ff_az_vf.m

%% Solve One Asset Dynamic Programming Problem (Loop)
% *back to <https://fanwangecon.github.io Fan>'s
% <https://fanwangecon.github.io/CodeDynaAsset/ Dynamic Assets Repository>
% Table of Content.*

%%
function result_map = ff_az_vf(varargin)
%% FF_AZ_VF solve infinite horizon exo shock + endo asset problem
% This program solves the infinite horizon dynamic single asset and single
% shock problem with loops. It is useful to have a version of code that is
% looped for easy debugging. This is the standard dynamic exogenous
% incomplete savings problem.
%
% See
% <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf.html
% ff_abz_vf> for the version of the problem that accommodates both borrowing
% and savings.
%
% @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
% * 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
%
%    % Get Default Parameters
%    it_param_set = 2;
%    [param_map, support_map] = ffs_abz_set_default_param(it_param_set);
%    % Change Keys in param_map
%    param_map('it_a_n') = 50;
%    param_map('it_z_n') = 5;
%    param_map('fl_a_max') = 100;
%    param_map('fl_w') = 1.3;
%    % Change Keys support_map
%    support_map('bl_display') = false;
%    support_map('bl_post') = true;
%    support_map('bl_display_final') = false;
%    % Call Program with external parameters that override defaults
%    % Note this program works very slowly if the grid sizes are too large
%    ff_az_vf(param_map, support_map);
%
% @include
%
% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/paramfunc/html/ffs_az_set_default_param.html ffs_az_set_default_param>
% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/paramfunc/html/ffs_az_get_funcgrid.html ffs_az_get_funcgrid>
% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/solvepost/html/ff_az_vf_post.html ff_az_vf_post>
%
% @seealso
%
% * save loop: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf.html ff_az_vf>
% * save vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf_vec.html ff_az_vf_vec>
% * save optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf_vecsv.html ff_az_vf_vecsv>
% * save + borr loop: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf.html ff_abz_vf>
% * save + borr vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf_vec.html ff_abz_vf_vec>
% * save + borr optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf_vecsv.html ff_abz_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 = 4;
bl_input_override = true;
[param_map, support_map] = ffs_az_set_default_param(it_param_set);

% Note: param_map and support_map can be adjusted here or outside to override defaults
param_map('it_a_n') = 75;
param_map('it_z_n') = 15;

[armt_map, func_map] = ffs_az_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_az_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_az_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'});
[ar_a, mt_z_trans, ar_z] = 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_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_nan_replace'});
[it_a_n, it_z_n, fl_crra, fl_beta, fl_nan_replace] = 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),length(ar_z));
mt_val = mt_val_cur - 1;
mt_pol_a = zeros(length(ar_a),length(ar_z));
mt_pol_a_cur = mt_pol_a - 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)
        fl_z = ar_z(it_z_i);

        % loop 2: over endogenous states
        for it_a_j = 1:length(ar_a)
            fl_a = ar_a(it_a_j);
            ar_val_cur = zeros(size(ar_a));

            % loop 3: over choices
            for it_ap_k = 1:length(ar_a)
                fl_ap = ar_a(it_ap_k);
                fl_c = f_cons(fl_z, fl_a, fl_ap);

                % 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_zp_q = 1:length(ar_z)
                    ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + fl_beta*mt_z_trans(it_z_i,it_zp_q)*mt_val_cur(it_ap_k,it_zp_q);
                end

                % Replace if negative consumption
                if fl_c <= 0
                    ar_val_cur(it_ap_k) = fl_nan_replace;
                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_a_j,it_z_i) = ar_val_cur(it_max_lin_idx(1));
            mt_pol_a(it_a_j,it_z_i) = ar_a(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);
    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
% for choices outcomes, store as cell with two elements, first element is
% the y(a,z), outcome given states, the second element will be solved found
% in
% <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_ds_vf.html
% ff_ds_vf> and other distributions files. It stores what are the
% probability mass function of y, along with sorted unique values of y.

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, ar_a'), zeros(1)};
result_map('cl_mt_pol_c') = {f_coh(ar_z, ar_a') - mt_pol_a, zeros(1)};
result_map('ar_st_pol_names') = ["mt_val", "cl_mt_pol_a", "cl_mt_coh", "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_az_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);
end

end