dynare/matlab/+occbin/solve_one_constraint.m

function [data, SS_out, error_flag ] = solve_one_constraint(M_,dr, opts_simul_, solve_DM)
%function [data, SS_out, error_flag ] = solve_one_constraint(M_,dr, opts_simul_, solve_DM)
%
% INPUT: 
% - M_                  [structure]     Matlab's structure describing the model (M_).
% - dr                  [structure]     decision rules for the model
% - opts_simul          [structure]     Matlab's structure containing the Occbin options (opts_simul).
% - solve_DM            [double]        indicator on whether to recompute decision rules
%
% OUTPUT:
% - data                [structure]     simulation result containing fields:
%                                           - linear: paths for endogenous variables ignoring OBC (linear solution)
%                                           - piecewise: paths for endogenous variables satisfying the OBC (occbin/piecewise solution)
%                                           - ys: vector of steady state values
%                                           - regime_history: information on number and time of regime transitions
% - SS_out              [structure]     State space solution
%                                           - T: [n_vars by n_vars by n_shock_period] array of transition matrices
%                                           - R: [n_vars by n_exo by n_shock_period] array of shock response matrices
%                                           - C: [n_vars by n_shock_period] array of constants
% - error_flag          [integer]       1 if a problem was encoutered, 0 otherwise

% Original authors: Luca Guerrieri and Matteo Iacoviello 
% Original file downloaded from:
% https://www.matteoiacoviello.com/research_files/occbin_20140630.zip
% Adapted for Dynare by Dynare Team.
%
% This code is in the public domain and may be used freely.
% However the authors would appreciate acknowledgement of the source by
% citation of any of the following papers:
%
% Luca Guerrieri and Matteo Iacoviello (2015): "OccBin: A toolkit for solving
% dynamic models with occasionally binding constraints easily"
% Journal of Monetary Economics 70, 22-38

persistent DM

if isempty(DM)
    solve_DM=true;
end

data.shocks_sequence = opts_simul_.SHOCKS;                   % sequence of unforeseen shocks under which one wants to solve the model
n_periods = opts_simul_.periods;                        % simulation horizon (can be longer than the sequence of shocks defined in shockssequence; must be long enough to ensure convergence back to the reference model at the end of the simulation horizon and may need to be varied depending on the sequence of shocks).
curb_retrench = opts_simul_.curb_retrench;              % 0: updates guess based on previous iteration; 1: updates similar to Gauss-Jacobi scheme, slowing iterations down by updating guess only one period at a time
max_iter = opts_simul_.maxit;                           % maximum number of iterations allowed for the solution algorithm
endo_init = opts_simul_.endo_init;                      % initial condition for state variables, in deviation from steady state in declaration order
binding_indicator = opts_simul_.init_binding_indicator;    % initial guess for constraint violations
regime_history_guess = opts_simul_.init_regime;              % initial guess for constraint violations
periodic_solution = opts_simul_.periodic_solution;

data.exo_pos = opts_simul_.exo_pos;

n_shocks_periods = size(data.shocks_sequence,1);

if n_periods < n_shocks_periods
    n_periods = n_shocks_periods;
end
nperiods_0 = max(opts_simul_.check_ahead_periods,n_periods-n_shocks_periods);

error_flag=0;

M_base = M_;
dr_base = dr;

% ensure that the two models have the same parameters
% use the parameters for the base model.
%Mstar_.params = Mbase_.params;

data.ys = dr_base.ys;

if solve_DM
    DM.n_vars = M_base.endo_nbr;
    DM.n_exo = M_base.exo_nbr;

    % get the matrices holding the first derivatives for the model
    % each regime is treated separately
    [DM.Cbarmat, DM.Bbarmat, DM.Abarmat, DM.Jbarmat] = occbin.get_deriv(M_base,data.ys);
    
    Mstar_= M_base;
    Mstar_.params(M_.occbin.pswitch(1))= 1;
    [DM.Cstarbarmat, DM.Bstarbarmat, DM.Astarbarmat, DM.Jstarbarmat, DM.Dstarbarmat] = occbin.get_deriv(Mstar_,data.ys);
    
    [DM.decrulea,DM.decruleb]=occbin.get_pq(dr_base);
    
    update_flag=true;    
else
    update_flag=false;
end

endo_names = M_base.endo_names;
exo_names =  M_base.exo_names;


% set some initial conditions and loop through the shocks
% period by period
init_orig_ = endo_init;
zdatapiecewise_ = zeros(n_periods,DM.n_vars);
% nwishes_ = size(wishlist_,1);
if ~exist('binding_indicator','var')
    binding_indicator = false(nperiods_0+1,1);
else
    if length(binding_indicator)<(nperiods_0+1)
        binding_indicator = [binding_indicator; false(nperiods_0+1-length(binding_indicator),1)];
    end
end
SS_out.T = NaN(DM.n_vars,DM.n_vars,n_shocks_periods);
SS_out.R = NaN(DM.n_vars,DM.n_exo,n_shocks_periods);
SS_out.C = nan(DM.n_vars,n_shocks_periods);
if isempty(regime_history_guess)
    regime_history = struct();
    guess_history = false;
else
    guess_history = true;
    regime_history = regime_history_guess;
end

if opts_simul_.waitbar
    hh_fig = dyn_waitbar(0,'Occbin: Solving the model');
    set(hh_fig,'Name','Occbin: Solving the model.');
end

for shock_period = 1:n_shocks_periods
    if opts_simul_.waitbar
        dyn_waitbar(shock_period/n_shocks_periods, hh_fig, sprintf('Period %u of %u', shock_period,n_shocks_periods));
    end
    
    regime_change_this_iteration=true;
    iter = 0;
    nperiods_endogenously_increased = false;
    guess_history_it = false;
    if guess_history && (shock_period<=length(regime_history_guess)) %beyond guess regime history
        guess_history_it = true;
    end
    
    is_periodic=false;
    is_periodic_loop=false;
    binding_indicator_history={};
    max_err = NaN(max_iter,1);
    regime_violates_constraint_in_expectation = false(max_iter,1);
    number_of_periods_with_violations = zeros(max_iter,1);
    regime_exit_period = ones(max_iter,1);
    
    while (regime_change_this_iteration && iter<max_iter && ~is_periodic && ~is_periodic_loop)
        iter = iter +1;
        if binding_indicator(end) && nperiods_0<opts_simul_.max_check_ahead_periods
            binding_indicator = [binding_indicator; false ];
            nperiods_0 = nperiods_0 + 1;
            nperiods_endogenously_increased = true;
            disp_verbose(['nperiods has been endogenously increased up to ' int2str(nperiods_0) '.'],opts_simul_.debug)
        elseif nperiods_0>=opts_simul_.max_check_ahead_periods
            % enforce endogenously increased nperiods to not violate max_check_ahead_periods
            binding_indicator = binding_indicator(1:opts_simul_.max_check_ahead_periods+1);
            binding_indicator(end)=false;
        end
        if length(binding_indicator)<(nperiods_0 + 1)
            binding_indicator=[binding_indicator; false(nperiods_0 + 1-length(binding_indicator),1)];
        end
               
        if iter==1 && guess_history_it
            regime = regime_history_guess(shock_period).regime;
            regime_start = regime_history_guess(shock_period).regimestart;
            binding_indicator(:,1) = regime(end);
            for ir=1:length(regime)-1
                binding_indicator(regime_start(ir):regime_start(ir+1)-1,1) = regime(ir);
            end
            nperiods_0 = size(binding_indicator,1)-1; %if history is present, update may be required
        end
        binding_indicator_history{iter}=binding_indicator;
        % analyze when each regime starts based on current guess
        [regime, regime_start, error_code_period]=occbin.map_regime(binding_indicator,opts_simul_.debug);
        regime_history(shock_period).regime = regime;
        regime_history(shock_period).regimestart = regime_start;
        
        % get the hypothesized piece wise linear solution
        if shock_period==1 || shock_period>1 && any(data.shocks_sequence(shock_period,:))
            if iter==1 && opts_simul_.reset_regime_in_new_period
                if opts_simul_.reset_check_ahead_periods_in_new_period
                    % I re-set check ahead periods to initial value, when in previous period it was endogenously increased
                    nperiods_0 = max(opts_simul_.check_ahead_periods,n_periods-n_shocks_periods);
                    binding_indicator = false(nperiods_0+1,1);
                else
                    binding_indicator=false(size(binding_indicator));
                end
                binding_indicator_history{iter}=binding_indicator;
                % analyse violvec and isolate contiguous periods in the other regime.
                [regime, regime_start, error_code_period]=occbin.map_regime(binding_indicator,opts_simul_.debug);
                regime_history(shock_period).regime = regime;
                regime_history(shock_period).regimestart = regime_start;
            end
            
            [zdatalinear_, SS_out.T(:,:,shock_period), SS_out.R(:,:,shock_period), SS_out.C(:,shock_period), SS, update_flag]=occbin.mkdatap_anticipated_dyn(nperiods_0,DM,...
                regime_start(end)-1,binding_indicator,...
                data.exo_pos,data.shocks_sequence(shock_period,:),endo_init,update_flag);
            
            [binding, relax, err]=feval([M_.fname,'.occbin_difference'],zdatalinear_+repmat(dr_base.ys',size(zdatalinear_,1),1),M_.params,dr_base.ys);

            if ~isinf(opts_simul_.max_check_ahead_periods) && opts_simul_.max_check_ahead_periods<length(binding_indicator)
                end_periods = opts_simul_.max_check_ahead_periods;
                last_indicator = false(length(binding_indicator)-end_periods,1);
                regime_violates_constraint_in_last_period(iter) = any(binding.constraint_1(end_periods+1:end));
            else
                end_periods = length(binding_indicator);
                last_indicator = false(0);
                regime_violates_constraint_in_last_period(iter) = binding.constraint_1(end_periods);
            end
            % check if changes to the hypothesis of the duration for each
            % regime
            if any(binding.constraint_1(1:end_periods) & ~binding_indicator(1:end_periods)) || any(relax.constraint_1(1:end_periods) & binding_indicator(1:end_periods))

                err_viol = err.binding_constraint_1(binding.constraint_1(1:end_periods) & ~binding_indicator(1:end_periods));
                err_relax = err.relax_constraint_1(relax.constraint_1(1:end_periods) & binding_indicator(1:end_periods));
                max_err(iter) = max(abs([err_viol;err_relax]));
                regime_change_this_iteration = true;
                regime_violates_constraint_in_expectation(iter) = any(binding.constraint_1(1:end_periods) & ~binding_indicator(1:end_periods));
            else
                regime_change_this_iteration = false;
                max_err(iter) = 0;
            end

            % if max_check_ahead_periods<inf, enforce unconstrained regime for period larger than max_check_ahead_periods 
            binding_constraint_new=[binding.constraint_1(1:end_periods);last_indicator];
            relaxed_constraint_new = [relax.constraint_1(1:end_periods);not(last_indicator)];
            number_of_periods_with_violations(iter) = sum(binding_indicator -((binding_indicator | binding_constraint_new) & ~(binding_indicator & relaxed_constraint_new)));
            regime_exit_period(iter) = max(regime_history(shock_period).regimestart);

            if curb_retrench   % apply Gauss-Seidel idea of slowing down the change in the guess
                % for the constraint -- only relax one
                % period at a time starting from the last
                % one when each of the constraints is true.
                retrench = false(numel(binding_indicator),1);
                max_relax_constraint_1=find(relax.constraint_1(1:end_periods) & binding_indicator(1:end_periods),1,'last');
                if ~isempty(max_relax_constraint_1) && find(relax.constraint_1(1:end_periods),1,'last')>=find(binding_indicator(1:end_periods),1,'last')
                    retrench(max_relax_constraint_1) = true;
                end                
                binding_indicator = (binding_indicator | binding_constraint_new) & ~ retrench;
           else
                binding_indicator = (binding_indicator | binding_constraint_new) & ~(binding_indicator & relaxed_constraint_new);
            end
            
            if iter>1 && regime_change_this_iteration && ~nperiods_endogenously_increased
                % check for periodic solution only if nperiods is not
                % increased endogenously
                % first check for infinite loop
                is_periodic_loop = false(iter-1,1);
                for kiter=1:iter-1
                    if size(binding_indicator,1)== size(binding_indicator_history{kiter},1)
                        %                     vvv = [binding_indicator_history{kiter}; false(size(binding_indicator,1)- size(binding_indicator_history{kiter},1), 1)];
                        %                     is_periodic(kiter) = isequal(vvv, binding_indicator);
                        is_periodic_loop(kiter) = isequal(binding_indicator_history{kiter}, binding_indicator);
                    else
                        is_periodic_loop(kiter) = false;
                    end
                end
                is_periodic_loop_all =is_periodic_loop;
                is_periodic_loop =  any(is_periodic_loop);
                % only accept periodicity where regimes differ by one
                % period!
                is_periodic = false(iter-1,1);
                for kiter=iter-1
                    if size(binding_indicator,1)== size(binding_indicator_history{kiter},1)
                        %                     vvv = [binding_indicator_history{kiter}; false(size(binding_indicator,1)- size(binding_indicator_history{kiter},1), 1)];
                        %                     is_periodic(kiter) = isequal(vvv, binding_indicator);
                        is_periodic(kiter) = isequal(binding_indicator_history{kiter}, binding_indicator) && sum(binding_indicator_history{iter}-binding_indicator)<=opts_simul_.periodic_solution_threshold;
                    else
                        is_periodic(kiter)=false;
                    end
                end
                is_periodic_all =is_periodic;
                is_periodic =  any(is_periodic);
                is_periodic_strict = is_periodic;
                
                if is_periodic_loop && ~is_periodic
                    if ~opts_simul_.periodic_solution_strict && any(number_of_periods_with_violations(~regime_violates_constraint_in_expectation(1:iter))<=opts_simul_.periodic_solution_threshold)
                        is_periodic=true;
                        is_periodic_all=false(size(is_periodic_loop_all));
                        is_periodic_all(1) = true; % here we consider all guesses and pick the best one according to the criteria below
                    else
                        do_nothing=true;
                    end
                end
                if is_periodic && periodic_solution
                    inx = find(is_periodic_all,1):iter;
                    inx1 = inx(find(~regime_violates_constraint_in_expectation(inx)));
                    if not(isempty(inx1))
                        inx=inx1;
                    end
                    if is_periodic_strict || isempty(inx1)
                        [merr,imerr]=min(max_err(inx));
                    else
                        [merr,imerr]=min(number_of_periods_with_violations(inx));
                    end
                    inx = inx(imerr);
                    binding_indicator=binding_indicator_history{inx};
                    if inx<iter
                        [regime, regime_start, error_code_period]=occbin.map_regime(binding_indicator,opts_simul_.debug);
                        regime_history(shock_period).regime = regime;
                        regime_history(shock_period).regimestart = regime_start;
                        
                        % get the hypothesized piece wise linear solution
                        [zdatalinear_, SS_out.T(:,:,shock_period), SS_out.R(:,:,shock_period), SS_out.C(:,shock_period), SS, update_flag]=occbin.mkdatap_anticipated_dyn(nperiods_0,DM,...
                            regime_start(end)-1,binding_indicator,...
                            data.exo_pos,data.shocks_sequence(shock_period,:),endo_init,update_flag);                        
                    end                    
                end
            end
            
        else
            regime_change_this_iteration=false;
            zdatalinear_(1:end-1,:)=zdatalinear_(2:end,:);
            zdatalinear_(end,:) = DM.decrulea*zdatalinear_(end-1,:)';
            if length(SS)>1
                SS=SS(2:end);
            else
                SS=[];
            end
            if isempty(SS)
                SS_out.T(:,:,shock_period)= DM.decrulea;
                SS_out.R(:,:,shock_period)= DM.decruleb;
                SS_out.C(:,shock_period)= 0;
            else
                SS_out.T(:,:,shock_period)= SS(1).T;
                SS_out.R(:,:,shock_period)= SS(1).R;
                SS_out.C(:,shock_period)= SS(1).C;
            end
            binding_indicator_history{iter}=binding_indicator;
        end
        
    end
    
    if regime_change_this_iteration ==1 
        if max_iter>opts_simul_.algo_truncation
            disp_verbose(['occbin solver:: period ' int2str(shock_period) '::'],opts_simul_.debug)
            if is_periodic
                disp_verbose('Occbin solver loops between two regimes.',opts_simul_.debug)
                if periodic_solution
                    disp_verbose(['Max error:' num2str(merr) '.'],opts_simul_.debug)
                else
                    if opts_simul_.waitbar; dyn_waitbar_close(hh_fig); end
                    error_flag = 310;
                    return
                end
            else
                if is_periodic_loop
                    disp_verbose('Did not converge -- infinite loop of guess regimes.',opts_simul_.debug)
                    error_flag = 313;
                else
                disp_verbose('Did not converge -- increase maxit.',opts_simul_.debug)
                    error_flag = 311;
                end
                if opts_simul_.waitbar; dyn_waitbar_close(hh_fig); end
                return
            end
        else
            binding_indicator = binding_indicator_history{end};
        end
    end
    if any(error_code_period)
        disp_verbose('Increase nperiods.',opts_simul_.debug)
        if opts_simul_.waitbar; dyn_waitbar_close(hh_fig); end
        error_flag = 312;
        return
    end
    
    endo_init = zdatalinear_(1,:);
    zdatapiecewise_(shock_period,:)=endo_init;
    endo_init= endo_init';
    
    % reset binding_indicator for next period's shock -- this resetting is
    % consistent with expecting no additional shocks
    binding_indicator=[binding_indicator(2:end); false];
    
end

% if necessary, fill in the rest of the path with the remainder of the
% last IRF computed.
zdatapiecewise_(n_shocks_periods+1:end,:)=zdatalinear_(2:n_periods-n_shocks_periods+1,:);

data.piecewise=zdatapiecewise_;
data.regime_history=regime_history;

if ~opts_simul_.piecewise_only
    % get the linear responses
    data.linear = occbin.mkdata(max(n_periods,size(data.shocks_sequence,1)),...
        DM.decrulea,DM.decruleb,endo_names,exo_names,...
        [],data.exo_pos,data.shocks_sequence,init_orig_);
end

if opts_simul_.waitbar
    dyn_waitbar_close(hh_fig); 
end