function [result_map] = ff_iwkz_ds_vec(varargin)

%% FF_IWKZ_DS_VEC finds the stationary asset distributions

% Building on the Two Assets Two-Step Interpolated Dynamic Programming

% Problem

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

% ff_iwkz_vf_vecsv>, here we solve for the asset distribution. This version

% of the program is vectorized

%

% This is the two-stage with interpolation version of

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

% ff_akz_ds_vec>. See that file for additional descriptions and

% comparisons. These two functions are nearly identical

%

% The code here works when we are looking for the distribution of f(a,z),

% where a'(a,z,z'), meaning that the a next period is determined by a last

% period and some shock last period as well as shock this period. a here is

% cash-on-hand. This contrasts with

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

% ff_az_ds>, which works for a'(a,z), a' can not be a function of z'.

%

% @example

%

%    % Get Default Parameters

%    it_param_set = 6;

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

%    % Change Keys in param_map

%    param_map('it_w_n') = 750;

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

%    param_map('it_z_n') = 11;

%    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

%    ff_iwkz_ds_vec(param_map, support_map);

%

% @include

%

% * <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_iwkz_vf_vecsv.html ff_wkz_vf_vecsv>

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

% * <https://fanwangecon.github.io/CodeDynaAsset/tools/html/fft_disc_rand_var_stats.html fft_disc_rand_var_stats>

% * <https://fanwangecon.github.io/CodeDynaAsset/tools/html/fft_disc_rand_var_mass2outcomes.html fft_disc_rand_var_mass2outcomes>

%

% @seealso

%

% * derive distribution f(y'(y,z)) one asset *loop*: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_ds.html ff_az_ds>

% * derive distribution f(y'({x,y},z)) two assets *loop*: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_akz_ds.html ff_akz_ds>

% * derive distribution f(y'({x,y},z, *z'*)) two assets *loop*: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_iwkz_ds.html ff_iwkz_ds>

% * derive distribution f(y'({y},z)) or f(y'({x,y},z)) *vectorized*: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_ds_vec.html ff_az_ds_vec>

% * derive distribution f(y'({y},z, *z'*)) or f(y'({x,y},z, *z'*)) *vectorized*: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_iwkz_ds_vec.html ff_iwkz_ds_vec>

% * derive distribution f(y'({y},z)) or f(y'({x,y},z)) *semi-analytical*: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_ds_vecsv.html ff_az_ds_vecsv>

% * derive distribution f(y'({y},z, *z'*)) or f(y'({x,y},z, *z'*)) *semi-analytical*: <https://fanwangecon.github.io/CodeDynaAsset/m_akz/solve/html/ff_iwkz_ds_vecsv.html ff_iwkz_ds_vecsv>

%

%% Default

% Program can be externally invoked with _az_, _abz_ or various other

% programs. By default, program invokes using _az_ model programs:

%

% # it_subset = 5 is basic invoke quick test

% # it_subset = 6 is invoke full test

% # it_subset = 7 is profiling invoke

% # it_subset = 8 is matlab publish

% # it_subset = 9 is invoke operational (only final stats) and coh graph

%

if (~isempty(varargin))

    % if invoked from outside override fully

    [param_map, support_map, armt_map, func_map, result_map] = varargin{:};

else

    % default invoke

    close all;

    it_param_set = 7;

    st_akz_or_iwkz = 'iwkz';

    % 1. Generate Parameters

    [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;

    % 2. Generate function and grids

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

    % 3. Solve value and policy function using ff_iwkz_vf_vecsv

    if (strcmp(st_akz_or_iwkz, 'iwkz'))

        [result_map] = ff_iwkz_vf_vecsv(param_map, support_map, armt_map, func_map);

    end

end

%% Parse Parameters

% append function name

st_func_name = 'ff_iwkz_ds_vec';

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')];

% result_map

% ar_st_pol_names is from section _Process Optimal Choices_ in the value

% function code.

params_group = values(result_map, {'cl_mt_pol_a', 'cl_mt_pol_k'});

[cl_mt_pol_a, cl_mt_pol_k] = params_group{:};

[mt_pol_a, mt_pol_k] = deal(cl_mt_pol_a{1}, cl_mt_pol_k{1});

% func_map

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

[f_coh] = params_group{:};

% 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_interp_coh_grid'});

[ar_interp_coh_grid] = params_group{:};

% param_map

params_group = values(param_map, {'it_z_n', 'it_maxiter_dist', 'fl_tol_dist'});

[it_z_n, it_maxiter_dist, fl_tol_dist] = params_group{:};

% support_map

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

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

    'bl_time', 'bl_display_dist', 'it_display_every'});

[bl_profile_dist, st_profile_path, ...

    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...

    bl_time, bl_display_dist, it_display_every] = params_group{:};

%% Start Profiler and Timer

% Start Profile

if (bl_profile_dist)

    close all;

    profile off;

    profile on;

end 

% Start Timer

if (bl_time) 

    tic; 

end 

%% A. Get Size of Endogenous and Exogenous State

it_endostates_n = length(ar_interp_coh_grid); 

it_exostates_n = length(ar_z); 

%% B. Initialize Output Matrixes

% Initialize the distribution to be uniform

mt_dist_akz_init = ones(it_endostates_n,it_exostates_n)/it_endostates_n/it_exostates_n; 

mt_dist_akz_cur = mt_dist_akz_init; 

mt_dist_akz_zeros = zeros(it_endostates_n,it_exostates_n); 

%% C. Initialize Convergence Conditions

bl_histiter_continue = true; 

it_iter = 0; 

ar_dist_diff_norm = zeros([it_maxiter_dist, 1]); 

mt_dist_perc_change = zeros([it_maxiter_dist, it_z_n]); 

%% D. Solve for Index

% The model is solved by interpolating over cash-on-hand. The optimal

% choices do not map to specific points on the cash-on-hand grid. Find the

% index of the cash-on-hand vector that is the closest to the

% coh'(a'(coh,z),k'(coh,z),z'). 

%

% Since we have *z_n* elements of shocks, and *coh_n* elements of the

% cash-on-hand grid, there are (coh_n x z_n) possible combinations of

% states at period t. In period t+1, there are (coh_n x z_n) by (z_n)

% possible/reachable cash-on-hand points. We find the index of all these

% reachable coh' points on the interpolation cash-on-hand grid.

%

% 1. *mt_coh_prime* is (coh_n x z_n) by (z_n)

% coh'(z', a'(coh,z), k'(coh,z))    

mt_coh_prime = f_coh(ar_z, mt_pol_a(:), mt_pol_k(:)); 

% 2. *mt_coh_prime_on_grid_idx* is (coh_n x z_n) by (z_n):

% index for coh'(a,k,z')

mt_coh_prime_on_grid_idx = zeros(size(mt_coh_prime)); 

for it_zprime_ctr=1:size(mt_coh_prime, 2) 

    ar_coh_prime = mt_coh_prime(:,it_zprime_ctr); 

    [~, ar_coh_prime_on_grid_idx] = min(abs(ar_coh_prime(:)' - ar_interp_coh_grid')); 

    mt_coh_prime_on_grid_idx(:,it_zprime_ctr) = ar_coh_prime_on_grid_idx; 

end 

%% E. Solve for Unique Index

% For each z', there are (coh_n x z_n) possible coh'(z') reachable points,

% which have been converted to index: *mt_coh_prime_on_grid_idx* along the

% cash-on-hand grid in the previous code segment. Now, we find the number

% of unique coh' grid points among the (coh_n x z_n) grid indexes:

% *ar_idx_of_unique*. We also find the positions of these unique indexes in

% the full (coh_n x z_n) grid: *ar_idx_full*

% 

cl_ar_idx_full = cell([it_exostates_n, 1]); 

cl_ar_idx_of_unique = cell([it_exostates_n, 1]); 

for it_z_i = 1:it_exostates_n 

    % 5. Cumulative probability received at state from zi

    [ar_idx_full, ~, ar_idx_of_unique] = unique(mt_coh_prime_on_grid_idx(:, it_z_i)); 

    cl_ar_idx_full{it_z_i} = ar_idx_full; 

    cl_ar_idx_of_unique{it_z_i} = ar_idx_of_unique; 

end 

%% F. Derive Stationary Distribution

% Iterate until convergence

while (bl_histiter_continue) 

    it_iter = it_iter + 1; 

    %% F1. Iterate over z' Shocks

    % The code below loops over future states, note that the structure here is

    % significant different from

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

    % ff_akz_ds>, where we looped over current shocks. Here we loop over future

    % shocks because coh' is a function of z' as well as choices last period. 

    %

    % 1. initialize empty

    mt_dist_akz = mt_dist_akz_zeros; 

    % 2. loop over next period exo shocks

    for it_z_i = 1:it_exostates_n 

        % 3. *ar_zi_prob* is (coh_n x z_n) by (1):

        % mt_z_trans(:, it_z_i)': for all z today, prob(z'|z) fixing z' 

        % overall: f(coh,z)*f(z'|z) fixing z' for all z

        mt_zi_prob = mt_dist_akz_cur .* mt_z_trans(:,it_z_i)'; 

        ar_zi_prob = mt_zi_prob(:); 

        % 4. Cumulative probability received at state from zi

        mt_zi_cumu_prob = accumarray(cl_ar_idx_of_unique{it_z_i}, ar_zi_prob); 

        % 5. Adding up

        mt_dist_akz(cl_ar_idx_full{it_z_i}, it_z_i) = mt_zi_cumu_prob +  mt_dist_akz(cl_ar_idx_full{it_z_i}, it_z_i); 

    end 

    %% F2. Check Tolerance and Continuation

    % Difference across iterations

    ar_dist_diff_norm(it_iter) = norm(mt_dist_akz - mt_dist_akz_cur); 

    mt_dist_perc_change(it_iter, :) = sum((mt_dist_akz ~= mt_dist_akz))/it_endostates_n; 

    % Update

    mt_dist_akz_cur = mt_dist_akz; 

    % Print Iteration Results

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

        fprintf('Dist it_iter:%d, fl_dist_diff:%d\n', it_iter, ar_dist_diff_norm(it_iter));

        tb_hist_iter = array2table([sum(mt_dist_akz_cur,1); std(mt_dist_akz_cur,1); ...

                                    mt_dist_akz_cur(1,:); mt_dist_akz_cur(it_endostates_n,:)]);

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

        tb_hist_iter.Properties.RowNames = {'mdist','sddist', 'Ldist', 'Hdist'};

        disp('mdist = sum(mt_dist_akz_cur,1) = sum_{a,k}(p({a,k})|z)')

        disp('sddist = std(mt_pol_ak_cur,1) = std_{a,k}(p({a,k})|z)')

        disp('Ldist = mt_dist_akz_cur(1,:) = p(min({a,k})|z)')

        disp('Hdist = mt_dist_akz_cur(it_a_n,:) = p(max({a,k})|z)')

        disp(tb_hist_iter);

    end

    % Continuation Conditions:

    if (it_iter == (it_maxiter_dist + 1)) 

        bl_histiter_continue = false; 

    elseif ((it_iter == it_maxiter_dist) || ... 

            (ar_dist_diff_norm(it_iter) < fl_tol_dist)) 

        it_iter_last = it_iter; 

        it_iter = it_maxiter_dist; 

    end 

end 

%% End Time and Profiler

% End Timer

if (bl_time) 

    toc; 

end 

% End Profile

if (bl_profile_dist) 

    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

%% *f(y), f(c), f(a), f(k)*: Generate Key Distributional Statistics for Each outcome

% Having derived f({a,k},z) the probability mass function of the joint discrete

% random variables, we now obtain distributional statistics. Note that we

% know f({a,k},z), and we also know relevant policy functions a'(a,k,z), k'(a,k,z),

% or other policy functions. We can simulate any choices that are a

% function of the random variables (coh(a,k),z), using f(coh(a,k),z). We call function

% <https://fanwangecon.github.io/CodeDynaAsset/m_az/solvepost/html/ff_az_ds_post_stats.html

% ff_az_ds_post_stats> which uses

% <https://fanwangecon.github.io/CodeDynaAsset/tools/html/fft_disc_rand_var_stats.html

% fft_disc_rand_var_stats> and

% <https://fanwangecon.github.io/CodeDynaAsset/tools/html/fft_disc_rand_var_mass2outcomes.html

% fft_disc_rand_var_mass2outcomes> to compute various statistics of

% interest.

result_map = ff_az_ds_post_stats(support_map, result_map, mt_dist_akz);

end