function result_map = ff_akz_vf(varargin)

%% FF_AKZ_VF solve infinite horizon exo shock + endo asset problem

% This program solves the infinite horizon dynamic savings and risky

% capital asset problem with some ar1 shock. The two assets could be a safe

% bond and a risky stock if the risky asset has constant return to scale.

% Alternatively, the risky asset could be a capital investment asset with

% decreasing return to scale. There is risky component to the risky capital

% investment, but one could also potentially resale a fraction of the risky

% capital after depreciation, giving the household/investor/entrepreur a

% safe minimum return to risky investment. The state variable is the

% cash-on-hand, which is determined by risky and safe asset as well as the

% shock jointly.

%

% This problem is more computationally intensive to solve

% compared to the single asset problem, shown here:

% <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf.html

% ff_az_vf>. Here I show the looped solution. As before, as we expand the 

% state and choices spaces to have a looped slow version of the code so

% that one could debug and make sure the model works. 

%

% Vectorized, optimized vectorized versions of the code are shown here:

% <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_akz_vf_vec.html

% ff_akz_vf_vec> and here:

% <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_akz_vf_vecsv.html

% ff_akz_vf_vecsv>. These improve upon the speed, yet the

% speed is still not as fast as we need for some applications. 

%

% The basic forms of the one and two asset problems have analytically

% tractable mathmatical solutions. The benefit of these grid based solution

% algorithm is that we are able to add very flexible constraints to the

% problem or incorporate additional discrete choices that make the

% underlying problem non-continous and non-differentiable and mathamtically

% untractable.

%

% @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 safe asset

% * mt_pol_k matrix states_n by shock_n matrix of converged policy function

% grid risky asset

% * 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

%

%   it_param_set = 2;

%   [param_map, support_map] = ffs_akz_set_default_param(it_param_set);   

%   % Simulation Accuracy

%   param_map('it_w_n') = 750;

%   param_map('it_ak_n') = param_map('it_w_n');

%   param_map('it_z_n') = 11;

%   % Display Parameters

%   support_map('bl_display') = false;

%   support_map('bl_display_final') = false;

%   support_map('bl_time') = true;

%   support_map('bl_profile') = false;

%   % Call Program with external parameters that override defaults

%   ff_akz_vf(param_map, support_map);

% 

% @include

%

% * <https://fanwangecon.github.io/CodeDynaAsset/m_akz/paramfunc/html/ffs_akz_set_default_param.html ffs_akz_set_default_param>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_akz/paramfunc/html/ffs_akz_get_funcgrid.html ffs_akz_get_funcgrid>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solvepost/html/ff_akz_vf_post.html ff_akz_vf_post>

%

% @seealso

%

% * concurrent (safe + risky) loop: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_akz_vf.html ff_akz_vf>

% * concurrent (safe + risky) vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_akz_vf_vec.html ff_akz_vf_vec>

% * concurrent (safe + risky) optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_akz_vf_vecsv.html ff_akz_vf_vecsv>

% * two-stage (safe + risky) loop: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_wkz_vf.html ff_wkz_vf>

% * two-stage (safe + risky) vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_wkz_vf_vec.html ff_wkz_vf_vec>

% * two-stage (safe + risky) optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_wkz_vf_vecsv.html ff_wkz_vf_vecsv>

% * two-stage + interpolate (safe + risky) loop: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_iwkz_vf.html ff_iwkz_vf>

% * two-stage + interpolate (safe + risky) vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_iwkz_vf_vec.html ff_iwkz_vf_vec>

% * two-stage + interpolate (safe + risky) optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_iwkz_vf_vecsv.html ff_iwkz_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 = 2;

bl_input_override = true;

[param_map, support_map] = ffs_akz_set_default_param(it_param_set);

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

% param_map('it_w_n') = 50;

% param_map('it_z_n') = 15;

% get armt and func map

[armt_map, func_map] = ffs_akz_get_funcgrid(param_map, support_map, bl_input_override); % 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_akz_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_akz_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, {'mt_z_trans', 'ar_z'});

[ mt_z_trans, ar_z] = params_group{:};

params_group = values(armt_map, {'ar_a_meshk', 'ar_k_mesha', 'mt_coh_wkb', 'it_ameshk_n'});

[ar_a_meshk, ar_k_mesha, mt_coh_wkb, it_ameshk_n] = params_group{:};

% func_map

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

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

% param_map

params_group = values(param_map, {'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min'});

[it_z_n, fl_crra, fl_beta, fl_c_min] = 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{:};

% support_map

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

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

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

[bl_profile, st_profile_path, ...

    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...

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

%% Initialize Output Matrixes

mt_val_cur = zeros(length(ar_a_meshk),length(ar_z));

mt_val = mt_val_cur - 1;

mt_pol_a = zeros(length(ar_a_meshk),length(ar_z));

mt_pol_a_cur = mt_pol_a - 1;

mt_pol_k = zeros(length(ar_a_meshk),length(ar_z));

mt_pol_k_cur = mt_pol_k - 1;

%% 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 

% Value Function Iteration

while bl_vfi_continue 

    it_iter = it_iter + 1; 

    %% Solve Optimization Problem Current Iteration

    % loop 1: over exogenous states

    for it_z_i = 1:length(ar_z) 

        % loop 2: over endogenous states

        for it_coh_j = 1:length(ar_a_meshk) 

            % Get cash-on-hand which include k,b,z

            fl_coh = mt_coh_wkb(it_coh_j, it_z_i); 

            % loop 3: over choices

            ar_val_cur = zeros(size(ar_a_meshk)); 

            for it_cohp_k = 1:length(ar_a_meshk) 

                fl_ap = ar_a_meshk(it_cohp_k); 

                fl_kp = ar_k_mesha(it_cohp_k); 

                % consumption

                fl_c = f_cons(fl_coh, fl_ap, fl_kp); 

                % current utility

                if (fl_crra == 1) 

                    ar_val_cur(it_cohp_k) = f_util_log(fl_c);

                    fl_u_neg_c = f_util_log(fl_c_min);

                else 

                    ar_val_cur(it_cohp_k) = f_util_crra(fl_c); 

                    fl_u_neg_c = f_util_crra(fl_c_min); 

                end 

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

                for it_zp_q = 1:length(ar_z) 

                    ar_val_cur(it_cohp_k) = ar_val_cur(it_cohp_k) + fl_beta*mt_z_trans(it_z_i,it_zp_q)*mt_val_cur(it_cohp_k,it_zp_q); 

                end 

                % Replace if negative consumption

                if fl_c <= 0 

                    ar_val_cur(it_cohp_k) = fl_u_neg_c; 

                end 

            end 

            % maximization over loop 3 choices for loop 1+2 states

            it_max_lin_idx = find(ar_val_cur == max(ar_val_cur)); 

            mt_val(it_coh_j,it_z_i) = ar_val_cur(it_max_lin_idx(1)); 

            mt_pol_a(it_coh_j,it_z_i) = ar_a_meshk(it_max_lin_idx(1)); 

            mt_pol_k(it_coh_j,it_z_i) = ar_k_mesha(it_max_lin_idx(1)); 

        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) + norm(mt_pol_k - mt_pol_k_cur); 

    ar_pol_a_perc_change = sum((mt_pol_a ~= mt_pol_a_cur))/(it_ameshk_n); 

    ar_pol_k_perc_change = sum((mt_pol_k ~= mt_pol_k_cur))/(it_ameshk_n);     

    mt_pol_perc_change(it_iter, :) = mean([ar_pol_a_perc_change;ar_pol_k_perc_change]); 

    % Update

    mt_val_cur = mt_val; 

    mt_pol_a_cur = mt_pol_a; 

    mt_pol_k_cur = mt_pol_k; 

    % 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); ...

                                      mean(mt_pol_k_cur,1); ...

                                      mt_val_cur(it_ameshk_n,:); ...

                                      mt_pol_a_cur(it_ameshk_n,:); ...

                                      mt_pol_k_cur(it_ameshk_n,:)]);

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

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

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

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

        disp('mkp  = mean(mt_pol_k_cur,1), average choice over k')

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

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

        disp('mak = mt_pol_k_cur(it_ameshk_n,:), highest k 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;

mt_coh = f_coh(ar_z, ar_a_meshk, ar_k_mesha);

result_map('cl_mt_pol_coh') = {mt_coh, zeros(1)};

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

result_map('cl_mt_pol_k') = {mt_pol_k, zeros(1)};

result_map('cl_mt_pol_c') = {f_cons(mt_coh, mt_pol_a, mt_pol_k), zeros(1)};

result_map('ar_st_pol_names') = ["cl_mt_pol_coh", "cl_mt_pol_a", "cl_mt_pol_k", "cl_mt_pol_c"];

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, :);

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

end

end