function [mt_ev_condi_z_max, mt_ev_condi_z_max_idx, mt_ev_condi_z_max_kp, mt_ev_condi_z_max_bp] = ff_ipwkbzr_evf(varargin)

%% FF_IPWKBZR_EVF solves the k' vs b' problem given aggregate savings

% This function follows the structure set up here:

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

% ff_wkz_evf> but now we solve the second stage with percentage choice grid

%

% We solve along a vector of w_n vector, that is an interpolation vector,

% not a vector of actual w choices picked in the first stage. k' choices

% are in terms of percentages. Compared to ff_wkz_evf where we only had an

% upper triangle of choices, now we have a full matrix of percentage

% choices.

%

% @param mt_val matrix state_n I^2 by shock_n. This is the value

% matrix each row is a feasible reachable state given the choice

% vectors/matrix and each column is a shock state.

%

% @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

%

% @return mt_ev_condi_z_max matrix choice_w_n by shock_n

% max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) conditional on z and w, at the

% optimal k' choice (w=k'+b') what is the expected utility? This is the

% value result from the 2nd stage problem. Note the result integrates over

% z'.

%

% @return mt_ev_condi_z_max_idx matrix choice_w_n by shock_n this is the

% argmax from max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)). Given the vector of k'

% choices, which index maximized conditional on z and w integrating over

% z'/

%

% @return mt_ev_condi_z_max_kp matrix choice_w_level_n by shock_n the k'

% choice at max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w))

%

% @return mt_ev_condi_z_max_bp matrix choice_w_n by shock_n the b'=w-k'

% choice at max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w))

%

% @example

%

% @include

%

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

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

%

%% Default

if (~isempty(varargin)) 

    % override when called from outside

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

else

    close all;

    % Not default parameters, but parameters that generate defaults

    [param_map, support_map] = ffs_ipwkbzr_set_default_param();

    support_map('bl_graph_evf') = true;

    bl_display_evf = true;

    support_map('bl_display_evf') = bl_display_evf;        

    st_param_which = 'default';

    if (ismember(st_param_which, ['default']))

        param_map('it_ak_perc_n') = 250;        

    elseif ismember(st_param_which, ['small'])

        param_map('fl_z_r_borr_n') = 2;

        param_map('it_z_wage_n') = 3;

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

        param_map('fl_b_bd') = -20; % borrow bound, = 0 if save only

        param_map('fl_default_aprime') = 0;

        param_map('bl_default') = 0; % if borrowing is default allowed

        param_map('fl_w_min') = param_map('fl_b_bd');

        param_map('it_w_perc_n') = 7;

        param_map('it_ak_perc_n') = 7;

        param_map('fl_w_interp_grid_gap') = 2;

        param_map('fl_coh_interp_grid_gap') = 2;

        param_map('fl_z_r_borr_min') = 0.025;

        param_map('fl_z_r_borr_max') = 0.95;

        param_map('fl_z_r_borr_n') = 3;

    elseif ismember(st_param_which, ['ff_ipwkbzr_evf'])

        % ff_ipwkbzr_evf default

        param_map('fl_z_r_borr_min') = 0.025;

        param_map('fl_z_r_borr_max') = 0.025;

        param_map('fl_z_r_borr_n') = 1;

        param_map('it_ak_perc_n') = 250;

        param_map('fl_r_save') = 0.025;

    end

    % Dimension Adjustments

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

    param_map('fl_w_interp_grid_gap') = (param_map('fl_w_max')-param_map('fl_b_bd'))/param_map('it_ak_perc_n');

    % Generate Grids

    [armt_map, func_map] = ffs_ipwkbzr_get_funcgrid(param_map, support_map);

    % Get Defaults

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

    [it_z_n, fl_z_r_borr_n] = params_group{:};    

    params_group = values(param_map, {'st_v_coh_z_interp_method'});

    [st_v_coh_z_interp_method] = params_group{:};    

    params_group = values(armt_map, {'mt_coh_wkb', 'ar_z_r_borr', 'ar_ak_perc', 'ar_w_level'});

    [mt_coh_wkb, ar_z_r_borr, ar_ak_perc, ar_w_level] = params_group{:};

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

    [f_util_standin_coh] = params_group{:};

    % Note that for the testing function below, ar_z_r_borr does not need

    % to matter for testing, meaning V(coh, zw, zr_j) = V(coh, zw, zr_i).

    % With integration it matters. This is an important point, for just

    % last period debt, if no new borrowing choices are made, it does not

    % matter what new zr shocks are, just what last period rates are. But

    % once the problem is dynamic. But the object of interest here is:

    % EV(k', b', zw, zr), conditionally on the same k'/b', will zr have an

    % impact? yes it will, even just through interest rate on b'.

    % mt_coh_wkb is: (I^k x I^w x M^r) by (M^z)

    % mt_coh_wkb(:) is: (I^k x I^w x M^r x M^z) by 1

    % ar_z_r_borr is: 1 by M^r

    % mt_val is: (I^k x I^w x M^r x M^z) by (M^r)

    mt_val = f_util_standin_coh(mt_coh_wkb(:), ar_z_r_borr);

    % mt_val is: (I^k x I^w x M^r) by (M^z x M^r)

    mt_val = reshape(mt_val, [size(mt_coh_wkb, 1), it_z_n]);

    if (ismember(st_v_coh_z_interp_method, ["method_idx_a", "method_idx_b", "method_cell"]))

        it_ak_perc_n = length(ar_ak_perc);

        it_w_interp_n = length(ar_w_level);

        it_wak_n = it_w_interp_n*it_ak_perc_n;

        clmt_val_wkb_interpolated = cell([fl_z_r_borr_n, 1]);

        for it_z_r_borr_ctr = 1:1:fl_z_r_borr_n

            it_mt_val_row_start = it_wak_n*(it_z_r_borr_ctr-1) + 1;

            it_mt_val_row_end = it_mt_val_row_start + it_wak_n - 1;

            clmt_val_wkb_interpolated{it_z_r_borr_ctr} = ...

                mt_val(it_mt_val_row_start:it_mt_val_row_end, :);

        end

    elseif (ismember(st_v_coh_z_interp_method, ["method_matrix", "method_mat_seg"]))

        clmt_val_wkb_interpolated = mt_val;

    end

    % Display Parameters

    if (bl_display_evf)

        fft_container_map_display(param_map);

        fft_container_map_display(support_map);

    end

end 

%% Parse Parameters

% armt_map

params_group = values(armt_map, {'ar_z_r_borr_mesh_wage_w1r2', 'ar_z_wage_mesh_r_borr_w1r2'}); 

[ar_z_r_borr_mesh_wage_w1r2, ar_z_wage_mesh_r_borr_w1r2] = params_group{:}; 

params_group = values(armt_map, {'mt_z_trans', 'ar_ak_perc', 'ar_w_level', 'ar_k_mesha', 'ar_a_meshk', 'ar_aplusk_mesh'}); 

[mt_z_trans, ar_ak_perc, ar_w_level, ar_k_mesha, ar_a_meshk, ar_aplusk_mesh] = params_group{:}; 

% param_map

params_group = values(param_map, {'it_z_n', 'fl_z_r_borr_n', 'it_z_wage_n'}); 

[it_z_n, fl_z_r_borr_n, it_z_wage_n] = params_group{:}; 

params_group = values(param_map, {'fl_nan_replace', 'fl_b_bd'}); 

[fl_nan_replace, fl_b_bd] = params_group{:}; 

params_group = values(param_map, {'st_v_coh_z_interp_method'}); 

[st_v_coh_z_interp_method] = params_group{:}; 

% support_map

params_group = values(support_map, {'bl_graph_onebyones','bl_display_evf', 'bl_graph_evf'}); 

[bl_graph_onebyones, bl_display_evf, bl_graph_evf] = params_group{:}; 

params_group = values(support_map, {'bl_img_save', 'st_img_path', 'st_img_prefix', 'st_img_name_main', 'st_img_suffix'}); 

[bl_img_save, st_img_path, st_img_prefix, st_img_name_main, st_img_suffix] = 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{:}; 

% append function name

st_func_name = 'ff_ipwkbzr_evf'; 

st_img_name_main = [st_func_name st_img_name_main]; 

%% Integrate *E(V(coh(k',b',zr),zw',zr')|zw,zr)*

% start with E(V(coh(k',b',zr),zw',zr')|zw,zr), integrate to find

% EV(k',b';zw,zr).

%

% Each column for a different state z, to integrate:

% *E(V(coh(k',b',zr),zw',zr')|zw,zr)*. Each column is a different shock,

% from the combinations of zw and zr shocks. Each row is a different unique

% level of reacheable cash-on-hand level, which is determined by the choice

% grid for w = k' + b', k' and b', as well as the borrowing shock vector

% zr. 

%

% The issue here is, unlike the productivity shock, where only the z'

% matters tomorrow, and z matters via conditional probability of p(z'|z),

% for the interest rate shock, both r and r' matter. For the z case, z'

% impacts the cash-on-hand, and z''. For r case, r impacts cash-on-hand

% tomorrow, since interest is known at the time when the loan is taken out,

% and r' also matters because it is the rate that decision maker next

% period faces when making b'' borrowing choices. 

%

% With the structure below, the interest rate r draw that households face

% today will impact the cash-on-hand tomorrow; the r' draw will impact

% tomorrow's value function through its effect on b'' choice; r impacts r'

% through conditional probability.

%

% Note that: mt_ev_condi_z = mt_val*mt_z_trans' work if we did not have the

% interest rate shock. With the interest rate shock, we have to proceed

% differently. 

%

% Note that mt_ev_condi_z rows are less by length of r rate shock times.

%

% # mt_val = (it_w_interp_n*it_ak_perc_n*length(fl_z_r_borr_n)) by (it_z_wage_n*length(fl_z_r_borr_n))

% # mt_ev_condi_z = (it_w_interp_n*it_ak_perc_n) by (it_z_wage_n*length(fl_z_r_borr_n))

%

% 1. Number of W/B/K Choice Combinations

it_ak_perc_n = length(ar_ak_perc); 

it_w_interp_n = length(ar_w_level); 

it_wak_n = it_w_interp_n*it_ak_perc_n; 

% 2. Initialize mt_ev_condi_z = E(V(coh(k',b',zr'),zw',zr')|zw,zr)

% rows = it_wak_n

% cols = it_z_n

mt_ev_condi_z = zeros([it_wak_n, it_z_n]); 

for it_z_r_borr_ctr = 1:1:fl_z_r_borr_n 

    % Transition Row Subset: ((M^z) by (M^z x M^r))' for one m^r

    it_mt_z_trans_row_start = it_z_wage_n*(it_z_r_borr_ctr-1) + 1; 

    it_mt_z_trans_row_end = it_mt_z_trans_row_start + it_z_wage_n - 1;     

    mt_z_trans_cur_z_r_borr = mt_z_trans(it_mt_z_trans_row_start:it_mt_z_trans_row_end, :); 

    if (ismember(st_v_coh_z_interp_method, ["method_idx_a", "method_idx_b", "method_cell"])) 

        mt_ev_condi_z(:, it_mt_z_trans_row_start:it_mt_z_trans_row_end) = ... 

            clmt_val_wkb_interpolated{it_z_r_borr_ctr}*mt_z_trans_cur_z_r_borr'; 

    elseif (ismember(st_v_coh_z_interp_method, ["method_matrix", "method_mat_seg"]))

        % Val Segment : ((M^z) by (M^z x M^r))' for one m^r

        it_mt_val_row_start = it_wak_n*(it_z_r_borr_ctr-1) + 1;

        it_mt_val_row_end = it_mt_val_row_start + it_wak_n - 1;

        mt_val_cur_z_r_borr = clmt_val_wkb_interpolated(it_mt_val_row_start:it_mt_val_row_end, :);

        % EV(k',b';zw,zr) = E(V(coh(k',b',zr),zw',zr')|zw,zr) for one zr and all zw

        mt_ev_condi_z(:, it_mt_z_trans_row_start:it_mt_z_trans_row_end) = ...

            mt_val_cur_z_r_borr*mt_z_trans_cur_z_r_borr';

    end

end 

if(bl_display_evf) 

    disp('----------------------------------------');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    disp('Expected Value: mt_ev_condi_z');

    disp("EV(k', b', zw, zr) = (V(coh(k',b',zr'),zw',zr')|zw,zr)");       

    disp("rows = k'/b' combos, cols = zw/zr combos");

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    it_col_n_keep = it_z_wage_n*2;

    it_row_n_keep = it_ak_perc_n*3;

    [it_row_n, it_col_n] = size(mt_ev_condi_z);

    [ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);    

    cl_st_full_cols = cellstr([num2str(ar_z_r_borr_mesh_wage_w1r2', 'r%3.2f;'), ...

                               num2str(ar_z_wage_mesh_r_borr_w1r2', 'w%3.2f')]);

    cl_st_full_rows = cellstr([num2str(ar_aplusk_mesh, 'w%3.2f'), ...

                               num2str(ar_k_mesha, 'k%3.2f'),...

                               num2str(ar_a_meshk, 'a%3.2f')]);

    tb_mt_exp_val = array2table(round(mt_ev_condi_z(ar_it_rows, ar_it_cols),6));

    cl_col_names = strcat('i', num2str(ar_it_cols'), ':', cl_st_full_cols(ar_it_cols));

    cl_row_names = strcat('i', num2str(ar_it_rows'), ':', cl_st_full_rows(ar_it_rows));

    tb_mt_exp_val.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);

    tb_mt_exp_val.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);

    disp(size(mt_ev_condi_z));

    disp(tb_mt_exp_val(1:round(it_row_n_keep/2), :));

    disp(tb_mt_exp_val((round(it_row_n_keep/2)+1):it_row_n_keep, :));

end

%% Reshape *E(V(coh,z'|z,w))* to allow for maxing

% dim(mt_ev_condi_z): *IxJ by M*

mt_ev_condi_z_full = reshape(mt_ev_condi_z, [it_ak_perc_n, it_w_interp_n*it_z_n]); 

%% Maximize *max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w))* optimal value and index

% Maximization, find optimal k'/b' combination given z and w=k'+b'

[ar_ev_condi_z_max, ar_ev_condi_z_max_idx] = max(mt_ev_condi_z_full); 

mt_ev_condi_z_max = reshape(ar_ev_condi_z_max, [it_w_interp_n, it_z_n]); 

mt_ev_condi_z_max_idx = reshape(ar_ev_condi_z_max_idx, [it_w_interp_n, it_z_n]); 

if(bl_display_evf) 

    disp('----------------------------------------');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    disp('mt_ev_condi_z_full: J by IxM');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    disp(size(mt_ev_condi_z_full));

%     disp(head(array2table(mt_ev_condi_z_full), 20));

%     disp(tail(array2table(mt_ev_condi_z_full), 20));

    disp('----------------------------------------');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    disp('mt_ev_condi_z_max: I by M');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    it_col_n_keep = it_z_wage_n*2;    

    it_row_n_keep = round(it_w_interp_n);

    [it_row_n, it_col_n] = size(mt_ev_condi_z_max);

    [ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);    

    cl_st_full_cols = cellstr([num2str(ar_z_r_borr_mesh_wage_w1r2', 'r%3.2f;'), ...

                               num2str(ar_z_wage_mesh_r_borr_w1r2', 'w%3.2f')]);

    cl_st_full_rows = cellstr([num2str(ar_w_level', 'w%3.2f')]);

    tb_mt_ev_condi_z_max = array2table(round(mt_ev_condi_z_max(ar_it_rows, ar_it_cols), 6));

    cl_col_names = strcat('i', num2str(ar_it_cols'), ':', cl_st_full_cols(ar_it_cols));

    cl_row_names = strcat('i', num2str(ar_it_rows'), ':', cl_st_full_rows(ar_it_rows));

    tb_mt_ev_condi_z_max.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);

    tb_mt_ev_condi_z_max.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);    

    disp(size(mt_ev_condi_z_max));

    disp(tb_mt_ev_condi_z_max(1:round(it_row_n_keep/2), :));

    disp(tb_mt_ev_condi_z_max((round(it_row_n_keep/2)+1):it_row_n_keep, :));

    disp('----------------------------------------');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    disp('mt_ev_condi_z_max_idx: I by M');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    tb_mt_ev_condi_z_max_idx = array2table(mt_ev_condi_z_max_idx(ar_it_rows, ar_it_cols));

    tb_mt_ev_condi_z_max_idx.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);

    tb_mt_ev_condi_z_max_idx.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);    

    disp(size(mt_ev_condi_z_max_idx));

    disp(tb_mt_ev_condi_z_max_idx(1:round(it_row_n_keep/2), :));

    disp(tb_mt_ev_condi_z_max_idx((round(it_row_n_keep/2)+1):it_row_n_keep, :));

end

%% Reindex K' and B' Choices for each State at the Optimal *w'=k'+b'* choice

% The K' and B' Optimal Choices Associated with EV opti

% dim(mt_ev_condi_z_max_kp): *I by M*

ar_add_grid = linspace(0, it_ak_perc_n*(it_w_interp_n-1), it_w_interp_n); 

mt_ev_condi_z_max_idx = mt_ev_condi_z_max_idx + ar_add_grid'; 

mt_ev_condi_z_max_kp = reshape(ar_k_mesha(mt_ev_condi_z_max_idx), [it_w_interp_n, it_z_n]); 

mt_ev_condi_z_max_bp = reshape(ar_a_meshk(mt_ev_condi_z_max_idx), [it_w_interp_n, it_z_n]); 

if(bl_display_evf) 

    disp('----------------------------------------');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    disp('mt_ev_condi_z_max_kp: I by M');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    tb_ev_condi_z_max_kp = array2table(mt_ev_condi_z_max_kp(ar_it_rows, ar_it_cols));

    tb_ev_condi_z_max_kp.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);

    tb_ev_condi_z_max_kp.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);    

    disp(size(mt_ev_condi_z_max_kp));

    disp(tb_ev_condi_z_max_kp(1:round(it_row_n_keep/2), :));

    disp(tb_ev_condi_z_max_kp((round(it_row_n_keep/2)+1):it_row_n_keep, :));

    disp('----------------------------------------');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    disp('mt_ev_condi_z_max_bp: I by M');

    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    tb_ev_condi_z_max_bp = array2table(mt_ev_condi_z_max_bp(ar_it_rows, ar_it_cols));

    tb_ev_condi_z_max_bp.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);

    tb_ev_condi_z_max_bp.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);    

    disp(size(mt_ev_condi_z_max_kp));

    disp(tb_ev_condi_z_max_bp(1:round(it_row_n_keep/2), :));

    disp(tb_ev_condi_z_max_bp((round(it_row_n_keep/2)+1):it_row_n_keep, :));

end

%% Graph

if (bl_graph_evf) 

    %% Generate Limited Legends

    % 8 graph points, 2 levels of borrow rates, and 4 levels of rbr rates

    ar_it_z_r_borr = ([1 round((fl_z_r_borr_n)/2) (fl_z_r_borr_n)]);

    ar_it_z_wage = ([1 round((it_z_wage_n)/2) (it_z_wage_n)]);

    % combine by index

    mt_it_z_graph = ar_it_z_wage' + it_z_wage_n*(ar_it_z_r_borr-1);

    ar_it_z_graph = mt_it_z_graph(:)';

    % legends index final

    cl_st_legendCell = cellstr([num2str(ar_z_r_borr_mesh_wage_w1r2', 'zr=%3.2f;'), ...

                                num2str(ar_z_wage_mesh_r_borr_w1r2', 'zw=%3.2f')]);

    %% Graph 1, V and EV

%     if (~bl_graph_onebyones)

%         figure('PaperPosition', [0 0 14 4]);

%         hold on;

%     end

%     

%     

%     for subplot_j=1:1:2

%         

%         if (~bl_graph_onebyones)

%             hAxis(subplot_j) = subplot(1,2,subplot_j);

%         else

%             figure('PaperPosition', [0 0 7 4]);

%         end

%         

% %         cl_val_wkb_interpolated

%         if (subplot_j==1)

%             chart = plot(mt_val);

%         end

%         if (subplot_j==2)

%             chart = plot(mt_ev_condi_z);

%         end

%         

%         clr = jet(numel(chart));

%         for m = 1:numel(chart)

%             set(chart(m),'Color',clr(m,:))

%         end

%         

%         legend(chart(ar_it_z_graph), cl_st_legendCell(ar_it_z_graph), 'Location','southeast');

%         

%         if (subplot_j==1)

%             title('V(coh,zp); w(k+b),k,z');

%         end

%         if (subplot_j==2)

%             title('E_z(V(coh,zp|z))');

%         end

%         

%         ylabel('Next Period Value');

%         xlabel({'Index of Cash-on-Hand Discrete Point'...

%             'Each Segment is a w=k+b; within segment increasing k'...

%             'EV and V identical if shock is fully persistent'});

%         grid on;

%         grid minor;

%     end

%     

%     % Share y axis

%     if (~bl_graph_onebyones)

%         linkaxes(hAxis,'y');

%     end

%     

%     % save file

%     if (bl_img_save)

%         mkdir(support_map('st_img_path'));

%         st_file_name = [st_img_prefix st_img_name_main '_vev' st_img_suffix];

%         saveas(gcf, strcat(st_img_path, st_file_name));

%     end

    %% Graph 2, max(EV)

    if(~bl_graph_onebyones)

        figure('PaperPosition', [0 0 7 4]);

    end

    for sub_j=1:1:1

        if(sub_j==1)

            mt_outcome = mt_ev_condi_z_max;

            st_y_label = 'max_{k''}(E(V(coh(k'',b''=w-k''),z''|z,w))';

        end

        if(~bl_graph_onebyones)

            subplot(1,1,sub_j)

        else

            figure('PaperPosition', [0 0 7 4]);

        end

        hold on;

        clr = jet(length(ar_it_z_graph));

        i_ctr = 0;

        for i = ar_it_z_graph

            i_ctr = i_ctr + 1;

            ar_x = ar_w_level;

            ar_y = mt_outcome(:, i);

            scatter(ar_x, ar_y, 5, ...

                'MarkerEdgeColor', clr(i_ctr,:), ...

                'MarkerFaceColor', clr(i_ctr,:));

        end

        grid on;

        grid minor;

        title(['2nd Stage Exp Value at Optimal K given W=K''+B'''])

        ylabel(st_y_label)

        xlabel({'Aggregate Savings'})

        legendCell_here = cl_st_legendCell;

        legendCell_here{length(legendCell_here) + 1} = 'max-agg-save';

        legend(legendCell_here([ar_it_z_graph length(legendCell_here)]), 'Location','southeast');

        xline0 = xline(0);

        xline0.HandleVisibility = 'off';

        yline0 = yline(0);

        yline0.HandleVisibility = 'off';

    end

    % save file

    if (bl_img_save)

        mkdir(support_map('st_img_path'));

        st_file_name = [st_img_prefix st_img_name_main '_maxev' st_img_suffix];

        saveas(gcf, strcat(st_img_path, st_file_name));

    end

    %% Graph 3, at max(EV) optimal choice category, color regions, borrow save

    % Borrow Vs Save

    [ar_z_mw, ar_w_mz] = meshgrid(ar_z_wage_mesh_r_borr_w1r2, ar_w_level);

    mt_it_borr_idx = (mt_ev_condi_z_max_bp < 0);

    mt_it_riskyhalf_idx = ((mt_ev_condi_z_max_kp./mt_ev_condi_z_max_bp) > 0.5);

    mt_it_kzero_idx = (mt_ev_condi_z_max_kp == 0);

    mt_it_isnan_idx = (isnan(mt_ev_condi_z_max_kp));

    figure('PaperPosition', [0 0 7 4]);

    % States: ar_w, ar_z

    % Choices: mt_ev_condi_z_max_kp, mt_ev_condi_z_max_bp

    hold on;

    it_sca_size = 10;

    chart_br = scatter(ar_w_mz(mt_it_borr_idx),...

        ar_z_mw(mt_it_borr_idx),...

        it_sca_size, 'blue', 'filled');

    %     legend([chart_br], {'Borrow'}, 'Location','northeast');

    chart_khalf = scatter(ar_w_mz(~mt_it_borr_idx & mt_it_riskyhalf_idx),...

        ar_z_mw(~mt_it_borr_idx & mt_it_riskyhalf_idx),...

        it_sca_size, 'black', 'filled');

    %     legend([chart_khalf], {'Save >0.5 K'}, 'Location','northeast');

    chart_sv = scatter(ar_w_mz(~mt_it_borr_idx & ~mt_it_riskyhalf_idx),...

        ar_z_mw(~mt_it_borr_idx & ~mt_it_riskyhalf_idx),...

        it_sca_size, 'red', 'filled');

    %     legend([chart_sv], {'Save <0.5 K'}, 'Location','northeast');

    chart_invalid = scatter(ar_w_mz(mt_it_kzero_idx | mt_it_isnan_idx),...

        ar_z_mw(mt_it_kzero_idx | mt_it_isnan_idx),...

        it_sca_size, 'yellow', 'filled');

    legend([chart_br, chart_khalf, chart_sv, chart_invalid], ...

        {'Borrow','Save >0.5 K','Save <0.5 K', 'k=0 or k=nan'}, 'Location','northeast');

    title('Borrow and Save Regions')

    ylabel('Shocks')

    xlabel({'Total Savings w=k+b'})

    grid on;

    % save file

    if (bl_img_save)

        mkdir(support_map('st_img_path'));

        st_file_name = [st_img_prefix st_img_name_main '_maxbrsv' st_img_suffix];

        saveas(gcf, strcat(st_img_path, st_file_name));

    end

    %% Graph 4, Optimal K' and B' Levels

    [~, ar_w_mz] = meshgrid(ar_z_wage_mesh_r_borr_w1r2, ar_w_level);

    for sub_j=1:1:4

        if (bl_graph_onebyones)

            figure('PaperPosition', [0 0 7 4]);

        end

        if (sub_j==1)

            if(~bl_graph_onebyones)

                figure('PaperPosition', [0 0 14 4]);

                subplot(1,2,sub_j);

            end

            mt_y = mt_ev_condi_z_max_bp;

        end

        if (sub_j==2)

            if(~bl_graph_onebyones)

                subplot(1,2,sub_j);

            end

            mt_y = mt_ev_condi_z_max_kp;

        end

        if (sub_j==3)

            if(~bl_graph_onebyones)

                figure('PaperPosition', [0 0 14 4]);

                subplot(1,2,sub_j-2);

            end

            mt_y = zeros(size(mt_ev_condi_z_max_bp));

            mt_it_borr_idx = (mt_ev_condi_z_max_bp < 0);

            mt_y(mt_it_borr_idx) = -mt_ev_condi_z_max_bp(mt_it_borr_idx)/fl_b_bd;

            mt_y(~mt_it_borr_idx) = mt_ev_condi_z_max_bp(~mt_it_borr_idx)./ar_w_mz(~mt_it_borr_idx);

        end

        if (sub_j==4)

            if(~bl_graph_onebyones)

                subplot(1,2,sub_j-2);

            end

            mt_y = mt_ev_condi_z_max_kp./(ar_w_level'-fl_b_bd);

        end

        hold on;

        chart = plot(ar_w_level, mt_y);

        clr = jet(numel(chart));

        if (length(ar_w_level) <= 100)

            scatter(ar_w_mz(:), mt_y(:), 3, 'filled', 'MarkerEdgeColor', 'b', 'MarkerFaceColor', 'b');

        end

        for m = 1:numel(chart)

            set(chart(m),'Color',clr(m,:))

        end

        legend2plot = fliplr(ar_it_z_graph);

        legendCell = cl_st_legendCell;

        xline0 = xline(0);

        xline0.HandleVisibility = 'off';

        yline0 = yline(0);

        yline0.HandleVisibility = 'off';

        grid on;

        if (sub_j<=2)

            hline = refline([1 0]);

            hline.Color = 'k';

            hline.LineStyle = ':';

            hline.HandleVisibility = 'off';

        end

        if (sub_j==1)

            title('B Choices of W');

            ylabel('B Choices');

            xlabel({'Total Savings w=k+b'});

            legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');

        end

        if (sub_j==2)

            title('K Choices of W');

            ylabel('K Choices');

            xlabel({'Total Savings w=k+b'});

            legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');

        end

        if (sub_j==3)