Risky + Safe Asset Dyna Prog Two-Step Solution (Optimized-Vectorized)

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Contents

function result_map = ff_wkz_vf_vecsv(varargin)

FF_WKZ_VF_VECSV solve infinite horizon exo shock + endo asset problem

This program solves the infinite horizon dynamic savings and risky capital asset problem with some ar1 shock. This is the efficient vectorized version of ff_wkz_vf. See that file for more descriptions.

@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:

@include

@seealso

Default

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

% Note: param_map and support_map can be adjusted here or outside to override defaults
% param_map('it_w_n') = 50;
% param_map('it_z_n') = 15;

% get armt and func map
[armt_map, func_map] = ffs_akz_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_akz_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_wkz_vf_vecsv';
support_map('st_profile_name_main') = [st_func_name support_map('st_profile_name_main')];
support_map('st_mat_name_main') = [st_func_name support_map('st_mat_name_main')];
support_map('st_img_name_main') = [st_func_name support_map('st_img_name_main')];

Parse Parameters 2

% armt_map
params_group = values(armt_map, {'ar_w', 'ar_z'});
[ar_w, ar_z] = params_group{:};
params_group = values(armt_map, {'ar_a_meshk', 'ar_k_mesha', 'mt_coh_wkb', 'it_ameshk_n'});
[ar_a_meshk, ar_k_mesha, mt_coh_wkb, it_ameshk_n] = params_group{:};
% func_map
params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_cons', 'f_coh'});
[f_util_log, f_util_crra, f_cons, f_coh] = params_group{:};
% param_map
params_group = values(param_map, {'fl_r_save', 'fl_r_borr', 'fl_w',...
    'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min'});
[fl_r_save, fl_r_borr, fl_wage, it_z_n, fl_crra, fl_beta, fl_c_min] = params_group{:};
params_group = values(param_map, {'it_maxiter_val', 'fl_tol_val', 'fl_tol_pol', 'it_tol_pol_nochange'});
[it_maxiter_val, fl_tol_val, fl_tol_pol, it_tol_pol_nochange] = params_group{:};
% support_map
params_group = values(support_map, {'bl_profile', 'st_profile_path', ...
    'st_profile_prefix', 'st_profile_name_main', 'st_profile_suffix',...
    'bl_time', 'bl_display', 'it_display_every', 'bl_post'});
[bl_profile, st_profile_path, ...
    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...
    bl_time, bl_display, it_display_every, bl_post] = params_group{:};

Initialize Output Matrixes

mt_val_cur = zeros(length(ar_a_meshk),length(ar_z));
mt_val = mt_val_cur - 1;
mt_pol_a = zeros(length(ar_a_meshk),length(ar_z));
mt_pol_a_cur = mt_pol_a - 1;
mt_pol_k = zeros(length(ar_a_meshk),length(ar_z));
mt_pol_k_cur = mt_pol_k - 1;
mt_pol_idx = zeros(length(ar_a_meshk),length(ar_z));
mt_ev_condi_z_max_kp = zeros(length(ar_w),length(ar_z));
mt_ev_condi_z_max_kp_cur = mt_ev_condi_z_max_kp - 1;

% We did not need these in ff_oz_vf or ff_oz_vf_vec
% see
% <https://fanwangecon.github.io/M4Econ/support/speed/partupdate/fs_u_c_partrepeat_main.html
% fs_u_c_partrepeat_main> for why store using cells.
cl_u_c_store = cell([it_z_n, 1]);
cl_c_valid_idx = cell([it_z_n, 1]);

Initialize Convergence Conditions

bl_vfi_continue = true;
it_iter = 0;
ar_val_diff_norm = zeros([it_maxiter_val, 1]);
ar_pol_diff_norm = zeros([it_maxiter_val, 1]);
mt_pol_perc_change = zeros([it_maxiter_val, it_z_n]);

Iterate Value Function

Loop solution with 4 nested loops

  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

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

Solve Second Stage Problem k*(w,z)

This is the key difference between this function and ffs_akz_set_functions which solves the two stages jointly Across iterations, only some k*(w,z) is changing, we only update consumption matrix when k*(w,z) is changing note in ff_wkz_evf a = b

    bl_input_override = true;
    [mt_ev_condi_z_max, ~, mt_ev_condi_z_max_kp, mt_ev_condi_z_max_bp] = ...
        ff_wkz_evf(mt_val_cur, param_map, support_map, armt_map, bl_input_override);

Find which k choice differ across iterations?

    mt_w_kstar_diff_idx = (mt_ev_condi_z_max_kp_cur ~= mt_ev_condi_z_max_kp);

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

    % loop 1: over exogenous states
    for it_z_i = 1:length(ar_z)
        % State Array fixed
        ar_coh_z = mt_coh_wkb(:,it_z_i);

        % Get 2nd Stage Choice Arrays
        % Update rows where opti k given w=k'+b' is changing
        ar_w_kstar_diff_idx = mt_w_kstar_diff_idx(:, it_z_i);
        ar_w_kstar_z = mt_ev_condi_z_max_kp(ar_w_kstar_diff_idx, it_z_i);
        ar_w_astar_z = mt_ev_condi_z_max_bp(ar_w_kstar_diff_idx, it_z_i);

        % Consumption Update
        % Note that compared to
        % <https://fanwangecon.github.io/CodeDynaAsset/m_akz/paramfunc/html/ffs_akz_set_functions.html
        % ffs_akz_set_functions> the mt_c here is much smaller the same
        % number of columns (states) as in the ffs_akz_set_functions file,
        % but the number of rows equal to ar_w length.
        mt_c = f_cons(ar_coh_z', ar_w_astar_z, ar_w_kstar_z);

        % EVAL current utility: N by N, f_util defined earlier
        if (fl_crra == 1)
            mt_utility_update = f_util_log(mt_c);
            fl_u_neg_c = f_util_log(fl_c_min);
        else
            mt_utility_update = f_util_crra(mt_c);
            fl_u_neg_c = f_util_crra(fl_c_min);
        end

        % Eliminate Complex Numbers
        mt_it_c_valid_idx = (mt_c <= fl_c_min);
        mt_utility_update(mt_it_c_valid_idx) = fl_u_neg_c;

        % Update Storage
        if (it_iter == 1)
            cl_u_c_store{it_z_i} = mt_utility_update;
            cl_c_valid_idx{it_z_i} = mt_it_c_valid_idx;
        else
            cl_u_c_store{it_z_i}(ar_w_kstar_diff_idx,:) = mt_utility_update;
            cl_c_valid_idx{it_z_i}(ar_w_kstar_diff_idx,:) = mt_it_c_valid_idx;
        end

        % EVAL add on future utility, N by N + N by 1
        ar_evzp_ak_condi_z = mt_ev_condi_z_max(:, it_z_i);
        mt_utility = cl_u_c_store{it_z_i} + fl_beta*ar_evzp_ak_condi_z;

        % Index update
        % using the method below is much faster than index replace
        % see <https://fanwangecon.github.io/M4Econ/support/speed/index/fs_subscript.html fs_subscript>
        mt_it_c_valid_idx = cl_c_valid_idx{it_z_i};
        mt_utility = mt_utility.*(~mt_it_c_valid_idx) + fl_u_neg_c*(mt_it_c_valid_idx);

        % Optimization: remember matlab is column major, rows must be
        % choices, columns must be states
        % <https://en.wikipedia.org/wiki/Row-_and_column-major_order COLUMN-MAJOR>
        [ar_opti_val1_z, ar_opti_idx_z] = max(mt_utility);
        mt_val(:,it_z_i) = ar_opti_val1_z;
        mt_pol_a(:,it_z_i) = mt_ev_condi_z_max_bp(ar_opti_idx_z, it_z_i);
        mt_pol_k(:,it_z_i) = mt_ev_condi_z_max_kp(ar_opti_idx_z, it_z_i);

Obtain Choice Index for Vectorized/Analytical Distribution Programs

For deriving distributions using vectorized and semi-analytical methods, at convergence, what index do optimal choices correspond to in terms of the rows of mt_val and mt_pol_a, and mt_pol_k. For the LHS matrixes here, each column a different optimal choice, each row a different element of the a_meshk and k_mesha vectors. For each column (one optimal choice), which row has that optimal choice's k' and b' values. Note the code is shorter than code in ff_wkz_vf_vec.

        if (it_iter == (it_maxiter_val + 1))
            [~, ar_opti_fullakvec_idx_z] = max((ar_a_meshk == mt_pol_a(:,it_z_i)').*(ar_k_mesha == mt_pol_k(:,it_z_i)'));
            mt_pol_idx(:,it_z_i) = ar_opti_fullakvec_idx_z;
        end
    end

Check Tolerance and Continuation

    % Difference across iterations
    ar_val_diff_norm(it_iter) = norm(mt_val - mt_val_cur);
    ar_pol_diff_norm(it_iter) = norm(mt_pol_a - mt_pol_a_cur) + norm(mt_pol_k - mt_pol_k_cur);
    ar_pol_a_perc_change = sum((mt_pol_a ~= mt_pol_a_cur))/(it_ameshk_n);
    ar_pol_k_perc_change = sum((mt_pol_k ~= mt_pol_k_cur))/(it_ameshk_n);
    mt_pol_perc_change(it_iter, :) = mean([ar_pol_a_perc_change;ar_pol_k_perc_change]);

    % Update
    mt_val_cur = mt_val;
    mt_pol_a_cur = mt_pol_a;
    mt_pol_k_cur = mt_pol_k;
    mt_ev_condi_z_max_kp_cur = mt_ev_condi_z_max_kp;

    % Print Iteration Results
    if (bl_display && (rem(it_iter, it_display_every)==0))
        fprintf('VAL it_iter:%d, fl_diff:%d, fl_diff_pol:%d\n', ...
            it_iter, ar_val_diff_norm(it_iter), ar_pol_diff_norm(it_iter));
        tb_valpol_iter = array2table([mean(mt_val_cur,1);...
                                      mean(mt_pol_a_cur,1); ...
                                      mean(mt_pol_k_cur,1); ...
                                      mt_val_cur(it_ameshk_n,:); ...
                                      mt_pol_a_cur(it_ameshk_n,:); ...
                                      mt_pol_k_cur(it_ameshk_n,:)]);
        tb_valpol_iter.Properties.VariableNames = strcat('z', string((1:size(mt_val_cur,2))));
        tb_valpol_iter.Properties.RowNames = {'mval', 'map', 'mak', 'Hval', 'Hap', 'Hak'};
        disp('mval = mean(mt_val_cur,1), average value over a')
        disp('map  = mean(mt_pol_a_cur,1), average choice over a')
        disp('mkp  = mean(mt_pol_k_cur,1), average choice over k')
        disp('Hval = mt_val_cur(it_ameshk_n,:), highest a state val')
        disp('Hap = mt_pol_a_cur(it_ameshk_n,:), highest a state choice')
        disp('mak = mt_pol_k_cur(it_ameshk_n,:), highest k state choice')
        disp(tb_valpol_iter);
    end

    % Continuation Conditions:
    % 1. if value function convergence criteria reached
    % 2. if policy function variation over iterations is less than
    % threshold
    if (it_iter == (it_maxiter_val + 1))
        bl_vfi_continue = false;
    elseif ((it_iter == it_maxiter_val) || ...
            (ar_val_diff_norm(it_iter) < fl_tol_val) || ...
            (sum(ar_pol_diff_norm(max(1, it_iter-it_tol_pol_nochange):it_iter)) < fl_tol_pol))
        % Fix to max, run again to save results if needed
        it_iter_last = it_iter;
        it_iter = it_maxiter_val;
    end
end

% End Timer
if (bl_time)
    toc;
end

% End Profile
if (bl_profile)
    profile off
    profile viewer
    st_file_name = [st_profile_prefix st_profile_name_main st_profile_suffix];
    profsave(profile('info'), strcat(st_profile_path, st_file_name));
end

Process Optimal Choices

result_map = containers.Map('KeyType','char', 'ValueType','any');
result_map('mt_val') = mt_val;
result_map('mt_pol_idx') = mt_pol_idx;

result_map('cl_mt_pol_coh') = {mt_coh_wkb, zeros(1)};
result_map('cl_mt_pol_a') = {mt_pol_a, zeros(1)};
result_map('cl_mt_pol_k') = {mt_pol_k, zeros(1)};
result_map('cl_mt_pol_c') = {f_cons(mt_coh_wkb, mt_pol_a, mt_pol_k), zeros(1)};
result_map('ar_st_pol_names') = ["cl_mt_pol_coh", "cl_mt_pol_a", "cl_mt_pol_k", "cl_mt_pol_c"];

if (bl_post)
    bl_input_override = true;
    result_map('ar_val_diff_norm') = ar_val_diff_norm(1:it_iter_last);
    result_map('ar_pol_diff_norm') = ar_pol_diff_norm(1:it_iter_last);
    result_map('mt_pol_perc_change') = mt_pol_perc_change(1:it_iter_last, :);
    result_map = ff_akz_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))+sum((mt_pol_k ~= mt_pol_k_cur)))/(2*it_ameshk_n):percentage of state space points conditional on shock where the policy function is changing across iterations
                valgap     polgap        z1            z2            z3            z4            z5            z6            z7            z8            z9           z10           z11           z12           z13           z14           z15    
                _______    ______    __________    __________    __________    __________    __________    __________    __________    __________    __________    __________    __________    __________    __________    __________    __________

    iter=1       227.04    276.59             1             1             1             1             1             1             1             1             1             1             1             1             1             1             1
    iter=2       179.64    2790.4       0.99137       0.99137       0.98549       0.98549       0.97804       0.97804       0.96902       0.95804       0.94588       0.92039       0.88745       0.84824       0.80157          0.72       0.63529
    iter=3       151.16    920.98       0.65176       0.65098       0.52314       0.52275       0.61882       0.62196       0.71686       0.62275       0.89216       0.51608       0.69725       0.54235       0.63294        0.5949       0.62627
    iter=4        130.1    448.85       0.57725       0.57922       0.49608       0.49608       0.55608       0.57137        0.6251       0.52157       0.78431       0.48863       0.63765       0.50039       0.59569       0.50784       0.51647
    iter=5        113.5    266.36       0.53608       0.53569        0.4749       0.47529       0.55882       0.59333       0.58627       0.49137       0.71569       0.47176       0.56196       0.48588       0.51529       0.47686       0.48863
    iter=6       99.938     188.1       0.46471       0.46471       0.42588       0.42549       0.46627           0.5       0.54431       0.44627       0.73922       0.43647       0.54745       0.46471       0.47412       0.44902       0.45412
    iter=7       88.609    140.12       0.37294       0.37569       0.35176       0.35412       0.39608       0.43098       0.46471       0.37333       0.62392       0.37647       0.50431       0.40941       0.41451       0.40314       0.40824
    iter=8           79    120.94       0.27137       0.27412       0.26275        0.2651       0.28627       0.33098       0.32745       0.28588       0.73373       0.29059       0.42902       0.34549       0.33255        0.3298       0.33569
    iter=9       70.745    98.728        0.2051       0.20667       0.20078        0.2051       0.22235       0.26471          0.26       0.21529       0.72157       0.21961       0.36275        0.3102       0.25176       0.25294       0.27059
    iter=10      63.581    88.163       0.16118       0.16431       0.15412       0.15686        0.1698       0.21098       0.20275       0.17725       0.69804       0.17804       0.27686       0.32588       0.20471       0.21725       0.21922
    iter=11      57.334    71.859       0.13059       0.12863       0.12431       0.12431       0.13255       0.16235       0.15529       0.13137       0.61412       0.14353       0.25412       0.26549       0.16431       0.16392       0.17216
    iter=12      51.832    69.137      0.098431       0.10039      0.096863      0.096078       0.10902       0.12314       0.13569       0.12431       0.57569       0.11725       0.20902       0.21451       0.13451       0.14941       0.15333
    iter=13       46.97    54.289      0.086275      0.086275      0.083529      0.086275      0.093725       0.12431       0.11059      0.092157       0.43373      0.094902       0.16745       0.18824       0.11882       0.10941       0.12196
    iter=14      42.649     50.95      0.074118      0.074902      0.071765      0.072941      0.080784       0.13922      0.087059       0.07451       0.42902      0.082353       0.12784       0.11647      0.097255      0.099216       0.10039
    iter=15      38.799    44.356      0.056471      0.055686       0.05451      0.055294      0.064314       0.20196      0.073725      0.071373       0.29569      0.073725       0.15098      0.083137      0.072549      0.090588      0.094118
    iter=16      35.368    47.104      0.047451      0.049412      0.045882      0.047843      0.051765       0.23922      0.067451      0.065882       0.32314      0.060784       0.15451      0.094902      0.069804      0.072549      0.086275
    iter=17      32.283     40.36      0.042353      0.043529      0.043137      0.042353      0.047059       0.25137      0.058039      0.052941       0.22431      0.049804       0.12667      0.088627      0.060784      0.061176      0.061569
    iter=18      29.497    32.552      0.040784      0.040392      0.035686      0.041176      0.041569       0.13647       0.04902      0.042353       0.19529      0.042745        0.1302      0.088235      0.058039      0.051765      0.053333
    iter=19      26.977    34.912      0.034118      0.033725      0.038431      0.035686      0.039216       0.11608      0.041961      0.035686       0.21686      0.039608       0.11961      0.057647      0.056471      0.045098       0.04902
    iter=20      24.704    35.339      0.026275      0.031373      0.027451      0.030588       0.03098       0.19216      0.033333      0.027843       0.21529      0.034902      0.074902      0.040392          0.04      0.045098      0.063529
    iter=21      22.656    25.724      0.026275      0.024706      0.024706      0.024706      0.023529        0.1102      0.026275      0.027059       0.12745      0.034902      0.049804       0.04902      0.032157      0.043529      0.081961
    iter=22      20.807    24.188      0.019216      0.018431      0.020392      0.016863      0.021176       0.06902      0.025098      0.023922        0.1098      0.028627      0.083922      0.031765      0.027059      0.038431          0.08
    iter=23       19.13    28.633      0.018824      0.017647      0.016863      0.019608      0.018824       0.10941      0.021569      0.021176       0.15098      0.021569      0.089804      0.038824      0.025098       0.02902      0.073333
    iter=24      17.602    21.949      0.013725      0.016863      0.014902      0.014118      0.016863      0.087843      0.021961      0.018824      0.092549          0.02      0.087451       0.03451      0.021176      0.021961      0.065098
    iter=25      16.207    24.666      0.014902      0.013333      0.013725      0.014118      0.013725       0.10863       0.01451      0.017255       0.11686      0.019216      0.043529      0.031373      0.022745      0.021569      0.043137
    iter=26      14.932    25.232      0.011373      0.010588      0.012941      0.012549      0.016471      0.070588      0.016863      0.016078       0.12353      0.012941      0.036078      0.039216      0.016863      0.018431      0.061961
    iter=27      13.764    21.592       0.01098      0.013333     0.0090196      0.011373      0.012157      0.089412      0.015294      0.014902      0.055686      0.012549          0.04      0.019216      0.016863      0.015294      0.061961
    iter=28      12.694    21.639     0.0090196      0.010588      0.010196      0.010588      0.012941      0.087451      0.012941       0.01451      0.089412      0.011765      0.041176      0.014118      0.015686       0.01451      0.038039
    iter=29      11.714    23.752     0.0086275     0.0082353     0.0082353     0.0070588     0.0098039      0.072157      0.012941      0.011765       0.10549      0.012549      0.033333       0.01451      0.016078      0.011765      0.062745
    iter=30      10.819    19.707     0.0070588     0.0062745     0.0078431      0.007451     0.0070588      0.072941      0.010588      0.012549      0.013333     0.0098039      0.014118      0.011373       0.01451       0.01098      0.038431
    iter=31      10.001    20.629     0.0078431      0.005098     0.0047059     0.0082353     0.0058824      0.065098     0.0078431     0.0094118      0.081569     0.0082353      0.011765      0.011373       0.01098      0.012549      0.037255
    iter=32      9.2538    18.997     0.0039216     0.0058824     0.0058824     0.0035294      0.010196      0.027451      0.010588     0.0082353      0.070196     0.0094118     0.0094118      0.021569      0.013333      0.010196      0.037647
    iter=33      8.5706    18.069     0.0043137     0.0047059     0.0023529     0.0054902     0.0043137      0.044314     0.0062745     0.0054902      0.033725     0.0078431      0.010196     0.0070588      0.011765     0.0090196      0.061569
    iter=34      7.9453    10.089     0.0031373     0.0047059      0.007451     0.0062745     0.0035294     0.0070588     0.0062745     0.0047059      0.019608     0.0035294     0.0086275     0.0066667      0.010196     0.0098039     0.0094118
    iter=35      7.3729     16.84     0.0027451     0.0031373     0.0023529     0.0027451     0.0058824      0.032157     0.0070588     0.0054902       0.05451     0.0066667     0.0062745      0.007451     0.0070588     0.0090196      0.037647
    iter=36      6.8481    13.579     0.0039216     0.0027451     0.0019608     0.0015686     0.0043137      0.027451     0.0043137     0.0039216     0.0031373      0.005098     0.0094118     0.0039216     0.0090196      0.005098      0.034902
    iter=37      6.3662    14.429     0.0015686     0.0027451     0.0035294     0.0039216     0.0019608      0.020392     0.0062745     0.0023529      0.039216     0.0031373     0.0043137      0.020392     0.0047059      0.007451      0.034118
    iter=38       5.923    4.8384     0.0023529     0.0015686             0     0.0019608     0.0019608     0.0031373     0.0031373     0.0035294     0.0023529     0.0035294     0.0043137     0.0023529     0.0054902     0.0043137     0.0035294
    iter=39       5.515    13.871    0.00078431    0.00078431     0.0031373    0.00039216     0.0035294     0.0031373     0.0023529     0.0019608     0.0027451     0.0019608     0.0047059     0.0039216     0.0070588     0.0043137      0.036471
    iter=40      5.1387    4.6995     0.0015686     0.0011765     0.0023529     0.0019608     0.0031373     0.0015686     0.0011765     0.0019608    0.00039216     0.0031373     0.0027451     0.0039216     0.0027451      0.005098     0.0043137
    iter=41      4.7913    14.522    0.00078431     0.0023529     0.0019608     0.0023529     0.0019608     0.0031373     0.0015686    0.00078431          0.04     0.0031373     0.0031373     0.0015686     0.0035294     0.0039216      0.035294
    iter=42      4.4701    11.807     0.0023529     0.0011765    0.00078431    0.00078431    0.00078431     0.0011765     0.0031373     0.0023529      0.026667     0.0015686     0.0011765     0.0011765     0.0023529     0.0027451     0.0047059
    iter=43      4.1728    5.4465    0.00039216    0.00039216    0.00078431     0.0011765     0.0011765     0.0023529    0.00078431     0.0015686     0.0023529    0.00078431     0.0031373     0.0043137     0.0035294     0.0043137     0.0054902
    iter=44      3.8974    12.575    0.00039216    0.00078431     0.0011765     0.0015686    0.00078431    0.00078431     0.0015686    0.00039216     0.0019608     0.0019608     0.0011765     0.0031373     0.0015686     0.0023529      0.029804
    iter=45      3.6419    13.302             0             0    0.00078431    0.00039216    0.00039216             0    0.00039216     0.0015686    0.00039216     0.0011765    0.00039216    0.00078431    0.00078431     0.0031373      0.033333
    iter=46      3.4048    2.4995             0     0.0011765             0     0.0011765             0     0.0023529    0.00039216             0     0.0027451    0.00039216    0.00078431     0.0015686     0.0015686     0.0015686     0.0011765
    iter=47      3.1844    3.2577    0.00039216    0.00039216             0             0    0.00078431     0.0019608     0.0011765    0.00039216             0    0.00039216     0.0015686    0.00078431     0.0011765     0.0019608     0.0039216
    iter=48      2.9795    2.7878     0.0011765    0.00039216             0    0.00039216    0.00078431    0.00078431     0.0011765             0    0.00039216     0.0011765    0.00039216    0.00039216    0.00039216     0.0015686     0.0011765
    iter=49      2.7887    2.2817    0.00039216             0    0.00039216    0.00078431     0.0015686    0.00039216     0.0019608     0.0011765             0    0.00078431     0.0011765    0.00078431     0.0019608     0.0011765     0.0019608
    iter=50       2.611    14.289             0    0.00078431    0.00039216    0.00039216    0.00039216             0    0.00039216    0.00078431      0.038431    0.00078431    0.00039216     0.0011765    0.00078431    0.00078431    0.00078431
    iter=51      2.4454    3.7202    0.00039216             0             0             0    0.00078431    0.00039216    0.00039216    0.00039216    0.00039216    0.00039216    0.00039216             0     0.0015686     0.0011765     0.0019608
    iter=52       2.291    3.3021             0             0    0.00039216    0.00039216    0.00078431     0.0011765             0    0.00078431    0.00039216             0             0    0.00078431             0     0.0019608     0.0011765
    iter=53      2.1469    4.5043    0.00039216             0    0.00039216    0.00039216             0    0.00078431             0             0     0.0019608     0.0015686    0.00078431    0.00039216     0.0011765    0.00039216             0
    iter=54      2.0123    2.2817             0             0             0    0.00078431    0.00039216             0             0             0             0    0.00039216    0.00078431     0.0011765    0.00078431    0.00078431     0.0019608
    iter=55      1.8866    13.458             0    0.00039216    0.00078431             0     0.0011765             0    0.00039216    0.00039216             0    0.00039216    0.00078431             0             0    0.00078431      0.034118
    iter=56      1.7691    18.926    0.00039216             0             0             0             0             0             0             0    0.00078431    0.00078431    0.00039216             0             0    0.00078431      0.067451
    iter=57      1.6593    1.0204             0    0.00039216             0             0             0    0.00039216             0             0    0.00039216             0             0    0.00039216             0             0             0
    iter=58      1.5565    1.0204    0.00039216             0             0    0.00039216             0             0             0             0             0             0             0    0.00078431             0             0             0
    iter=59      1.4603    1.4431             0             0             0             0             0    0.00039216    0.00039216             0    0.00078431             0             0    0.00039216    0.00039216             0             0
    iter=60      1.3703    1.7674    0.00039216    0.00039216             0             0             0    0.00078431             0             0             0             0     0.0011765             0             0             0             0
    iter=61      1.2861    1.4431             0             0             0             0             0    0.00039216    0.00039216             0             0    0.00039216    0.00078431             0             0             0             0
    iter=62      1.2071    1.4431             0             0    0.00039216             0             0             0             0             0             0             0             0             0             0    0.00078431             0
    iter=63      1.1332    1.0204             0             0             0             0             0    0.00039216             0             0             0             0             0             0             0             0             0
    iter=64      1.0639    1.0204    0.00039216             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=65     0.99889    1.0204             0             0             0             0             0             0             0             0             0    0.00039216    0.00039216             0             0             0             0
    iter=66     0.93798    1.0204             0             0             0    0.00039216             0             0             0             0             0    0.00039216             0             0             0    0.00039216             0
    iter=67     0.88086    1.0204             0             0             0             0             0             0             0             0             0             0             0             0             0    0.00039216    0.00039216
    iter=68     0.82728    1.0204             0             0             0             0             0             0             0             0             0             0             0    0.00039216             0             0    0.00039216
    iter=69     0.77702    1.0204    0.00039216             0             0             0             0    0.00039216             0             0             0             0             0             0             0             0             0
    iter=70     0.72986    1.0204             0             0             0             0             0             0             0             0             0             0             0             0             0    0.00039216    0.00039216
    iter=71      0.6856         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=72     0.64407         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=73     0.60508         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=74     0.56848    1.0204             0             0             0             0             0             0             0             0             0    0.00039216             0             0             0             0             0
    iter=75     0.53411         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=76     0.50184         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=77     0.47154         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=78     0.44308         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=79     0.41636         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=80     0.39125         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=81     0.36767         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=82     0.34552         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=83     0.32471         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=84     0.30516         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=85     0.28679         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=86     0.26953         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=87     0.25331         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=88     0.23808         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=89     0.22376         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=90      0.2103         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=91     0.19766         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=92     0.18578         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=93     0.17461         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=94     0.16412         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=95     0.15426         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=96     0.14499         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=97     0.13628         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=98     0.12809         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=99      0.1204         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0
    iter=100    0.11317         0             0             0             0             0             0             0             0             0             0             0             0             0             0             0             0

tb_val: V(a,z) value at each state space point
                                   z1_0_34741    z2_0_40076    z3_0_4623    z4_0_5333    z5_0_61519    z6_0_70966    z10_1_2567    z11_1_4496    z12_1_6723    z13_1_9291    z14_2_2253    z15_2_567
                                   __________    __________    _________    _________    __________    __________    __________    __________    __________    __________    __________    _________

    coh1:k=0,b=0                    -16.679       -16.679       -16.679      -16.679      -16.679       -16.679       -16.679       -16.679       -16.679       -16.679       -16.679       -16.679 
    coh2:k=1.02041,b=0               1.6951        1.9479        2.2271       2.5214       2.8265        3.1427        4.6343        5.0876        5.5573        6.0229        6.4636        6.8568 
    coh3:k=0,b=1.02041               2.2448        2.5822        2.9487       3.3322       3.7278        4.1353        6.0791        6.7832        7.4306        8.0338        8.5908        9.0897 
    coh4:k=2.04082,b=0               2.9914        3.2625        3.5574       3.8626       4.1718        4.4834        5.9294        6.3827        6.8524        7.3179        7.7586        8.1519 
    coh5:k=1.02041,b=1.02041         3.5061        3.8576        4.2358       4.6264       5.0226        5.4221        7.0898        7.5454        8.0444        8.6067        9.1318        9.6083 
    coh6:k=0,b=2.04082               3.4934        3.8679        4.2667       4.6754       5.0871        5.4996        7.1962        7.7648        8.3175        8.8438        9.3405        9.8339 
    coh7:k=3.06122,b=0               4.2237        4.4947        4.7897       5.0949       5.4041        5.7157        7.0339        7.4054        7.7937        8.1869         8.569         8.919 
    coh8:k=2.04082,b=1.02041         4.3374        4.6305        4.9498       5.3357       5.7345        6.1368        7.7599        8.1816        8.6138         9.051        9.5545        10.014 
    coh9:k=1.02041,b=2.04082          4.334        4.6334        4.9765       5.3827       5.7967        6.2118         7.864        8.2883        8.7762         9.281        9.7589        10.197 
    coh10:k=0,b=3.06122              4.3183         4.623        4.9609       5.3839       5.8119        6.2385        7.9162        8.3803        8.8955        9.3883         9.856        10.354 
    coh11:k=4.08163,b=0              4.9498        5.1987        5.4824       5.7892       6.1044        6.4219        7.7053        8.0447        8.3966        8.7558        9.1106        9.4413 
    coh12:k=3.06122,b=1.02041        5.0609        5.3315        5.6389       5.9718       6.3154        6.6635         8.246        8.6521        9.0659        9.4844        9.9108        10.356 
    coh13:k=2.04082,b=2.04082        5.0576        5.3343        5.6481       5.9875       6.3377        6.7307         8.348        8.7568         9.172        9.6484        10.111        10.536 
    coh14:k=1.02041,b=3.06122        5.0423        5.3242        5.6432       5.9879       6.3465        6.7567        8.3992        8.8106        9.2765        9.7536        10.207        10.653 
    coh15:k=0,b=4.08163              5.0203        5.3072        5.6313        5.981       6.3412        6.7626        8.4302        8.8525         9.346        9.8176        10.266         10.75 
    coh16:k=5.10204,b=0              5.5962         5.816        6.0667       6.3398       6.6306        6.9351        8.1927        8.5182        8.8533        9.1951        9.5337        9.8508 
    coh17:k=4.08163,b=1.02041        5.7049        5.9458        6.2199       6.5185       6.8372        7.1718        8.6475        9.0427        9.4435         9.848        10.247        10.655 
    coh18:k=3.06122,b=2.04082        5.7016        5.9486        6.2289       6.5339       6.8591        7.2002        8.7473        9.1454        9.5478        9.9687        10.418        10.832 
    coh19:k=2.04082,b=3.06122        5.6866        5.9387        6.2241       6.5343       6.8646        7.2107        8.7977        9.1984        9.6082        10.072        10.512         10.92 
    coh20:k=1.02041,b=4.08163        5.6651        5.9221        6.2124       6.5275       6.8625        7.2131        8.8281        9.2315        9.6762        10.135        10.571        11.016 
    coh21:k=0,b=5.10204              5.6387        5.9008        6.1961       6.5161       6.8557        7.2107        8.8479         9.254        9.7218        10.178        10.613        11.079 
    coh22:k=6.12245,b=0              6.1694         6.367        6.5911       6.8365       7.0995        7.3793        8.5954        8.9117        9.2353        9.5644        9.8905        10.205 
    coh23:k=5.10204,b=1.02041        6.2756         6.494        6.7409       7.0114       7.3017        7.6112        8.9965        9.3819        9.7719        10.165        10.552        10.922 
    coh24:k=4.08163,b=2.04082        6.2725        6.4967        6.7498       7.0266       7.3233        7.6391        9.0943        9.4828        9.8745        10.268        10.692        11.096 
    coh25:k=3.06122,b=3.06122        6.2577         6.487        6.7451        7.027       7.3287        7.6494        9.1437        9.5348        9.9281        10.355        10.785        11.181 
    coh26:k=2.04082,b=4.08163        6.2367        6.4707        6.7336       7.0203       7.3267        7.6518        9.1737        9.5674        9.9705        10.417        10.842        11.258 
    coh27:k=1.02041,b=5.10204        6.2109        6.4499        6.7176        7.009         7.32        7.6494        9.1931        9.5896        10.015         10.46        10.882        11.321 
    coh28:k=0,b=6.12245               6.181        6.4252        6.6981       6.9944       7.3099        7.6437         9.206        9.6053        10.047        10.491        10.918        11.366 
    coh29:k=7.14286,b=0              6.6824        6.8619        7.0655        7.289       7.5286        7.7849        8.9456        9.2589        9.5824        9.9115        10.238        10.543 
    coh30:k=6.12245,b=1.02041        6.7864        6.9862        7.2122       7.4603       7.7268        8.0122        9.3111        9.6849        10.064        10.447        10.824        11.182 
    coh31:k=5.10204,b=2.04082        6.7833        6.9889        7.2209       7.4752       7.7479        8.0396        9.4061         9.784        10.165        10.548        10.942        11.337 
    coh32:k=4.08163,b=3.06122        6.7689        6.9793        7.2162       7.4756       7.7533        8.0498        9.4546        9.8352        10.218        10.613        11.033         11.42 
    coh33:k=3.06122,b=4.08163        6.7482        6.9634         7.205        7.469       7.7512        8.0521         9.484        9.8673        10.252        10.674         11.09        11.482 
    coh34:k=2.04082,b=5.10204         6.723         6.943        7.1894        7.458       7.7447        8.0498        9.5031        9.8892        10.281        10.716        11.129        11.544 
    coh35:k=1.02041,b=6.12245        6.6938        6.9188        7.1702       7.4436       7.7348        8.0442        9.5158        9.9047        10.313        10.746        11.159        11.589 
    coh36:k=0,b=7.14286              6.6606        6.8912        7.1479       7.4263       7.7223         8.036         9.524        9.9158        10.336         10.77         11.19        11.623 
    coh37:k=8.16327,b=0              7.1458        7.3107        7.4979       7.7039       7.9242        8.1603        9.2863        9.5944        9.9086        10.227        10.543        10.839 
    coh38:k=7.14286,b=1.02041        7.2476        7.4324        7.6415       7.8717       8.1183        8.3831        9.6194        9.9597         10.33        10.703        11.072        11.422 
    coh39:k=6.12245,b=2.04082        7.2445         7.435          7.65       7.8863       8.1391        8.4101        9.6892        10.057        10.429        10.803        11.173         11.56 
    coh40:k=5.10204,b=3.06122        7.2304        7.4256        7.6455       7.8867       8.1443        8.4201        9.7368        10.107        10.481        10.856        11.263        11.642 
    coh41:k=4.08163,b=4.08163        7.2102          7.41        7.6345       7.8802       8.1424        8.4224        9.7657        10.139        10.515        10.912        11.319        11.694 
    coh42:k=3.06122,b=5.10204        7.1855          7.39        7.6191       7.8694       8.1359        8.4201        9.7846        10.161        10.538        10.953        11.358        11.753 
    coh43:k=2.04082,b=6.12245        7.1569        7.3663        7.6003       7.8553       8.1262        8.4146         9.797        10.176         10.56        10.983        11.387        11.797 
    coh44:k=1.02041,b=7.14286        7.1246        7.3393        7.5785       7.8384       8.1139        8.4065        9.8051        10.187        10.583        11.006        11.409        11.831 
    coh45:k=0,b=8.16327              7.0883         7.309        7.5538       7.8189       8.0994        8.3964        9.8098        10.195          10.6        11.024        11.436        11.858 
    coh46:k=9.18367,b=0              7.5679        7.7208        7.8945        8.086       8.2903        8.5093        9.5949        9.8939        10.199        10.508        10.815        11.103 
    coh47:k=8.16327,b=1.02041        7.6674        7.8399        8.0352       8.2504       8.4806        8.7277        9.8991        10.228        10.577        10.941        11.301        11.643 
    coh48:k=7.14286,b=2.04082        7.6645        7.8425        8.0436       8.2648        8.501        8.7542        9.9554        10.312        10.674        11.039          11.4        11.769 
    coh49:k=6.12245,b=3.06122        7.6506        7.8333        8.0392       8.2652       8.5062        8.7641        10.002        10.362        10.726        11.092        11.478         11.85 
    coh50:k=5.10204,b=4.08163        7.6309         7.818        8.0283       8.2588       8.5042        8.7664        10.031        10.393        10.759        11.134        11.533        11.901 
    coh1226:k=50,b=0                 14.953        14.999        15.052       15.111       15.177        15.247        15.595        15.701        15.818        15.945        16.077        16.208 
    coh1227:k=48.9796,b=1.02041      14.975        15.026        15.085        15.15       15.222        15.301        15.694        15.817         15.95        16.092        16.242        16.392 
    coh1228:k=47.9592,b=2.04082      14.975        15.027        15.087       15.154       15.228        15.308        15.717        15.842        15.978        16.124        16.282        16.439 
    coh1229:k=46.9388,b=3.06122      14.971        15.024        15.086       15.154       15.229        15.311        15.729        15.857        15.995        16.149        16.309        16.467 
    coh1230:k=45.9184,b=4.08163      14.967        15.021        15.083       15.153       15.229        15.312        15.737        15.866         16.01        16.165        16.327        16.488 
    coh1231:k=44.898,b=5.10204       14.961        15.016        15.079        15.15       15.227        15.311        15.742        15.873         16.02        16.177         16.34        16.506 
    coh1232:k=43.8776,b=6.12245      14.955        15.011        15.075       15.146       15.224         15.31        15.746        15.879        16.028        16.187        16.352        16.521 
    coh1233:k=42.8571,b=7.14286      14.948        15.005         15.07       15.142       15.221        15.307        15.748        15.884        16.035        16.194        16.363        16.532 
    coh1234:k=41.8367,b=8.16327      14.941        14.998        15.064       15.137       15.217        15.304         15.75        15.887        16.039          16.2        16.372        16.542 
    coh1235:k=40.8163,b=9.18367      14.934        14.992        15.058       15.132       15.213        15.301         15.75        15.889        16.043        16.205        16.379         16.55 
    coh1236:k=39.7959,b=10.2041      14.926        14.984        15.052       15.126       15.208        15.297         15.75        15.891        16.046        16.209        16.386        16.557 
    coh1237:k=38.7755,b=11.2245      14.917        14.977        15.045        15.12       15.203        15.293         15.75        15.892        16.048        16.213        16.391        16.563 
    coh1238:k=37.7551,b=12.2449      14.908        14.969        15.037       15.114       15.198        15.289        15.749        15.892         16.05        16.216        16.395        16.568 
    coh1239:k=36.7347,b=13.2653      14.899         14.96         15.03       15.108       15.192        15.284        15.748        15.892        16.051        16.219        16.399        16.572 
    coh1240:k=35.7143,b=14.2857      14.892        14.951        15.022       15.101       15.186        15.279        15.746        15.891        16.051        16.221        16.402        16.576 
    coh1241:k=34.6939,b=15.3061      14.884        14.943        15.014       15.093        15.18        15.274        15.744         15.89        16.051        16.222        16.404         16.58 
    coh1242:k=33.6735,b=16.3265      14.877        14.937        15.005       15.086       15.173        15.268        15.742        15.889        16.051        16.224        16.407        16.582 
    coh1243:k=32.6531,b=17.3469      14.869        14.929        14.998       15.078       15.166        15.262         15.74        15.887        16.051        16.224        16.408        16.585 
    coh1244:k=31.6327,b=18.3673      14.861        14.922        14.992       15.069       15.159        15.256        15.737        15.885         16.05        16.225         16.41        16.587 
    coh1245:k=30.6122,b=19.3878      14.853        14.914        14.985       15.063       15.152         15.25        15.734        15.882        16.049        16.225        16.411        16.589 
    coh1246:k=29.5918,b=20.4082      14.844        14.906        14.977       15.056       15.144        15.243        15.731         15.88        16.048        16.225        16.412        16.591 
    coh1247:k=28.5714,b=21.4286      14.835        14.898         14.97        15.05       15.136        15.236        15.727        15.877        16.046        16.224        16.413        16.592 
    coh1248:k=27.551,b=22.449        14.826        14.889        14.962       15.043        15.13        15.229        15.724        15.874        16.044        16.223        16.413        16.594 
    coh1249:k=26.5306,b=23.4694      14.816        14.881        14.954       15.036       15.124        15.222         15.72        15.872        16.043        16.222        16.413        16.595 
    coh1250:k=25.5102,b=24.4898      14.806        14.871        14.946       15.028       15.117        15.214        15.716        15.869         16.04        16.221        16.413        16.595 
    coh1251:k=24.4898,b=25.5102      14.796        14.862        14.937        15.02       15.111        15.208        15.712        15.866        16.038         16.22        16.413        16.596 
    coh1252:k=23.4694,b=26.5306      14.787        14.852        14.928       15.012       15.104        15.202        15.707        15.863        16.036        16.218        16.413        16.597 
    coh1253:k=22.449,b=27.551        14.779        14.842        14.919       15.004       15.096        15.196        15.703         15.86        16.033        16.216        16.412        16.597 
    coh1254:k=21.4286,b=28.5714      14.771        14.834         14.91       14.996       15.089        15.189        15.698        15.857         16.03        16.214        16.411        16.597 
    coh1255:k=20.4082,b=29.5918      14.762        14.826          14.9       14.987       15.081        15.183        15.693        15.853        16.027        16.212        16.411        16.597 
    coh1256:k=19.3878,b=30.6122      14.753        14.818        14.892       14.978       15.073        15.176        15.688         15.85        16.024         16.21         16.41        16.597 
    coh1257:k=18.3673,b=31.6327      14.744         14.81        14.885       14.968       15.065        15.169        15.683        15.846        16.021        16.208        16.409        16.597 
    coh1258:k=17.3469,b=32.6531      14.735        14.801        14.877       14.961       15.056        15.161        15.677        15.842        16.017        16.206        16.407        16.597 
    coh1259:k=16.3265,b=33.6735      14.725        14.792        14.869       14.953       15.048        15.154        15.672        15.838        16.014        16.204        16.406        16.597 
    coh1260:k=15.3061,b=34.6939      14.715        14.783         14.86       14.946       15.038        15.146        15.668        15.834         16.01        16.202        16.404        16.596 
    coh1261:k=14.2857,b=35.7143      14.705        14.774        14.852       14.938       15.031        15.138        15.664        15.829        16.006        16.199        16.403        16.596 
    coh1262:k=13.2653,b=36.7347      14.694        14.764        14.843        14.93       15.024         15.13        15.659        15.825        16.002        16.197        16.401        16.595 
    coh1263:k=12.2449,b=37.7551      14.683        14.754        14.834       14.922       15.017        15.121        15.654         15.82        15.998        16.194        16.399        16.594 
    coh1264:k=11.2245,b=38.7755      14.675        14.743        14.824       14.913       15.009        15.112        15.649        15.815        15.994        16.191        16.397        16.593 
    coh1265:k=10.2041,b=39.7959      14.666        14.733        14.814       14.905       15.002        15.106        15.644         15.81        15.991        16.189        16.395        16.592 
    coh1266:k=9.18367,b=40.8163      14.657        14.725        14.804       14.895       14.994        15.099        15.639        15.805        15.987        16.186        16.393        16.591 
    coh1267:k=8.16327,b=41.8367      14.648        14.716        14.794       14.886       14.986        15.092        15.633          15.8        15.984        16.183        16.391         16.59 
    coh1268:k=7.14286,b=42.8571      14.639        14.708        14.786       14.876       14.977        15.084        15.628        15.794         15.98         16.18        16.389        16.589 
    coh1269:k=6.12245,b=43.8776      14.629        14.699        14.778       14.866       14.968        15.077        15.622        15.789        15.976        16.176        16.386        16.588 
    coh1270:k=5.10204,b=44.898       14.619         14.69         14.77       14.857       14.959        15.069        15.616        15.784        15.972        16.173        16.384        16.587 
    coh1271:k=4.08163,b=45.9184      14.609         14.68        14.761        14.85        14.95        15.061         15.61         15.78        15.968         16.17        16.381        16.586 
    coh1272:k=3.06122,b=46.9388      14.598         14.67        14.752       14.842        14.94        15.053        15.604        15.775        15.964        16.166        16.378        16.584 
    coh1273:k=2.04082,b=47.9592      14.587         14.66        14.743       14.834       14.931        15.045        15.597         15.77        15.959        16.162        16.376        16.583 
    coh1274:k=1.02041,b=48.9796      14.576         14.65        14.734       14.825       14.924        15.036        15.591        15.765        15.955        16.158        16.373        16.581 
    coh1275:k=0,b=50                 14.566        14.639        14.724       14.817       14.916        15.027        15.584        15.761         15.95        16.155         16.37        16.579 

tb_pol_a: optimal safe savings choice for each state space point
                                   z1_0_34741    z2_0_40076    z3_0_4623    z4_0_5333    z5_0_61519    z6_0_70966    z10_1_2567    z11_1_4496    z12_1_6723    z13_1_9291    z14_2_2253    z15_2_567
                                   __________    __________    _________    _________    __________    __________    __________    __________    __________    __________    __________    _________

    coh1:k=0,b=0                          0             0            0            0             0             0             0             0             0             0             0            0  
    coh2:k=1.02041,b=0                    0             0            0            0             0             0             0             0             0             0             0            0  
    coh3:k=0,b=1.02041                    0             0            0            0             0             0             0             0             0             0             0            0  
    coh4:k=2.04082,b=0                    0             0            0            0             0             0             0             0             0             0             0            0  
    coh5:k=1.02041,b=1.02041              0             0            0            0             0             0             0             0             0             0             0            0  
    coh6:k=0,b=2.04082                    0             0            0            0             0             0             0             0             0             0             0            0  
    coh7:k=3.06122,b=0                    0             0            0            0             0             0             0             0             0             0             0            0  
    coh8:k=2.04082,b=1.02041              0             0            0            0             0             0             0             0             0             0             0            0  
    coh9:k=1.02041,b=2.04082              0             0            0            0             0             0             0             0             0             0             0            0  
    coh10:k=0,b=3.06122                   0             0            0            0             0             0             0             0             0             0             0            0  
    coh11:k=4.08163,b=0              1.0204        1.0204            0            0             0             0             0             0             0             0             0            0  
    coh12:k=3.06122,b=1.02041        1.0204        1.0204            0            0             0             0             0             0             0             0             0            0  
    coh13:k=2.04082,b=2.04082        1.0204        1.0204            0            0             0             0             0             0             0             0             0            0  
    coh14:k=1.02041,b=3.06122        1.0204        1.0204            0            0             0             0             0             0             0             0             0            0  
    coh15:k=0,b=4.08163              1.0204        1.0204            0            0             0             0             0             0             0             0             0            0  
    coh16:k=5.10204,b=0              2.0408        2.0408       1.0204       1.0204             0             0             0             0             0             0             0            0  
    coh17:k=4.08163,b=1.02041        2.0408        2.0408       1.0204       1.0204             0             0             0             0             0             0             0            0  
    coh18:k=3.06122,b=2.04082        2.0408        2.0408       1.0204       1.0204             0             0             0             0             0             0             0            0  
    coh19:k=2.04082,b=3.06122        2.0408        2.0408       1.0204       1.0204             0             0             0             0             0             0             0            0  
    coh20:k=1.02041,b=4.08163        2.0408        2.0408       1.0204       1.0204             0             0             0             0             0             0             0            0  
    coh21:k=0,b=5.10204              2.0408        2.0408       1.0204       1.0204             0             0             0             0             0             0             0            0  
    coh22:k=6.12245,b=0              3.0612        3.0612       2.0408       2.0408        1.0204             0             0             0             0             0             0            0  
    coh23:k=5.10204,b=1.02041        3.0612        3.0612       2.0408       2.0408        1.0204             0             0             0             0             0             0            0  
    coh24:k=4.08163,b=2.04082        3.0612        3.0612       2.0408       2.0408        1.0204             0             0             0             0             0             0            0  
    coh25:k=3.06122,b=3.06122        3.0612        3.0612       2.0408       2.0408        1.0204             0             0             0             0             0             0            0  
    coh26:k=2.04082,b=4.08163        3.0612        3.0612       2.0408       2.0408        1.0204             0             0             0             0             0             0            0  
    coh27:k=1.02041,b=5.10204        3.0612        3.0612       2.0408       2.0408        1.0204             0             0             0             0             0             0            0  
    coh28:k=0,b=6.12245              3.0612        3.0612       2.0408       2.0408        1.0204             0             0             0             0             0             0            0  
    coh29:k=7.14286,b=0              4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh30:k=6.12245,b=1.02041        4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh31:k=5.10204,b=2.04082        4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh32:k=4.08163,b=3.06122        4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh33:k=3.06122,b=4.08163        4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh34:k=2.04082,b=5.10204        4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh35:k=1.02041,b=6.12245        4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh36:k=0,b=7.14286              4.0816        4.0816       3.0612       3.0612        2.0408        1.0204             0             0             0             0             0            0  
    coh37:k=8.16327,b=0               5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh38:k=7.14286,b=1.02041         5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh39:k=6.12245,b=2.04082         5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh40:k=5.10204,b=3.06122         5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh41:k=4.08163,b=4.08163         5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh42:k=3.06122,b=5.10204         5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh43:k=2.04082,b=6.12245         5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh44:k=1.02041,b=7.14286         5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh45:k=0,b=8.16327               5.102         5.102       4.0816       4.0816        3.0612        2.0408             0             0             0             0             0            0  
    coh46:k=9.18367,b=0              6.1224        6.1224        5.102        5.102        4.0816        4.0816             0             0             0             0             0            0  
    coh47:k=8.16327,b=1.02041        6.1224        6.1224        5.102        5.102        4.0816        4.0816             0             0             0             0             0            0  
    coh48:k=7.14286,b=2.04082        6.1224        6.1224        5.102        5.102        4.0816        4.0816             0             0             0             0             0            0  
    coh49:k=6.12245,b=3.06122        6.1224        6.1224        5.102        5.102        4.0816        4.0816             0             0             0             0             0            0  
    coh50:k=5.10204,b=4.08163        6.1224        6.1224        5.102        5.102        4.0816        4.0816             0             0             0             0             0            0  
    coh1226:k=50,b=0                 44.898        44.898       43.878       43.878        42.857        42.857        37.755        35.714        32.653        30.612        27.551        24.49  
    coh1227:k=48.9796,b=1.02041      44.898        44.898       43.878       43.878        42.857        42.857        38.776        36.735        34.694        32.653        29.592       26.531  
    coh1228:k=47.9592,b=2.04082      44.898        44.898       43.878       43.878        42.857        42.857        38.776        36.735        34.694        32.653        30.612       27.551  
    coh1229:k=46.9388,b=3.06122      44.898        44.898       43.878       43.878        42.857        42.857        38.776        36.735        34.694        33.673        30.612       27.551  
    coh1230:k=45.9184,b=4.08163      44.898        44.898       43.878       43.878        42.857        42.857        38.776        36.735        35.714        33.673        30.612       29.592  
    coh1231:k=44.898,b=5.10204       44.898        44.898       43.878       43.878        42.857        42.857        38.776        36.735        35.714        33.673        30.612       29.592  
    coh1232:k=43.8776,b=6.12245      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        33.673        31.633       29.592  
    coh1233:k=42.8571,b=7.14286      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        33.673        31.633       29.592  
    coh1234:k=41.8367,b=8.16327      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        33.673        31.633       29.592  
    coh1235:k=40.8163,b=9.18367      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        33.673        31.633       29.592  
    coh1236:k=39.7959,b=10.2041      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        33.673        31.633       29.592  
    coh1237:k=38.7755,b=11.2245      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1238:k=37.7551,b=12.2449      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1239:k=36.7347,b=13.2653      44.898        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1240:k=35.7143,b=14.2857      43.878        44.898       43.878       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1241:k=34.6939,b=15.3061      43.878        43.878       43.878       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1242:k=33.6735,b=16.3265      43.878        43.878       43.878       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1243:k=32.6531,b=17.3469      43.878        43.878       42.857       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1244:k=31.6327,b=18.3673      43.878        43.878       42.857       43.878        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1245:k=30.6122,b=19.3878      43.878        43.878       42.857       42.857        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1246:k=29.5918,b=20.4082      43.878        43.878       42.857       42.857        42.857        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1247:k=28.5714,b=21.4286      43.878        43.878       42.857       42.857        41.837        42.857        38.776        37.755        35.714        34.694        31.633       29.592  
    coh1248:k=27.551,b=22.449        43.878        43.878       42.857       42.857        41.837        42.857        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1249:k=26.5306,b=23.4694      43.878        43.878       42.857       42.857        41.837        42.857        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1250:k=25.5102,b=24.4898      43.878        43.878       42.857       42.857        41.837        42.857        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1251:k=24.4898,b=25.5102      43.878        43.878       42.857       42.857        41.837        41.837        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1252:k=23.4694,b=26.5306      42.857        43.878       42.857       42.857        41.837        41.837        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1253:k=22.449,b=27.551        42.857        43.878       42.857       42.857        41.837        41.837        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1254:k=21.4286,b=28.5714      42.857        42.857       42.857       42.857        41.837        41.837        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1255:k=20.4082,b=29.5918      42.857        42.857       41.837       42.857        41.837        41.837        38.776        36.735        35.714        34.694        31.633       29.592  
    coh1256:k=19.3878,b=30.6122      42.857        42.857       41.837       42.857        41.837        41.837        38.776        36.735        35.714        33.673        31.633       29.592  
    coh1257:k=18.3673,b=31.6327      42.857        42.857       41.837       42.857        41.837        41.837        38.776        36.735        35.714        33.673        31.633       29.592  
    coh1258:k=17.3469,b=32.6531      42.857        42.857       41.837       41.837        41.837        41.837        38.776        36.735        35.714        33.673        31.633       29.592  
    coh1259:k=16.3265,b=33.6735      42.857        42.857       41.837       41.837        41.837        41.837        37.755        36.735        35.714        33.673        31.633       29.592  
    coh1260:k=15.3061,b=34.6939      42.857        42.857       41.837       41.837        41.837        41.837        37.755        36.735        35.714        33.673        31.633       29.592  
    coh1261:k=14.2857,b=35.7143      42.857        42.857       41.837       41.837        40.816        41.837        37.755        36.735        35.714        33.673        31.633       29.592  
    coh1262:k=13.2653,b=36.7347      42.857        42.857       41.837       41.837        40.816        41.837        37.755        36.735        35.714        33.673        31.633       29.592  
    coh1263:k=12.2449,b=37.7551      42.857        42.857       41.837       41.837        40.816        41.837        37.755        36.735        35.714        33.673        31.633       29.592  
    coh1264:k=11.2245,b=38.7755      41.837        42.857       41.837       41.837        40.816        40.816        37.755        36.735        34.694        33.673        31.633       29.592  
    coh1265:k=10.2041,b=39.7959      41.837        41.837       41.837       41.837        40.816        40.816        37.755        36.735        34.694        33.673        31.633       29.592  
    coh1266:k=9.18367,b=40.8163      41.837        41.837       41.837       41.837        40.816        40.816        37.755        36.735        34.694        33.673        31.633       29.592  
    coh1267:k=8.16327,b=41.8367      41.837        41.837       40.816       41.837        40.816        40.816        37.755        36.735        34.694        33.673        31.633       29.592  
    coh1268:k=7.14286,b=42.8571      41.837        41.837       40.816       41.837        40.816        40.816        37.755        36.735        34.694        33.673        31.633       29.592  
    coh1269:k=6.12245,b=43.8776      41.837        41.837       40.816       41.837        40.816        40.816        37.755        36.735        34.694        33.673        31.633       29.592  
    coh1270:k=5.10204,b=44.898       41.837        41.837       40.816       40.816        40.816        40.816        37.755        35.714        34.694        33.673        31.633       29.592  
    coh1271:k=4.08163,b=45.9184      41.837        41.837       40.816       40.816        40.816        40.816        37.755        35.714        34.694        33.673        31.633       29.592  
    coh1272:k=3.06122,b=46.9388      41.837        41.837       40.816       40.816        40.816        40.816        37.755        35.714        34.694        33.673        31.633       29.592  
    coh1273:k=2.04082,b=47.9592      41.837        41.837       40.816       40.816        39.796        40.816        37.755        35.714        34.694        33.673        31.633       29.592  
    coh1274:k=1.02041,b=48.9796      41.837        41.837       40.816       40.816        39.796        40.816        37.755        35.714        34.694        33.673        31.633       29.592  
    coh1275:k=0,b=50                 40.816        41.837       40.816       40.816        39.796        40.816        37.755        35.714        34.694        33.673        31.633       29.592  

tb_pol_k: optimal risky investment choice for each state space point
                                   z1_0_34741    z2_0_40076    z3_0_4623    z4_0_5333    z5_0_61519    z6_0_70966    z10_1_2567    z11_1_4496    z12_1_6723    z13_1_9291    z14_2_2253    z15_2_567
                                   __________    __________    _________    _________    __________    __________    __________    __________    __________    __________    __________    _________

    coh1:k=0,b=0                          0             0            0            0             0             0             0             0             0             0             0            0  
    coh2:k=1.02041,b=0               1.0204        1.0204       1.0204       1.0204        1.0204        1.0204        1.0204        1.0204        1.0204        1.0204        1.0204       1.0204  
    coh3:k=0,b=1.02041               1.0204        1.0204       1.0204       1.0204        1.0204        1.0204        2.0408        2.0408        2.0408        2.0408        2.0408       2.0408  
    coh4:k=2.04082,b=0               2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        1.0204        1.0204        1.0204        1.0204        1.0204       1.0204  
    coh5:k=1.02041,b=1.02041         2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        2.0408        2.0408        3.0612        3.0612        3.0612       3.0612  
    coh6:k=0,b=2.04082               2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        2.0408        3.0612        3.0612        3.0612        3.0612       4.0816  
    coh7:k=3.06122,b=0               2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        2.0408        2.0408        2.0408        2.0408        2.0408       2.0408  
    coh8:k=2.04082,b=1.02041         2.0408        2.0408       2.0408       3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        4.0816       4.0816  
    coh9:k=1.02041,b=2.04082         2.0408        2.0408       3.0612       3.0612        3.0612        3.0612        3.0612        3.0612        4.0816        4.0816        4.0816       4.0816  
    coh10:k=0,b=3.06122              2.0408        2.0408       3.0612       3.0612        3.0612        3.0612        3.0612        4.0816        4.0816        4.0816        4.0816        5.102  
    coh11:k=4.08163,b=0              2.0408        2.0408       3.0612       3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        3.0612       3.0612  
    coh12:k=3.06122,b=1.02041        2.0408        2.0408       3.0612       3.0612        3.0612        3.0612        4.0816        4.0816        4.0816        4.0816         5.102        5.102  
    coh13:k=2.04082,b=2.04082        2.0408        2.0408       3.0612       3.0612        3.0612        4.0816        4.0816        4.0816        4.0816         5.102         5.102        5.102  
    coh14:k=1.02041,b=3.06122        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        4.0816        4.0816         5.102         5.102         5.102       6.1224  
    coh15:k=0,b=4.08163              2.0408        2.0408       3.0612       3.0612        3.0612        4.0816        4.0816         5.102         5.102         5.102         5.102       6.1224  
    coh16:k=5.10204,b=0              2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        4.0816        4.0816        4.0816        4.0816        4.0816       4.0816  
    coh17:k=4.08163,b=1.02041        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816         5.102         5.102         5.102         5.102         5.102       6.1224  
    coh18:k=3.06122,b=2.04082        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816         5.102         5.102         5.102        6.1224        6.1224       6.1224  
    coh19:k=2.04082,b=3.06122        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816         5.102         5.102        6.1224        6.1224        6.1224       7.1429  
    coh20:k=1.02041,b=4.08163        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816         5.102         5.102        6.1224        6.1224        6.1224       7.1429  
    coh21:k=0,b=5.10204              2.0408        2.0408       3.0612       3.0612        4.0816        4.0816         5.102         5.102        6.1224        6.1224        7.1429       7.1429  
    coh22:k=6.12245,b=0              2.0408        2.0408       3.0612       3.0612        4.0816         5.102         5.102         5.102         5.102         5.102         5.102       4.0816  
    coh23:k=5.10204,b=1.02041        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        6.1224        6.1224        6.1224        6.1224       7.1429  
    coh24:k=4.08163,b=2.04082        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        6.1224        6.1224        6.1224        7.1429       7.1429  
    coh25:k=3.06122,b=3.06122        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        6.1224        6.1224        7.1429        7.1429       7.1429  
    coh26:k=2.04082,b=4.08163        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        6.1224        7.1429        7.1429        7.1429       8.1633  
    coh27:k=1.02041,b=5.10204        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        6.1224        7.1429        7.1429        7.1429       8.1633  
    coh28:k=0,b=6.12245              2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        6.1224        7.1429        7.1429        8.1633       8.1633  
    coh29:k=7.14286,b=0              2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224         5.102         5.102         5.102         5.102        5.102  
    coh30:k=6.12245,b=1.02041        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        7.1429        7.1429        7.1429        7.1429       7.1429  
    coh31:k=5.10204,b=2.04082        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        7.1429        7.1429        7.1429        7.1429        8.1633       8.1633  
    coh32:k=4.08163,b=3.06122        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        7.1429        7.1429        7.1429        8.1633        8.1633       8.1633  
    coh33:k=3.06122,b=4.08163        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        7.1429        7.1429        7.1429        8.1633        8.1633       9.1837  
    coh34:k=2.04082,b=5.10204        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        7.1429        7.1429        8.1633        8.1633        8.1633       9.1837  
    coh35:k=1.02041,b=6.12245        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        7.1429        7.1429        8.1633        8.1633        8.1633       9.1837  
    coh36:k=0,b=7.14286              2.0408        2.0408       3.0612       3.0612        4.0816         5.102        7.1429        7.1429        8.1633        8.1633        9.1837       9.1837  
    coh37:k=8.16327,b=0              2.0408        2.0408       3.0612       3.0612        4.0816         5.102        6.1224        6.1224        6.1224        6.1224        6.1224       6.1224  
    coh38:k=7.14286,b=1.02041        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        7.1429        8.1633        8.1633        8.1633        8.1633       8.1633  
    coh39:k=6.12245,b=2.04082        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        8.1633        8.1633        8.1633        8.1633        9.1837       9.1837  
    coh40:k=5.10204,b=3.06122        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        8.1633        8.1633        8.1633        8.1633        9.1837       9.1837  
    coh41:k=4.08163,b=4.08163        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        8.1633        8.1633        8.1633        9.1837        9.1837       9.1837  
    coh42:k=3.06122,b=5.10204        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        8.1633        8.1633        8.1633        9.1837        9.1837       10.204  
    coh43:k=2.04082,b=6.12245        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        8.1633        8.1633        9.1837        9.1837        9.1837       10.204  
    coh44:k=1.02041,b=7.14286        2.0408        2.0408       3.0612       3.0612        4.0816         5.102        8.1633        8.1633        9.1837        9.1837        9.1837       10.204  
    coh45:k=0,b=8.16327              2.0408        2.0408       3.0612       3.0612        4.0816         5.102        8.1633        8.1633        9.1837        9.1837        10.204       10.204  
    coh46:k=9.18367,b=0              2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        7.1429        7.1429        7.1429        7.1429        7.1429       7.1429  
    coh47:k=8.16327,b=1.02041        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        8.1633        8.1633        9.1837        9.1837        9.1837       9.1837  
    coh48:k=7.14286,b=2.04082        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        9.1837        9.1837        9.1837        9.1837       10.204  
    coh49:k=6.12245,b=3.06122        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        9.1837        9.1837        9.1837        10.204       10.204  
    coh50:k=5.10204,b=4.08163        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        9.1837        9.1837        10.204        10.204       10.204  
    coh1226:k=50,b=0                 2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       21.429  
    coh1227:k=48.9796,b=1.02041      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       21.429  
    coh1228:k=47.9592,b=2.04082      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       21.429  
    coh1229:k=46.9388,b=3.06122      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       21.429  
    coh1230:k=45.9184,b=4.08163      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1231:k=44.898,b=5.10204       2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1232:k=43.8776,b=6.12245      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1233:k=42.8571,b=7.14286      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1234:k=41.8367,b=8.16327      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1235:k=40.8163,b=9.18367      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1236:k=39.7959,b=10.2041      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1237:k=38.7755,b=11.2245      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1238:k=37.7551,b=12.2449      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1239:k=36.7347,b=13.2653      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1240:k=35.7143,b=14.2857      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1241:k=34.6939,b=15.3061      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1242:k=33.6735,b=16.3265      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1243:k=32.6531,b=17.3469      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1244:k=31.6327,b=18.3673      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1245:k=30.6122,b=19.3878      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1246:k=29.5918,b=20.4082      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1247:k=28.5714,b=21.4286      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1248:k=27.551,b=22.449        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1249:k=26.5306,b=23.4694      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1250:k=25.5102,b=24.4898      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1251:k=24.4898,b=25.5102      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1252:k=23.4694,b=26.5306      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1253:k=22.449,b=27.551        2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1254:k=21.4286,b=28.5714      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1255:k=20.4082,b=29.5918      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1256:k=19.3878,b=30.6122      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1257:k=18.3673,b=31.6327      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1258:k=17.3469,b=32.6531      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1259:k=16.3265,b=33.6735      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1260:k=15.3061,b=34.6939      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1261:k=14.2857,b=35.7143      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1262:k=13.2653,b=36.7347      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1263:k=12.2449,b=37.7551      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1264:k=11.2245,b=38.7755      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1265:k=10.2041,b=39.7959      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1266:k=9.18367,b=40.8163      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1267:k=8.16327,b=41.8367      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1268:k=7.14286,b=42.8571      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1269:k=6.12245,b=43.8776      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1270:k=5.10204,b=44.898       2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1271:k=4.08163,b=45.9184      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1272:k=3.06122,b=46.9388      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1273:k=2.04082,b=47.9592      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1274:k=1.02041,b=48.9796      2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  
    coh1275:k=0,b=50                 2.0408        2.0408       3.0612       3.0612        4.0816        4.0816        9.1837        11.224        13.265        15.306        18.367       20.408  

tb_pol_w: risky + safe investment choices (first stage choice, choose within risky vs safe)
                                   z1_0_34741    z2_0_40076    z3_0_4623    z4_0_5333    z5_0_61519    z6_0_70966    z10_1_2567    z11_1_4496    z12_1_6723    z13_1_9291    z14_2_2253    z15_2_567
                                   __________    __________    _________    _________    __________    __________    __________    __________    __________    __________    __________    _________

    coh1:k=0,b=0                          0             0            0            0             0             0             0             0             0             0             0            0  
    coh2:k=1.02041,b=0               1.0204        1.0204       1.0204       1.0204        1.0204        1.0204        1.0204        1.0204        1.0204        1.0204        1.0204       1.0204  
    coh3:k=0,b=1.02041               1.0204        1.0204       1.0204       1.0204        1.0204        1.0204        2.0408        2.0408        2.0408        2.0408        2.0408       2.0408  
    coh4:k=2.04082,b=0               2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        1.0204        1.0204        1.0204        1.0204        1.0204       1.0204  
    coh5:k=1.02041,b=1.02041         2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        2.0408        2.0408        3.0612        3.0612        3.0612       3.0612  
    coh6:k=0,b=2.04082               2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        2.0408        3.0612        3.0612        3.0612        3.0612       4.0816  
    coh7:k=3.06122,b=0               2.0408        2.0408       2.0408       2.0408        2.0408        2.0408        2.0408        2.0408        2.0408        2.0408        2.0408       2.0408  
    coh8:k=2.04082,b=1.02041         2.0408        2.0408       2.0408       3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        4.0816       4.0816  
    coh9:k=1.02041,b=2.04082         2.0408        2.0408       3.0612       3.0612        3.0612        3.0612        3.0612        3.0612        4.0816        4.0816        4.0816       4.0816  
    coh10:k=0,b=3.06122              2.0408        2.0408       3.0612       3.0612        3.0612        3.0612        3.0612        4.0816        4.0816        4.0816        4.0816        5.102  
    coh11:k=4.08163,b=0              3.0612        3.0612       3.0612       3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        3.0612        3.0612       3.0612  
    coh12:k=3.06122,b=1.02041        3.0612        3.0612       3.0612       3.0612        3.0612        3.0612        4.0816        4.0816        4.0816        4.0816         5.102        5.102  
    coh13:k=2.04082,b=2.04082        3.0612        3.0612       3.0612       3.0612        3.0612        4.0816        4.0816        4.0816        4.0816         5.102         5.102        5.102  
    coh14:k=1.02041,b=3.06122        3.0612        3.0612       3.0612       3.0612        4.0816        4.0816        4.0816        4.0816         5.102         5.102         5.102       6.1224  
    coh15:k=0,b=4.08163              3.0612        3.0612       3.0612       3.0612        3.0612        4.0816        4.0816         5.102         5.102         5.102         5.102       6.1224  
    coh16:k=5.10204,b=0              4.0816        4.0816       4.0816       4.0816        4.0816        4.0816        4.0816        4.0816        4.0816        4.0816        4.0816       4.0816  
    coh17:k=4.08163,b=1.02041        4.0816        4.0816       4.0816       4.0816        4.0816        4.0816         5.102         5.102         5.102         5.102         5.102       6.1224  
    coh18:k=3.06122,b=2.04082        4.0816        4.0816       4.0816       4.0816        4.0816        4.0816         5.102         5.102         5.102        6.1224        6.1224       6.1224  
    coh19:k=2.04082,b=3.06122        4.0816        4.0816       4.0816       4.0816        4.0816        4.0816         5.102         5.102        6.1224        6.1224        6.1224       7.1429  
    coh20:k=1.02041,b=4.08163        4.0816        4.0816       4.0816       4.0816        4.0816        4.0816         5.102         5.102        6.1224        6.1224        6.1224       7.1429  
    coh21:k=0,b=5.10204              4.0816        4.0816       4.0816       4.0816        4.0816        4.0816         5.102         5.102        6.1224        6.1224        7.1429       7.1429  
    coh22:k=6.12245,b=0               5.102         5.102        5.102        5.102         5.102         5.102         5.102         5.102         5.102         5.102         5.102       4.0816  
    coh23:k=5.10204,b=1.02041         5.102         5.102        5.102        5.102         5.102         5.102        6.1224        6.1224        6.1224        6.1224        6.1224       7.1429  
    coh24:k=4.08163,b=2.04082         5.102         5.102        5.102        5.102         5.102         5.102        6.1224        6.1224        6.1224        6.1224        7.1429       7.1429  
    coh25:k=3.06122,b=3.06122         5.102         5.102        5.102        5.102         5.102         5.102        6.1224        6.1224        6.1224        7.1429        7.1429       7.1429  
    coh26:k=2.04082,b=4.08163         5.102         5.102        5.102        5.102         5.102         5.102        6.1224        6.1224        7.1429        7.1429        7.1429       8.1633  
    coh27:k=1.02041,b=5.10204         5.102         5.102        5.102        5.102         5.102         5.102        6.1224        6.1224        7.1429        7.1429        7.1429       8.1633  
    coh28:k=0,b=6.12245               5.102         5.102        5.102        5.102         5.102         5.102        6.1224        6.1224        7.1429        7.1429        8.1633       8.1633  
    coh29:k=7.14286,b=0              6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        6.1224         5.102         5.102         5.102         5.102        5.102  
    coh30:k=6.12245,b=1.02041        6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        6.1224        7.1429        7.1429        7.1429        7.1429       7.1429  
    coh31:k=5.10204,b=2.04082        6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        7.1429        7.1429        7.1429        7.1429        8.1633       8.1633  
    coh32:k=4.08163,b=3.06122        6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        7.1429        7.1429        7.1429        8.1633        8.1633       8.1633  
    coh33:k=3.06122,b=4.08163        6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        7.1429        7.1429        7.1429        8.1633        8.1633       9.1837  
    coh34:k=2.04082,b=5.10204        6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        7.1429        7.1429        8.1633        8.1633        8.1633       9.1837  
    coh35:k=1.02041,b=6.12245        6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        7.1429        7.1429        8.1633        8.1633        8.1633       9.1837  
    coh36:k=0,b=7.14286              6.1224        6.1224       6.1224       6.1224        6.1224        6.1224        7.1429        7.1429        8.1633        8.1633        9.1837       9.1837  
    coh37:k=8.16327,b=0              7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        6.1224        6.1224        6.1224        6.1224        6.1224       6.1224  
    coh38:k=7.14286,b=1.02041        7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        7.1429        8.1633        8.1633        8.1633        8.1633       8.1633  
    coh39:k=6.12245,b=2.04082        7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        8.1633        8.1633        8.1633        8.1633        9.1837       9.1837  
    coh40:k=5.10204,b=3.06122        7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        8.1633        8.1633        8.1633        8.1633        9.1837       9.1837  
    coh41:k=4.08163,b=4.08163        7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        8.1633        8.1633        8.1633        9.1837        9.1837       9.1837  
    coh42:k=3.06122,b=5.10204        7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        8.1633        8.1633        8.1633        9.1837        9.1837       10.204  
    coh43:k=2.04082,b=6.12245        7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        8.1633        8.1633        9.1837        9.1837        9.1837       10.204  
    coh44:k=1.02041,b=7.14286        7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        8.1633        8.1633        9.1837        9.1837        9.1837       10.204  
    coh45:k=0,b=8.16327              7.1429        7.1429       7.1429       7.1429        7.1429        7.1429        8.1633        8.1633        9.1837        9.1837        10.204       10.204  
    coh46:k=9.18367,b=0              8.1633        8.1633       8.1633       8.1633        8.1633        8.1633        7.1429        7.1429        7.1429        7.1429        7.1429       7.1429  
    coh47:k=8.16327,b=1.02041        8.1633        8.1633       8.1633       8.1633        8.1633        8.1633        8.1633        8.1633        9.1837        9.1837        9.1837       9.1837  
    coh48:k=7.14286,b=2.04082        8.1633        8.1633       8.1633       8.1633        8.1633        8.1633        9.1837        9.1837        9.1837        9.1837        9.1837       10.204  
    coh49:k=6.12245,b=3.06122        8.1633        8.1633       8.1633       8.1633        8.1633        8.1633        9.1837        9.1837        9.1837        9.1837        10.204       10.204  
    coh50:k=5.10204,b=4.08163        8.1633        8.1633       8.1633       8.1633        8.1633        8.1633        9.1837        9.1837        9.1837        10.204        10.204       10.204  
    coh1226:k=50,b=0                 46.939        46.939       46.939       46.939        46.939        46.939        46.939        46.939        45.918        45.918        45.918       45.918  
    coh1227:k=48.9796,b=1.02041      46.939        46.939       46.939       46.939        46.939        46.939        47.959        47.959        47.959        47.959        47.959       47.959  
    coh1228:k=47.9592,b=2.04082      46.939        46.939       46.939       46.939        46.939        46.939        47.959        47.959        47.959        47.959         48.98        48.98  
    coh1229:k=46.9388,b=3.06122      46.939        46.939       46.939       46.939        46.939        46.939        47.959        47.959        47.959         48.98         48.98        48.98  
    coh1230:k=45.9184,b=4.08163      46.939        46.939       46.939       46.939        46.939        46.939        47.959        47.959         48.98         48.98         48.98           50  
    coh1231:k=44.898,b=5.10204       46.939        46.939       46.939       46.939        46.939        46.939        47.959        47.959         48.98         48.98         48.98           50  
    coh1232:k=43.8776,b=6.12245      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98         48.98            50           50  
    coh1233:k=42.8571,b=7.14286      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98         48.98            50           50  
    coh1234:k=41.8367,b=8.16327      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98         48.98            50           50  
    coh1235:k=40.8163,b=9.18367      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98         48.98            50           50  
    coh1236:k=39.7959,b=10.2041      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98         48.98            50           50  
    coh1237:k=38.7755,b=11.2245      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1238:k=37.7551,b=12.2449      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1239:k=36.7347,b=13.2653      46.939        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1240:k=35.7143,b=14.2857      45.918        46.939       46.939       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1241:k=34.6939,b=15.3061      45.918        45.918       46.939       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1242:k=33.6735,b=16.3265      45.918        45.918       46.939       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1243:k=32.6531,b=17.3469      45.918        45.918       45.918       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1244:k=31.6327,b=18.3673      45.918        45.918       45.918       46.939        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1245:k=30.6122,b=19.3878      45.918        45.918       45.918       45.918        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1246:k=29.5918,b=20.4082      45.918        45.918       45.918       45.918        46.939        46.939        47.959         48.98         48.98            50            50           50  
    coh1247:k=28.5714,b=21.4286      45.918        45.918       45.918       45.918        45.918        46.939        47.959         48.98         48.98            50            50           50  
    coh1248:k=27.551,b=22.449        45.918        45.918       45.918       45.918        45.918        46.939        47.959        47.959         48.98            50            50           50  
    coh1249:k=26.5306,b=23.4694      45.918        45.918       45.918       45.918        45.918        46.939        47.959        47.959         48.98            50            50           50  
    coh1250:k=25.5102,b=24.4898      45.918        45.918       45.918       45.918        45.918        46.939        47.959        47.959         48.98            50            50           50  
    coh1251:k=24.4898,b=25.5102      45.918        45.918       45.918       45.918        45.918        45.918        47.959        47.959         48.98            50            50           50  
    coh1252:k=23.4694,b=26.5306      44.898        45.918       45.918       45.918        45.918        45.918        47.959        47.959         48.98            50            50           50  
    coh1253:k=22.449,b=27.551        44.898        45.918       45.918       45.918        45.918        45.918        47.959        47.959         48.98            50            50           50  
    coh1254:k=21.4286,b=28.5714      44.898        44.898       45.918       45.918        45.918        45.918        47.959        47.959         48.98            50            50           50  
    coh1255:k=20.4082,b=29.5918      44.898        44.898       44.898       45.918        45.918        45.918        47.959        47.959         48.98            50            50           50  
    coh1256:k=19.3878,b=30.6122      44.898        44.898       44.898       45.918        45.918        45.918        47.959        47.959         48.98         48.98            50           50  
    coh1257:k=18.3673,b=31.6327      44.898        44.898       44.898       45.918        45.918        45.918        47.959        47.959         48.98         48.98            50           50  
    coh1258:k=17.3469,b=32.6531      44.898        44.898       44.898       44.898        45.918        45.918        47.959        47.959         48.98         48.98            50           50  
    coh1259:k=16.3265,b=33.6735      44.898        44.898       44.898       44.898        45.918        45.918        46.939        47.959         48.98         48.98            50           50  
    coh1260:k=15.3061,b=34.6939      44.898        44.898       44.898       44.898        45.918        45.918        46.939        47.959         48.98         48.98            50           50  
    coh1261:k=14.2857,b=35.7143      44.898        44.898       44.898       44.898        44.898        45.918        46.939        47.959         48.98         48.98            50           50  
    coh1262:k=13.2653,b=36.7347      44.898        44.898       44.898       44.898        44.898        45.918        46.939        47.959         48.98         48.98            50           50  
    coh1263:k=12.2449,b=37.7551      44.898        44.898       44.898       44.898        44.898        45.918        46.939        47.959         48.98         48.98            50           50  
    coh1264:k=11.2245,b=38.7755      43.878        44.898       44.898       44.898        44.898        44.898        46.939        47.959        47.959         48.98            50           50  
    coh1265:k=10.2041,b=39.7959      43.878        43.878       44.898       44.898        44.898        44.898        46.939        47.959        47.959         48.98            50           50  
    coh1266:k=9.18367,b=40.8163      43.878        43.878       44.898       44.898        44.898        44.898        46.939        47.959        47.959         48.98            50           50  
    coh1267:k=8.16327,b=41.8367      43.878        43.878       43.878       44.898        44.898        44.898        46.939        47.959        47.959         48.98            50           50  
    coh1268:k=7.14286,b=42.8571      43.878        43.878       43.878       44.898        44.898        44.898        46.939        47.959        47.959         48.98            50           50  
    coh1269:k=6.12245,b=43.8776      43.878        43.878       43.878       44.898        44.898        44.898        46.939        47.959        47.959         48.98            50           50  
    coh1270:k=5.10204,b=44.898       43.878        43.878       43.878       43.878        44.898        44.898        46.939        46.939        47.959         48.98            50           50  
    coh1271:k=4.08163,b=45.9184      43.878        43.878       43.878       43.878        44.898        44.898        46.939        46.939        47.959         48.98            50           50  
    coh1272:k=3.06122,b=46.9388      43.878        43.878       43.878       43.878        44.898        44.898        46.939        46.939        47.959         48.98            50           50  
    coh1273:k=2.04082,b=47.9592      43.878        43.878       43.878       43.878        43.878        44.898        46.939        46.939        47.959         48.98            50           50  
    coh1274:k=1.02041,b=48.9796      43.878        43.878       43.878       43.878        43.878        44.898        46.939        46.939        47.959         48.98            50           50  
    coh1275:k=0,b=50                 42.857        43.878       43.878       43.878        43.878        44.898        46.939        46.939        47.959         48.98            50           50  

end
ans = 

  Map with properties:

        Count: 15
      KeyType: char
    ValueType: any