Solve For+Inf+Borr+Save Dynamic Programming Problem (Loop)

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Contents

function result_map = ff_abz_fibs_vf(varargin)

FF_ABZR_FIBS_VF borr + save one asset formal informal + loop

This program solves the infinite horizon dynamic single asset and single shock problem with loops. This file contains codes that processes borrowing and handles formal and informal choices. R shock.

@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:

@example

@include

@seealso

Default

it_param_set = 4;
bl_input_override = true;
[param_map, support_map] = ffs_abz_fibs_set_default_param(it_param_set);

% Note: param_map and support_map can be adjusted here or outside to override defaults
% To generate results as if formal informal do not matter
param_map('it_a_n') = 35;
param_map('it_z_n') = 7;
param_map('it_maxiter_val') = 20;
% param_map('fl_r_fsv') = 0.025;
% param_map('fl_r_inf') = 0.035;
% param_map('fl_r_inf_bridge') = 0.035;
% param_map('fl_r_fbr') = 0.035;
% param_map('bl_b_is_principle') = false;
% param_map('st_forbrblk_type') = 'seg3';
% param_map('fl_forbrblk_brmost') = -19;
% param_map('fl_forbrblk_brleast') = -1;
% param_map('fl_forbrblk_gap') = -1.5;
% param_map('bl_b_is_principle') = false;

[armt_map, func_map] = ffs_abz_fibs_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_abz_fibs_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_abz_fibs_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{:};

% Formal choice Menu/Grid and Interest Rate Menu/Grid
params_group = values(armt_map, {'ar_forbrblk_r', 'ar_forbrblk'});
[ar_forbrblk_r, ar_forbrblk] = params_group{:};

% func_map
params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_coh', 'f_cons_coh_fbis', 'f_cons_coh_save'});
[f_util_log, f_util_crra, f_coh, f_cons_coh_fbis, f_cons_coh_save] = params_group{:};

% param_map
params_group = values(param_map, {'it_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min',...
    'fl_nan_replace', 'bl_default', 'bl_bridge', 'bl_rollover', 'fl_default_aprime'});
[it_a_n, it_z_n, fl_crra, fl_beta, fl_c_min, ...
    fl_nan_replace, bl_default, bl_bridge, bl_rollover, fl_default_aprime] = 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{:};

% param_map, Formal informal
params_group = values(param_map, {'fl_r_inf', 'fl_r_fsv', 'bl_b_is_principle'});
[fl_r_inf, fl_r_fsv, bl_b_is_principle] = 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_display_minccost', 'bl_display_infbridge', ...
    '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_display_minccost, bl_display_infbridge, ...
    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;
mt_pol_cons = zeros(length(ar_a),length(ar_z));

% collect optimal borrowing formal and informal choices
mt_pol_b_bridge = zeros(length(ar_a),length(ar_z));
mt_pol_inf_borr_nobridge = zeros(length(ar_a),length(ar_z));
mt_pol_for_borr = zeros(length(ar_a),length(ar_z));
mt_pol_for_save = zeros(length(ar_a),length(ar_z));

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

  1. loop 1: over exogenous states
  2. loop 2: over endogenous states
  3. loop 3: over choices
  4. 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

% Utility at-Default/at-limiting-case-when-nodefault
if (fl_crra == 1)
    fl_u_cmin = f_util_log(fl_c_min);
else
    fl_u_cmin = f_util_crra(fl_c_min);
end


% Value Function Iteration
while bl_vfi_continue
    it_iter = it_iter + 1;

Iterate over a and z states

handling borrowing and default possibility

    % 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)
            % Get asset state
            fl_a = ar_a(it_a_j);

            % Initialize storage
            ar_val_cur = zeros(size(ar_a));
            ar_c_cur = zeros(size(ar_a));
            ar_b_bridge = zeros(size(ar_a));
            ar_inf_borr_nobridge = zeros(size(ar_a));
            ar_for_borr = zeros(size(ar_a));
            ar_for_save = zeros(size(ar_a));

            % calculate cash on hand
            fl_coh = f_coh(fl_z, fl_a);

            % loop 3: over choices
            for it_ap_k = 1:length(ar_a)
                % get next period asset choice
                fl_ap = ar_a(it_ap_k);

Compute Consumption given Borrowing and Savings

find the today's consumption maximizing formal and informal choices given a' and coh. The formal and informal choices need to generate exactly a', but depending on which formal and informal joint choice is used, the consumption cost today a' is different. Note here, a is principle + interests. Three areas:

                if (fl_ap < 0)

                    % Calculate Bridge Loan Borrowing
                    if (bl_bridge && fl_coh < 0)

                        bl_input_override = true;
                        [fl_aprime_nobridge, fl_b_bridge, fl_c_bridge] = ffs_fibs_inf_bridge(...
                            bl_b_is_principle, fl_r_inf, fl_ap, fl_coh, ...
                            bl_display_infbridge, bl_input_override);

                    else

                        fl_aprime_nobridge = fl_ap;
                        fl_b_bridge = 0;
                        fl_c_bridge = 0;

                    end

                    % Find Optimal Formal Informal Borrow Save Combo
                    % calculate consumption gain from formal + informal
                    % borrowing and savings choices.
                    bl_input_override = true;
                    [fl_max_c_nobridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...
                        ffs_fibs_min_c_cost(...
                        bl_b_is_principle, fl_r_inf, fl_r_fsv, ...
                        ar_forbrblk_r, ar_forbrblk, ...
                        fl_aprime_nobridge, bl_display_minccost, bl_input_override);

                    % Compute Consumption given Formal and Informal joint
                    % consumption with formal borrow menu + bridge loans.
                    fl_c = f_cons_coh_fbis(fl_coh, fl_max_c_nobridge + fl_c_bridge);

                else

                    % consumption with savings
                    fl_c = f_cons_coh_save(fl_coh, fl_ap);

                    % assign values for formal and informal choices
                    % possible that fl_coh < 0, but if then fl_ap > 0 is
                    % not valid choice
                    [fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = deal(0, 0, 0, fl_ap);

                end

Compute Utility With Default

if rollover is not allowed and bridge is not allowed, then as long as coh <= 0, also treat as not allowed states. assign u(c)

                if (fl_c <= fl_c_min || ...
                    ( ~bl_rollover && ~bl_bridge && fl_coh < fl_c_min))

                    if (bl_default)
                        % defaults
                        % current utility: only today u(cmin)
                        ar_val_cur(it_ap_k) = fl_u_cmin;
                        % transition out next period, debt wiped out
                        for it_az_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_az_q)*mt_val_cur((ar_a == fl_default_aprime), it_az_q);
                        end

                        % Replace Consumption if default cmin
                        fl_c = fl_c_min;
                    else
                        % if default is not allowed: v = fl_nan_replace
                        ar_val_cur(it_ap_k) = fl_nan_replace;

                        % Replace Consumption if no default nan
                        fl_c = 0;
                    end

                    % no action, defaulting
                    fl_b_bridge = 0;
                    fl_inf_borr_nobridge = 0;
                    fl_for_borr = 0;
                    fl_for_save = 0;

                else
                    % Solve Optimization Problem: max_{a'} u(c(a,a',z)) + beta*EV(a',z')
                    % borrowed enough to pay debt (and borrowing limit not exceeded)
                    % saved only the coh available.
                    % 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_az_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_az_q)*mt_val_cur(it_ap_k, it_az_q);
                    end
                end

Store Values

                % Could get the formal and informal values from
                % ffs_fibs_min_c_cost_bridge.m
%                 bl_input_override = true;
%                 [fl_c, fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...
%                     ffs_fibs_min_c_cost_bridge(fl_ap, fl_coh, ...
%                     param_map, support_map, armt_map, func_map, bl_input_override);

                % Store consumption
                ar_c_cur(it_ap_k) = fl_c;

                % Save/Update Borrowing Information
                ar_b_bridge(it_ap_k) = fl_b_bridge;
                ar_inf_borr_nobridge(it_ap_k) = fl_inf_borr_nobridge;
                ar_for_borr(it_ap_k) = fl_for_borr;
                ar_for_save(it_ap_k) = fl_for_save;
            end

Optimize over Next Period Asset Choices

optimal choice value

            [fl_opti_val_z, fl_opti_idx_z] = max(ar_val_cur);
            fl_opti_aprime_z = ar_a(fl_opti_idx_z);
            fl_opti_c_z = ar_c_cur(fl_opti_idx_z);

            % corresponding optimal borrowing and savings choices
            fl_opti_b_bridge = ar_b_bridge(fl_opti_idx_z);
            fl_opti_inf_borr_nobridge = ar_inf_borr_nobridge(fl_opti_idx_z);
            fl_opti_for_borr = ar_for_borr(fl_opti_idx_z);
            fl_opti_for_save = ar_for_save(fl_opti_idx_z);

Find Optimal Choices for Defaults or Not

Handle Default is optimal or not

            if (fl_opti_c_z <= fl_c_min)
                if (bl_default)
                    % if defaulting is optimal choice, at these states, not required
                    % to default, non-default possible, but default could be optimal
                    fl_opti_aprime_z = fl_default_aprime;
                else
                    % if default is not allowed, then next period same state as now
                    % this is absorbing state, this is the limiting case, single
                    % state space point, lowest a and lowest shock has this.
                    fl_opti_aprime_z = min(ar_a);
                end
            end

Store Optimal Choices and Value Given(a,z)

            % store overal savings, value and consumption
            mt_val(it_a_j,it_z_i) = fl_opti_val_z;
            mt_pol_a(it_a_j,it_z_i) = fl_opti_aprime_z;
            mt_pol_cons(it_a_j,it_z_i) = fl_opti_c_z;

            % store savings and borrowing formal and inf optimal choices
            mt_pol_b_bridge(it_a_j,it_z_i) = fl_opti_b_bridge;
            mt_pol_inf_borr_nobridge(it_a_j,it_z_i) = fl_opti_inf_borr_nobridge;
            mt_pol_for_borr(it_a_j,it_z_i) = fl_opti_for_borr;
            mt_pol_for_save(it_a_j,it_z_i) = fl_opti_for_save;
        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

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') = {mt_pol_cons, zeros(1)};
result_map('cl_mt_pol_b_bridge') = {mt_pol_b_bridge, zeros(1)};
result_map('cl_mt_pol_inf_borr_nobridge') = {mt_pol_inf_borr_nobridge, zeros(1)};
result_map('cl_mt_pol_for_borr') = {mt_pol_for_borr, zeros(1)};
result_map('cl_mt_pol_for_save') = {mt_pol_for_save, zeros(1)};

result_map('ar_st_pol_names') = ["cl_mt_pol_a", "cl_mt_coh", "cl_mt_pol_c", ...
    "cl_mt_pol_b_bridge", "cl_mt_pol_inf_borr_nobridge", "cl_mt_pol_for_borr", "cl_mt_pol_for_save"];

% Get Discrete Choice Outcomes
result_map = ffs_fibs_identify_discrete(result_map, bl_input_override);

Post Solution Graph and Table Generation

Note in comparison with abz, results here, even when using identical parameters would differ because in abz solved where choices are principle. Here choices are principle + interests in order to facilitate using the informal choice functions.

Note that this means two things are different, on the one hand, the value of asset for to coh is different based on the grid of assets. If the asset grid is negative, now per grid point, there is more coh because that grid point of asset no longer has interest rates. On the other hand, if one has positive asset grid point on arrival, that is worth less to coh. Additionally, when making choices for the next period, now choices aprime includes interests. What these mean is that the a grid no longer has the same meaning. We should expect at higher savings levels, for the same grid points, if optimal grid choices are the same as before, consumption should be lower when b includes interest rates and principle. This is however, not true when arriving in a period with negative a levels, for the same negative a level and same a prime negative choice, could have higher consumption here becasue have to pay less interests on debt. This tends to happen for smaller levels of borrowing choices.

Graphically, when using interest + principle, big difference in consumption as a fraction of (coh - aprime) figure. In those figures, when counting in principles only, the gap in coh and aprime is consumption, but now, as more is borrowed only a small fraction of coh and aprime gap is consumption, becuase aprime/(1+r) is put into consumption.

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, :);

    % Standard AZ graphs
    result_map = ff_az_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);

    % Graphs for results_map with FIBS contents
    result_map = ff_az_fibs_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);
end
valgap = norm(mt_val - mt_val_cur): value function difference across iterations
polgap = norm(mt_pol_a - mt_pol_a_cur): policy function difference across iterations
z1 = z1 perc change: sum((mt_pol_a ~= mt_pol_a_cur))/(it_a_n): percentage of state space points conditional on shock where the policy function is changing across iterations
               valgap    polgap    z1_0_34387    z2_0_47991    z3_0_66977    z4_0_93474    z5_1_3045    z6_1_8206    z7_2_5409
               ______    ______    __________    __________    __________    __________    _________    _________    _________

    iter=1     35.191    293.38            1             1             1             1            1            1            1 
    iter=2     27.601    324.29      0.97143       0.97143       0.97143       0.97143      0.97143      0.97143      0.97143 
    iter=3     22.977    106.04      0.91429       0.91429       0.91429       0.91429      0.91429      0.91429      0.91429 
    iter=4     19.813    53.871      0.82857       0.82857           0.8           0.8      0.85714      0.85714      0.85714 
    iter=5     16.321    33.097      0.68571       0.68571       0.62857       0.71429      0.68571      0.71429      0.74286 
    iter=6     13.909    21.392      0.54286       0.54286       0.51429       0.51429      0.57143      0.54286      0.62857 
    iter=7     11.127    22.625      0.45714       0.37143           0.4       0.34286      0.42857      0.51429          0.4 
    iter=8     8.4903    14.262      0.28571       0.28571       0.31429       0.34286      0.31429      0.34286      0.28571 
    iter=9     6.6273    11.528      0.22857       0.28571       0.22857       0.22857      0.28571          0.2      0.25714 
    iter=10    5.6641    11.097          0.2           0.2       0.25714       0.22857      0.14286      0.14286          0.2 
    iter=11     4.823    7.9882      0.17143       0.11429       0.14286       0.14286      0.14286      0.17143      0.17143 
    iter=12    4.2445    5.8971     0.085714      0.057143      0.085714       0.11429      0.17143      0.14286      0.11429 
    iter=13    3.7603    6.6642      0.11429       0.17143      0.085714       0.11429     0.085714     0.085714      0.14286 
    iter=14      3.31    6.2938     0.057143      0.085714      0.085714       0.14286     0.057143      0.11429      0.11429 
    iter=15    2.9058    6.3178      0.11429      0.085714      0.085714      0.085714     0.085714     0.085714     0.085714 
    iter=16    2.5574    5.0958     0.057143      0.028571      0.028571      0.057143     0.057143     0.057143     0.085714 
    iter=17    2.2837     3.674     0.028571      0.028571      0.028571             0     0.057143     0.028571     0.028571 
    iter=18    2.0703     3.674     0.028571      0.028571      0.028571      0.028571     0.057143     0.057143     0.028571 
    iter=19    1.8945    2.9998     0.028571      0.028571      0.057143      0.028571     0.057143     0.028571            0 
    iter=20    1.7333    2.9998     0.028571      0.028571      0.028571      0.057143     0.057143     0.028571     0.028571 

tb_val: V(a,z) value at each state space point
                     z1_0_34387    z2_0_47991    z3_0_66977    z4_0_93474    z5_1_3045    z6_1_8206    z7_2_5409
                     __________    __________    __________    __________    _________    _________    _________

    a1=-20             -11.044       -10.241       -9.2889       -8.3621      -7.5016      -6.7048      -5.3397 
    a2=-17.8788         -9.977       -9.1339       -8.2393       -7.3605       -6.519      -5.6938      -4.2847 
    a3=-15.7576         -8.736       -7.9628       -7.1441         -6.33      -5.5253      -4.5465      -3.1422 
    a4=-13.6364        -7.4521       -6.7644       -6.0286       -5.2803      -4.5088      -3.3123      -1.9426 
    a5=-11.5152        -6.1692       -5.5648       -4.9081         -4.22      -3.4736      -2.1366     -0.80055 
    a6=-9.39394        -4.9082       -4.3786       -3.7893       -3.1579      -2.3267     -0.88477      0.61727 
    a7=-7.27273         -3.679       -3.2109       -2.6799       -2.0822     -0.82437       0.6701       2.6629 
    a8=-5.15152        -2.4853       -2.0673       -1.5784      -0.75221      0.78049        2.306        4.477 
    a9=-3.0303         -1.3262      -0.94073      -0.41556        1.1772       2.6939        4.092       5.9132 
    a10=-0.909091     -0.19337       0.26579        1.8079        3.2235       4.4981       5.7598       6.8568 
    a11=0              0.50858        1.3489        2.6932        3.9516       5.0928       6.1272       7.1231 
    a12=1.21212         1.5426        2.4208         3.463        4.5495       5.5982       6.5624       7.4093 
    a13=3.33333         2.8352        3.5754        4.4061        5.3204        6.266       7.1567         7.95 
    a14=5.45455         3.9817        4.5899        5.2735        6.0329       6.8859       7.7101        8.454 
    a15=7.57576         4.9965        5.4984        6.0671        6.6953       7.4673       8.2304       8.9275 
    a16=9.69697          5.901        6.3185        6.7945        7.3284       8.0195       8.7211       9.3707 
    a17=11.8182         6.7136         7.064        7.4687        7.9325       8.5393       9.1794       9.7827 
    a18=13.9394         7.4494        7.7478        8.0971        8.5025       9.0249       9.6061       10.165 
    a19=16.0606         8.1182        8.3765        8.6814        9.0357        9.478       10.003       10.519 
    a20=18.1818         8.7307        8.9567        9.2241        9.5327       9.9023       10.375       10.847 
    a21=20.303          9.2933         9.492        9.7269        9.9952       10.306       10.721       11.147 
    a22=22.4242         9.8096         9.985        10.192        10.428       10.698       11.031       11.423 
    a23=24.5455         10.201        10.367        10.563        10.785       11.034       11.316       11.684 
    a24=26.6667         10.535        10.694        10.882        11.094       11.331       11.595       11.924 
    a25=28.7879         10.834        10.988        11.169        11.375       11.603       11.855       12.137 
    a26=30.9091         11.091        11.241        11.417        11.617       11.839       12.082       12.331 
    a27=33.0303         11.336        11.471         11.63        11.821       12.038       12.275       12.519 
    a28=35.1515         11.566        11.689        11.837        12.014       12.223       12.454       12.693 
    a29=37.2727         11.784        11.898        12.037        12.198       12.396       12.619       12.852 
    a30=39.3939         11.991        12.099        12.228        12.379       12.566       12.781       13.008 
    a31=41.5152          12.19        12.291        12.412        12.555       12.731       12.939        13.16 
    a32=43.6364          12.38        12.476        12.591        12.726       12.892       13.093       13.307 
    a33=45.7576         12.563        12.654        12.763        12.892       13.048       13.242        13.45 
    a34=47.8788          12.74        12.826        12.931        13.053         13.2       13.386       13.589 
    a35=50              12.911        12.993        13.093         13.21       13.348       13.528       13.725 

tb_pol_a: optimal asset choice for each state space point
                     z1_0_34387    z2_0_47991    z3_0_66977    z4_0_93474    z5_1_3045    z6_1_8206    z7_2_5409
                     __________    __________    __________    __________    _________    _________    _________

    a1=-20                   0             0             0             0            0            0          -20 
    a2=-17.8788            -20           -20           -20           -20          -20          -20      -17.879 
    a3=-15.7576        -17.879       -17.879       -17.879       -17.879      -17.879      -15.758      -15.758 
    a4=-13.6364        -15.758       -15.758       -15.758       -15.758      -15.758      -13.636      -13.636 
    a5=-11.5152        -13.636       -13.636       -13.636       -13.636      -13.636      -11.515      -11.515 
    a6=-9.39394        -11.515       -11.515       -11.515       -11.515      -9.3939      -9.3939      -7.2727 
    a7=-7.27273        -9.3939       -9.3939       -9.3939       -9.3939      -7.2727      -7.2727      -5.1515 
    a8=-5.15152        -7.2727       -7.2727       -7.2727       -5.1515      -5.1515      -5.1515      -3.0303 
    a9=-3.0303         -5.1515       -5.1515       -5.1515       -3.0303      -3.0303      -3.0303     -0.90909 
    a10=-0.909091      -3.0303      -0.90909      -0.90909      -0.90909     -0.90909            0            0 
    a11=0             -0.90909             0             0             0            0            0       1.2121 
    a12=1.21212              0             0             0        1.2121       1.2121       1.2121       1.2121 
    a13=3.33333         1.2121        1.2121        1.2121        3.3333       3.3333       3.3333       3.3333 
    a14=5.45455         3.3333        3.3333        3.3333        5.4545       5.4545       5.4545       5.4545 
    a15=7.57576         5.4545        5.4545        5.4545        7.5758       7.5758       7.5758       7.5758 
    a16=9.69697         7.5758        7.5758        7.5758        7.5758        9.697        9.697        9.697 
    a17=11.8182          9.697         9.697         9.697         9.697       11.818       11.818       11.818 
    a18=13.9394         11.818        11.818        11.818        11.818       13.939       13.939       13.939 
    a19=16.0606         13.939        13.939        13.939        13.939       16.061       16.061       16.061 
    a20=18.1818         16.061        16.061        16.061        16.061       18.182       18.182       18.182 
    a21=20.303          18.182        18.182        18.182        18.182       18.182       20.303       20.303 
    a22=22.4242         20.303        20.303        20.303        20.303       20.303       22.424       22.424 
    a23=24.5455         22.424        22.424        22.424        22.424       22.424       24.545       24.545 
    a24=26.6667         24.545        24.545        24.545        24.545       24.545       24.545       26.667 
    a25=28.7879         26.667        26.667        26.667        26.667       26.667       26.667       28.788 
    a26=30.9091         28.788        28.788        28.788        28.788       28.788       28.788       28.788 
    a27=33.0303         28.788        28.788        28.788        30.909       30.909       30.909       30.909 
    a28=35.1515         30.909        30.909        30.909         33.03        33.03        33.03        33.03 
    a29=37.2727          33.03         33.03         33.03         33.03       35.152       35.152       35.152 
    a30=39.3939         35.152        35.152        35.152        35.152       37.273       37.273       37.273 
    a31=41.5152         37.273        37.273        37.273        37.273       39.394       39.394       39.394 
    a32=43.6364         39.394        39.394        39.394        39.394       41.515       41.515       41.515 
    a33=45.7576         41.515        41.515        41.515        41.515       43.636       43.636       43.636 
    a34=47.8788         43.636        43.636        43.636        43.636       45.758       45.758       45.758 
    a35=50              45.758        45.758        45.758        45.758       45.758       47.879       47.879 

mt_pol_b_bridge_print: bridge loans
                       z1_0_34387    z2_0_47991    z3_0_66977    z4_0_93474    z5_1_3045    z6_1_8206    z7_2_5409
                       __________    __________    __________    __________    _________    _________    _________

    coh1=-19.5598              0             0             0            0             0            0      -18.339 
    coh2=-17.4386        -19.095       -18.905       -18.639      -18.267       -17.749      -17.025      -16.016 
    coh3=-15.3174        -16.773       -16.582       -16.316      -15.944       -15.426      -14.703      -13.693 
    coh4=-13.1962         -14.45       -14.259       -13.993      -13.622       -13.103       -12.38      -11.371 
    coh5=-11.075         -12.127       -11.936        -11.67      -11.299       -10.781      -10.057      -9.0478 
    coh6=-8.95379        -9.8044       -9.6137       -9.3476      -8.9762       -8.4579      -7.7346      -6.7251 
    coh7=-6.83257        -7.4817        -7.291       -7.0249      -6.6535       -6.1352      -5.4119      -4.4023 
    coh8=-4.71136        -5.1589       -4.9683       -4.7022      -4.3308       -3.8125      -3.0891      -2.0796 
    coh9=-2.59015        -2.8362       -2.6455       -2.3794      -2.0081       -1.4898      -0.7664            0 
    coh10=-0.468937     -0.51349      -0.32281     -0.056707            0             0            0            0 
    coh11=0.440154             0             0             0            0             0            0            0 
    coh12=1.65228              0             0             0            0             0            0            0 
    coh13=3.77349              0             0             0            0             0            0            0 
    coh14=5.8947               0             0             0            0             0            0            0 
    coh15=8.01591              0             0             0            0             0            0            0 
    coh16=10.1371              0             0             0            0             0            0            0 
    coh17=12.2583              0             0             0            0             0            0            0 
    coh18=14.3795              0             0             0            0             0            0            0 
    coh19=16.5008              0             0             0            0             0            0            0 
    coh20=18.622               0             0             0            0             0            0            0 
    coh21=20.7432              0             0             0            0             0            0            0 
    coh22=22.8644              0             0             0            0             0            0            0 
    coh23=24.9856              0             0             0            0             0            0            0 
    coh24=27.1068              0             0             0            0             0            0            0 
    coh25=29.228               0             0             0            0             0            0            0 
    coh26=31.3492              0             0             0            0             0            0            0 
    coh27=33.4705              0             0             0            0             0            0            0 
    coh28=35.5917              0             0             0            0             0            0            0 
    coh29=37.7129              0             0             0            0             0            0            0 
    coh30=39.8341              0             0             0            0             0            0            0 
    coh31=41.9553              0             0             0            0             0            0            0 
    coh32=44.0765              0             0             0            0             0            0            0 
    coh33=46.1977              0             0             0            0             0            0            0 
    coh34=48.3189              0             0             0            0             0            0            0 
    coh35=50.4402              0             0             0            0             0            0            0 

mt_pol_inf_borr_nobridge_print: Informal loans that is not bridge loan
                       z1_0_34387    z2_0_47991    z3_0_66977    z4_0_93474    z5_1_3045    z6_1_8206    z7_2_5409
                       __________    __________    __________    __________    _________    _________    _________

    coh1=-19.5598              0             0             0             0             0           0      -0.5963 
    coh2=-17.4386              0     -0.030369      -0.29647      -0.66785             0    -0.31201     -0.79781 
    coh3=-15.3174      -0.041211      -0.23188      -0.49799      -0.86937             0           0            0 
    coh4=-13.1962       -0.24273       -0.4334      -0.69951             0             0    -0.19133            0 
    coh5=-11.075        -0.44424      -0.63491      -0.90102             0       -0.1932    -0.39284            0 
    coh6=-8.95379       -0.64576      -0.83643             0             0             0    -0.59436     -0.54766 
    coh7=-6.83257       -0.84727             0             0     -0.077931     -0.072521    -0.79587            0 
    coh8=-4.71136              0             0             0             0      -0.27404           0            0 
    coh9=-2.59015              0             0      -0.10958             0      -0.47555           0            0 
    coh10=-0.468937            0      -0.58628             0             0             0           0            0 
    coh11=0.440154             0             0             0             0             0           0            0 
    coh12=1.65228              0             0             0             0             0           0            0 
    coh13=3.77349              0             0             0             0             0           0            0 
    coh14=5.8947               0             0             0             0             0           0            0 
    coh15=8.01591              0             0             0             0             0           0            0 
    coh16=10.1371              0             0             0             0             0           0            0 
    coh17=12.2583              0             0             0             0             0           0            0 
    coh18=14.3795              0             0             0             0             0           0            0 
    coh19=16.5008              0             0             0             0             0           0            0 
    coh20=18.622               0             0             0             0             0           0            0 
    coh21=20.7432              0             0             0             0             0           0            0 
    coh22=22.8644              0             0             0             0             0           0            0 
    coh23=24.9856              0             0             0             0             0           0            0 
    coh24=27.1068              0             0             0             0             0           0            0 
    coh25=29.228               0             0             0             0             0           0            0 
    coh26=31.3492              0             0             0             0             0           0            0 
    coh27=33.4705              0             0             0             0             0           0            0 
    coh28=35.5917              0             0             0             0             0           0            0 
    coh29=37.7129              0             0             0             0             0           0            0 
    coh30=39.8341              0             0             0             0             0           0            0 
    coh31=41.9553              0             0             0             0             0           0            0 
    coh32=44.0765              0             0             0             0             0           0            0 
    coh33=46.1977              0             0             0             0             0           0            0 
    coh34=48.3189              0             0             0             0             0           0            0 
    coh35=50.4402              0             0             0             0             0           0            0 

mt_pol_for_borr_print: formal borrowing
                       z1_0_34387    z2_0_47991    z3_0_66977    z4_0_93474    z5_1_3045    z6_1_8206    z7_2_5409
                       __________    __________    __________    __________    _________    _________    _________

    coh1=-19.5598             0             0             0             0             0            0       -1.065 
    coh2=-17.4386        -1.065        -1.065        -1.065        -1.065       -2.6625      -2.6625       -1.065 
    coh3=-15.3174        -1.065        -1.065        -1.065        -1.065       -2.6625       -1.065      -2.6625 
    coh4=-13.1962        -1.065        -1.065        -1.065       -2.6625       -2.6625       -1.065      -2.6625 
    coh5=-11.075         -1.065        -1.065        -1.065       -2.6625       -2.6625       -1.065      -2.6625 
    coh6=-8.95379        -1.065        -1.065       -2.6625       -2.6625        -1.065       -1.065            0 
    coh7=-6.83257        -1.065       -2.6625       -2.6625       -2.6625        -1.065       -1.065       -1.065 
    coh8=-4.71136       -2.6625       -2.6625       -2.6625        -1.065        -1.065      -2.6625       -1.065 
    coh9=-2.59015       -2.6625       -2.6625       -2.6625        -1.065        -1.065      -2.6625       -1.065 
    coh10=-0.468937     -2.6625             0        -1.065        -1.065        -1.065            0            0 
    coh11=0.440154       -1.065             0             0             0             0            0            0 
    coh12=1.65228             0             0             0             0             0            0            0 
    coh13=3.77349             0             0             0             0             0            0            0 
    coh14=5.8947              0             0             0             0             0            0            0 
    coh15=8.01591             0             0             0             0             0            0            0 
    coh16=10.1371             0             0             0             0             0            0            0 
    coh17=12.2583             0             0             0             0             0            0            0 
    coh18=14.3795             0             0             0             0             0            0            0 
    coh19=16.5008             0             0             0             0             0            0            0 
    coh20=18.622              0             0             0             0             0            0            0 
    coh21=20.7432             0             0             0             0             0            0            0 
    coh22=22.8644             0             0             0             0             0            0            0 
    coh23=24.9856             0             0             0             0             0            0            0 
    coh24=27.1068             0             0             0             0             0            0            0 
    coh25=29.228              0             0             0             0             0            0            0 
    coh26=31.3492             0             0             0             0             0            0            0 
    coh27=33.4705             0             0             0             0             0            0            0 
    coh28=35.5917             0             0             0             0             0            0            0 
    coh29=37.7129             0             0             0             0             0            0            0 
    coh30=39.8341             0             0             0             0             0            0            0 
    coh31=41.9553             0             0             0             0             0            0            0 
    coh32=44.0765             0             0             0             0             0            0            0 
    coh33=46.1977             0             0             0             0             0            0            0 
    coh34=48.3189             0             0             0             0             0            0            0 
    coh35=50.4402             0             0             0             0             0            0            0 

mt_pol_for_save_print: formal savings
                       z1_0_34387    z2_0_47991    z3_0_66977    z4_0_93474    z5_1_3045    z6_1_8206    z7_2_5409
                       __________    __________    __________    __________    _________    _________    _________

    coh1=-19.5598             0             0              0             0             0           0            0 
    coh2=-17.4386        0.1603             0              0             0       0.41134           0            0 
    coh3=-15.3174             0             0              0             0       0.20983     0.01019      0.59817 
    coh4=-13.1962             0             0              0       0.52661     0.0083121           0      0.39666 
    coh5=-11.075              0             0              0        0.3251             0           0      0.19514 
    coh6=-8.95379             0             0        0.49496       0.12358       0.12899           0            0 
    coh7=-6.83257             0       0.55956        0.29345             0             0           0      0.31583 
    coh8=-4.71136       0.54871       0.35804       0.091934       0.24427             0     0.60011      0.11431 
    coh9=-2.59015        0.3472       0.15652              0      0.042751             0      0.3986      0.15591 
    coh10=-0.468937     0.14568             0        0.21262       0.15591       0.15591           0            0 
    coh11=0.440154      0.15591             0              0             0             0           0       1.2121 
    coh12=1.65228             0             0              0        1.2121        1.2121      1.2121       1.2121 
    coh13=3.77349        1.2121        1.2121         1.2121        3.3333        3.3333      3.3333       3.3333 
    coh14=5.8947         3.3333        3.3333         3.3333        5.4545        5.4545      5.4545       5.4545 
    coh15=8.01591        5.4545        5.4545         5.4545        7.5758        7.5758      7.5758       7.5758 
    coh16=10.1371        7.5758        7.5758         7.5758        7.5758         9.697       9.697        9.697 
    coh17=12.2583         9.697         9.697          9.697         9.697        11.818      11.818       11.818 
    coh18=14.3795        11.818        11.818         11.818        11.818        13.939      13.939       13.939 
    coh19=16.5008        13.939        13.939         13.939        13.939        16.061      16.061       16.061 
    coh20=18.622         16.061        16.061         16.061        16.061        18.182      18.182       18.182 
    coh21=20.7432        18.182        18.182         18.182        18.182        18.182      20.303       20.303 
    coh22=22.8644        20.303        20.303         20.303        20.303        20.303      22.424       22.424 
    coh23=24.9856        22.424        22.424         22.424        22.424        22.424      24.545       24.545 
    coh24=27.1068        24.545        24.545         24.545        24.545        24.545      24.545       26.667 
    coh25=29.228         26.667        26.667         26.667        26.667        26.667      26.667       28.788 
    coh26=31.3492        28.788        28.788         28.788        28.788        28.788      28.788       28.788 
    coh27=33.4705        28.788        28.788         28.788        30.909        30.909      30.909       30.909 
    coh28=35.5917        30.909        30.909         30.909         33.03         33.03       33.03        33.03 
    coh29=37.7129         33.03         33.03          33.03         33.03        35.152      35.152       35.152 
    coh30=39.8341        35.152        35.152         35.152        35.152        37.273      37.273       37.273 
    coh31=41.9553        37.273        37.273         37.273        37.273        39.394      39.394       39.394 
    coh32=44.0765        39.394        39.394         39.394        39.394        41.515      41.515       41.515 
    coh33=46.1977        41.515        41.515         41.515        41.515        43.636      43.636       43.636 
    coh34=48.3189        43.636        43.636         43.636        43.636        45.758      45.758       45.758 
    coh35=50.4402        45.758        45.758         45.758        45.758        45.758      47.879       47.879 

Display Various Containers

bl_display_defparam = true;
if (bl_display_defparam)

Display 1 support_map

    fft_container_map_display(support_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
----------------------------------------
  Map with properties:

        Count: 42
      KeyType: char
    ValueType: any

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xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = bl_display ; val = false
pos = 2 ; key = bl_display_dist ; val = false
pos = 3 ; key = bl_display_final ; val = true
pos = 4 ; key = bl_display_final_dist ; val = false
pos = 5 ; key = bl_display_final_dist_detail ; val = false
pos = 6 ; key = bl_display_funcgrids ; val = false
pos = 7 ; key = bl_display_infbridge ; val = false
pos = 8 ; key = bl_display_minccost ; val = false
pos = 9 ; key = bl_graph ; val = true
pos = 10 ; key = bl_graph_coh_t_coh ; val = true
pos = 11 ; key = bl_graph_discrete ; val = true
pos = 12 ; key = bl_graph_forinf_discrete ; val = true
pos = 13 ; key = bl_graph_forinf_pol_lvl ; val = true
pos = 14 ; key = bl_graph_forinf_pol_pct ; val = true
pos = 15 ; key = bl_graph_funcgrids ; val = false
pos = 16 ; key = bl_graph_onebyones ; val = true
pos = 17 ; key = bl_graph_pol_lvl ; val = true
pos = 18 ; key = bl_graph_pol_pct ; val = true
pos = 19 ; key = bl_graph_val ; val = true
pos = 20 ; key = bl_img_save ; val = false
pos = 21 ; key = bl_mat ; val = false
pos = 22 ; key = bl_post ; val = true
pos = 23 ; key = bl_profile ; val = false
pos = 24 ; key = bl_profile_dist ; val = false
pos = 25 ; key = bl_time ; val = false
pos = 26 ; key = it_display_every ; val = 5
pos = 27 ; key = it_display_final_colmax ; val = 12
pos = 28 ; key = it_display_final_rowmax ; val = 100
pos = 29 ; key = st_img_name_main ; val = ff_abz_fibs_vf_default
pos = 30 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_fibs//m_abz_solve/img/
pos = 31 ; key = st_img_prefix ; val = 
pos = 32 ; key = st_img_suffix ; val = _p4.png
pos = 33 ; key = st_mat_name_main ; val = ff_abz_fibs_vf_default
pos = 34 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_fibs//m_abz_solve/mat/
pos = 35 ; key = st_mat_prefix ; val = 
pos = 36 ; key = st_mat_suffix ; val = _p4
pos = 37 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_fibs/
pos = 38 ; key = st_profile_name_main ; val = ff_abz_fibs_vf_default
pos = 39 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_fibs//m_abz_solve/profile/
pos = 40 ; key = st_profile_prefix ; val = 
pos = 41 ; key = st_profile_suffix ; val = _p4
pos = 42 ; key = st_title_prefix ; val = 
----------------------------------------
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Scalars in Container and Sizes and Basic Statistics
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                                    i     idx    value
                                    __    ___    _____

    bl_display                       1     1        0 
    bl_display_dist                  2     2        0 
    bl_display_final                 3     3        1 
    bl_display_final_dist            4     4        0 
    bl_display_final_dist_detail     5     5        0 
    bl_display_funcgrids             6     6        0 
    bl_display_infbridge             7     7        0 
    bl_display_minccost              8     8        0 
    bl_graph                         9     9        1 
    bl_graph_coh_t_coh              10    10        1 
    bl_graph_discrete               11    11        1 
    bl_graph_forinf_discrete        12    12        1 
    bl_graph_forinf_pol_lvl         13    13        1 
    bl_graph_forinf_pol_pct         14    14        1 
    bl_graph_funcgrids              15    15        0 
    bl_graph_onebyones              16    16        1 
    bl_graph_pol_lvl                17    17        1 
    bl_graph_pol_pct                18    18        1 
    bl_graph_val                    19    19        1 
    bl_img_save                     20    20        0 
    bl_mat                          21    21        0 
    bl_post                         22    22        1 
    bl_profile                      23    23        0 
    bl_profile_dist                 24    24        0 
    bl_time                         25    25        0 
    it_display_every                26    26        5 
    it_display_final_colmax         27    27       12 
    it_display_final_rowmax         28    28      100 

----------------------------------------
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Strings in Container and Sizes and Basic Statistics
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                            i     idx
                            __    ___

    st_img_name_main         1    29 
    st_img_path              2    30 
    st_img_prefix            3    31 
    st_img_suffix            4    32 
    st_mat_name_main         5    33 
    st_mat_path              6    34 
    st_mat_prefix            7    35 
    st_mat_suffix            8    36 
    st_matimg_path_root      9    37 
    st_profile_name_main    10    38 
    st_profile_path         11    39 
    st_profile_prefix       12    40 
    st_profile_suffix       13    41 
    st_title_prefix         14    42 

Display 2 armt_map

    fft_container_map_display(armt_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: ARMT_MAP
----------------------------------------
  Map with properties:

        Count: 6
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = ar_a ;rown= 1 ,coln= 35
ar_a :mu= 14.5714 ,sd= 20.9645 ,min= -20 ,max= 50
               zi_1_C1    zi_2_C2    zi_3_C3    zi_18_c18    zi_33_c33    zi_34_c34    zi_35_c35
               _______    _______    _______    _________    _________    _________    _________

    zi_1_r1      -20      -17.879    -15.758     13.939       45.758       47.879         50    

pos = 2 ; key = ar_forbrblk ;rown= 1 ,coln= 9
ar_forbrblk :mu= -7.0556 ,sd= 6.3809 ,min= -19 ,max= 0
               zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
               _______    _______    _______    _______    _______    _______    _______

    zi_1_r1      -19       -14.5       -10       -5.5       -2.5        -1          0   

pos = 3 ; key = ar_forbrblk_r ;rown= 1 ,coln= 9
ar_forbrblk_r :mu= 0.065 ,sd= 0 ,min= 0.065 ,max= 0.065
               zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
               _______    _______    _______    _______    _______    _______    _______

    zi_1_r1     0.065      0.065      0.065      0.065      0.065      0.065      0.065 

pos = 4 ; key = ar_stationary ;rown= 1 ,coln= 7
ar_stationary :mu= 0.14286 ,sd= 0.13646 ,min= 0.0093649 ,max= 0.35951
                zi_1_c1     zi_2_c2     zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6      zi_7_c7 
               _________    ________    _______    _______    _______    ________    _________

    zi_1_r1    0.0093649    0.071014    0.23987    0.35951    0.23987    0.071014    0.0093649

pos = 5 ; key = ar_z ;rown= 1 ,coln= 7
ar_z :mu= 1.1563 ,sd= 0.79411 ,min= 0.34387 ,max= 2.5409
               zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
               _______    _______    _______    _______    _______    _______    _______

    zi_1_r1    0.34387    0.47991    0.66977    0.93474    1.3045     1.8206     2.5409 

pos = 6 ; key = mt_z_trans ;rown= 7 ,coln= 7
mt_z_trans :mu= 0.14286 ,sd= 0.20394 ,min= 1.1102e-16 ,max= 0.59534
                zi_1_c1       zi_2_c2       zi_3_c3       zi_4_c4       zi_5_c5       zi_6_c6       zi_7_c7  
               __________    __________    __________    __________    __________    __________    __________

    zi_1_r1       0.43382       0.49938      0.066036    0.00077031    6.7129e-07     4.016e-11    1.1102e-16
    zi_2_r2      0.066807       0.49938       0.40044      0.033144    0.00023251    1.1915e-07    4.1482e-12
    zi_3_r3     0.0023033       0.11937       0.56979       0.29341      0.015067     6.319e-05     1.899e-08
    zi_4_r4    1.5454e-05     0.0061942       0.19612       0.59534       0.19612     0.0061942    1.5454e-05
    zi_5_r5     1.899e-08     6.319e-05      0.015067       0.29341       0.56979       0.11937     0.0023033
    zi_6_r6    4.1482e-12    1.1915e-07    0.00023251      0.033144       0.40044       0.49938      0.066807
    zi_7_r7    1.5851e-16     4.016e-11    6.7129e-07    0.00077031      0.066036       0.49938       0.43382

----------------------------------------
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Matrix in Container and Sizes and Basic Statistics
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                     i    idx    rowN    colN     mean        std         min          max  
                     _    ___    ____    ____    _______    _______    __________    _______

    ar_a             1     1      1       35      14.571     20.964           -20         50
    ar_forbrblk      2     2      1        9     -7.0556     6.3809           -19          0
    ar_forbrblk_r    3     3      1        9       0.065          0         0.065      0.065
    ar_stationary    4     4      1        7     0.14286    0.13646     0.0093649    0.35951
    ar_z             5     5      1        7      1.1563    0.79411       0.34387     2.5409
    mt_z_trans       6     6      7        7     0.14286    0.20394    1.1102e-16    0.59534

Display 3 param_map

    fft_container_map_display(param_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
----------------------------------------
  Map with properties:

        Count: 37
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = bl_b_is_principle ; val = false
pos = 2 ; key = bl_bridge ; val = true
pos = 3 ; key = bl_default ; val = true
pos = 4 ; key = bl_loglin ; val = false
pos = 5 ; key = bl_rollover ; val = true
pos = 6 ; key = fl_a_max ; val = 50
pos = 7 ; key = fl_a_min ; val = 0
pos = 8 ; key = fl_b_bd ; val = -20
pos = 9 ; key = fl_beta ; val = 0.94
pos = 10 ; key = fl_c_min ; val = 0.02
pos = 11 ; key = fl_crra ; val = 1.5
pos = 12 ; key = fl_default_aprime ; val = 0
pos = 13 ; key = fl_forbrblk_brleast ; val = -1
pos = 14 ; key = fl_forbrblk_brmost ; val = -19
pos = 15 ; key = fl_forbrblk_gap ; val = -1.5
pos = 16 ; key = fl_loglin_threshold ; val = 1
pos = 17 ; key = fl_nan_replace ; val = -99999
pos = 18 ; key = fl_r_fbr ; val = 0.065
pos = 19 ; key = fl_r_fsv ; val = 0.025
pos = 20 ; key = fl_r_inf ; val = 0.095
pos = 21 ; key = fl_r_inf_bridge ; val = 0.095
pos = 22 ; key = fl_tol_dist ; val = 1e-05
pos = 23 ; key = fl_tol_pol ; val = 1e-05
pos = 24 ; key = fl_tol_val ; val = 1e-05
pos = 25 ; key = fl_w ; val = 1.28
pos = 26 ; key = fl_z_mu ; val = 0
pos = 27 ; key = fl_z_rho ; val = 0.8
pos = 28 ; key = fl_z_sig ; val = 0.2
pos = 29 ; key = it_a_n ; val = 35
pos = 30 ; key = it_maxiter_dist ; val = 1000
pos = 31 ; key = it_maxiter_val ; val = 20
pos = 32 ; key = it_tol_pol_nochange ; val = 25
pos = 33 ; key = it_trans_power_dist ; val = 1000
pos = 34 ; key = it_z_n ; val = 7
pos = 35 ; key = st_analytical_stationary_type ; val = eigenvector
pos = 36 ; key = st_forbrblk_type ; val = seg3
pos = 37 ; key = st_model ; val = abz_fibs
----------------------------------------
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Scalars in Container and Sizes and Basic Statistics
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                           i     idx    value 
                           __    ___    ______

    bl_b_is_principle       1     1          0
    bl_bridge               2     2          1
    bl_default              3     3          1
    bl_loglin               4     4          0
    bl_rollover             5     5          1
    fl_a_max                6     6         50
    fl_a_min                7     7          0
    fl_b_bd                 8     8        -20
    fl_beta                 9     9       0.94
    fl_c_min               10    10       0.02
    fl_crra                11    11        1.5
    fl_default_aprime      12    12          0
    fl_forbrblk_brleast    13    13         -1
    fl_forbrblk_brmost     14    14        -19
    fl_forbrblk_gap        15    15       -1.5
    fl_loglin_threshold    16    16          1
    fl_nan_replace         17    17     -99999
    fl_r_fbr               18    18      0.065
    fl_r_fsv               19    19      0.025
    fl_r_inf               20    20      0.095
    fl_r_inf_bridge        21    21      0.095
    fl_tol_dist            22    22      1e-05
    fl_tol_pol             23    23      1e-05
    fl_tol_val             24    24      1e-05
    fl_w                   25    25       1.28
    fl_z_mu                26    26          0
    fl_z_rho               27    27        0.8
    fl_z_sig               28    28        0.2
    it_a_n                 29    29         35
    it_maxiter_dist        30    30       1000
    it_maxiter_val         31    31         20
    it_tol_pol_nochange    32    32         25
    it_trans_power_dist    33    33       1000
    it_z_n                 34    34          7

----------------------------------------
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Strings in Container and Sizes and Basic Statistics
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                                     i    idx
                                     _    ___

    st_analytical_stationary_type    1    35 
    st_forbrblk_type                 2    36 
    st_model                         3    37 

Display 4 func_map

    fft_container_map_display(func_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: FUNC_MAP
----------------------------------------
  Map with properties:

        Count: 8
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = f_bprime ; val = @(fl_r_inf,ar_for_borr,ar_inf_borr,ar_for_save)(ar_for_borr./(1+fl_r_fbr)+ar_inf_borr./(1+fl_r_inf)+ar_for_save./(1+fl_r_fsv))
pos = 2 ; key = f_coh ; val = @(ar_z,ar_b)(ar_z*fl_w+ar_b)
pos = 3 ; key = f_cons_coh_fbis ; val = @(coh,ar_bprime_in_c)(coh+ar_bprime_in_c)
pos = 4 ; key = f_cons_coh_save ; val = @(coh,ar_for_save)(coh-ar_for_save./(1+fl_r_fsv))
pos = 5 ; key = f_inc ; val = @(ar_z,fl_r_inf,ar_for_borr,ar_inf_borr,ar_for_save)(ar_z*fl_w+((ar_for_borr./(1+fl_r_fbr))*fl_r_fbr+(ar_inf_borr./(1+fl_r_inf))*fl_r_inf+(ar_for_save./(1+fl_r_fsv))*fl_r_fsv))
pos = 6 ; key = f_util_crra ; val = @(c)(((c).^(1-fl_crra)-1)./(1-fl_crra))
pos = 7 ; key = f_util_log ; val = @(c)log(c)
pos = 8 ; key = f_util_standin ; val = @(z,b)f_util_log(f_coh_simple(z,b).*(f_coh_simple(z,b)>0)+fl_c_min.*(f_coh_simple(z,b)<=0))
----------------------------------------
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Scalars in Container and Sizes and Basic Statistics
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                       i    idx    xFunction
                       _    ___    _________

    f_bprime           1     1         1    
    f_coh              2     2         2    
    f_cons_coh_fbis    3     3         3    
    f_cons_coh_save    4     4         4    
    f_inc              5     5         5    
    f_util_crra        6     6         6    
    f_util_log         7     7         7    
    f_util_standin     8     8         8    

Display 5 result_map

    fft_container_map_display(result_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: RESULT_MAP
----------------------------------------
  Map with properties:

        Count: 21
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = ar_pol_diff_norm ;rown= 20 ,coln= 1
ar_pol_diff_norm :mu= 47.1596 ,sd= 92.8277 ,min= 2.9998 ,max= 324.2902
                 zi_1_c1
                 _______

    zi_1_R1      293.38 
    zi_2_R2      324.29 
    zi_3_R3      106.04 
    zi_4_R4      53.871 
    zi_5_R5      33.097 
    zi_16_r16    5.0958 
    zi_17_r17     3.674 
    zi_18_r18     3.674 
    zi_19_r19    2.9998 
    zi_20_r20    2.9998 

pos = 2 ; key = ar_st_pol_names ; val = cl_mt_pol_a cl_mt_coh cl_mt_pol_c cl_mt_pol_b_bridge cl_mt_pol_inf_borr_nobridge cl_mt_pol_for_borr cl_mt_pol_for_save
pos = 3 ; key = ar_val_diff_norm ;rown= 20 ,coln= 1
ar_val_diff_norm :mu= 9.8652 ,sd= 9.7427 ,min= 1.7333 ,max= 35.1911
                 zi_1_c1
                 _______

    zi_1_R1      35.191 
    zi_2_R2      27.601 
    zi_3_R3      22.977 
    zi_4_R4      19.813 
    zi_5_R5      16.321 
    zi_16_r16    2.5574 
    zi_17_r17    2.2837 
    zi_18_r18    2.0703 
    zi_19_r19    1.8945 
    zi_20_r20    1.7333 

pos = 4 ; key = cl_mt_coh ;rown= 35 ,coln= 7
cl_mt_coh :mu= 16.0515 ,sd= 20.7266 ,min= -19.5598 ,max= 53.2523
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       -19.56    -19.386    -19.143    -18.804     -18.33     -17.67    -16.748
    zi_2_R2      -17.439    -17.265    -17.021    -16.682    -16.209    -15.548    -14.626
    zi_3_R3      -15.317    -15.143      -14.9    -14.561    -14.088    -13.427    -12.505
    zi_4_R4      -13.196    -13.022    -12.779     -12.44    -11.967    -11.306    -10.384
    zi_5_R5      -11.075    -10.901    -10.658    -10.319    -9.8454    -9.1848    -8.2628
    zi_31_r31     41.955     42.129     42.372     42.712     43.185     43.846     44.767
    zi_32_r32     44.077     44.251     44.494     44.833     45.306     45.967     46.889
    zi_33_r33     46.198     46.372     46.615     46.954     47.427     48.088      49.01
    zi_34_r34     48.319     48.493     48.736     49.075     49.549     50.209     51.131
    zi_35_r35      50.44     50.614     50.857     51.196      51.67      52.33     53.252

pos = 5 ; key = cl_mt_pol_a ;rown= 35 ,coln= 7
cl_mt_pol_a :mu= 13.384 ,sd= 19.2751 ,min= -20 ,max= 47.8788
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1            0          0          0          0          0          0        -20
    zi_2_R2          -20        -20        -20        -20        -20        -20    -17.879
    zi_3_R3      -17.879    -17.879    -17.879    -17.879    -17.879    -15.758    -15.758
    zi_4_R4      -15.758    -15.758    -15.758    -15.758    -15.758    -13.636    -13.636
    zi_5_R5      -13.636    -13.636    -13.636    -13.636    -13.636    -11.515    -11.515
    zi_31_r31     37.273     37.273     37.273     37.273     39.394     39.394     39.394
    zi_32_r32     39.394     39.394     39.394     39.394     41.515     41.515     41.515
    zi_33_r33     41.515     41.515     41.515     41.515     43.636     43.636     43.636
    zi_34_r34     43.636     43.636     43.636     43.636     45.758     45.758     45.758
    zi_35_r35     45.758     45.758     45.758     45.758     45.758     47.879     47.879

pos = 6 ; key = cl_mt_pol_b_bridge ;rown= 35 ,coln= 7
cl_mt_pol_b_bridge :mu= -2.3257 ,sd= 4.9856 ,min= -19.0953 ,max= 0
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1            0          0          0          0          0          0    -18.339
    zi_2_R2      -19.095    -18.905    -18.639    -18.267    -17.749    -17.025    -16.016
    zi_3_R3      -16.773    -16.582    -16.316    -15.944    -15.426    -14.703    -13.693
    zi_4_R4       -14.45    -14.259    -13.993    -13.622    -13.103     -12.38    -11.371
    zi_5_R5      -12.127    -11.936     -11.67    -11.299    -10.781    -10.057    -9.0478
    zi_31_r31          0          0          0          0          0          0          0
    zi_32_r32          0          0          0          0          0          0          0
    zi_33_r33          0          0          0          0          0          0          0
    zi_34_r34          0          0          0          0          0          0          0
    zi_35_r35          0          0          0          0          0          0          0

pos = 7 ; key = cl_mt_pol_c ;rown= 35 ,coln= 7
cl_mt_pol_c :mu= 3.2911 ,sd= 1.7598 ,min= 0.02 ,max= 7.0283
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1         0.02      0.02       0.02       0.02       0.02        0.02    1.5446 
    zi_2_R2      0.84361    1.0277     1.2708     1.6099     2.0987      2.7849    1.7286 
    zi_3_R3       1.0376    1.2118     1.4548     1.7939     2.2953     0.99006    1.9164 
    zi_4_R4       1.2217    1.3958     1.6388     1.9862     2.4919      1.1747     2.113 
    zi_5_R5       1.4057    1.5798     1.8228     2.1828     2.6764      1.3588    2.3096 
    zi_31_r31     5.5917    5.7658     6.0088      6.348     4.7518      5.4124    6.3344 
    zi_32_r32     5.6434    5.8175     6.0606     6.3997     4.8036      5.4642    6.3861 
    zi_33_r33     5.6951    5.8693     6.1123     6.4515     4.8553      5.5159    6.4378 
    zi_34_r34     5.7469     5.921      6.164     6.5032      4.907      5.5676    6.4896 
    zi_35_r35     5.7986    5.9727     6.2158     6.5549     7.0283      5.6194    6.5413 

pos = 8 ; key = cl_mt_pol_for_borr ;rown= 35 ,coln= 7
cl_mt_pol_for_borr :mu= -0.42165 ,sd= 0.83111 ,min= -2.6625 ,max= 0
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1           0          0          0           0          0          0     -1.065
    zi_2_R2      -1.065     -1.065     -1.065      -1.065    -2.6625    -2.6625     -1.065
    zi_3_R3      -1.065     -1.065     -1.065      -1.065    -2.6625     -1.065    -2.6625
    zi_4_R4      -1.065     -1.065     -1.065     -2.6625    -2.6625     -1.065    -2.6625
    zi_5_R5      -1.065     -1.065     -1.065     -2.6625    -2.6625     -1.065    -2.6625
    zi_31_r31         0          0          0           0          0          0          0
    zi_32_r32         0          0          0           0          0          0          0
    zi_33_r33         0          0          0           0          0          0          0
    zi_34_r34         0          0          0           0          0          0          0
    zi_35_r35         0          0          0           0          0          0          0

pos = 9 ; key = cl_mt_pol_for_save ;rown= 35 ,coln= 7
cl_mt_pol_for_save :mu= 16.1899 ,sd= 15.7711 ,min= 0 ,max= 47.8788
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4     zi_5_c5     zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _________    _______    _______

    zi_1_R1           0          0          0           0            0          0          0
    zi_2_R2      0.1603          0          0           0      0.41134          0          0
    zi_3_R3           0          0          0           0      0.20983    0.01019    0.59817
    zi_4_R4           0          0          0     0.52661    0.0083121          0    0.39666
    zi_5_R5           0          0          0      0.3251            0          0    0.19514
    zi_31_r31    37.273     37.273     37.273      37.273       39.394     39.394     39.394
    zi_32_r32    39.394     39.394     39.394      39.394       41.515     41.515     41.515
    zi_33_r33    41.515     41.515     41.515      41.515       43.636     43.636     43.636
    zi_34_r34    43.636     43.636     43.636      43.636       45.758     45.758     45.758
    zi_35_r35    45.758     45.758     45.758      45.758       45.758     47.879     47.879

pos = 10 ; key = cl_mt_pol_inf_borr_nobridge ;rown= 35 ,coln= 7
cl_mt_pol_inf_borr_nobridge :mu= -0.058521 ,sd= 0.18119 ,min= -0.90102 ,max= 0
                  zi_1_c1      zi_2_c2     zi_3_c3     zi_4_c4     zi_5_c5    zi_6_c6     zi_7_c7 
                 _________    _________    ________    ________    _______    ________    ________

    zi_1_R1              0            0           0           0          0           0     -0.5963
    zi_2_R2              0    -0.030369    -0.29647    -0.66785          0    -0.31201    -0.79781
    zi_3_R3      -0.041211     -0.23188    -0.49799    -0.86937          0           0           0
    zi_4_R4       -0.24273      -0.4334    -0.69951           0          0    -0.19133           0
    zi_5_R5       -0.44424     -0.63491    -0.90102           0    -0.1932    -0.39284           0
    zi_31_r31            0            0           0           0          0           0           0
    zi_32_r32            0            0           0           0          0           0           0
    zi_33_r33            0            0           0           0          0           0           0
    zi_34_r34            0            0           0           0          0           0           0
    zi_35_r35            0            0           0           0          0           0           0

pos = 11 ; key = mt_it_b_bridge_idx ;rown= 35 ,coln= 7
mt_it_b_bridge_idx :mu= 0.24082 ,sd= 0.42845 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      true  
    zi_2_R2       true       true       true       true       true       true       true  
    zi_3_R3       true       true       true       true       true       true       true  
    zi_4_R4       true       true       true       true       true       true       true  
    zi_5_R5       true       true       true       true       true       true       true  
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 12 ; key = mt_it_for_only_nbdg ;rown= 35 ,coln= 7
mt_it_for_only_nbdg :mu= 0 ,sd= 0 ,min= 0 ,max= 0
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      false 
    zi_2_R2       false      false      false      false      false      false      false 
    zi_3_R3       false      false      false      false      false      false      false 
    zi_4_R4       false      false      false      false      false      false      false 
    zi_5_R5       false      false      false      false      false      false      false 
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 13 ; key = mt_it_fr_brrsv_nbdg ;rown= 35 ,coln= 7
mt_it_fr_brrsv_nbdg :mu= 0.13061 ,sd= 0.33767 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      false 
    zi_2_R2       true       false      false      false      true       false      false 
    zi_3_R3       false      false      false      false      true       true       true  
    zi_4_R4       false      false      false      true       true       false      true  
    zi_5_R5       false      false      false      true       false      false      true  
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 14 ; key = mt_it_frin_brr_nbdg ;rown= 35 ,coln= 7
mt_it_frin_brr_nbdg :mu= 0.11837 ,sd= 0.3237 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      true  
    zi_2_R2       false      true       true       true       false      true       true  
    zi_3_R3       true       true       true       true       false      false      false 
    zi_4_R4       true       true       true       false      false      true       false 
    zi_5_R5       true       true       true       false      true       true       false 
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 15 ; key = mt_it_frmsavng_only ;rown= 35 ,coln= 7
mt_it_frmsavng_only :mu= 0.67755 ,sd= 0.46837 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      false 
    zi_2_R2       false      false      false      false      false      false      false 
    zi_3_R3       false      false      false      false      false      false      false 
    zi_4_R4       false      false      false      false      false      false      false 
    zi_5_R5       false      false      false      false      false      false      false 
    zi_31_r31     true       true       true       true       true       true       true  
    zi_32_r32     true       true       true       true       true       true       true  
    zi_33_r33     true       true       true       true       true       true       true  
    zi_34_r34     true       true       true       true       true       true       true  
    zi_35_r35     true       true       true       true       true       true       true  

pos = 16 ; key = mt_it_inf_only_nbdg ;rown= 35 ,coln= 7
mt_it_inf_only_nbdg :mu= 0.0081633 ,sd= 0.090165 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      false 
    zi_2_R2       false      false      false      false      false      false      false 
    zi_3_R3       false      false      false      false      false      false      false 
    zi_4_R4       false      false      false      false      false      false      false 
    zi_5_R5       false      false      false      false      false      false      false 
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 17 ; key = mt_pol_perc_change ;rown= 20 ,coln= 7
mt_pol_perc_change :mu= 0.34388 ,sd= 0.34377 ,min= 0 ,max= 1
                 zi_1_c1     zi_2_c2     zi_3_c3     zi_4_c4     zi_5_c5     zi_6_c6     zi_7_c7 
                 ________    ________    ________    ________    ________    ________    ________

    zi_1_R1             1           1           1           1           1           1           1
    zi_2_R2       0.97143     0.97143     0.97143     0.97143     0.97143     0.97143     0.97143
    zi_3_R3       0.91429     0.91429     0.91429     0.91429     0.91429     0.91429     0.91429
    zi_4_R4       0.82857     0.82857         0.8         0.8     0.85714     0.85714     0.85714
    zi_5_R5       0.68571     0.68571     0.62857     0.71429     0.68571     0.71429     0.74286
    zi_16_r16    0.057143    0.028571    0.028571    0.057143    0.057143    0.057143    0.085714
    zi_17_r17    0.028571    0.028571    0.028571           0    0.057143    0.028571    0.028571
    zi_18_r18    0.028571    0.028571    0.028571    0.028571    0.057143    0.057143    0.028571
    zi_19_r19    0.028571    0.028571    0.057143    0.028571    0.057143    0.028571           0
    zi_20_r20    0.028571    0.028571    0.028571    0.057143    0.057143    0.028571    0.028571

pos = 18 ; key = mt_val ;rown= 35 ,coln= 7
mt_val :mu= 6.2523 ,sd= 6.7613 ,min= -11.0436 ,max= 13.7247
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7 
                 _______    _______    _______    _______    _______    _______    ________

    zi_1_R1      -11.044    -10.241    -9.2889    -8.3621    -7.5016    -6.7048     -5.3397
    zi_2_R2       -9.977    -9.1339    -8.2393    -7.3605     -6.519    -5.6938     -4.2847
    zi_3_R3       -8.736    -7.9628    -7.1441      -6.33    -5.5253    -4.5465     -3.1422
    zi_4_R4      -7.4521    -6.7644    -6.0286    -5.2803    -4.5088    -3.3123     -1.9426
    zi_5_R5      -6.1692    -5.5648    -4.9081      -4.22    -3.4736    -2.1366    -0.80055
    zi_31_r31      12.19     12.291     12.412     12.555     12.731     12.939       13.16
    zi_32_r32      12.38     12.476     12.591     12.726     12.892     13.093      13.307
    zi_33_r33     12.563     12.654     12.763     12.892     13.048     13.242       13.45
    zi_34_r34      12.74     12.826     12.931     13.053       13.2     13.386      13.589
    zi_35_r35     12.911     12.993     13.093      13.21     13.348     13.528      13.725

pos = 19 ; key = tb_pol_a ;rown= 35 ,coln= 7
tb_pol_a :mu= 13.384 ,sd= 19.2751 ,min= -20 ,max= 47.8788
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1            0          0          0          0          0          0        -20
    zi_2_R2          -20        -20        -20        -20        -20        -20    -17.879
    zi_3_R3      -17.879    -17.879    -17.879    -17.879    -17.879    -15.758    -15.758
    zi_4_R4      -15.758    -15.758    -15.758    -15.758    -15.758    -13.636    -13.636
    zi_5_R5      -13.636    -13.636    -13.636    -13.636    -13.636    -11.515    -11.515
    zi_31_r31     37.273     37.273     37.273     37.273     39.394     39.394     39.394
    zi_32_r32     39.394     39.394     39.394     39.394     41.515     41.515     41.515
    zi_33_r33     41.515     41.515     41.515     41.515     43.636     43.636     43.636
    zi_34_r34     43.636     43.636     43.636     43.636     45.758     45.758     45.758
    zi_35_r35     45.758     45.758     45.758     45.758     45.758     47.879     47.879

pos = 20 ; key = tb_val ;rown= 35 ,coln= 7
tb_val :mu= 6.2523 ,sd= 6.7613 ,min= -11.0436 ,max= 13.7247
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_4_c4    zi_5_c5    zi_6_c6    zi_7_c7 
                 _______    _______    _______    _______    _______    _______    ________

    zi_1_R1      -11.044    -10.241    -9.2889    -8.3621    -7.5016    -6.7048     -5.3397
    zi_2_R2       -9.977    -9.1339    -8.2393    -7.3605     -6.519    -5.6938     -4.2847
    zi_3_R3       -8.736    -7.9628    -7.1441      -6.33    -5.5253    -4.5465     -3.1422
    zi_4_R4      -7.4521    -6.7644    -6.0286    -5.2803    -4.5088    -3.3123     -1.9426
    zi_5_R5      -6.1692    -5.5648    -4.9081      -4.22    -3.4736    -2.1366    -0.80055
    zi_31_r31      12.19     12.291     12.412     12.555     12.731     12.939       13.16
    zi_32_r32      12.38     12.476     12.591     12.726     12.892     13.093      13.307
    zi_33_r33     12.563     12.654     12.763     12.892     13.048     13.242       13.45
    zi_34_r34      12.74     12.826     12.931     13.053       13.2     13.386      13.589
    zi_35_r35     12.911     12.993     13.093      13.21     13.348     13.528      13.725

pos = 21 ; key = tb_valpol_alliter ;rown= 20 ,coln= 9
tb_valpol_alliter :mu= 6.6035 ,sd= 33.7702 ,min= 0 ,max= 324.2902
                 zi_1_c1    zi_2_c2    zi_3_c3     zi_5_c5     zi_7_c7     zi_8_c8     zi_9_c9 
                 _______    _______    ________    ________    ________    ________    ________

    zi_1_R1      35.191     293.38            1           1           1           1           1
    zi_2_R2      27.601     324.29      0.97143     0.97143     0.97143     0.97143     0.97143
    zi_3_R3      22.977     106.04      0.91429     0.91429     0.91429     0.91429     0.91429
    zi_4_R4      19.813     53.871      0.82857         0.8     0.85714     0.85714     0.85714
    zi_5_R5      16.321     33.097      0.68571     0.62857     0.68571     0.71429     0.74286
    zi_16_r16    2.5574     5.0958     0.057143    0.028571    0.057143    0.057143    0.085714
    zi_17_r17    2.2837      3.674     0.028571    0.028571    0.057143    0.028571    0.028571
    zi_18_r18    2.0703      3.674     0.028571    0.028571    0.057143    0.057143    0.028571
    zi_19_r19    1.8945     2.9998     0.028571    0.057143    0.057143    0.028571           0
    zi_20_r20    1.7333     2.9998     0.028571    0.028571    0.057143    0.028571    0.028571

----------------------------------------
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Matrix in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                                   i     idx    rowN    colN      mean         std         min        max  
                                   __    ___    ____    ____    _________    ________    ________    ______

    ar_pol_diff_norm                1     1      20      1          47.16      92.828      2.9998    324.29
    ar_val_diff_norm                2     3      20      1         9.8652      9.7427      1.7333    35.191
    cl_mt_coh                       3     4      35      7         16.052      20.727      -19.56    53.252
    cl_mt_pol_a                     4     5      35      7         13.384      19.275         -20    47.879
    cl_mt_pol_b_bridge              5     6      35      7        -2.3257      4.9856     -19.095         0
    cl_mt_pol_c                     6     7      35      7         3.2911      1.7598        0.02    7.0283
    cl_mt_pol_for_borr              7     8      35      7       -0.42165     0.83111     -2.6625         0
    cl_mt_pol_for_save              8     9      35      7          16.19      15.771           0    47.879
    cl_mt_pol_inf_borr_nobridge     9    10      35      7      -0.058521     0.18119    -0.90102         0
    mt_it_b_bridge_idx             10    11      35      7        0.24082     0.42845           0         1
    mt_it_for_only_nbdg            11    12      35      7              0           0           0         0
    mt_it_fr_brrsv_nbdg            12    13      35      7        0.13061     0.33767           0         1
    mt_it_frin_brr_nbdg            13    14      35      7        0.11837      0.3237           0         1
    mt_it_frmsavng_only            14    15      35      7        0.67755     0.46837           0         1
    mt_it_inf_only_nbdg            15    16      35      7      0.0081633    0.090165           0         1
    mt_pol_perc_change             16    17      20      7        0.34388     0.34377           0         1
    mt_val                         17    18      35      7         6.2523      6.7613     -11.044    13.725
    tb_pol_a                       18    19      35      7         13.384      19.275         -20    47.879
    tb_val                         19    20      35      7         6.2523      6.7613     -11.044    13.725
    tb_valpol_alliter              20    21      20      9         6.6035       33.77           0    324.29

----------------------------------------
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Strings in Container and Sizes and Basic Statistics
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                       i    idx
                       _    ___

    ar_st_pol_names    1     2 

end
end