking equations
FL_RANK=rank(AA0); % nfwrd+nboth; % min total no of forward looking equations and vars

try
    % call [G1pi,C,impact,nmat,TT1,TT2,gev,eu]=PI_gensys(a0,a1,a2,c,PSI,NX,NETA,NO_FL_EQS)
    % System given as
    %        a0*E_t[y(t+1])+a1*y(t)=a2*y(t-1)+c+psi*eps(t)
    % with eps an exogenous variable process.
    % Returned system is
    %       [s(t)' x(t)' E_t x(t+1)']'=G1pi [s(t-1)' x(t-1)' x(t)]'+C+impact*eps(t),
    %  and (a) the matrix nmat satisfying   nmat*E_t z(t)+ E_t x(t+1)=0
    %      (b) matrices TT1, TT2  that relate y(t) to these states:
    %      y(t)=[TT1 TT2][s(t)' x(t)']'.

    if(options_.ACES_solver)
        if isfield(lq_instruments,'xsopt_SS')
            SSbar= diag([lq_instruments.xsopt_SS(m_var)]);% lq_instruments.xsopt_SS(lq_instruments.inst_var_indices)]);
            insSSbar=repmat(lq_instruments.xsopt_SS(lq_instruments.inst_var_indices)',nendo-num_inst,1);
        else
            SSbar= diag([dr.ys(m_var)]);%; dr.ys(lq_instruments.inst_var_indices)]);%(oo_.steady_state);
            insSSbar=repmat(dr.ys(lq_instruments.inst_var_indices)',nendo-num_inst,1);
        end
        SSbar=diag([diag(SSbar);diag(eye(num_inst))]);
        insSSbar=[insSSbar;diag(eye(num_inst))];

        AA0=AA0*SSbar;
        AA1=AA1*SSbar;
        AA2=AA2*SSbar;
        lq_instruments.B1=(lq_instruments.B1).*insSSbar;
    end
    %% for expectational models when complete
    if any(AA3)
        AA3=AA3*SSbar;
        [G1pi,CC,impact,nmat,TT1,TT2,gev,eu, DD, E2,E5, GAMMA, FL_RANK]=PI_gensysEXP(AA0,AA1,-AA2,AA3,cc,PSI,NX,NETA,FL_RANK, M_, options_);
    else
        [G1pi,CC,impact,nmat,TT1,TT2,gev,eu, DD, E2,E5, GAMMA, FL_RANK]=PI_gensys(AA0,AA1,-AA2,AA3,cc,PSI,NX,NETA,FL_RANK, M_, options_);
    end

    % reuse some of the bypassed code and tests that may be needed
    if (eu(1) ~= 1 || eu(2) ~= 1) && ~options_.ACES_solver
        info(1) = abs(eu(1)+eu(2));
        info(2) = 1.0e+8;
        %     return
    end

    dr.PI_ghx=G1pi;
    dr.PI_ghu=impact;
    dr.PI_TT1=TT1;
    dr.PI_TT2=TT2;
    dr.PI_nmat=nmat;
    dr.PI_CC=CC;
    dr.PI_gev=gev;
    dr.PI_eu=eu;
    dr.PI_FL_RANK=FL_RANK;
    %dr.ys=zeros(nendo); % zero steady state
    dr.ghx=G1pi;
    dr.ghu=impact;
    dr.eigval = eig(G1pi);
    dr.rank=FL_RANK;

    if options_.ACES_solver
        betap=options_.planner_discount;
        sigma_cov=M_.Sigma_e;
        % get W - BY
        W=(1-betap)*GAMMA'*DYN_Q*GAMMA;
        %W=[0]
        ACES.A=G1pi;
        ACES.C=impact; % (:,1);
        ACES.D=DD; %=impact (:,20);
        ACES.E2=E2;
        ACES.E5=E5;
        ACES.GAMMA=GAMMA;
        ACES_M=size(G1pi,2)-FL_RANK;
        ACES_NM=FL_RANK;
        ACES.M=ACES_M;
        ACES.NM=FL_RANK;
        % added by BY
        ACES.Q=DYN_Q;
        ACES.W=W;
        NY=nendo-num_inst;

        % save the followings in a subdirectory - BY
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_Matrices'], 'ACES');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_GAMMA'], 'GAMMA');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_A.txt'], 'G1pi', '-ascii', '-double', '-tabs');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_C.txt'], 'impact','-ascii', '-double', '-tabs');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_D.txt'], 'DD', '-ascii', '-double', '-tabs');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_E2.txt'], 'E2', '-ascii', '-double', '-tabs');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_E5.txt'], 'E5', '-ascii', '-double', '-tabs');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_GAMMA.txt'], 'GAMMA', '-ascii', '-double', '-tabs');
        %save ([M_.fname '_ACESLQ_M.txt'], 'ACES_M', '-ascii', '-tabs');
        %save ([M_.fname '_ACESLQ_NM.txt'], 'ACES_NM', '-ascii', '-tabs');
        %save ([M_.fname '_ACESLQ_betap.txt'], 'betap', '-ascii', '-tabs');
        %save ([M_.fname '_ACESLQ_NI.txt'], 'num_inst', '-ascii', '-tabs');
        %save ([M_.fname '_ACESLQ_ND.txt'], 'NX', '-ascii', '-tabs');
        %save ([M_.fname '_ACESLQ_NY.txt'], 'NY', '-ascii', '-tabs');
        ACES_VARS=char(M_.endo_names);
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_VARS.txt'], 'ACES_VARS', '-ascii', '-tabs');
        % added by BY
        % save the char array ACES_VARS into .txt as it is
        fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_VARnames.txt'),'wt');
        ACES_VARS =[ACES_VARS repmat(sprintf('\n'),size(ACES_VARS,1),1)];
        fwrite(fid,ACES_VARS.');
        fclose(fid);
        % save as integers
        fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_M.txt'),'wt');
        fprintf(fid,'%d\n',ACES_M);
        fclose(fid);
        fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_NM.txt'),'wt');
        fprintf(fid,'%d\n',ACES_NM);
        fclose(fid);
        fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_betap.txt'),'wt');
        fprintf(fid,'%d\n',betap);
        fclose(fid);
        fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_NI.txt'),'wt');
        fprintf(fid,'%d\n',num_inst);
        fclose(fid);
        fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_ND.txt'),'wt');
        fprintf(fid,'%d\n',NX);
        fclose(fid);
        fid = fopen(strcat(ACES_DirectoryName,'/',M_.fname,'_ACESLQ_NY.txt'),'wt');
        fprintf(fid,'%d\n',NY);
        fclose(fid);
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_Q.txt'], 'DYN_Q', '-ascii', '-double', '-tabs');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_W.txt'], 'W', '-ascii', '-double', '-tabs');
        save ([ACES_DirectoryName,'/',M_.fname '_ACESLQ_SIGMAE.txt'], 'sigma_cov', '-ascii', '-double', '-tabs');
    end

catch
    lerror=lasterror;
    if options_.ACES_solver
        disp('Problem with using Part Info ACES solver:');
        error(lerror.message);
    else
        disp('Problem with using Part Info solver');
        error(lerror.message);
    end
end

% TODO:
% if options_.loglinear == 1
% if exogenous deterministic variables