function result_map = ff_ipwkz_vf_vecsv(varargin)

%% FF_IPWKZ_VF_VECSV 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. This is the two step solution

% with interpolation and with percentage asset grids version of

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

% ff_iwkz_vf_vecsv>. See that file for more descriptions. This is the

% optimized-vectorized version of the program.

%

% @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

%

% @include

%

% * <https://github.com/FanWangEcon/CodeDynaAsset/blob/master/m_ipwkz/paramfunc/ff_ipwkz_evf.m ff_ipwkz_evf>

% * <https://github.com/FanWangEcon/CodeDynaAsset/blob/master/m_ipwkz/paramfunc/ffs_ipwkz_set_default_param.m ffs_ipwkz_set_default_param>

% * <https://github.com/FanWangEcon/CodeDynaAsset/blob/master/m_ipwkz/paramfunc/ffs_ipwkz_get_funcgrid.m ffs_ipwkz_get_funcgrid>

% * <https://github.com/FanWangEcon/CodeDynaAsset/blob/master/m_akz/solvepost/ff_akz_vf_post.m ff_akz_vf_post>

%

%% 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;

bl_input_override = true;

[param_map, support_map] = ffs_ipwkz_set_default_param(it_param_set);

% parameters can be set inside ffs_ipwkz_set_default_param or updated here

% param_map('it_w_perc_n') = 50;

% param_map('it_ak_perc_n') = param_map('it_w_perc_n');

% param_map('it_z_n') = 15;

% param_map('fl_coh_interp_grid_gap') = 0.025;

% param_map('it_c_interp_grid_gap') = 0.001;

% param_map('fl_w_interp_grid_gap') = 0.25;

% param_map('it_w_perc_n') = 100;

% param_map('it_ak_perc_n') = param_map('it_w_perc_n');

% param_map('it_z_n') = 11;

% param_map('fl_coh_interp_grid_gap') = 0.1;

% param_map('it_c_interp_grid_gap') = 10^-4;

% param_map('fl_w_interp_grid_gap') = 0.1;

% get armt and func map

[armt_map, func_map] = ffs_ipwkz_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_ipwkz_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_ipwkz_vf_vecsv';

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_w_perc', 'ar_w_level', 'ar_z'});

[ar_w_perc, ar_w_level, ar_z] = params_group{:};

params_group = values(armt_map, {'ar_interp_c_grid', 'ar_interp_coh_grid', ...

    'mt_interp_coh_grid_mesh_z', 'mt_z_mesh_coh_interp_grid',...

    'mt_interp_coh_grid_mesh_w_perc', ...

    'mt_w_by_interp_coh_interp_grid'});

[ar_interp_c_grid, ar_interp_coh_grid, ...

    mt_interp_coh_grid_mesh_z, mt_z_mesh_coh_interp_grid, ...

    mt_interp_coh_grid_mesh_w_perc,...

    mt_w_by_interp_coh_interp_grid] = params_group{:};

params_group = values(armt_map, {'mt_coh_wkb', 'mt_z_mesh_coh_wkb'});

[mt_coh_wkb, mt_z_mesh_coh_wkb] = params_group{:};

% func_map

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

[f_util_log, f_util_crra, f_cons] = 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_defparam', 'bl_graph_evf', '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_defparam, bl_graph_evf, bl_display, it_display_every, bl_post] = params_group{:};

params_group = values(support_map, {'it_display_summmat_rowmax', 'it_display_summmat_colmax'});

[it_display_summmat_rowmax, it_display_summmat_colmax] = params_group{:};

%% Initialize Output Matrixes

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

mt_val = mt_val_cur - 1;

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

mt_pol_a_cur = mt_pol_a - 1;

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

mt_pol_k_cur = mt_pol_k - 1;

mt_pol_idx = zeros(length(ar_interp_coh_grid),length(ar_z));

% We did not need these in ff_oz_vf or ff_oz_vf_vec

% see

% <https://fanwangecon.github.io/M4Econ/support/speed/partupdate/fs_u_c_partrepeat_main.html

% fs_u_c_partrepeat_main> for why store using cells.

cl_u_c_store = cell([it_z_n, 1]);

cl_w_kstar_interp_z = cell([it_z_n, 1]);

for it_z_i = 1:length(ar_z)

    cl_w_kstar_interp_z{it_z_i} = zeros([length(ar_w_perc), length(ar_interp_coh_grid)]) - 1;

end

%% 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]);

%% Pre-calculate u(c)

% Interpolation, see

% <https://fanwangecon.github.io/M4Econ/support/speed/partupdate/fs_u_c_partrepeat_main.html

% fs_u_c_partrepeat_main> for why interpolate over u(c)

% Evaluate

if (fl_crra == 1)

    ar_interp_u_of_c_grid = f_util_log(ar_interp_c_grid);

    fl_u_neg_c = f_util_log(fl_c_min);

else

    ar_interp_u_of_c_grid = f_util_crra(ar_interp_c_grid);

    fl_u_neg_c = f_util_crra(fl_c_min);

end

ar_interp_u_of_c_grid(ar_interp_c_grid <= fl_c_min) = fl_u_neg_c;

% Get Interpolant

f_grid_interpolant_spln = griddedInterpolant(ar_interp_c_grid, ar_interp_u_of_c_grid, 'spline', 'nearest');

%% 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; 

    %% Interpolate (1) reacahble v(coh(k(w,z),b(w,z),z),z) given v(coh, z)

    % v(coh,z) solved on ar_interp_coh_grid, ar_z grids, see

    % ffs_ipwkz_get_funcgrid.m. Generate interpolant based on that, Then

    % interpolate for the coh reachable levels given the k(w,z) percentage

    % choice grids in the second stage of the problem

    % Generate Interpolant for v(coh,z)

    f_grid_interpolant_value = griddedInterpolant(... 

        mt_z_mesh_coh_interp_grid', mt_interp_coh_grid_mesh_z', mt_val_cur', 'linear', 'nearest'); 

    % Interpolate for v(coh(k(w,z),b(w,z),z),z)

    mt_val_wkb_interpolated = f_grid_interpolant_value(mt_z_mesh_coh_wkb, mt_coh_wkb); 

    %% Solve Second Stage Problem k*(w,z)

    % This is the key difference between this function and

    % <https://fanwangecon.github.io/CodeDynaAsset/m_akz/paramfunc/html/ffs_akz_set_functions.html

    % ffs_akz_set_functions> which solves the two stages jointly

    % Interpolation first, because solution coh grid is not the same as all

    % points reachable by k and b choices given w.

    support_map('bl_graph_evf') = false; 

    if (it_iter == (it_maxiter_val + 1)) 

        support_map('bl_graph_evf') = bl_graph_evf; 

    end 

    bl_input_override = true; 

    [mt_ev_condi_z_max, ~, mt_ev_condi_z_max_kp, ~] = ... 

        ff_ipwkz_evf(mt_val_wkb_interpolated, param_map, support_map, armt_map, bl_input_override); 

    %% Solve First Stage Problem w*(z) given k*(w,z)

    % loop 1: over exogenous states

    for it_z_i = 1:length(ar_z) 

        %% A. Interpolate FULL to get k*(w_perc, z), b*(k,w) based on k*(w_level, z)

        % Generate interpolant for (2) k*(ar_w_perc) from k*(ar_w_level,z)

        % There are two w=k'+b' arrays. ar_w_level is the level even grid based

        % on which we solve the 2nd stage problem in ff_ipwkz_evf.m. Here for

        % each coh level, we have a different vector of w levels, but the same

        % vector of percentage ws. So we need to interpolate to get the optimal

        % k* and b* choices at each percentage level of w.

        f_interpolante_w_level_kstar_z = griddedInterpolant(ar_w_level, mt_ev_condi_z_max_kp(:, it_z_i)', 'linear', 'nearest'); 

        % Interpolate (2), shift from w_level to w_perc

        mt_w_kstar_interp_z = f_interpolante_w_level_kstar_z(mt_w_by_interp_coh_interp_grid); 

        mt_w_astar_interp_z = mt_w_by_interp_coh_interp_grid - mt_w_kstar_interp_z; 

        % changes in w_perc kstar choices

        mt_w_kstar_diff_idx = (cl_w_kstar_interp_z{it_z_i} ~= mt_w_kstar_interp_z); 

        %% B. Calculate UPDATE u(c): u(c(coh_level, w_perc)) given k*_interp, b*_interp

        % Note that compared to

        % <https://fanwangecon.github.io/CodeDynaAsset/m_akz/paramfunc/html/ffs_akz_set_functions.html

        % ffs_akz_set_functions> the mt_c here is much smaller the same

        % number of columns (states) as in the ffs_akz_set_functions file,

        % but the number of rows equal to ar_w length.

        ar_c = f_cons(mt_interp_coh_grid_mesh_w_perc(mt_w_kstar_diff_idx), ... 

                      mt_w_astar_interp_z(mt_w_kstar_diff_idx), ... 

                      mt_w_kstar_interp_z(mt_w_kstar_diff_idx)); 

        % EVAL current utility: N by N, f_util defined earlier

        ar_utility_update = f_grid_interpolant_spln(ar_c); 

        % Update Storage

        if (it_iter == 1) 

            cl_u_c_store{it_z_i} = reshape(ar_utility_update, [length(ar_w_perc), length(ar_interp_coh_grid)]); 

        else 

            cl_u_c_store{it_z_i}(mt_w_kstar_diff_idx) = ar_utility_update; 

        end 

        cl_w_kstar_interp_z{it_z_i} = mt_w_kstar_interp_z; 

        %% C. Interpolate FULL EV(k*(coh_level, w_perc, z), w - b*|z) based on EV(k*(w_level, z))

        % Generate Interpolant for (3) EV(k*(ar_w_perc),Z)

        f_interpolante_ev_condi_z_max_z = griddedInterpolant(ar_w_level, mt_ev_condi_z_max(:, it_z_i)', 'linear', 'nearest'); 

        % Interpolate (3), EVAL add on future utility, N by N + N by N

        mt_ev_condi_z_max_interp_z = f_interpolante_ev_condi_z_max_z(mt_w_by_interp_coh_interp_grid); 

        %% D. Compute FULL U(coh_level, w_perc, z) over all w_perc

        mt_utility = cl_u_c_store{it_z_i} + fl_beta*mt_ev_condi_z_max_interp_z; 

        % percentage algorithm does not have invalid (check to make sure

        % min percent is not 0 in ffs_ipwkz_get_funcgrid.m)

        % mt_utility = mt_utility.*(~mt_it_c_valid_idx) + fl_u_neg_c*(mt_it_c_valid_idx);

        %% E. Optimize Over Choices: max_{w_perc} U(coh_level, w_perc, z)

        % Optimization: remember matlab is column major, rows must be

        % choices, columns must be states

        % <https://en.wikipedia.org/wiki/Row-_and_column-major_order COLUMN-MAJOR>

        [ar_opti_val1_z, ar_opti_idx_z] = max(mt_utility); 

        % Generate Linear Opti Index

        [it_choies_n, it_states_n] = size(mt_utility); 

        ar_add_grid = linspace(0, it_choies_n*(it_states_n-1), it_states_n); 

        ar_opti_linear_idx_z = ar_opti_idx_z + ar_add_grid; 

        %% F. Store Results

        mt_val(:,it_z_i) = ar_opti_val1_z; 

        mt_pol_a(:,it_z_i) = mt_w_astar_interp_z(ar_opti_linear_idx_z); 

        mt_pol_k(:,it_z_i) = mt_w_kstar_interp_z(ar_opti_linear_idx_z); 

        if (it_iter == (it_maxiter_val + 1)) 

            mt_pol_idx(:,it_z_i) = ar_opti_linear_idx_z; 

        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))/(length(ar_interp_coh_grid)); 

    ar_pol_k_perc_change = sum((mt_pol_k ~= mt_pol_k_cur))/(length(ar_interp_coh_grid)); 

    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(length(ar_interp_coh_grid),:); ...

                                      mt_pol_a_cur(length(ar_interp_coh_grid),:); ...

                                      mt_pol_k_cur(length(ar_interp_coh_grid),:)]);

        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;

result_map('mt_pol_idx') = mt_pol_idx;

result_map('cl_mt_coh') = {mt_interp_coh_grid_mesh_z, 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_interp_coh_grid_mesh_z, mt_pol_a, mt_pol_k), zeros(1)};

result_map('ar_st_pol_names') = ["cl_mt_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, :);

    % graphing based on coh_wkb, but that does not match optimal choice

    % matrixes for graphs.

    armt_map('mt_coh_wkb') = mt_interp_coh_grid_mesh_z;

    armt_map('it_ameshk_n') = length(ar_interp_coh_grid);

    armt_map('ar_a_meshk') = mt_interp_coh_grid_mesh_z(:,1);

    armt_map('ar_k_mesha') = zeros(size(mt_interp_coh_grid_mesh_z(:,1)) + 0);

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

end

%% Display Various Containers

if (bl_display_defparam)

    %% Display 1 support_map

    fft_container_map_display(support_map, it_display_summmat_rowmax, it_display_summmat_colmax);

    %% Display 2 armt_map

    fft_container_map_display(armt_map, it_display_summmat_rowmax, it_display_summmat_colmax);

    %% Display 3 param_map

    fft_container_map_display(param_map, it_display_summmat_rowmax, it_display_summmat_colmax);

    %% Display 4 func_map

    fft_container_map_display(func_map, it_display_summmat_rowmax, it_display_summmat_colmax);

    %% Display 5 result_map

    fft_container_map_display(result_map, it_display_summmat_rowmax, it_display_summmat_colmax);

end

end