function result_map = ff_abzr_fibs_vf(varargin)

%% FF_ABZ_FIBS_VF borr + save one asset formal informal + loop

% This program solves the infinite horizon dynamic single asset and single

% shock problem with loops. This file contains codes that processes

% borrowing and handles formal and informal choices. With R Shock.

%

% @param param_map container parameter container

%

% @param support_map container support container

%

% @param armt_map container container with states, choices and shocks

% grids that are inputs for grid based solution algorithm

%

% @param func_map container container with function handles for

% consumption cash-on-hand etc.

%

% @return result_map container contains policy function matrix, value

% function matrix, iteration results, and policy function, value function

% and iteration results tables.

%

% keys included in result_map:

%

% * mt_val matrix states_n by shock_n matrix of converged value function grid

% * mt_pol_a matrix states_n by shock_n matrix of converged policy function grid

% * mt_cons matrix states_n by shock_n matrix of optimal consumption

% levels, unlike modele without formal and informal choices, where we know

% c from coh and a, here this needed to be stored because it is the results

% from with joint category maximization problem.

% * ar_val_diff_norm array if bl_post = true it_iter_last by 1 val function

% difference between iteration

% * ar_pol_diff_norm array if bl_post = true it_iter_last by 1 policy

% function difference between iterations

% * mt_pol_perc_change matrix if bl_post = true it_iter_last by shock_n the

% proportion of grid points at which policy function changed between

% current and last iteration for each element of shock

%

% @example

%

% @include

%

% * <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/m_abzr_paramfunc/html/ffs_abzr_fibs_set_default_param.html ffs_abzr_fibs_set_default_param>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/m_abzr_paramfunc/html/ffs_abzr_fibs_get_funcgrid.html ffs_abzr_fibs_get_funcgrid>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_fibs_min_c_cost_bridge.html ffs_fibs_min_c_cost_bridge>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_fibs_inf_bridge.html ffs_fibs_inf_bridge>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_fibs_min_c_cost.html ffs_fibs_min_c_cost>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/solvepost/html/ff_az_vf_post.html ff_az_vf_post>

%

% @seealso

%

% * for/inf + save + borr loop: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/m_abzr_solve/html/ff_abzr_fibs_vf.html ff_abzr_fibs_vf>

% * for/inf + borr vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/m_abzr_solve/html/ff_abzr_fibs_vf_vec.html ff_abzr_fibs_vf_vec>

% * for/inf + borr optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/m_abzr_solve/html/ff_abzr_fibs_vf_vecsv.html ff_abzr_fibs_vf_vecsv>

%

%% Default

% * it_param_set = 1: quick test

% * it_param_set = 2: benchmark run

% * it_param_set = 3: benchmark profile

% * it_param_set = 4: press publish button

it_param_set = 3;

[param_map, support_map] = ffs_abzr_fibs_set_default_param(it_param_set);

% Note: param_map and support_map can be adjusted here or outside to override defaults

% To generate results as if formal informal do not matter

param_map('it_a_n') = 35;

param_map('fl_z_r_infbr_n') = 3;

param_map('it_z_wage_n') = 3;

param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_infbr_n');

param_map('it_maxiter_val') = 20;

% param_map('fl_r_fsv') = 0.025;

% param_map('fl_r_fbr') = 0.035;

% param_map('bl_b_is_principle') = false;

% param_map('st_forbrblk_type') = 'seg3';

% param_map('fl_forbrblk_brmost') = -19;

% param_map('fl_forbrblk_brleast') = -1;

% param_map('fl_forbrblk_gap') = -1.5;

% param_map('bl_b_is_principle') = false;

[armt_map, func_map] = ffs_abzr_fibs_get_funcgrid(param_map, support_map); % 1 for override

default_params = {param_map support_map armt_map func_map};

%% Parse Parameters 1

% if varargin only has param_map and support_map,

params_len = length(varargin);

[default_params{1:params_len}] = varargin{:};

param_map = [param_map; default_params{1}];

support_map = [support_map; default_params{2}];

if params_len >= 1 && params_len <= 2

    % If override param_map, re-generate armt and func if they are not

    % provided

    bl_input_override = true;

    [armt_map, func_map] = ffs_abzr_fibs_get_funcgrid(param_map, support_map, bl_input_override);

else

    % Override all

    armt_map = [armt_map; default_params{3}];

    func_map = [func_map; default_params{4}];

end

% append function name

st_func_name = 'ff_abzr_fibs_vf';

support_map('st_profile_name_main') = [st_func_name support_map('st_profile_name_main')];

support_map('st_mat_name_main') = [st_func_name support_map('st_mat_name_main')];

support_map('st_img_name_main') = [st_func_name support_map('st_img_name_main')];

%% Parse Parameters 2

% armt_map

params_group = values(armt_map, {'ar_a', 'mt_z_trans', 'ar_z_r_infbr_mesh_wage', 'ar_z_wage_mesh_r_infbr'});

[ar_a, mt_z_trans, ar_z_r_infbr_mesh_wage, ar_z_wage_mesh_r_infbr] = params_group{:};

% Formal choice Menu/Grid and Interest Rate Menu/Grid

params_group = values(armt_map, {'ar_forbrblk_r', 'ar_forbrblk'});

[ar_forbrblk_r, ar_forbrblk] = params_group{:};

% func_map

params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_coh', 'f_cons_coh_fbis', 'f_cons_coh_save'});

[f_util_log, f_util_crra, f_coh, f_cons_coh_fbis, f_cons_coh_save] = params_group{:};

% param_map

params_group = values(param_map, {'it_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min',...

    'fl_nan_replace', 'bl_default', 'bl_bridge', 'bl_rollover', 'fl_default_aprime'});

[it_a_n, it_z_n, fl_crra, fl_beta, fl_c_min, ...

    fl_nan_replace, bl_default, bl_bridge, bl_rollover, fl_default_aprime] = params_group{:};

params_group = values(param_map, {'it_maxiter_val', 'fl_tol_val', 'fl_tol_pol', 'it_tol_pol_nochange'});

[it_maxiter_val, fl_tol_val, fl_tol_pol, it_tol_pol_nochange] = params_group{:};

% param_map, Formal informal

params_group = values(param_map, {'fl_r_fsv', 'bl_b_is_principle'});

[fl_r_fsv, bl_b_is_principle] = params_group{:};

% support_map

params_group = values(support_map, {'bl_profile', 'st_profile_path', ...

    'st_profile_prefix', 'st_profile_name_main', 'st_profile_suffix',...

    'bl_display_minccost', 'bl_display_infbridge', ...

    'bl_time', 'bl_display_defparam', 'bl_display', 'it_display_every', 'bl_post'});

[bl_profile, st_profile_path, ...

    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...

    bl_display_minccost, bl_display_infbridge, ...

    bl_time, bl_display_defparam, bl_display, it_display_every, bl_post] = params_group{:};

%% Initialize Output Matrixes

mt_val_cur = zeros(it_a_n,it_z_n);

mt_val = mt_val_cur - 1;

mt_pol_a = zeros(it_a_n,it_z_n);

mt_pol_a_cur = mt_pol_a - 1;

mt_pol_cons = zeros(it_a_n,it_z_n);

% collect optimal borrowing formal and informal choices

mt_pol_b_bridge = zeros(it_a_n,it_z_n);

mt_pol_inf_borr_nobridge = zeros(it_a_n,it_z_n);

mt_pol_for_borr = zeros(it_a_n,it_z_n);

mt_pol_for_save = zeros(it_a_n,it_z_n);

%% Initialize Convergence Conditions

bl_vfi_continue = true;

it_iter = 0;

ar_val_diff_norm = zeros([it_maxiter_val, 1]);

ar_pol_diff_norm = zeros([it_maxiter_val, 1]);

mt_pol_perc_change = zeros([it_maxiter_val, it_z_n]);

%% Iterate Value Function

% Loop solution with 4 nested loops

%

% # loop 1: over exogenous states

% # loop 2: over endogenous states

% # loop 3: over choices

% # loop 4: add future utility, integration--loop over future shocks

%

% Start Profile

if (bl_profile)

    close all;

    profile off;

    profile on;

end 

% Start Timer

if (bl_time) 

    tic; 

end 

% Utility at-Default/at-limiting-case-when-nodefault

if (fl_crra == 1) 

    fl_u_cmin = f_util_log(fl_c_min);

else 

    fl_u_cmin = f_util_crra(fl_c_min); 

end 

% Value Function Iteration

while bl_vfi_continue 

    it_iter = it_iter + 1; 

    %% Iterate over a and z states

    % handling borrowing and default possibility

    % loop 1: over exogenous states

    for it_z_i = 1:it_z_n 

        fl_z_r_borr = ar_z_r_infbr_mesh_wage(it_z_i); 

        fl_z_wage = ar_z_wage_mesh_r_infbr(it_z_i); 

        % loop 2: over endogenous states

        for it_a_j = 1:it_a_n 

            % Get asset state

            fl_a = ar_a(it_a_j); 

            % Initialize storage

            ar_val_cur = zeros(size(ar_a)); 

            ar_c_cur = zeros(size(ar_a)); 

            ar_b_bridge = zeros(size(ar_a)); 

            ar_inf_borr_nobridge = zeros(size(ar_a)); 

            ar_for_borr = zeros(size(ar_a)); 

            ar_for_save = zeros(size(ar_a)); 

            % calculate cash on hand

            fl_coh = f_coh(fl_z_wage, fl_a); 

            % loop 3: over choices

            for it_ap_k = 1:it_a_n 

                % get next period asset choice

                fl_ap = ar_a(it_ap_k); 

                %% Compute Consumption given Borrowing and Savings

                % find the today's consumption maximizing formal and informal

                % choices given a' and coh. The formal and informal choices need to

                % generate exactly a', but depending on which formal and informal

                % joint choice is used, the consumption cost today a' is different.

                % Note here, a is principle + interests. Three areas:

                %

                % * *CASE A* a' > 0: savings, do not need to optimize over formal and

                % informal choices

                % * *CASE B* a' < 0 & coh < 0: need bridge loan to pay for unpaid debt, and

                % borrowing over-all, need to first pick bridge loan to pay for

                % debt, if bridge loan is insufficient, go into default. After

                % bridge loan, optimize over formal+informal, borrow+save joint

                % choices.

                % * *CASE C* $ a' < 0 & coh > 0: do not need to get informal bridge loans,

                % optimize over for+inf save, for+save+borr, inf+borr only, for

                % borrow only.

                %

                if (fl_ap < 0) 

                    % Calculate Bridge Loan Borrowing

                    if (bl_bridge && fl_coh < 0) 

                        bl_input_override = true; 

                        [fl_aprime_nobridge, fl_b_bridge, fl_c_bridge] = ffs_fibs_inf_bridge(... 

                            bl_b_is_principle, fl_z_r_borr, fl_ap, fl_coh, ... 

                            bl_display_infbridge, bl_input_override); 

                    else 

                        fl_aprime_nobridge = fl_ap; 

                        fl_b_bridge = 0; 

                        fl_c_bridge = 0; 

                    end 

                    % Find Optimal Formal Informal Borrow Save Combo

                    % calculate consumption gain from formal + informal

                    % borrowing and savings choices.

                    bl_input_override = true; 

                    [fl_max_c_nobridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ... 

                        ffs_fibs_min_c_cost(...

                        bl_b_is_principle, fl_z_r_borr, fl_r_fsv, ... 

                        ar_forbrblk_r, ar_forbrblk, ... 

                        fl_aprime_nobridge, bl_display_minccost, bl_input_override); 

                    % Compute Consumption given Formal and Informal joint

                    % consumption with formal borrow menu + bridge loans.

                    fl_c = f_cons_coh_fbis(fl_coh, fl_max_c_nobridge + fl_c_bridge); 

                else 

                    % consumption with savings

                    fl_c = f_cons_coh_save(fl_coh, fl_ap); 

                    % assign values for formal and informal choices

                    % possible that fl_coh < 0, but if then fl_ap > 0 is

                    % not valid choice

                    [fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = deal(0, 0, 0, fl_ap); 

                end 

                %% Compute Utility With Default

                % if rollover is not allowed and bridge is not allowed,

                % then as long as coh <= 0, also treat as not allowed

                % states.

                % assign u(c)

                if (fl_c <= fl_c_min || ... 

                    ( ~bl_rollover && ~bl_bridge && fl_coh < fl_c_min)) 

                    if (bl_default) 

                        % defaults

                        % current utility: only today u(cmin)

                        ar_val_cur(it_ap_k) = fl_u_cmin; 

                        % transition out next period, debt wiped out

                        for it_az_q = 1:it_z_n 

                            ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ... 

                                fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur((ar_a == fl_default_aprime), it_az_q); 

                        end 

                        % Replace Consumption if default cmin

                        fl_c = fl_c_min; 

                    else

                        % if default is not allowed: v = fl_nan_replace

                        ar_val_cur(it_ap_k) = fl_nan_replace;

                        % Replace Consumption if no default nan

                        fl_c = 0;

                    end 

                    % no action, defaulting

                    fl_b_bridge = 0; 

                    fl_inf_borr_nobridge = 0; 

                    fl_for_borr = 0; 

                    fl_for_save = 0; 

                else 

                    % Solve Optimization Problem: max_{a'} u(c(a,a',z)) + beta*EV(a',z')

                    % borrowed enough to pay debt (and borrowing limit not exceeded)

                    % saved only the coh available.

                    % current utility

                    if (fl_crra == 1) 

                        ar_val_cur(it_ap_k) = f_util_log(fl_c);

                    else 

                        ar_val_cur(it_ap_k) = f_util_crra(fl_c); 

                    end 

                    % loop 4: add future utility, integration--loop over future shocks

                    for it_az_q = 1:it_z_n 

                        ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ... 

                            fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur(it_ap_k, it_az_q); 

                    end 

                end 

                %% Store Values

                % Could get the formal and informal values from

                % ffs_fibs_min_c_cost_bridge.m

%                 bl_input_override = true;

%                 [fl_c, fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...

%                     ffs_fibs_min_c_cost_bridge(fl_ap, fl_coh, ...

%                     param_map, support_map, armt_map, func_map, bl_input_override);

                % Store consumption

                ar_c_cur(it_ap_k) = fl_c; 

                % Save/Update Borrowing Information

                ar_b_bridge(it_ap_k) = fl_b_bridge; 

                ar_inf_borr_nobridge(it_ap_k) = fl_inf_borr_nobridge; 

                ar_for_borr(it_ap_k) = fl_for_borr; 

                ar_for_save(it_ap_k) = fl_for_save; 

            end 

            %% Optimize over Next Period Asset Choices

            % optimal choice value

            [fl_opti_val_z, fl_opti_idx_z] = max(ar_val_cur); 

            fl_opti_aprime_z = ar_a(fl_opti_idx_z); 

            fl_opti_c_z = ar_c_cur(fl_opti_idx_z); 

            % corresponding optimal borrowing and savings choices

            fl_opti_b_bridge = ar_b_bridge(fl_opti_idx_z); 

            fl_opti_inf_borr_nobridge = ar_inf_borr_nobridge(fl_opti_idx_z); 

            fl_opti_for_borr = ar_for_borr(fl_opti_idx_z); 

            fl_opti_for_save = ar_for_save(fl_opti_idx_z); 

            %% Find Optimal Choices for Defaults or Not

            % Handle Default is optimal or not

            if (fl_opti_c_z <= fl_c_min) 

                if (bl_default) 

                    % if defaulting is optimal choice, at these states, not required

                    % to default, non-default possible, but default could be optimal

                    fl_opti_aprime_z = fl_default_aprime; 

                else

                    % if default is not allowed, then next period same state as now

                    % this is absorbing state, this is the limiting case, single

                    % state space point, lowest a and lowest shock has this.

                    fl_opti_aprime_z = min(ar_a);

                end 

            end 

            %% Store Optimal Choices and Value Given(a,z)

            % store overal savings, value and consumption

            mt_val(it_a_j,it_z_i) = fl_opti_val_z; 

            mt_pol_a(it_a_j,it_z_i) = fl_opti_aprime_z; 

            mt_pol_cons(it_a_j,it_z_i) = fl_opti_c_z; 

            % store savings and borrowing formal and inf optimal choices

            mt_pol_b_bridge(it_a_j,it_z_i) = fl_opti_b_bridge; 

            mt_pol_inf_borr_nobridge(it_a_j,it_z_i) = fl_opti_inf_borr_nobridge; 

            mt_pol_for_borr(it_a_j,it_z_i) = fl_opti_for_borr; 

            mt_pol_for_save(it_a_j,it_z_i) = fl_opti_for_save; 

        end 

    end 

    %% Check Tolerance and Continuation

    % Difference across iterations

    ar_val_diff_norm(it_iter) = norm(mt_val - mt_val_cur); 

    ar_pol_diff_norm(it_iter) = norm(mt_pol_a - mt_pol_a_cur); 

    mt_pol_perc_change(it_iter, :) = sum((mt_pol_a ~= mt_pol_a_cur))/(it_a_n); 

    % Update

    mt_val_cur = mt_val; 

    mt_pol_a_cur = mt_pol_a; 

    % Print Iteration Results

    if (bl_display && (rem(it_iter, it_display_every)==0)) 

        fprintf('VAL it_iter:%d, fl_diff:%d, fl_diff_pol:%d\n', ...

            it_iter, ar_val_diff_norm(it_iter), ar_pol_diff_norm(it_iter));

        tb_valpol_iter = array2table([mean(mt_val_cur,1); mean(mt_pol_a_cur,1); ...

            mt_val_cur(it_a_n,:); mt_pol_a_cur(it_a_n,:)]);

        tb_valpol_iter.Properties.VariableNames = strcat('z', string((1:size(mt_val_cur,2))));

        tb_valpol_iter.Properties.RowNames = {'mval', 'map', 'Hval', 'Hap'};

        disp('mval = mean(mt_val_cur,1), average value over a')

        disp('map  = mean(mt_pol_a_cur,1), average choice over a')

        disp('Hval = mt_val_cur(it_a_n,:), highest a state val')

        disp('Hap = mt_pol_a_cur(it_a_n,:), highest a state choice')

        disp(tb_valpol_iter);

    end

    % Continuation Conditions:

    % 1. if value function convergence criteria reached

    % 2. if policy function variation over iterations is less than

    % threshold

    if (it_iter == (it_maxiter_val + 1)) 

        bl_vfi_continue = false; 

    elseif ((it_iter == it_maxiter_val) || ... 

            (ar_val_diff_norm(it_iter) < fl_tol_val) || ... 

            (sum(ar_pol_diff_norm(max(1, it_iter-it_tol_pol_nochange):it_iter)) < fl_tol_pol)) 

        % Fix to max, run again to save results if needed

        it_iter_last = it_iter; 

        it_iter = it_maxiter_val; 

    end 

end 

% End Timer

if (bl_time) 

    toc; 

end 

% End Profile

if (bl_profile) 

    profile off 

    profile viewer

    st_file_name = [st_profile_prefix st_profile_name_main st_profile_suffix];

    profsave(profile('info'), strcat(st_profile_path, st_file_name));

end

%% Process Optimal Choices

result_map = containers.Map('KeyType','char', 'ValueType','any');

result_map('mt_val') = mt_val;

result_map('cl_mt_pol_a') = {mt_pol_a, zeros(1)};

result_map('cl_mt_coh') = {f_coh(ar_z_r_infbr_mesh_wage, ar_a'), zeros(1)};

result_map('cl_mt_pol_c') = {mt_pol_cons, zeros(1)};

result_map('cl_mt_pol_b_bridge') = {mt_pol_b_bridge, zeros(1)};

result_map('cl_mt_pol_inf_borr_nobridge') = {mt_pol_inf_borr_nobridge, zeros(1)};

result_map('cl_mt_pol_for_borr') = {mt_pol_for_borr, zeros(1)};

result_map('cl_mt_pol_for_save') = {mt_pol_for_save, zeros(1)};

result_map('ar_st_pol_names') = ["cl_mt_pol_a", "cl_mt_pol_coh", "cl_mt_pol_c", ...

    "cl_mt_pol_b_bridge", "cl_mt_pol_inf_borr_nobridge", "cl_mt_pol_for_borr", "cl_mt_pol_for_save"];

% Get Discrete Choice Outcomes

result_map = ffs_fibs_identify_discrete(result_map, bl_input_override);

%% Post Solution Graph and Table Generation

% Note in comparison with *abzr*, results here, even when using identical

% parameters would differ because in *abzr* solved where choices are

% principle. Here choices are principle + interests in order to facilitate

% using the informal choice functions.

%

% Note that this means two things are

% different, on the one hand, the value of asset for to coh is different

% based on the grid of assets. If the asset grid is negative, now per grid

% point, there is more coh because that grid point of asset no longer has

% interest rates. On the other hand, if one has positive asset grid point

% on arrival, that is worth less to coh. Additionally, when making choices

% for the next period, now choices aprime includes interests. What these

% mean is that the a grid no longer has the same meaning. We should expect

% at higher savings levels, for the same grid points, if optimal grid

% choices are the same as before, consumption should be lower when b

% includes interest rates and principle. This is however, not true when

% arriving in a period with negative a levels, for the same negative a

% level and same a prime negative choice, could have higher consumption

% here becasue have to pay less interests on debt. This tends to happen for

% smaller levels of borrowing choices.

%

% Graphically, when using interest + principle, big difference in

% consumption as a fraction of (coh - aprime) figure. In those figures,

% when counting in principles only, the gap in coh and aprime is

% consumption, but now, as more is borrowed only a small fraction of coh

% and aprime gap is consumption, becuase aprime/(1+r) is put into

% consumption.

if (bl_post)

    bl_input_override = true;

    result_map('ar_val_diff_norm') = ar_val_diff_norm(1:it_iter_last);

    result_map('ar_pol_diff_norm') = ar_pol_diff_norm(1:it_iter_last);

    result_map('mt_pol_perc_change') = mt_pol_perc_change(1:it_iter_last, :);

    % Standard AZ graphs

    result_map = ff_az_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);

    % Graphs for results_map with FIBS contents

    result_map = ff_az_fibs_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);

end

end