Generate States/Choices/Shocks Grids, get Functions (Interpolated + Percentage + Risky + Safe Asset + Save + Borrow)

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Contents

function [armt_map, func_map] = ffs_ipwkbz_get_funcgrid(varargin)

FFS_IPWKBZ_GET_FUNCGRID get funcs, params, states choices shocks grids

centralized gateway for retrieving parameters, and solution grids and functions. Similar to ffs_akz_get_funcgrid function. This code deals with problems with savings and borrowing.

The graphs below show the difference between percentage choice grid and level choice grid. See comments by graphs below for explanations of differences between the choice grids here and choice grids in the ffs_akz_get_funcgrid function.

Note that for borrowing, we can not start at the min(coh(k,w-k,z)) reacheable given the w and k choice grids. That would be: min(coh(k,w-k,z)) < min(w). At min(coh), there is a single point, and also for all values between min(coh) and min(w), all percentage w_perc choices are below min(w), requiring extrapolation. It is in some sense safer to extrapolate by starting solution at min(coh) = min(w). Now, for the lowest levels of coh(k, w-k, z), which are < min(w), we now require extrapolation. But this extrapolation is straight forward, when coh < min(w), households have to default, the utility from default is the same regardless of the level of coh at the time of default. So nearest extrapolation is fully correct.

Note that the first stage w grid is based on cash-on-hand level reached by the coh(k,w-k,z) possible choice and shock combinations. This coh(k,w-k,z) > max(w), which also means that at max(coh) grid, the w_perc choices at higher points require extrapolation. Extrapolation is based on nearest extrapolation.

Note that even when w = 0, as long as interest rate is low, only the lowest level of borrowing is invalid.

@param param_map container parameter container

@param support_map container support container

@param bl_input_override boolean if true varargin contained param_map and support_map fully overrides local default. Local default is not invoked. This could be important for speed if this function is getting invoked within certain loops. Default is 0.

@return armt_map container container with states, choices and shocks grids that are inputs for grid based solution algorithm

@return func_map container container with function handles for consumption cash-on-hand etc.

@example

  it_param_set = 2;
  bl_input_override = true;
  [param_map, support_map] = ffs_ipwkbz_set_default_param(it_param_set);
  [armt_map, func_map] = ffs_ipwkbz_get_funcgrid(param_map, support_map, bl_input_override);

@include

Default

if (~isempty(varargin))

    % override when called from outside
    [param_map, support_map] = varargin{:};

else
    % default internal run
    [param_map, support_map] = ffs_ipwkbz_set_default_param();
    support_map('bl_graph_funcgrids') = true;
    support_map('bl_graph_funcgrids_detail') = true;
    support_map('bl_display_funcgrids') = true;

    % to be able to visually see choice grid points
    param_map('fl_b_bd') = -20; % borrow bound, = 0 if save only
    param_map('fl_default_aprime') = 0;
    param_map('bl_default') = 0; % if borrowing is default allowed

    param_map('fl_w_min') = param_map('fl_b_bd');
    param_map('it_w_perc_n') = 25;
    param_map('it_ak_perc_n') = 45;
    param_map('fl_w_interp_grid_gap') = 2;
    param_map('fl_coh_interp_grid_gap') = 2;

    default_maps = {param_map, support_map};

    % numvarargs is the number of varagin inputted
    [default_maps{1:length(varargin)}] = varargin{:};
    param_map = [param_map; default_maps{1}];
    support_map = [support_map; default_maps{2}];
end
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Display Parameters Specific to IPWKBZR
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Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
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  Map with properties:

        Count: 9
      KeyType: char
    ValueType: any

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pos = 1 ; key = bl_default ; val = true
pos = 2 ; key = fl_b_bd ; val = -20
pos = 3 ; key = fl_c_min ; val = 0.02
pos = 4 ; key = fl_default_wprime ; val = 0
pos = 5 ; key = fl_k_max ; val = 70
pos = 6 ; key = fl_w_max ; val = 50
pos = 7 ; key = fl_w_min ; val = -20
pos = 8 ; key = st_model ; val = ipwkbz
pos = 9 ; key = st_v_coh_z_interp_method ; val = method_cell
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Scalars in Container and Sizes and Basic Statistics
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                         i    idx    value
                         _    ___    _____

    bl_default           1     1        1 
    fl_b_bd              2     2      -20 
    fl_c_min             3     3     0.02 
    fl_default_wprime    4     4        0 
    fl_k_max             5     5       70 
    fl_w_max             6     6       50 
    fl_w_min             7     7      -20 

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

    st_model                    1     8 
    st_v_coh_z_interp_method    2     9 

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Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
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  Map with properties:

        Count: 5
      KeyType: char
    ValueType: any

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pos = 1 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/img/
pos = 2 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/mat/
pos = 3 ; key = st_mat_test_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//test/ff_ipwkbz_ds_vecsv/mat/
pos = 4 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr/
pos = 5 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/profile/
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Strings in Container and Sizes and Basic Statistics
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                           i    idx
                           _    ___

    st_img_path            1     1 
    st_mat_path            2     2 
    st_mat_test_path       3     3 
    st_matimg_path_root    4     4 
    st_profile_path        5     5 

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Display All Parameters with IPWKBZR overriding IPWKBZR
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Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
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  Map with properties:

        Count: 35
      KeyType: char
    ValueType: any

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pos = 1 ; key = bl_default ; val = true
pos = 2 ; key = fl_Amean ; val = 1
pos = 3 ; key = fl_alpha ; val = 0.36
pos = 4 ; key = fl_b_bd ; val = -20
pos = 5 ; key = fl_beta ; val = 0.94
pos = 6 ; key = fl_c_min ; val = 0.02
pos = 7 ; key = fl_coh_interp_grid_gap ; val = 0.1
pos = 8 ; key = fl_crra ; val = 1.5
pos = 9 ; key = fl_default_wprime ; val = 0
pos = 10 ; key = fl_delta ; val = 0.08
pos = 11 ; key = fl_k_max ; val = 70
pos = 12 ; key = fl_k_min ; val = 0
pos = 13 ; key = fl_nan_replace ; val = -9999
pos = 14 ; key = fl_r_borr ; val = 0.095
pos = 15 ; key = fl_r_save ; val = 0.025
pos = 16 ; key = fl_tol_dist ; val = 1e-05
pos = 17 ; key = fl_tol_pol ; val = 1e-05
pos = 18 ; key = fl_tol_val ; val = 1e-05
pos = 19 ; key = fl_w ; val = 0.44365
pos = 20 ; key = fl_w_interp_grid_gap ; val = 0.1
pos = 21 ; key = fl_w_max ; val = 50
pos = 22 ; key = fl_w_min ; val = -20
pos = 23 ; key = fl_z_mu ; val = 0
pos = 24 ; key = fl_z_rho ; val = 0.8
pos = 25 ; key = fl_z_sig ; val = 0.2
pos = 26 ; key = it_ak_perc_n ; val = 50
pos = 27 ; key = it_c_interp_grid_gap ; val = 0.0001
pos = 28 ; key = it_maxiter_dist ; val = 1000
pos = 29 ; key = it_maxiter_val ; val = 250
pos = 30 ; key = it_tol_pol_nochange ; val = 25
pos = 31 ; key = it_w_perc_n ; val = 50
pos = 32 ; key = it_z_n ; val = 15
pos = 33 ; key = st_analytical_stationary_type ; val = eigenvector
pos = 34 ; key = st_model ; val = ipwkbz
pos = 35 ; key = st_v_coh_z_interp_method ; val = method_cell
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Scalars in Container and Sizes and Basic Statistics
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                              i     idx     value 
                              __    ___    _______

    bl_default                 1     1           1
    fl_Amean                   2     2           1
    fl_alpha                   3     3        0.36
    fl_b_bd                    4     4         -20
    fl_beta                    5     5        0.94
    fl_c_min                   6     6        0.02
    fl_coh_interp_grid_gap     7     7         0.1
    fl_crra                    8     8         1.5
    fl_default_wprime          9     9           0
    fl_delta                  10    10        0.08
    fl_k_max                  11    11          70
    fl_k_min                  12    12           0
    fl_nan_replace            13    13       -9999
    fl_r_borr                 14    14       0.095
    fl_r_save                 15    15       0.025
    fl_tol_dist               16    16       1e-05
    fl_tol_pol                17    17       1e-05
    fl_tol_val                18    18       1e-05
    fl_w                      19    19     0.44365
    fl_w_interp_grid_gap      20    20         0.1
    fl_w_max                  21    21          50
    fl_w_min                  22    22         -20
    fl_z_mu                   23    23           0
    fl_z_rho                  24    24         0.8
    fl_z_sig                  25    25         0.2
    it_ak_perc_n              26    26          50
    it_c_interp_grid_gap      27    27      0.0001
    it_maxiter_dist           28    28        1000
    it_maxiter_val            29    29         250
    it_tol_pol_nochange       30    30          25
    it_w_perc_n               31    31          50
    it_z_n                    32    32          15

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

    st_analytical_stationary_type    1    33 
    st_model                         2    34 
    st_v_coh_z_interp_method         3    35 

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Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
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  Map with properties:

        Count: 43
      KeyType: char
    ValueType: any

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pos = 1 ; key = bl_display ; val = false
pos = 2 ; key = bl_display_defparam ; val = true
pos = 3 ; key = bl_display_dist ; val = false
pos = 4 ; key = bl_display_evf ; val = false
pos = 5 ; key = bl_display_final ; val = true
pos = 6 ; key = bl_display_final_dist ; val = false
pos = 7 ; key = bl_display_final_dist_detail ; val = false
pos = 8 ; key = bl_display_funcgrids ; val = false
pos = 9 ; key = bl_graph ; val = true
pos = 10 ; key = bl_graph_coh_t_coh ; val = true
pos = 11 ; key = bl_graph_evf ; val = false
pos = 12 ; key = bl_graph_funcgrids ; val = false
pos = 13 ; key = bl_graph_funcgrids_detail ; val = false
pos = 14 ; key = bl_graph_onebyones ; val = true
pos = 15 ; key = bl_graph_pol_lvl ; val = true
pos = 16 ; key = bl_graph_pol_pct ; val = true
pos = 17 ; key = bl_graph_val ; val = true
pos = 18 ; key = bl_img_save ; val = false
pos = 19 ; key = bl_mat ; val = false
pos = 20 ; key = bl_post ; val = true
pos = 21 ; key = bl_profile ; val = false
pos = 22 ; key = bl_profile_dist ; val = false
pos = 23 ; key = bl_time ; val = false
pos = 24 ; key = it_display_every ; val = 5
pos = 25 ; key = it_display_final_colmax ; val = 12
pos = 26 ; key = it_display_final_rowmax ; val = 100
pos = 27 ; key = it_display_summmat_colmax ; val = 7
pos = 28 ; key = it_display_summmat_rowmax ; val = 7
pos = 29 ; key = st_img_name_main ; val = _default
pos = 30 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/img/
pos = 31 ; key = st_img_prefix ; val = 
pos = 32 ; key = st_img_suffix ; val = _p4.png
pos = 33 ; key = st_mat_name_main ; val = _default
pos = 34 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/mat/
pos = 35 ; key = st_mat_prefix ; val = 
pos = 36 ; key = st_mat_suffix ; val = _p4
pos = 37 ; key = st_mat_test_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//test/ff_ipwkbz_ds_vecsv/mat/
pos = 38 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr/
pos = 39 ; key = st_profile_name_main ; val = _default
pos = 40 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/profile/
pos = 41 ; key = st_profile_prefix ; val = 
pos = 42 ; key = st_profile_suffix ; val = _p4
pos = 43 ; key = st_title_prefix ; val = 
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Scalars in Container and Sizes and Basic Statistics
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                                    i     idx    value
                                    __    ___    _____

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

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

    st_img_name_main         1    29 
    st_img_path              2    30 
    st_img_prefix            3    31 
    st_img_suffix            4    32 
    st_mat_name_main         5    33 
    st_mat_path              6    34 
    st_mat_prefix            7    35 
    st_mat_suffix            8    36 
    st_mat_test_path         9    37 
    st_matimg_path_root     10    38 
    st_profile_name_main    11    39 
    st_profile_path         12    40 
    st_profile_prefix       13    41 
    st_profile_suffix       14    42 
    st_title_prefix         15    43 

Parse Parameters

params_group = values(param_map, {'it_z_n', 'fl_z_mu', 'fl_z_rho', 'fl_z_sig'});
[it_z_n, fl_z_mu, fl_z_rho, fl_z_sig] = params_group{:};

params_group = values(param_map, {'bl_default', 'fl_b_bd', 'fl_w_min', 'fl_w_max', ...
    'it_w_perc_n', 'fl_w_interp_grid_gap', 'fl_coh_interp_grid_gap'});
[bl_default, fl_b_bd, fl_w_min, fl_w_max, ...
    it_w_perc_n, fl_w_interp_grid_gap, fl_coh_interp_grid_gap] = params_group{:};

params_group = values(param_map, {'fl_k_min', 'fl_k_max', 'it_ak_perc_n'});
[fl_k_min, fl_k_max, it_ak_perc_n] = params_group{:};

params_group = values(param_map, {'fl_crra', 'fl_c_min', 'it_c_interp_grid_gap'});
[fl_crra, fl_c_min, it_c_interp_grid_gap] = params_group{:};

params_group = values(param_map, {'fl_Amean', 'fl_alpha', 'fl_delta'});
[fl_Amean, fl_alpha, fl_delta] = params_group{:};

params_group = values(param_map, {'fl_r_save', 'fl_r_borr', 'fl_w'});
[fl_r_save, fl_r_borr, fl_w] = params_group{:};

params_group = values(support_map, {'bl_graph_funcgrids', 'bl_graph_funcgrids_detail', 'bl_display_funcgrids'});
[bl_graph_funcgrids, bl_graph_funcgrids_detail, bl_display_funcgrids] = params_group{:};
params_group = values(support_map, {'it_display_summmat_rowmax', 'it_display_summmat_colmax'});
[it_display_summmat_rowmax, it_display_summmat_colmax] = params_group{:};

Generate Asset and Choice Grid for 2nd stage Problem

This generate triangular choice structure. Household choose total aggregate savings, and within that how much to put into risky capital and how much to put into safe assets, in percentages. See ffs_ipwkbz_set_default_param for details.

if (~bl_default)
    fl_w_min_use = max(fl_w_min, -(fl_w)/fl_r_borr);
    fl_b_bd = fl_w_min_use;
else
    fl_w_min_use = fl_w_min;
end

% percentage grid for 1st stage choice problem, level grid for 2nd stage
% solving optimal k given w and z.
ar_w_perc = linspace(0, 1, it_w_perc_n);
it_w_interp_n = (fl_w_max-fl_w_min_use)/(fl_w_interp_grid_gap);
ar_w_level_full = fft_array_add_zero(linspace(fl_w_min_use, fl_w_max, it_w_interp_n), true);
ar_w_level = ar_w_level_full;
it_w_interp_n = length(ar_w_level_full);

% max k given w, need to consider the possibility of borrowing.
ar_k_max = ar_w_level_full - fl_b_bd;

% k percentage choice grid
ar_ak_perc = linspace(0, 1, it_ak_perc_n);

% 2nd stage percentage choice matrixes
% (ar_k_max') is it_w_interp_n by 1, and (ar_ak_perc) is 1 by it_ak_perc_n
% mt_k is a it_w_interp_n by it_ak_perc_n matrix of choice points of k'
% conditional on w, each column is a different w, each row for each col a
% different k' value.
mt_k = (ar_k_max'*ar_ak_perc)';
mt_a = (ar_w_level_full - mt_k);

% can not have choice that are beyond feasible bound given the percentage
% structure here.
mt_bl_constrained = (mt_a < fl_b_bd);
if (sum(mt_bl_constrained) > 0 )
    error('at %s second stage choice points, percentage choice exceed bounds, can not happen',...
        num2str(sum(mt_bl_constrained)));
end

ar_a_meshk_full = mt_a(:);
ar_k_mesha_full = mt_k(:);

ar_a_meshk = ar_a_meshk_full;
ar_k_mesha = ar_k_mesha_full;

Get Shock Grids

[~, mt_z_trans, ar_stationary, ar_z] = ffto_gen_tauchen_jhl(fl_z_mu,fl_z_rho,fl_z_sig,it_z_n);

Get Equations

[f_util_log, f_util_crra, f_util_standin, f_prod, f_inc, f_coh, f_cons] = ...
    ffs_ipwkbz_set_functions(fl_crra, fl_c_min, fl_b_bd, fl_Amean, fl_alpha, fl_delta, fl_r_save, fl_r_borr, fl_w);

Generate Cash-on-Hand/State Matrix

The endogenous state variable is cash-on-hand, it has it_z_n*it_a_n number of points, covering all reachable points when ar_a is the choice vector and ar_z is the shock vector. requires inputs from get Asset and choice grids, get shock grids, and get equations above.

mt_coh_wkb_full = f_coh(ar_z, ar_a_meshk_full, ar_k_mesha_full);

if (bl_display_funcgrids)

    % Generate Aggregate Variables
    ar_aplusk_mesh = ar_a_meshk_full + ar_k_mesha_full;

    % Genereate Table
    tab_ak_choices = array2table([ar_aplusk_mesh, ar_k_mesha_full, ar_a_meshk_full]);
    cl_col_names = {'ar_aplusk_mesh', 'ar_k_mesha_full', 'ar_a_meshk_full'};
    tab_ak_choices.Properties.VariableNames = cl_col_names;

    % Label Table Variables
    tab_ak_choices.Properties.VariableDescriptions{'ar_aplusk_mesh'} = ...
        '*ar_aplusk_mesha*: ar_aplusk_mesha = ar_a_meshk_full + ar_k_mesha_full;';
    tab_ak_choices.Properties.VariableDescriptions{'ar_a_meshk_full'} = ...
        '*ar_a_meshk_full*:';
    tab_ak_choices.Properties.VariableDescriptions{'ar_k_mesha_full'} = ...
        '*ar_k_mesha_full*:';

    cl_var_desc = tab_ak_choices.Properties.VariableDescriptions;
    for it_var_name = 1:length(cl_var_desc)
        disp(cl_var_desc{it_var_name});
    end

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('tab_ak_choices');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    it_rows_toshow = length(ar_w_level)*2;
    disp(size(tab_ak_choices));
    disp(head(array2table(tab_ak_choices), it_rows_toshow));
    disp(tail(array2table(tab_ak_choices), it_rows_toshow));


    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_coh_wkb_full');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_coh_wkb_full));
    disp(head(array2table(mt_coh_wkb_full), it_rows_toshow));
    disp(tail(array2table(mt_coh_wkb_full), it_rows_toshow));

end
*ar_aplusk_mesha*: ar_aplusk_mesha = ar_a_meshk_full + ar_k_mesha_full;
*ar_k_mesha_full*:
*ar_a_meshk_full*:
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tab_ak_choices
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        1215           3

    tab_ak_choices1    tab_ak_choices2    tab_ak_choices3
    ar_aplusk_mesh     ar_k_mesha_full    ar_a_meshk_full
    _______________    _______________    _______________

         -4.67                  0               -4.67    
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         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
       -2.4832                  0             -2.4832    
       -2.4832             0.0497             -2.5329    
       -2.4832             0.0994             -2.5826    
       -2.4832             0.1491             -2.6323    
       -2.4832             0.1988              -2.682    
       -2.4832             0.2485             -2.7317    
       -2.4832             0.2982             -2.7814    
       -2.4832             0.3479             -2.8311    
       -2.4832             0.3976             -2.8808    

    tab_ak_choices1    tab_ak_choices2    tab_ak_choices3
    ar_aplusk_mesh     ar_k_mesha_full    ar_a_meshk_full
    _______________    _______________    _______________

        47.813             42.941              4.8724    
        47.813             44.134              3.6796    
        47.813             45.326              2.4868    
        47.813             46.519               1.294    
        47.813             47.712             0.10122    
        47.813             48.905             -1.0916    
        47.813             50.098             -2.2844    
        47.813              51.29             -3.4772    
        47.813             52.483               -4.67    
            50                  0                  50    
            50             1.2425              48.758    
            50              2.485              47.515    
            50             3.7275              46.273    
            50               4.97               45.03    
            50             6.2125              43.788    
            50              7.455              42.545    
            50             8.6975              41.303    
            50               9.94               40.06    
            50             11.182              38.818    
            50             12.425              37.575    
            50             13.667              36.333    
            50              14.91               35.09    
            50             16.152              33.848    
            50             17.395              32.605    
            50             18.637              31.363    
            50              19.88               30.12    
            50             21.122              28.878    
            50             22.365              27.635    
            50             23.607              26.393    
            50              24.85               25.15    
            50             26.092              23.908    
            50             27.335              22.665    
            50             28.577              21.423    
            50              29.82               20.18    
            50             31.062              18.938    
            50             32.305              17.695    
            50             33.547              16.453    
            50              34.79               15.21    
            50             36.032              13.968    
            50             37.275              12.725    
            50             38.517              11.483    
            50              39.76               10.24    
            50             41.002              8.9975    
            50             42.245               7.755    
            50             43.487              6.5125    
            50              44.73                5.27    
            50             45.972              4.0275    
            50             47.215               2.785    
            50             48.457              1.5425    
            50               49.7             0.30002    
            50             50.942            -0.94248    
            50             52.185              -2.185    
            50             53.427             -3.4275    
            50              54.67               -4.67    

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_coh_wkb_full
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        1215          15

    mt_coh_wkb_full1    mt_coh_wkb_full2    mt_coh_wkb_full3    mt_coh_wkb_full4    mt_coh_wkb_full5    mt_coh_wkb_full6    mt_coh_wkb_full7    mt_coh_wkb_full8    mt_coh_wkb_full9    mt_coh_wkb_full10    mt_coh_wkb_full11    mt_coh_wkb_full12    mt_coh_wkb_full13    mt_coh_wkb_full14    mt_coh_wkb_full15
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________    _________________    _________________    _________________    _________________

          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67                -4.67                -4.67                -4.67                -4.67     
        -2.2754             -2.2754             -2.2754             -2.2754             -2.2754             -2.2754             -2.2754             -2.2754             -2.2754              -2.2754              -2.2754              -2.2754              -2.2754              -2.2754              -2.2754     
        -2.1662             -2.1481             -2.1272             -2.1031             -2.0753             -2.0433             -2.0063             -1.9636             -1.9144              -1.8576              -1.7921              -1.7166              -1.6294              -1.5289              -1.4129     
        -2.1415             -2.1183             -2.0915             -2.0605             -2.0249             -1.9837             -1.9363             -1.8815             -1.8183              -1.7455              -1.6614              -1.5644              -1.4526              -1.3236              -1.1747     
        -2.1264             -2.0995             -2.0685             -2.0327             -1.9915             -1.9438             -1.8889             -1.8255             -1.7525              -1.6681              -1.5709              -1.4587              -1.3292              -1.1799              -1.0077     
         -2.116             -2.0862             -2.0518             -2.0121             -1.9663             -1.9135             -1.8526             -1.7823             -1.7012              -1.6077              -1.4998              -1.3754              -1.2318              -1.0662              -0.8752     
        -2.1085             -2.0761             -2.0389             -1.9959             -1.9462              -1.889              -1.823             -1.7468              -1.659              -1.5577              -1.4407              -1.3059              -1.1503             -0.97087             -0.76386     
        -2.1029             -2.0684             -2.0286             -1.9826             -1.9297             -1.8686             -1.7981             -1.7167             -1.6229              -1.5147              -1.3899              -1.2459              -1.0798             -0.88812             -0.66706     
        -2.0988             -2.0623             -2.0202             -1.9717             -1.9157             -1.8511             -1.7765             -1.6906             -1.5914               -1.477              -1.3451              -1.1928              -1.0172             -0.81468             -0.58101     
        -2.0958             -2.0575             -2.0133             -1.9624             -1.9036             -1.8359             -1.7577             -1.6675             -1.5634              -1.4434              -1.3049              -1.1452             -0.96098             -0.74844             -0.50326     

    mt_coh_wkb_full1    mt_coh_wkb_full2    mt_coh_wkb_full3    mt_coh_wkb_full4    mt_coh_wkb_full5    mt_coh_wkb_full6    mt_coh_wkb_full7    mt_coh_wkb_full8    mt_coh_wkb_full9    mt_coh_wkb_full10    mt_coh_wkb_full11    mt_coh_wkb_full12    mt_coh_wkb_full13    mt_coh_wkb_full14    mt_coh_wkb_full15
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________    _________________    _________________    _________________    _________________

         46.288              46.495              46.733              47.008              47.325              47.691              48.112              48.599               49.16              49.808               50.555               51.417               52.411               53.558               54.881      
         46.176              46.385              46.626              46.903              47.223              47.593              48.019               48.51              49.077              49.731               50.485               51.356                52.36               53.518               54.854      
         46.064              46.275              46.518              46.798              47.121              47.494              47.924               48.42              48.993              49.653               50.415               51.294               52.307               53.477               54.825      
         45.952              46.164               46.41              46.692              47.019              47.395              47.829               48.33              48.908              49.575               50.343                51.23               52.254               53.434               54.795      
         45.839              46.054              46.301              46.587              46.916              47.296              47.734              48.239              48.823              49.495               50.271               51.166               52.199                53.39               54.764      
          45.65              45.867              46.116              46.404              46.736               47.12              47.562              48.072               48.66              49.339               50.121               51.025               52.066               53.268               54.654      
         45.454              45.672              45.924              46.214              46.549              46.936              47.382              47.896               48.49              49.174               49.964               50.875               51.926               53.138               54.536      
         45.257              45.477              45.731              46.024              46.362              46.752              47.202               47.72              48.319              49.009               49.806               50.724               51.784               53.007               54.417      
          45.06              45.282              45.538              45.834              46.174              46.568              47.021              47.544              48.148              48.844               49.647               50.573               51.642               52.874               54.296      
         51.694              51.694              51.694              51.694              51.694              51.694              51.694              51.694              51.694              51.694               51.694               51.694               51.694               51.694               51.694      
         51.939              51.997              52.063               52.14              52.228              52.331              52.448              52.584              52.741              52.922               53.131               53.371               53.649               53.969               54.339      
         51.915              51.989              52.074              52.173              52.286              52.418              52.569              52.743              52.945              53.177               53.444               53.753                54.11               54.521               54.995      
          51.86              51.946              52.045              52.159               52.29              52.442              52.617              52.819              53.052               53.32                53.63               53.988                 54.4               54.876               55.425      
         51.791              51.886              51.995              52.122              52.268              52.436               52.63              52.854              53.112               53.41               53.754                54.15               54.608               55.135               55.744      
         51.712              51.815              51.934              52.071              52.229              52.411              52.621              52.864              53.144              53.467               53.839               54.269               54.765               55.336               55.996      
         51.627              51.737              51.864               52.01              52.179              52.373              52.598              52.857              53.156              53.501               53.899               54.357               54.887               55.497               56.202      
         51.537              51.654              51.788              51.942              52.121              52.326              52.564              52.838              53.154              53.518               53.939               54.424               54.983               55.628               56.373      
         51.444              51.566              51.707              51.869              52.056              52.272              52.521              52.809               53.14              53.523               53.964               54.473                55.06               55.737               56.518      
         51.348              51.475              51.622              51.791              51.987              52.212              52.472              52.772              53.118              53.517               53.977               54.508                55.12               55.827               56.642      
          51.25              51.382              51.534               51.71              51.913              52.147              52.417              52.728              53.088              53.502                53.98               54.531               55.168               55.901               56.748      
         51.149              51.286              51.444              51.626              51.836              52.078              52.357               52.68              53.051               53.48               53.975               54.546               55.204               55.963               56.839      
         51.047              51.188              51.351              51.539              51.755              52.005              52.294              52.626               53.01              53.452               53.963               54.551               55.231               56.014               56.918      
         50.943              51.089              51.256               51.45              51.672               51.93              52.226              52.569              52.963              53.419               53.944                54.55               55.249               56.056               56.986      
         50.839              50.988               51.16              51.358              51.587              51.851              52.156              52.508              52.913              53.381               53.921               54.543               55.261               56.089               57.045      
         50.733              50.885              51.062              51.265                51.5              51.771              52.083              52.444              52.859              53.339               53.892                54.53               55.266               56.115               57.095      
         50.625              50.782              50.963              51.171              51.411              51.688              52.008              52.377              52.802              53.293               53.859               54.512               55.266               56.135               57.137      
         50.518              50.677              50.862              51.075               51.32              51.604              51.931              52.307              52.742              53.244               53.823                54.49                55.26               56.148               57.173      
         50.409              50.572               50.76              50.978              51.228              51.518              51.851              52.236               52.68              53.192               53.783               54.464                55.25               56.157               57.203      
         50.299              50.466              50.658              50.879              51.135               51.43               51.77              52.162              52.615              53.137               53.739               54.434               55.236                56.16               57.227      
         50.189              50.358              50.554               50.78               51.04              51.341              51.687              52.087              52.548               53.08               53.693               54.401               55.217               56.159               57.245      
         50.078              50.251               50.45              50.679              50.944               51.25              51.603              52.009              52.479               53.02               53.644               54.365               55.195               56.154                57.26      
         49.967              50.142              50.345              50.578              50.848              51.158              51.517              51.931              52.408              52.958               53.593               54.326                55.17               56.145               57.269      
         49.854              50.033              50.239              50.476               50.75              51.066               51.43               51.85              52.335              52.894                53.54               54.284               55.142               56.133               57.275      
         49.742              49.923              50.132              50.373              50.651              50.972              51.342              51.769              52.261              52.829               53.484                54.24               55.111               56.117               57.277      
         49.629              49.813              50.025              50.269              50.551              50.877              51.252              51.686              52.185              52.761               53.426               54.193               55.078               56.099               57.276      
         49.516              49.702              49.917              50.165              50.451              50.781              51.162              51.601              52.108              52.693               53.367               54.145               55.042               56.077               57.271      
         49.402              49.591              49.809               50.06               50.35              50.685              51.071              51.516               52.03              52.622               53.306               54.094               55.004               56.053               57.263      
         49.287              49.479                49.7              49.954              50.248              50.587              50.978               51.43               51.95               52.55               53.243               54.042               54.963               56.026               57.253      
         49.173              49.367               49.59              49.848              50.146              50.489              50.885              51.342              51.869              52.477               53.179               53.988               54.921               55.997               57.239      
         49.058              49.254              49.481              49.742              50.043              50.391              50.791              51.254              51.787              52.403               53.113               53.932               54.876               55.966               57.223      
         48.943              49.141               49.37              49.635              49.939              50.291              50.697              51.165              51.705              52.327               53.046               53.874                54.83               55.933               57.205      
         48.827              49.028               49.26              49.527              49.835              50.191              50.601              51.075              51.621              52.251               52.977               53.815               54.782               55.898               57.184      
         48.711              48.914              49.148              49.419              49.731               50.09              50.505              50.984              51.536              52.173               52.908               53.755               54.733               55.861               57.162      
         48.595                48.8              49.037               49.31              49.625              49.989              50.408              50.892               51.45              52.094               52.837               53.693               54.682               55.822               57.137      
         48.478              48.686              48.925              49.201               49.52              49.887              50.311                50.8              51.364              52.014               52.765                53.63               54.629               55.781                57.11      
         48.362              48.571              48.813              49.092              49.414              49.785              50.213              50.707              51.277              51.934               52.692               53.566               54.575               55.739               57.081      
         48.245              48.456              48.701              48.982              49.307              49.682              50.114              50.613              51.188              51.852               52.618               53.501                54.52               55.695               57.051      
         48.128              48.341              48.588              48.872                49.2              49.579              50.015              50.519                51.1               51.77               52.543               53.435               54.463                55.65               57.019      
          48.01              48.226              48.475              48.762              49.093              49.475              49.916              50.424               51.01              51.687               52.467               53.367               54.405               55.603               56.985      
         47.893               48.11              48.361              48.651              48.985              49.371              49.815              50.328               50.92              51.603                52.39               53.298               54.346               55.555               56.949      
         47.709              47.929              48.182              48.474              48.811                49.2              49.649              50.166              50.763              51.452               52.246               53.163                54.22                55.44               56.846      
         47.504              47.725              47.981              48.276              48.616              49.008              49.461              49.983              50.585               51.28               52.081               53.005               54.072               55.302               56.721      
         47.299              47.522               47.78              48.077               48.42              48.816              49.272              49.799              50.406              51.107               51.915               52.847               53.923               55.163               56.594      
         47.093              47.319              47.579              47.878              48.224              48.623              49.083              49.614              50.227              50.933               51.748               52.688               53.772               55.023               56.466      

Check if COH is within Borrowing Bounds

some coh levels are below borrowing bound, can not borrow enough to pay debt

mt_bl_coh_wkb_invalid = (mt_coh_wkb_full < fl_b_bd);

% (k,a) invalid if coh(k,a,z) < bd for any z
ar_bl_wkb_invalid = max(mt_bl_coh_wkb_invalid,[], 2);
mt_bl_wkb_invalid = reshape(ar_bl_wkb_invalid, size(mt_a));

% find the first w_level choice where some k(w) percent choices are valid?
ar_bl_w_level_invalid =  min(mt_bl_wkb_invalid, [], 1);

% w choices can not be lower than fl_w_level_min_valid. If w choices are
% lower, given the current borrowing interest rate as well as the minimum
% income level in the future, and the maximum borrowing level available
% next period, and given the shock distribution, there exists some state in
% the future when the household when making this choice will be unable to
% borrow sufficiently to maintain positive consumption.
fl_w_level_min_valid = min(ar_w_level_full(~ar_bl_w_level_invalid));

Update Valid 2nd stage choice matrix

ar_w_level = linspace(fl_w_level_min_valid, fl_w_max, it_w_interp_n); ar_k_max = ar_w_level - fl_b_bd; mt_k = (ar_k_max'*ar_ak_perc)'; mt_a = (ar_w_level - mt_k); ar_a_meshk = mt_a(:); ar_k_mesha = mt_k(:);

Select only Valid (k(w), a) choices

% mt_coh_wkb = mt_coh_wkb_full(~ar_bl_wkb_invalid, :);
mt_coh_wkb = mt_coh_wkb_full;
mt_z_mesh_coh_wkb = repmat(ar_z, [size(mt_coh_wkb,1),1]);

Generate 1st Stage States: Interpolation Cash-on-hand Interpolation Grid

For the iwkz problems, we solve the problem along a grid of cash-on-hand values, the interpolate to find v(k',b',z) at (k',b') choices. Crucially, we have to coh matrxies

fl_max_mt_coh = max(max(mt_coh_wkb));

% This is savings only condition
% fl_min_mt_coh = min(min(mt_coh_wkb));

% This could be condition if no defaults are allowed
% fl_min_mt_coh = fl_w_level_min_valid;

% This is borrowing with default or not condition
fl_min_mt_coh = fl_b_bd;

it_coh_interp_n = (fl_max_mt_coh-fl_min_mt_coh)/(fl_coh_interp_grid_gap);
ar_interp_coh_grid = fft_array_add_zero(linspace(fl_min_mt_coh, fl_max_mt_coh, it_coh_interp_n), true);
[mt_interp_coh_grid_mesh_z, mt_z_mesh_coh_interp_grid] = ndgrid(ar_interp_coh_grid, ar_z);
mt_interp_coh_grid_mesh_w_perc = repmat(ar_interp_coh_grid, [it_w_perc_n, 1]);

Generate 1st Stage Choices: Interpolation Cash-on-hand Interpolation Grid

previously, our ar_w was the first stage choice grid, the grid was the same for all coh levels. Now, for each coh level, there is a different ar_w. ar_interp_coh_grid is (1 by ar_interp_coh_grid) and ar_w_perc is ( 1 by it_w_perc_n). Conditional on z, each choice matrix is (it_w_perc_n by ar_interp_coh_grid). Here we are pre-computing the choice matrix. This could be a large matrix if the choice grid is large. This is the matrix of aggregate savings choices

if (fl_min_mt_coh < 0)
    % borrowing bound is below zero
    mt_w_by_interp_coh_interp_grid = ((ar_interp_coh_grid-fl_min_mt_coh)'*ar_w_perc)' + fl_min_mt_coh;
else
    % savings only
    mt_w_by_interp_coh_interp_grid = ((ar_interp_coh_grid)'*ar_w_perc)';
end

Generate Interpolation Consumption Grid

We also interpolate over consumption to speed the program up. We only solve for u(c) at this grid for the iwkz problmes, and then interpolate other c values.

fl_c_max = max(max(mt_coh_wkb_full)) - fl_b_bd;
it_interp_c_grid_n = (fl_c_max-fl_c_min)/(it_c_interp_grid_gap);
ar_interp_c_grid = linspace(fl_c_min, fl_c_max, it_interp_c_grid_n);

Initialize armt_map to store, state, choice, shock matrixes

armt_map = containers.Map('KeyType','char', 'ValueType','any');
armtdesc_map = containers.Map('KeyType','char', 'ValueType','any');

Store armt_map (1): 2nd Stage Problem Arrays and Matrixes

armt_map('ar_ak_perc') = ar_ak_perc;
armt_map('mt_k') = mt_k;
armt_map('ar_a_meshk') = ar_a_meshk;
armt_map('ar_k_mesha') = ar_k_mesha;
armt_map('it_ameshk_n') = length(ar_a_meshk);
armt_map('mt_coh_wkb') = mt_coh_wkb_full;
armt_map('mt_z_mesh_coh_wkb') = mt_z_mesh_coh_wkb;

Store armt_map (2): First Stage Aggregate Savings

w = k' + b', w is aggregate Savings%

  1. ar_w_perc 1st stage, percentage w choice given coh, at each coh level the number of choice points is the same for this problem with percentage grid points.
  2. ar_w_level 2nd stage, level of w over which we solve the optimal percentage k' choices. Need to generate interpolant based on this so that we know optimal k* given ar_w_perc(coh) in the 1st stage
  3. mt_w_by_interp_coh_interp_grid 1st stage, generate w(coh, percent), meaning the level of w given coh and the percentage grid of ar_w_perc. Mesh this with the coh grid, Rows here correspond to percentage of w choices, columns correspond to cash-on-hand. The columns of cash-on-hand is determined by ar_interp_coh_grid, because we solve the 1st stage problem at that coh grid.
armt_map('ar_w_perc') = ar_w_perc;
armt_map('ar_w_level') = ar_w_level;
armt_map('mt_w_by_interp_coh_interp_grid') = mt_w_by_interp_coh_interp_grid;
armt_map('mt_interp_coh_grid_mesh_w_perc') = mt_interp_coh_grid_mesh_w_perc;

Store armt_map (3): First Stage Consumption and Cash-on-Hand Grids

armt_map('ar_interp_c_grid') = ar_interp_c_grid;
armt_map('ar_interp_coh_grid') = ar_interp_coh_grid;
armt_map('mt_interp_coh_grid_mesh_z') = mt_interp_coh_grid_mesh_z;
armt_map('mt_z_mesh_coh_interp_grid') = mt_z_mesh_coh_interp_grid;

Store armt_map (4): Shock Grids

armt_map('mt_z_trans') = mt_z_trans;
armt_map('ar_stationary') = ar_stationary;
armt_map('ar_z') = ar_z;

Store Function Map

func_map = containers.Map('KeyType','char', 'ValueType','any');
func_map('f_util_log') = f_util_log;
func_map('f_util_crra') = f_util_crra;
func_map('f_util_standin') = f_util_standin;
func_map('f_prod') = f_prod;
func_map('f_inc') = f_inc;
func_map('f_coh') = f_coh;
func_map('f_cons') = f_cons;

Graph

if (bl_graph_funcgrids)

Graph 1: a and k choice grid graphs

compare the figure here to the same figure in ffs_akz_get_funcgrid. there the grid points are on an even grid, half of the grid points have NA. for the grid here, the grid points get denser as we get closer to low w = k'+b' levels. This is what is different visually about percentage points based choice grid for the 2nd stage problem.

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

    chart = plot(mt_a, mt_k, 'blue');
    clr = jet(numel(chart));
    for m = 1:numel(chart)
        set(chart(m),'Color',clr(m,:))
    end
%     if (length(ar_w_level_full) <= 100)
        scatter(ar_a_meshk, ar_k_mesha, 3, 'filled', ...
            'MarkerEdgeColor', 'b', 'MarkerFaceColor', 'b');
%     end
    if (length(ar_w_level_full) <= 100)
        gf_invalid_scatter = scatter(ar_a_meshk_full(ar_bl_wkb_invalid),...
                                     ar_k_mesha_full(ar_bl_wkb_invalid),...
                20, 'O', 'MarkerEdgeColor', 'black', 'MarkerFaceColor', 'black');
    end

    xline(0);
    yline(0);

    title('Risky K Percentage Grids Given w=k+a (2nd Stage)')
    ylabel('Capital Choice (mt\_k)')
    xlabel({'Borrowing (<0) or Saving (>0) (mt\_a)'...
        'Each Diagonal Line a Different w=k+a level'...
        'Percentage for Risky K along Each Diagonal'})

    legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
    legendCell = cellstr(num2str(ar_w_level', 'k+a=%3.2f'));

    if (length(ar_w_level_full) <= 100)
        chart(length(chart)+1) = gf_invalid_scatter;
        legendCell{length(legendCell) + 1} = 'Invalid: COH(a,b,z)<bar(b) some z';
        legend(chart([legend2plot length(legendCell)]), legendCell([legend2plot length(legendCell)]), 'Location', 'northeast');
    else
        legend(chart([legend2plot]), legendCell([legend2plot]), 'Location', 'northeast');
    end

    grid on;

Graph 2: coh by shock

compare the figure here to the same figure in ffs_akz_get_funcgrid. there the grid points are on an even grid. Visually, one could see that the blue/red line segments here are always the same length, but in the ffs_akz_get_funcgrid figure, they are increasingly longer as we move towards the right. They are even because the number of percentage points available is constant regardless of w = k' + b' levels. But previously, the number of grid points available is increasing as w increases since choice grid is based on levels.

    figure('PaperPosition', [0 0 7 4]);
    chart = plot(0:1:(size(mt_coh_wkb_full,1)-1), mt_coh_wkb_full);
    clr = jet(numel(chart));
    for m = 1:numel(chart)
        set(chart(m),'Color',clr(m,:))
    end

    % zero lines
    xline(0);
    yline(0);

    % invalid points separating lines
    yline_borrbound = yline(fl_b_bd);
    yline_borrbound.HandleVisibility = 'on';
    yline_borrbound.LineStyle = '--';
    yline_borrbound.Color = 'blue';
    yline_borrbound.LineWidth = 2.5;

    title('Cash-on-Hand given w(k+b),k,z');
    ylabel('Cash-on-Hand (mt\_coh\_wkb\_full)');
    xlabel({'Index of Cash-on-Hand Discrete Point (0:1:(size(mt\_coh\_wkb\_full,1)-1))'...
        'Each Segment is a w=k+b; within segment increasing k'...
        'For each w and z, coh maximizing k is different'});

    legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
    legendCell = cellstr(num2str(ar_z', 'shock=%3.2f'));

    legendCell{length(legendCell) + 1} = 'borrow-constraint';
    chart(length(chart)+1) = yline_borrbound;
    legend(chart([legend2plot length(legendCell)]), legendCell([legend2plot length(legendCell)]), 'Location', 'southeast');

    grid on;

Graph 3: 1st State Aggregate Savings Choices by COH interpolation grids

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

    chart = plot(ar_interp_coh_grid, mt_w_by_interp_coh_interp_grid');

    clr = jet(numel(chart));
    for m = 1:numel(chart)
        set(chart(m),'Color',clr(m,:))
    end
    if (length(ar_interp_coh_grid) <= 100)
        [~, mt_interp_coh_grid_mesh_w_perc] = ndgrid(ar_w_perc, ar_interp_coh_grid);
        scatter(mt_interp_coh_grid_mesh_w_perc(:), mt_w_by_interp_coh_interp_grid(:), 3, 'filled', ...
            'MarkerEdgeColor', 'b', 'MarkerFaceColor', 'b');
    end

    % invalid points separating lines
    yline_borrbound = yline(fl_w_level_min_valid);
    yline_borrbound.HandleVisibility = 'on';
    yline_borrbound.LineStyle = '--';
    yline_borrbound.Color = 'red';
    yline_borrbound.LineWidth = 2.5;

    xline0 = xline(0);
    xline0.HandleVisibility = 'off';
    yline0 = yline(0);
    yline0.HandleVisibility = 'off';

    title({'Aggregate Savings Percentage Grids (1st Stage)' ...
           'y=mt\_w\_by\_interp\_coh\_interp\_grid, and, y=ar\_interp\_coh\_grid'});
    ylabel('1st Stage Aggregate Savings Choices');
    xlabel({'Cash-on-Hand Levels (Interpolation Points)'...
            'w(coh)>min-agg-save, coh(k(w),w-k)>=bar(b)'});

    legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
    legendCell = cellstr(num2str(ar_w_perc', 'ar w perc=%3.2f'));
    legendCell{length(legendCell) + 1} = 'min-agg-save';
    chart(length(chart)+1) = yline_borrbound;
    legend(chart([legend2plot length(legendCell)]), legendCell([legend2plot length(legendCell)]), 'Location', 'northwest');

    grid on;
end

Graph Details, Generally do Not Run

if (bl_graph_funcgrids_detail)

Graph 1: 2nd stage coh reached by k' b' choices by index

    figure('PaperPosition', [0 0 7 4]);
    ar_coh_kpzgrid_unique = unique(sort(mt_coh_wkb_full(:)));
    scatter(1:length(ar_coh_kpzgrid_unique), ar_coh_kpzgrid_unique);
    xline(0);
    yline(0);
    title('Cash-on-Hand given w(k+b),k,z');
    ylabel('Cash-on-Hand (y=ar\_coh\_kpzgrid\_unique)');
    xlabel({'Index of Cash-on-Hand Discrete Point' 'x = 1:length(ar\_coh\_kpzgrid\_unique)'});
    grid on;

Graph 2: 2nd stage coh reached by k' b' choices by coh

    figure('PaperPosition', [0 0 7 4]);
    ar_coh_kpzgrid_unique = unique(sort(mt_coh_wkb_full(:)));
    scatter(ar_coh_kpzgrid_unique, ar_coh_kpzgrid_unique, '.');
    xline(0);
    yline(0);
    title('Cash-on-Hand given w(k+b),k,z; See Clearly Sparsity Density of Grid across Z');
    ylabel('Cash-on-Hand (y = ar\_coh\_kpzgrid\_unique)');
    xlabel({'Cash-on-Hand' 'x = ar\_coh\_kpzgrid\_unique'});
    grid on;
end

Display

if (bl_display_funcgrids)

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_z');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(ar_z));
    disp(ar_z);

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_w_level_full');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(ar_w_level_full));
    disp(ar_w_level_full);

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_w_by_interp_coh_interp_grid');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_w_by_interp_coh_interp_grid));
    disp(head(array2table(mt_w_by_interp_coh_interp_grid), 10));
    disp(tail(array2table(mt_w_by_interp_coh_interp_grid), 10));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_z_trans');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_z_trans));
    disp(head(array2table(mt_z_trans), 10));
    disp(tail(array2table(mt_z_trans), 10));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_interp_coh_grid');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    summary(array2table(ar_interp_coh_grid'));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_interp_c_grid');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    summary(array2table(ar_interp_c_grid'));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_interp_coh_grid_mesh_z');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_interp_coh_grid_mesh_z));
    disp(head(array2table(mt_interp_coh_grid_mesh_z), 10));
    disp(tail(array2table(mt_interp_coh_grid_mesh_z), 10));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_a');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_a));
    disp(head(array2table(mt_a), 10));
    disp(tail(array2table(mt_a), 10));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_a_meshk');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    summary(array2table(ar_a_meshk));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_k');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_k));
    disp(head(array2table(mt_k), 10));
    disp(tail(array2table(mt_k), 10));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_k_mesha');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    summary(array2table(ar_k_mesha));

    param_map_keys = keys(func_map);
    param_map_vals = values(func_map);
    for i = 1:length(func_map)
        st_display = strjoin(['pos =' num2str(i) '; key =' string(param_map_keys{i}) '; val =' func2str(param_map_vals{i})]);
        disp(st_display);
    end

end
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_z
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
     1    15

  Columns 1 through 7

    0.3474    0.4008    0.4623    0.5333    0.6152    0.7097    0.8186

  Columns 8 through 14

    0.9444    1.0894    1.2567    1.4496    1.6723    1.9291    2.2253

  Column 15

    2.5670

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_w_level_full
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
     1    27

  Columns 1 through 7

   -4.6700   -2.4832   -0.2964         0    1.8904    4.0772    6.2640

  Columns 8 through 14

    8.4508   10.6376   12.8244   15.0112   17.1980   19.3848   21.5716

  Columns 15 through 21

   23.7584   25.9452   28.1320   30.3188   32.5056   34.6924   36.8792

  Columns 22 through 27

   39.0660   41.2528   43.4396   45.6264   47.8132   50.0000

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_w_by_interp_coh_interp_grid
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    25    30

    mt_w_by_interp_coh_interp_grid1    mt_w_by_interp_coh_interp_grid2    mt_w_by_interp_coh_interp_grid3    mt_w_by_interp_coh_interp_grid4    mt_w_by_interp_coh_interp_grid5    mt_w_by_interp_coh_interp_grid6    mt_w_by_interp_coh_interp_grid7    mt_w_by_interp_coh_interp_grid8    mt_w_by_interp_coh_interp_grid9    mt_w_by_interp_coh_interp_grid10    mt_w_by_interp_coh_interp_grid11    mt_w_by_interp_coh_interp_grid12    mt_w_by_interp_coh_interp_grid13    mt_w_by_interp_coh_interp_grid14    mt_w_by_interp_coh_interp_grid15    mt_w_by_interp_coh_interp_grid16    mt_w_by_interp_coh_interp_grid17    mt_w_by_interp_coh_interp_grid18    mt_w_by_interp_coh_interp_grid19    mt_w_by_interp_coh_interp_grid20    mt_w_by_interp_coh_interp_grid21    mt_w_by_interp_coh_interp_grid22    mt_w_by_interp_coh_interp_grid23    mt_w_by_interp_coh_interp_grid24    mt_w_by_interp_coh_interp_grid25    mt_w_by_interp_coh_interp_grid26    mt_w_by_interp_coh_interp_grid27    mt_w_by_interp_coh_interp_grid28    mt_w_by_interp_coh_interp_grid29    mt_w_by_interp_coh_interp_grid30
    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________

                 -4.67                               -4.67                              -4.67                              -4.67                              -4.67                              -4.67                              -4.67                              -4.67                              -4.67                               -4.67                               -4.67                               -4.67                               -4.67                               -4.67                              -4.67                                -4.67                               -4.67                               -4.67                               -4.67                              -4.67                               -4.67                                -4.67                               -4.67                               -4.67                               -4.67                               -4.67                               -4.67                              -4.67                               -4.67                               -4.67             
                 -4.67                             -4.5778                            -4.4856                            -4.4754                            -4.3934                            -4.3012                            -4.2091                            -4.1169                            -4.0247                             -3.9325                             -3.8403                             -3.7481                              -3.656                             -3.5638                            -3.4716                              -3.3794                             -3.2872                              -3.195                             -3.1029                            -3.0107                             -2.9185                              -2.8263                             -2.7341                             -2.6419                             -2.5498                             -2.4576                             -2.3654                            -2.2732                              -2.181                             -2.0888             
                 -4.67                             -4.4856                            -4.3012                            -4.2808                            -4.1169                            -3.9325                            -3.7481                            -3.5638                            -3.3794                              -3.195                             -3.0107                             -2.8263                             -2.6419                             -2.4576                            -2.2732                              -2.0888                             -1.9045                             -1.7201                             -1.5357                            -1.3514                              -1.167                             -0.98264                            -0.79828                            -0.61391                            -0.42954                            -0.24518                           -0.060809                            0.12356                             0.30792                             0.49229             
                 -4.67                             -4.3934                            -4.1169                            -4.0862                            -3.8403                            -3.5638                            -3.2872                            -3.0107                            -2.7341                             -2.4576                              -2.181                             -1.9045                             -1.6279                             -1.3514                            -1.0748                             -0.79828                            -0.52173                            -0.24518                            0.031374                            0.30792                             0.58447                              0.86102                              1.1376                              1.4141                              1.6907                              1.9672                              2.2438                             2.5203                              2.7969                              3.0734             
                 -4.67                             -4.3012                            -3.9325                            -3.8916                            -3.5638                             -3.195                            -2.8263                            -2.4576                            -2.0888                             -1.7201                             -1.3514                            -0.98264                            -0.61391                            -0.24518                            0.12356                              0.49229                             0.86102                              1.2298                              1.5985                             1.9672                               2.336                               2.7047                              3.0734                              3.4422                              3.8109                              4.1796                              4.5484                             4.9171                              5.2858                              5.6546             
                 -4.67                             -4.2091                            -3.7481                            -3.6971                            -3.2872                            -2.8263                            -2.3654                            -1.9045                            -1.4436                            -0.98264                            -0.52173                           -0.060809                             0.40011                             0.86102                             1.3219                               1.7829                              2.2438                              2.7047                              3.1656                             3.6265                              4.0874                               4.5484                              5.0093                              5.4702                              5.9311                               6.392                              6.8529                             7.3139                              7.7748                              8.2357             
                 -4.67                             -4.1169                            -3.5638                            -3.5025                            -3.0107                            -2.4576                            -1.9045                            -1.3514                           -0.79828                            -0.24518                             0.30792                             0.86102                              1.4141                              1.9672                             2.5203                               3.0734                              3.6265                              4.1796                              4.7327                             5.2858                              5.8389                                6.392                              6.9451                              7.4982                              8.0513                              8.6044                              9.1575                             9.7106                              10.264                              10.817             
                 -4.67                             -4.0247                            -3.3794                            -3.3079                            -2.7341                            -2.0888                            -1.4436                           -0.79828                           -0.15299                             0.49229                              1.1376                              1.7829                              2.4281                              3.0734                             3.7187                                4.364                              5.0093                              5.6546                              6.2998                             6.9451                              7.5904                               8.2357                               8.881                              9.5263                              10.172                              10.817                              11.462                             12.107                              12.753                              13.398             
                 -4.67                             -3.9325                             -3.195                            -3.1133                            -2.4576                            -1.7201                           -0.98264                           -0.24518                            0.49229                              1.2298                              1.9672                              2.7047                              3.4422                              4.1796                             4.9171                               5.6546                               6.392                              7.1295                               7.867                             8.6044                              9.3419                               10.079                              10.817                              11.554                              12.292                              13.029                              13.767                             14.504                              15.242                              15.979             
                 -4.67                             -3.8403                            -3.0107                            -2.9187                             -2.181                            -1.3514                           -0.52173                            0.30792                             1.1376                              1.9672                              2.7969                              3.6265                              4.4562                              5.2858                             6.1155                               6.9451                              7.7748                              8.6044                              9.4341                             10.264                              11.093                               11.923                              12.753                              13.582                              14.412                              15.242                              16.071                             16.901                              17.731                               18.56             

    mt_w_by_interp_coh_interp_grid1    mt_w_by_interp_coh_interp_grid2    mt_w_by_interp_coh_interp_grid3    mt_w_by_interp_coh_interp_grid4    mt_w_by_interp_coh_interp_grid5    mt_w_by_interp_coh_interp_grid6    mt_w_by_interp_coh_interp_grid7    mt_w_by_interp_coh_interp_grid8    mt_w_by_interp_coh_interp_grid9    mt_w_by_interp_coh_interp_grid10    mt_w_by_interp_coh_interp_grid11    mt_w_by_interp_coh_interp_grid12    mt_w_by_interp_coh_interp_grid13    mt_w_by_interp_coh_interp_grid14    mt_w_by_interp_coh_interp_grid15    mt_w_by_interp_coh_interp_grid16    mt_w_by_interp_coh_interp_grid17    mt_w_by_interp_coh_interp_grid18    mt_w_by_interp_coh_interp_grid19    mt_w_by_interp_coh_interp_grid20    mt_w_by_interp_coh_interp_grid21    mt_w_by_interp_coh_interp_grid22    mt_w_by_interp_coh_interp_grid23    mt_w_by_interp_coh_interp_grid24    mt_w_by_interp_coh_interp_grid25    mt_w_by_interp_coh_interp_grid26    mt_w_by_interp_coh_interp_grid27    mt_w_by_interp_coh_interp_grid28    mt_w_by_interp_coh_interp_grid29    mt_w_by_interp_coh_interp_grid30
    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    _______________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________    ________________________________

                 -4.67                             -3.2872                            -1.9045                            -1.7512                           -0.52173                            0.86102                            2.2438                             3.6265                             5.0093                               6.392                              7.7748                              9.1575                               10.54                              11.923                              13.306                              14.689                              16.071                              17.454                              18.837                               20.22                              21.602                              22.985                              24.368                              25.751                              27.133                              28.516                              29.899                              31.282                              32.664                              34.047             
                 -4.67                              -3.195                            -1.7201                            -1.5567                           -0.24518                             1.2298                            2.7047                             4.1796                             5.6546                              7.1295                              8.6044                              10.079                              11.554                              13.029                              14.504                              15.979                              17.454                              18.929                              20.404                              21.879                              23.354                              24.829                              26.304                              27.779                              29.254                              30.728                              32.203                              33.678                              35.153                              36.628             
                 -4.67                             -3.1029                            -1.5357                            -1.3621                           0.031374                             1.5985                            3.1656                             4.7327                             6.2998                               7.867                              9.4341                              11.001                              12.568                              14.135                              15.703                               17.27                              18.837                              20.404                              21.971                              23.538                              25.105                              26.672                              28.239                              29.807                              31.374                              32.941                              34.508                              36.075                              37.642                              39.209             
                 -4.67                             -3.0107                            -1.3514                            -1.1675                            0.30792                             1.9672                            3.6265                             5.2858                             6.9451                              8.6044                              10.264                              11.923                              13.582                              15.242                              16.901                               18.56                               20.22                              21.879                              23.538                              25.197                              26.857                              28.516                              30.175                              31.835                              33.494                              35.153                              36.813                              38.472                              40.131                               41.79             
                 -4.67                             -2.9185                             -1.167                           -0.97291                            0.58447                              2.336                            4.0874                             5.8389                             7.5904                              9.3419                              11.093                              12.845                              14.596                              16.348                              18.099                              19.851                              21.602                              23.354                              25.105                              26.857                              28.608                               30.36                              32.111                              33.863                              35.614                              37.366                              39.117                              40.869                               42.62                              44.372             
                 -4.67                             -2.8263                           -0.98264                           -0.77833                            0.86102                             2.7047                            4.5484                              6.392                             8.2357                              10.079                              11.923                              13.767                               15.61                              17.454                              19.298                              21.141                              22.985                              24.829                              26.672                              28.516                               30.36                              32.203                              34.047                              35.891                              37.734                              39.578                              41.422                              43.265                              45.109                              46.953             
                 -4.67                             -2.7341                           -0.79828                           -0.58375                             1.1376                             3.0734                            5.0093                             6.9451                              8.881                              10.817                              12.753                              14.689                              16.624                               18.56                              20.496                              22.432                              24.368                              26.304                              28.239                              30.175                              32.111                              34.047                              35.983                              37.919                              39.855                               41.79                              43.726                              45.662                              47.598                              49.534             
                 -4.67                             -2.6419                           -0.61391                           -0.38916                             1.4141                             3.4422                            5.4702                             7.4982                             9.5263                              11.554                              13.582                               15.61                              17.638                              19.666                              21.694                              23.723                              25.751                              27.779                              29.807                              31.835                              33.863                              35.891                              37.919                              39.947                              41.975                              44.003                              46.031                              48.059                              50.087                              52.115             
                 -4.67                             -2.5498                           -0.42954                           -0.19458                             1.6907                             3.8109                            5.9311                             8.0513                             10.172                              12.292                              14.412                              16.532                              18.652                              20.773                              22.893                              25.013                              27.133                              29.254                              31.374                              33.494                              35.614                              37.734                              39.855                              41.975                              44.095                              46.215                              48.335                              50.456                              52.576                              54.696             
                 -4.67                             -2.4576                           -0.24518                                  0                             1.9672                             4.1796                             6.392                             8.6044                             10.817                              13.029                              15.242                              17.454                              19.666                              21.879                              24.091                              26.304                              28.516                              30.728                              32.941                              35.153                              37.366                              39.578                               41.79                              44.003                              46.215                              48.428                               50.64                              52.852                              55.065                              57.277             

----------------------------------------
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mt_z_trans
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    15    15

    mt_z_trans1    mt_z_trans2    mt_z_trans3    mt_z_trans4    mt_z_trans5    mt_z_trans6    mt_z_trans7    mt_z_trans8    mt_z_trans9    mt_z_trans10    mt_z_trans11    mt_z_trans12    mt_z_trans13    mt_z_trans14    mt_z_trans15
    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ____________    ____________    ____________    ____________    ____________    ____________

       0.26016        0.26831        0.25551        0.14921       0.053403      0.011702       0.0015678     0.00012823     6.3911e-06      1.9381e-07      3.5701e-09      3.9889e-11      2.7001e-13      1.1102e-15               0 
       0.11232        0.19622         0.2763        0.23861        0.12635      0.040998       0.0081429     0.00098855     7.3236e-05      3.3054e-06      9.0736e-08      1.5125e-09      1.5289e-11      9.3592e-14      3.3307e-16 
      0.037073        0.10492         0.2185        0.27902         0.2185       0.10492        0.030863      0.0055558     0.00061112      4.1008e-05      1.6758e-06       4.164e-08      6.2811e-10      5.7438e-12      3.1863e-14 
     0.0092081       0.040998        0.12635        0.23861         0.2763       0.19622        0.085427       0.022782      0.0037167       0.0003704      2.2511e-05      8.3291e-07      1.8732e-08      2.5567e-10      2.1255e-12 
     0.0017026       0.011702       0.053403        0.14921        0.25551       0.26831         0.17279       0.068209       0.016489       0.0024379       0.0002201      1.2114e-05       4.058e-07      8.2598e-09      1.0277e-10 
    0.00023263      0.0024379       0.016489       0.068209        0.17279       0.26831         0.25551        0.14921       0.053403        0.011702       0.0015678      0.00012823      6.3911e-06      1.9381e-07      3.6102e-09 
    2.3363e-05      0.0003704      0.0037167       0.022782       0.085427       0.19622          0.2763        0.23861        0.12635        0.040998       0.0081429      0.00098855      7.3236e-05      3.3054e-06      9.2263e-08 
    1.7181e-06     4.1008e-05     0.00061112      0.0055558       0.030863       0.10492          0.2185        0.27902         0.2185         0.10492        0.030863       0.0055558      0.00061112      4.1008e-05      1.7181e-06 
    9.2263e-08     3.3054e-06     7.3236e-05     0.00098855      0.0081429      0.040998         0.12635        0.23861         0.2763         0.19622        0.085427        0.022782       0.0037167       0.0003704      2.3363e-05 
    3.6102e-09     1.9381e-07     6.3911e-06     0.00012823      0.0015678      0.011702        0.053403        0.14921        0.25551         0.26831         0.17279        0.068209        0.016489       0.0024379      0.00023263 

    mt_z_trans1    mt_z_trans2    mt_z_trans3    mt_z_trans4    mt_z_trans5    mt_z_trans6    mt_z_trans7    mt_z_trans8    mt_z_trans9    mt_z_trans10    mt_z_trans11    mt_z_trans12    mt_z_trans13    mt_z_trans14    mt_z_trans15
    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ____________    ____________    ____________    ____________    ____________    ____________

    0.00023263      0.0024379       0.016489       0.068209        0.17279        0.26831        0.25551        0.14921       0.053403       0.011702       0.0015678       0.00012823      6.3911e-06      1.9381e-07      3.6102e-09 
    2.3363e-05      0.0003704      0.0037167       0.022782       0.085427        0.19622         0.2763        0.23861        0.12635       0.040998       0.0081429       0.00098855      7.3236e-05      3.3054e-06      9.2263e-08 
    1.7181e-06     4.1008e-05     0.00061112      0.0055558       0.030863        0.10492         0.2185        0.27902         0.2185        0.10492        0.030863        0.0055558      0.00061112      4.1008e-05      1.7181e-06 
    9.2263e-08     3.3054e-06     7.3236e-05     0.00098855      0.0081429       0.040998        0.12635        0.23861         0.2763        0.19622        0.085427         0.022782       0.0037167       0.0003704      2.3363e-05 
    3.6102e-09     1.9381e-07     6.3911e-06     0.00012823      0.0015678       0.011702       0.053403        0.14921        0.25551        0.26831         0.17279         0.068209        0.016489       0.0024379      0.00023263 
    1.0277e-10     8.2598e-09      4.058e-07     1.2114e-05      0.0002201      0.0024379       0.016489       0.068209        0.17279        0.26831         0.25551          0.14921        0.053403        0.011702       0.0017026 
    2.1256e-12     2.5567e-10     1.8732e-08     8.3291e-07     2.2511e-05      0.0003704      0.0037167       0.022782       0.085427        0.19622          0.2763          0.23861         0.12635        0.040998       0.0092081 
    3.1909e-14     5.7438e-12     6.2811e-10      4.164e-08     1.6758e-06     4.1008e-05     0.00061112      0.0055558       0.030863        0.10492          0.2185          0.27902          0.2185         0.10492        0.037073 
     3.474e-16     9.3597e-14     1.5289e-11     1.5125e-09     9.0736e-08     3.3054e-06     7.3236e-05     0.00098855      0.0081429       0.040998         0.12635          0.23861          0.2763         0.19622         0.11232 
    2.7412e-18     1.1057e-15     2.6998e-13     3.9889e-11     3.5701e-09     1.9381e-07     6.3911e-06     0.00012823      0.0015678       0.011702        0.053403          0.14921         0.25551         0.26831         0.26016 

----------------------------------------
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ar_interp_coh_grid
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Variables:

    Var1: 30×1 double

        Values:

            Min        -4.67
            Median    25.197
            Max       57.277

----------------------------------------
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ar_interp_c_grid
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Variables:

    Var1: 619272×1 double

        Values:

            Min         0.02
            Median    30.984
            Max       61.947

----------------------------------------
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mt_interp_coh_grid_mesh_z
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    30    15

    mt_interp_coh_grid_mesh_z1    mt_interp_coh_grid_mesh_z2    mt_interp_coh_grid_mesh_z3    mt_interp_coh_grid_mesh_z4    mt_interp_coh_grid_mesh_z5    mt_interp_coh_grid_mesh_z6    mt_interp_coh_grid_mesh_z7    mt_interp_coh_grid_mesh_z8    mt_interp_coh_grid_mesh_z9    mt_interp_coh_grid_mesh_z10    mt_interp_coh_grid_mesh_z11    mt_interp_coh_grid_mesh_z12    mt_interp_coh_grid_mesh_z13    mt_interp_coh_grid_mesh_z14    mt_interp_coh_grid_mesh_z15
    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________

                -4.67                         -4.67                         -4.67                         -4.67                         -4.67                         -4.67                         -4.67                         -4.67                         -4.67                         -4.67                          -4.67                          -4.67                          -4.67                          -4.67                          -4.67          
              -2.4576                       -2.4576                       -2.4576                       -2.4576                       -2.4576                       -2.4576                       -2.4576                       -2.4576                       -2.4576                       -2.4576                        -2.4576                        -2.4576                        -2.4576                        -2.4576                        -2.4576          
             -0.24518                      -0.24518                      -0.24518                      -0.24518                      -0.24518                      -0.24518                      -0.24518                      -0.24518                      -0.24518                      -0.24518                       -0.24518                       -0.24518                       -0.24518                       -0.24518                       -0.24518          
                    0                             0                             0                             0                             0                             0                             0                             0                             0                             0                              0                              0                              0                              0                              0          
               1.9672                        1.9672                        1.9672                        1.9672                        1.9672                        1.9672                        1.9672                        1.9672                        1.9672                        1.9672                         1.9672                         1.9672                         1.9672                         1.9672                         1.9672          
               4.1796                        4.1796                        4.1796                        4.1796                        4.1796                        4.1796                        4.1796                        4.1796                        4.1796                        4.1796                         4.1796                         4.1796                         4.1796                         4.1796                         4.1796          
                6.392                         6.392                         6.392                         6.392                         6.392                         6.392                         6.392                         6.392                         6.392                         6.392                          6.392                          6.392                          6.392                          6.392                          6.392          
               8.6044                        8.6044                        8.6044                        8.6044                        8.6044                        8.6044                        8.6044                        8.6044                        8.6044                        8.6044                         8.6044                         8.6044                         8.6044                         8.6044                         8.6044          
               10.817                        10.817                        10.817                        10.817                        10.817                        10.817                        10.817                        10.817                        10.817                        10.817                         10.817                         10.817                         10.817                         10.817                         10.817          
               13.029                        13.029                        13.029                        13.029                        13.029                        13.029                        13.029                        13.029                        13.029                        13.029                         13.029                         13.029                         13.029                         13.029                         13.029          

    mt_interp_coh_grid_mesh_z1    mt_interp_coh_grid_mesh_z2    mt_interp_coh_grid_mesh_z3    mt_interp_coh_grid_mesh_z4    mt_interp_coh_grid_mesh_z5    mt_interp_coh_grid_mesh_z6    mt_interp_coh_grid_mesh_z7    mt_interp_coh_grid_mesh_z8    mt_interp_coh_grid_mesh_z9    mt_interp_coh_grid_mesh_z10    mt_interp_coh_grid_mesh_z11    mt_interp_coh_grid_mesh_z12    mt_interp_coh_grid_mesh_z13    mt_interp_coh_grid_mesh_z14    mt_interp_coh_grid_mesh_z15
    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________

              37.366                        37.366                        37.366                        37.366                        37.366                        37.366                        37.366                        37.366                        37.366                        37.366                         37.366                         37.366                         37.366                         37.366                         37.366           
              39.578                        39.578                        39.578                        39.578                        39.578                        39.578                        39.578                        39.578                        39.578                        39.578                         39.578                         39.578                         39.578                         39.578                         39.578           
               41.79                         41.79                         41.79                         41.79                         41.79                         41.79                         41.79                         41.79                         41.79                         41.79                          41.79                          41.79                          41.79                          41.79                          41.79           
              44.003                        44.003                        44.003                        44.003                        44.003                        44.003                        44.003                        44.003                        44.003                        44.003                         44.003                         44.003                         44.003                         44.003                         44.003           
              46.215                        46.215                        46.215                        46.215                        46.215                        46.215                        46.215                        46.215                        46.215                        46.215                         46.215                         46.215                         46.215                         46.215                         46.215           
              48.428                        48.428                        48.428                        48.428                        48.428                        48.428                        48.428                        48.428                        48.428                        48.428                         48.428                         48.428                         48.428                         48.428                         48.428           
               50.64                         50.64                         50.64                         50.64                         50.64                         50.64                         50.64                         50.64                         50.64                         50.64                          50.64                          50.64                          50.64                          50.64                          50.64           
              52.852                        52.852                        52.852                        52.852                        52.852                        52.852                        52.852                        52.852                        52.852                        52.852                         52.852                         52.852                         52.852                         52.852                         52.852           
              55.065                        55.065                        55.065                        55.065                        55.065                        55.065                        55.065                        55.065                        55.065                        55.065                         55.065                         55.065                         55.065                         55.065                         55.065           
              57.277                        57.277                        57.277                        57.277                        57.277                        57.277                        57.277                        57.277                        57.277                        57.277                         57.277                         57.277                         57.277                         57.277                         57.277           

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_a
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    45    27

    mt_a1     mt_a2      mt_a3       mt_a4       mt_a5     mt_a6     mt_a7     mt_a8     mt_a9     mt_a10    mt_a11    mt_a12    mt_a13    mt_a14    mt_a15    mt_a16    mt_a17    mt_a18    mt_a19    mt_a20    mt_a21    mt_a22    mt_a23    mt_a24    mt_a25    mt_a26    mt_a27
    _____    _______    ________    ________    _______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______

    -4.67    -2.4832    -0.29638           0     1.8904    4.0772     6.264    8.4508    10.638    12.824    15.011    17.198    19.385    21.572    23.758    25.945    28.132    30.319    32.506    34.692    36.879    39.066    41.253     43.44    45.626    47.813        50
    -4.67    -2.5329    -0.39578    -0.10614     1.7413    3.8784    6.0155    8.1526     10.29    12.427    14.564    16.701    18.838    20.975    23.112    25.249    27.387    29.524    31.661    33.798    35.935    38.072    40.209    42.346    44.483     46.62    48.758
    -4.67    -2.5826    -0.49518    -0.21227     1.5922    3.6796     5.767    7.8544    9.9418    12.029    14.117    16.204    18.291    20.379    22.466    24.554    26.641    28.728    30.816    32.903    34.991    37.078    39.165    41.253     43.34    45.428    47.515
    -4.67    -2.6323    -0.59458    -0.31841     1.4431    3.4808    5.5185    7.5562    9.5939    11.632    13.669    15.707    17.745    19.782     21.82    23.858    25.896    27.933    29.971    32.009    34.046    36.084    38.122    40.159    42.197    44.235    46.273
    -4.67     -2.682    -0.69398    -0.42454      1.294     3.282      5.27     7.258     9.246    11.234    13.222     15.21    17.198    19.186    21.174    23.162     25.15    27.138    29.126    31.114    33.102     35.09    37.078    39.066    41.054    43.042     45.03
    -4.67    -2.7317    -0.79338    -0.53068     1.1449    3.0832    5.0215    6.9598    8.8981    10.836    12.775    14.713    16.651     18.59    20.528    22.466    24.405    26.343    28.281    30.219    32.158    34.096    36.034    37.973    39.911    41.849    43.788
    -4.67    -2.7814    -0.89278    -0.63682    0.99582    2.8844     4.773    6.6616    8.5502    10.439    12.327    14.216    16.105    17.993    19.882     21.77    23.659    25.548    27.436    29.325    31.213    33.102    34.991    36.879    38.768    40.656    42.545
    -4.67    -2.8311    -0.99218    -0.74295    0.84672    2.6856    4.5245    6.3634    8.2023    10.041     11.88    13.719    15.558    17.397    19.236    21.075    22.914    24.752    26.591     28.43    30.269    32.108    33.947    35.786    37.625    39.464    41.303
    -4.67    -2.8808     -1.0916    -0.84909    0.69762    2.4868     4.276    6.0652    7.8544    9.6436    11.433    13.222    15.011      16.8     18.59    20.379    22.168    23.957    25.746    27.536    29.325    31.114    32.903    34.692    36.482    38.271     40.06
    -4.67    -2.9305      -1.191    -0.95522    0.54852     2.288    4.0275     5.767    7.5065     9.246    10.986    12.725    14.465    16.204    17.944    19.683    21.423    23.162    24.902    26.641    28.381     30.12     31.86    33.599    35.339    37.078    38.818

    mt_a1     mt_a2      mt_a3      mt_a4      mt_a5      mt_a6      mt_a7      mt_a8      mt_a9     mt_a10      mt_a11      mt_a12      mt_a13      mt_a14      mt_a15      mt_a16      mt_a17      mt_a18      mt_a19      mt_a20      mt_a21      mt_a22      mt_a23      mt_a24      mt_a25      mt_a26      mt_a27 
    _____    _______    _______    _______    _______    _______    _______    _______    _______    _______    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    _________    _______    ________

    -4.67    -4.2227    -3.7754    -3.7148    -3.3281    -2.8808    -2.4335    -1.9862    -1.5389    -1.0916    -0.64428    -0.19698     0.25032     0.69762      1.1449      1.5922      2.0395      2.4868      2.9341      3.3814      3.8287       4.276      4.7233      5.1706       5.6179     6.0652      6.5125
    -4.67    -4.2724    -3.8748    -3.8209    -3.4772    -3.0796     -2.682    -2.2844    -1.8868    -1.4892     -1.0916    -0.69398    -0.29638     0.10122     0.49882     0.89642       1.294      1.6916      2.0892      2.4868      2.8844       3.282      3.6796      4.0772       4.4748     4.8724        5.27
    -4.67    -4.3221    -3.9742     -3.927    -3.6263    -3.2784    -2.9305    -2.5826    -2.2347    -1.8868     -1.5389      -1.191    -0.84308    -0.49518    -0.14728     0.20062     0.54852     0.89642      1.2443      1.5922      1.9401       2.288      2.6359      2.9838       3.3317     3.6796      4.0275
    -4.67    -4.3718    -4.0736    -4.0332    -3.7754    -3.4772     -3.179    -2.8808    -2.5826    -2.2844     -1.9862      -1.688     -1.3898     -1.0916    -0.79338    -0.49518    -0.19698     0.10122     0.39942     0.69762     0.99582       1.294      1.5922      1.8904       2.1886     2.4868       2.785
    -4.67    -4.4215     -4.173    -4.1393    -3.9245     -3.676    -3.4275     -3.179    -2.9305     -2.682     -2.4335      -2.185     -1.9365      -1.688     -1.4395      -1.191    -0.94248    -0.69398    -0.44548    -0.19698    0.051519     0.30002     0.54852     0.79702       1.0455      1.294      1.5425
    -4.67    -4.4712    -4.2724    -4.2454    -4.0736    -3.8748     -3.676    -3.4772    -3.2784    -3.0796     -2.8808      -2.682     -2.4832     -2.2844     -2.0856     -1.8868      -1.688     -1.4892     -1.2904     -1.0916    -0.89278    -0.69398    -0.49518    -0.29638    -0.097581    0.10122     0.30002
    -4.67    -4.5209    -4.3718    -4.3516    -4.2227    -4.0736    -3.9245    -3.7754    -3.6263    -3.4772     -3.3281      -3.179     -3.0299     -2.8808     -2.7317     -2.5826     -2.4335     -2.2844     -2.1353     -1.9862     -1.8371      -1.688     -1.5389     -1.3898      -1.2407    -1.0916    -0.94248
    -4.67    -4.5706    -4.4712    -4.4577    -4.3718    -4.2724     -4.173    -4.0736    -3.9742    -3.8748     -3.7754      -3.676     -3.5766     -3.4772     -3.3778     -3.2784      -3.179     -3.0796     -2.9802     -2.8808     -2.7814      -2.682     -2.5826     -2.4832      -2.3838    -2.2844      -2.185
    -4.67    -4.6203    -4.5706    -4.5638    -4.5209    -4.4712    -4.4215    -4.3718    -4.3221    -4.2724     -4.2227      -4.173     -4.1233     -4.0736     -4.0239     -3.9742     -3.9245     -3.8748     -3.8251     -3.7754     -3.7257      -3.676     -3.6263     -3.5766      -3.5269    -3.4772     -3.4275
    -4.67      -4.67      -4.67      -4.67      -4.67      -4.67      -4.67      -4.67      -4.67      -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67       -4.67        -4.67      -4.67       -4.67

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_a_meshk
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Variables:

    ar_a_meshk: 1215×1 double

        Values:

            Min           -4.67   
            Median       4.7233   
            Max              50   

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_k
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    45    27

    mt_k1    mt_k2     mt_k3      mt_k4     mt_k5     mt_k6     mt_k7     mt_k8     mt_k9     mt_k10    mt_k11    mt_k12    mt_k13    mt_k14    mt_k15    mt_k16    mt_k17    mt_k18    mt_k19    mt_k20    mt_k21    mt_k22    mt_k23    mt_k24    mt_k25    mt_k26    mt_k27
    _____    ______    ______    _______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______

      0           0         0          0         0         0         0         0         0         0         0        0          0         0         0         0         0         0         0         0         0        0          0         0         0         0         0
      0      0.0497    0.0994    0.10614    0.1491    0.1988    0.2485    0.2982    0.3479    0.3976    0.4473    0.497     0.5467    0.5964    0.6461    0.6958    0.7455    0.7952    0.8449    0.8946    0.9443    0.994     1.0437    1.0934    1.1431    1.1928    1.2425
      0      0.0994    0.1988    0.21227    0.2982    0.3976     0.497    0.5964    0.6958    0.7952    0.8946    0.994     1.0934    1.1928    1.2922    1.3916     1.491    1.5904    1.6898    1.7892    1.8886    1.988     2.0874    2.1868    2.2862    2.3856     2.485
      0      0.1491    0.2982    0.31841    0.4473    0.5964    0.7455    0.8946    1.0437    1.1928    1.3419    1.491     1.6401    1.7892    1.9383    2.0874    2.2365    2.3856    2.5347    2.6838    2.8329    2.982     3.1311    3.2802    3.4293    3.5784    3.7275
      0      0.1988    0.3976    0.42454    0.5964    0.7952     0.994    1.1928    1.3916    1.5904    1.7892    1.988     2.1868    2.3856    2.5844    2.7832     2.982    3.1808    3.3796    3.5784    3.7772    3.976     4.1748    4.3736    4.5724    4.7712      4.97
      0      0.2485     0.497    0.53068    0.7455     0.994    1.2425     1.491    1.7395     1.988    2.2365    2.485     2.7335     2.982    3.2305     3.479    3.7275     3.976    4.2245     4.473    4.7215     4.97     5.2185     5.467    5.7155     5.964    6.2125
      0      0.2982    0.5964    0.63682    0.8946    1.1928     1.491    1.7892    2.0874    2.3856    2.6838    2.982     3.2802    3.5784    3.8766    4.1748     4.473    4.7712    5.0694    5.3676    5.6658    5.964     6.2622    6.5604    6.8586    7.1568     7.455
      0      0.3479    0.6958    0.74295    1.0437    1.3916    1.7395    2.0874    2.4353    2.7832    3.1311    3.479     3.8269    4.1748    4.5227    4.8706    5.2185    5.5664    5.9143    6.2622    6.6101    6.958     7.3059    7.6538    8.0017    8.3496    8.6975
      0      0.3976    0.7952    0.84909    1.1928    1.5904     1.988    2.3856    2.7832    3.1808    3.5784    3.976     4.3736    4.7712    5.1688    5.5664     5.964    6.3616    6.7592    7.1568    7.5544    7.952     8.3496    8.7472    9.1448    9.5424      9.94
      0      0.4473    0.8946    0.95522    1.3419    1.7892    2.2365    2.6838    3.1311    3.5784    4.0257    4.473     4.9203    5.3676    5.8149    6.2622    6.7095    7.1568    7.6041    8.0514    8.4987    8.946     9.3933    9.8406    10.288    10.735    11.182

    mt_k1    mt_k2     mt_k3     mt_k4     mt_k5     mt_k6     mt_k7     mt_k8     mt_k9     mt_k10    mt_k11    mt_k12    mt_k13    mt_k14    mt_k15    mt_k16    mt_k17    mt_k18    mt_k19    mt_k20    mt_k21    mt_k22    mt_k23    mt_k24    mt_k25    mt_k26    mt_k27
    _____    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______    ______

      0      1.7395     3.479    3.7148    5.2185     6.958    8.6975    10.437    12.176    13.916    15.655    17.395    19.134    20.874    22.613    24.353    26.092    27.832    29.571    31.311     33.05     34.79    36.529    38.269    40.008    41.748    43.487
      0      1.7892    3.5784    3.8209    5.3676    7.1568     8.946    10.735    12.524    14.314    16.103    17.892    19.681     21.47     23.26    25.049    26.838    28.627    30.416    32.206    33.995    35.784    37.573    39.362    41.152    42.941     44.73
      0      1.8389    3.6778     3.927    5.5167    7.3556    9.1945    11.033    12.872    14.711     16.55    18.389    20.228    22.067    23.906    25.745    27.583    29.422    31.261      33.1    34.939    36.778    38.617    40.456    42.295    44.134    45.972
      0      1.8886    3.7772    4.0332    5.6658    7.5544     9.443    11.332     13.22    15.109    16.997    18.886    20.775    22.663    24.552     26.44    28.329    30.218    32.106    33.995    35.883    37.772    39.661    41.549    43.438    45.326    47.215
      0      1.9383    3.8766    4.1393    5.8149    7.7532    9.6915     11.63    13.568    15.506    17.445    19.383    21.321     23.26    25.198    27.136    29.074    31.013    32.951    34.889    36.828    38.766    40.704    42.643    44.581    46.519    48.457
      0       1.988     3.976    4.2454     5.964     7.952      9.94    11.928    13.916    15.904    17.892     19.88    21.868    23.856    25.844    27.832     29.82    31.808    33.796    35.784    37.772     39.76    41.748    43.736    45.724    47.712      49.7
      0      2.0377    4.0754    4.3516    6.1131    8.1508    10.188    12.226    14.264    16.302    18.339    20.377    22.415    24.452     26.49    28.528    30.565    32.603    34.641    36.679    38.716    40.754    42.792    44.829    46.867    48.905    50.942
      0      2.0874    4.1748    4.4577    6.2622    8.3496    10.437    12.524    14.612    16.699    18.787    20.874    22.961    25.049    27.136    29.224    31.311    33.398    35.486    37.573    39.661    41.748    43.835    45.923     48.01    50.098    52.185
      0      2.1371    4.2742    4.5638    6.4113    8.5484    10.685    12.823     14.96    17.097    19.234    21.371    23.508    25.645    27.782    29.919    32.056    34.194    36.331    38.468    40.605    42.742    44.879    47.016    49.153     51.29    53.427
      0      2.1868    4.3736      4.67    6.5604    8.7472    10.934    13.121    15.308    17.494    19.681    21.868    24.055    26.242    28.428    30.615    32.802    34.989    37.176    39.362    41.549    43.736    45.923     48.11    50.296    52.483     54.67

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_k_mesha
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Variables:

    ar_k_mesha: 1215×1 double

        Values:

            Min               0   
            Median       9.3933   
            Max           54.67   

pos = 1 ; key = f_coh ; val = @(z,b,k)(f_prod(z,k)+k*(1-fl_delta)+fl_w+b.*(1+fl_r_save).*(b>0)+b.*(1+fl_r_borr).*(b<=0))
pos = 2 ; key = f_cons ; val = @(coh,bprime,kprime)(coh-kprime-bprime)
pos = 3 ; key = f_inc ; val = @(z,b,k)(f_prod(z,k)-(fl_delta)*k+fl_w+b.*(fl_r_save).*(b>0)+b.*(fl_r_borr).*(b<=0))
pos = 4 ; key = f_prod ; val = @(z,k)((fl_Amean.*(z)).*(k.^(fl_alpha)))
pos = 5 ; key = f_util_crra ; val = @(c)(((c).^(1-fl_crra)-1)./(1-fl_crra))
pos = 6 ; key = f_util_log ; val = @(c)log(c)
pos = 7 ; key = f_util_standin ; val = @(z,b,k)f_util_log((f_coh(z,b,k)-fl_b_bd).*((f_coh(z,b,k)-fl_b_bd)>fl_c_min)+fl_c_min.*((f_coh(z,b,k)-fl_b_bd)<=fl_c_min))

Display

if (bl_display_funcgrids)
    fft_container_map_display(armt_map, it_display_summmat_rowmax, it_display_summmat_colmax);
    fft_container_map_display(func_map, it_display_summmat_rowmax, it_display_summmat_colmax);
end
----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: ARMT_MAP
----------------------------------------
  Map with properties:

        Count: 18
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = ar_a_meshk ;rown= 1215 ,coln= 1
ar_a_meshk :mu= 8.5778 ,sd= 12.4414 ,min= -4.67 ,max= 50
                     zi_1_c1
                     _______

    zi_1_R1            -4.67
    zi_2_R2            -4.67
    zi_3_R3            -4.67
    zi_608_R608       8.4508
    zi_1213_r1213     -2.185
    zi_1214_r1214    -3.4275
    zi_1215_r1215      -4.67

pos = 2 ; key = ar_ak_perc ;rown= 1 ,coln= 45
ar_ak_perc :mu= 0.5 ,sd= 0.2985 ,min= 0 ,max= 1
               zi_1_C1    zi_2_C2     zi_3_C3     zi_23_c23    zi_43_c43    zi_44_c44    zi_45_c45
               _______    ________    ________    _________    _________    _________    _________

    zi_1_r1       0       0.022727    0.045455       0.5        0.95455      0.97727         1    

pos = 3 ; key = ar_interp_c_grid ;rown= 1 ,coln= 619272
ar_interp_c_grid :mu= 30.9836 ,sd= 17.8769 ,min= 0.02 ,max= 61.9472
               zi_1_C1    zi_2_C2    zi_3_C3    zi_309636_c309636    zi_619270_c619270    zi_619271_c619271    zi_619272_c619272
               _______    _______    _______    _________________    _________________    _________________    _________________

    zi_1_r1     0.02      0.0201     0.0202          30.984               61.947               61.947               61.947      

pos = 4 ; key = ar_interp_coh_grid ;rown= 1 ,coln= 30
ar_interp_coh_grid :mu= 25.4269 ,sd= 19.1231 ,min= -4.67 ,max= 57.2773
               zi_1_C1    zi_2_C2    zi_3_C3     zi_15_c15    zi_28_c28    zi_29_c29    zi_30_c30
               _______    _______    ________    _________    _________    _________    _________

    zi_1_r1     -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  

pos = 5 ; key = ar_k_mesha ;rown= 1215 ,coln= 1
ar_k_mesha :mu= 13.2478 ,sd= 12.4414 ,min= 0 ,max= 54.67
                     zi_1_c1
                     _______

    zi_1_R1               0 
    zi_2_R2               0 
    zi_3_R3               0 
    zi_608_R608      13.121 
    zi_1213_r1213    52.185 
    zi_1214_r1214    53.427 
    zi_1215_r1215     54.67 

pos = 6 ; key = ar_stationary ;rown= 1 ,coln= 15
ar_stationary :mu= 0.066667 ,sd= 0.060897 ,min= 0.0027089 ,max= 0.16757
                zi_1_C1      zi_2_C2     zi_3_C3     zi_8_C8    zi_13_c13    zi_14_c14    zi_15_c15
               _________    _________    ________    _______    _________    _________    _________

    zi_1_r1    0.0027089    0.0069499    0.018507    0.16757    0.018507     0.0069499    0.0027089

pos = 7 ; key = ar_w_level ;rown= 1 ,coln= 27
ar_w_level :mu= 21.8256 ,sd= 16.9711 ,min= -4.67 ,max= 50
               zi_1_C1    zi_2_C2    zi_3_C3     zi_14_c14    zi_25_c25    zi_26_c26    zi_27_c27
               _______    _______    ________    _________    _________    _________    _________

    zi_1_r1     -4.67     -2.4832    -0.29638     21.572       45.626       47.813         50    

pos = 8 ; key = ar_w_perc ;rown= 1 ,coln= 25
ar_w_perc :mu= 0.5 ,sd= 0.30666 ,min= 0 ,max= 1
               zi_1_C1    zi_2_C2     zi_3_C3     zi_13_c13    zi_23_c23    zi_24_c24    zi_25_c25
               _______    ________    ________    _________    _________    _________    _________

    zi_1_r1       0       0.041667    0.083333       0.5        0.91667      0.95833         1    

pos = 9 ; key = ar_z ;rown= 1 ,coln= 15
ar_z :mu= 1.1347 ,sd= 0.69878 ,min= 0.34741 ,max= 2.567
               zi_1_C1    zi_2_C2    zi_3_C3    zi_8_C8    zi_13_c13    zi_14_c14    zi_15_c15
               _______    _______    _______    _______    _________    _________    _________

    zi_1_r1    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  

pos = 10 ; key = it_ameshk_n ; val = 1215
pos = 11 ; key = mt_coh_wkb ;rown= 1215 ,coln= 15
mt_coh_wkb :mu= 23.8417 ,sd= 17.1131 ,min= -4.67 ,max= 57.2773
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_8_C8    zi_13_c13    zi_14_c14    zi_15_c15
                     _______    _______    _______    _______    _________    _________    _________

    zi_1_R1           -4.67      -4.67      -4.67      -4.67       -4.67        -4.67        -4.67  
    zi_2_R2           -4.67      -4.67      -4.67      -4.67       -4.67        -4.67        -4.67  
    zi_3_R3           -4.67      -4.67      -4.67      -4.67       -4.67        -4.67        -4.67  
    zi_608_R608      22.054     22.189     22.345     23.562       26.05       26.798       27.662  
    zi_1213_r1213    47.504     47.725     47.981     49.983      54.072       55.302       56.721  
    zi_1214_r1214    47.299     47.522      47.78     49.799      53.923       55.163       56.594  
    zi_1215_r1215    47.093     47.319     47.579     49.614      53.772       55.023       56.466  

pos = 12 ; key = mt_interp_coh_grid_mesh_w_perc ;rown= 25 ,coln= 30
mt_interp_coh_grid_mesh_w_perc :mu= 25.4269 ,sd= 18.8142 ,min= -4.67 ,max= 57.2773
                 zi_1_C1    zi_2_C2    zi_3_C3     zi_15_c15    zi_28_c28    zi_29_c29    zi_30_c30
                 _______    _______    ________    _________    _________    _________    _________

    zi_1_R1       -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  
    zi_2_R2       -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  
    zi_3_R3       -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  
    zi_13_r13     -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  
    zi_23_r23     -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  
    zi_24_r24     -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  
    zi_25_r25     -4.67     -2.4576    -0.24518     24.091       52.852       55.065       57.277  

pos = 13 ; key = mt_interp_coh_grid_mesh_z ;rown= 30 ,coln= 15
mt_interp_coh_grid_mesh_z :mu= 25.4269 ,sd= 18.8226 ,min= -4.67 ,max= 57.2773
                 zi_1_C1     zi_2_C2     zi_3_C3     zi_8_C8     zi_13_c13    zi_14_c14    zi_15_c15
                 ________    ________    ________    ________    _________    _________    _________

    zi_1_R1         -4.67       -4.67       -4.67       -4.67       -4.67        -4.67        -4.67 
    zi_2_R2       -2.4576     -2.4576     -2.4576     -2.4576     -2.4576      -2.4576      -2.4576 
    zi_3_R3      -0.24518    -0.24518    -0.24518    -0.24518    -0.24518     -0.24518     -0.24518 
    zi_15_r15      24.091      24.091      24.091      24.091      24.091       24.091       24.091 
    zi_28_r28      52.852      52.852      52.852      52.852      52.852       52.852       52.852 
    zi_29_r29      55.065      55.065      55.065      55.065      55.065       55.065       55.065 
    zi_30_r30      57.277      57.277      57.277      57.277      57.277       57.277       57.277 

pos = 14 ; key = mt_k ;rown= 45 ,coln= 27
mt_k :mu= 13.2478 ,sd= 12.4414 ,min= 0 ,max= 54.67
                 zi_1_C1    zi_2_C2    zi_3_C3    zi_14_c14    zi_25_c25    zi_26_c26    zi_27_c27
                 _______    _______    _______    _________    _________    _________    _________

    zi_1_R1         0            0          0           0            0            0            0  
    zi_2_R2         0       0.0497     0.0994      0.5964       1.1431       1.1928       1.2425  
    zi_3_R3         0       0.0994     0.1988      1.1928       2.2862       2.3856        2.485  
    zi_23_r23       0       1.0934     2.1868      13.121       25.148       26.242       27.335  
    zi_43_r43       0       2.0874     4.1748      25.049        48.01       50.098       52.185  
    zi_44_r44       0       2.1371     4.2742      25.645       49.153        51.29       53.427  
    zi_45_r45       0       2.1868     4.3736      26.242       50.296       52.483        54.67  

pos = 15 ; key = mt_w_by_interp_coh_interp_grid ;rown= 25 ,coln= 30
mt_w_by_interp_coh_interp_grid :mu= 10.3784 ,sd= 14.2244 ,min= -4.67 ,max= 57.2773
                 zi_1_C1    zi_2_C2    zi_3_C3     zi_15_c15    zi_28_c28    zi_29_c29    zi_30_c30
                 _______    _______    ________    _________    _________    _________    _________

    zi_1_R1       -4.67       -4.67       -4.67       -4.67        -4.67        -4.67        -4.67 
    zi_2_R2       -4.67     -4.5778     -4.4856     -3.4716      -2.2732       -2.181      -2.0888 
    zi_3_R3       -4.67     -4.4856     -4.3012     -2.2732      0.12356      0.30792      0.49229 
    zi_13_r13     -4.67     -3.5638     -2.4576      9.7106       24.091       25.197       26.304 
    zi_23_r23     -4.67     -2.6419    -0.61391      21.694       48.059       50.087       52.115 
    zi_24_r24     -4.67     -2.5498    -0.42954      22.893       50.456       52.576       54.696 
    zi_25_r25     -4.67     -2.4576    -0.24518      24.091       52.852       55.065       57.277 

pos = 16 ; key = mt_z_mesh_coh_interp_grid ;rown= 30 ,coln= 15
mt_z_mesh_coh_interp_grid :mu= 1.1347 ,sd= 0.67583 ,min= 0.34741 ,max= 2.567
                 zi_1_C1    zi_2_C2    zi_3_C3    zi_8_C8    zi_13_c13    zi_14_c14    zi_15_c15
                 _______    _______    _______    _______    _________    _________    _________

    zi_1_R1      0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_2_R2      0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_3_R3      0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_15_r15    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_28_r28    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_29_r29    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_30_r30    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  

pos = 17 ; key = mt_z_mesh_coh_wkb ;rown= 1215 ,coln= 15
mt_z_mesh_coh_wkb :mu= 1.1347 ,sd= 0.6751 ,min= 0.34741 ,max= 2.567
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_8_C8    zi_13_c13    zi_14_c14    zi_15_c15
                     _______    _______    _______    _______    _________    _________    _________

    zi_1_R1          0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_2_R2          0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_3_R3          0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_608_R608      0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_1213_r1213    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_1214_r1214    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  
    zi_1215_r1215    0.34741    0.40076    0.4623     0.94436     1.9291       2.2253        2.567  

pos = 18 ; key = mt_z_trans ;rown= 15 ,coln= 15
mt_z_trans :mu= 0.066667 ,sd= 0.095337 ,min= 0 ,max= 0.27902
                  zi_1_C1       zi_2_C2       zi_3_C3       zi_8_C8      zi_13_c13     zi_14_c14     zi_15_c15 
                 __________    __________    __________    __________    __________    __________    __________

    zi_1_R1         0.26016       0.26831       0.25551    0.00012823    2.7001e-13    1.1102e-15             0
    zi_2_R2         0.11232       0.19622        0.2763    0.00098855    1.5289e-11    9.3592e-14    3.3307e-16
    zi_3_R3        0.037073       0.10492        0.2185     0.0055558    6.2811e-10    5.7438e-12    3.1863e-14
    zi_8_R8      1.7181e-06    4.1008e-05    0.00061112       0.27902    0.00061112    4.1008e-05    1.7181e-06
    zi_13_r13    3.1909e-14    5.7438e-12    6.2811e-10     0.0055558        0.2185       0.10492      0.037073
    zi_14_r14     3.474e-16    9.3597e-14    1.5289e-11    0.00098855        0.2763       0.19622       0.11232
    zi_15_r15    2.7412e-18    1.1057e-15    2.6998e-13    0.00012823       0.25551       0.26831       0.26016

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

    ar_a_meshk                         1     1     1215             1      8.5778      12.441        -4.67         50
    ar_ak_perc                         2     2        1            45         0.5      0.2985            0          1
    ar_interp_c_grid                   3     3        1    6.1927e+05      30.984      17.877         0.02     61.947
    ar_interp_coh_grid                 4     4        1            30      25.427      19.123        -4.67     57.277
    ar_k_mesha                         5     5     1215             1      13.248      12.441            0      54.67
    ar_stationary                      6     6        1            15    0.066667    0.060897    0.0027089    0.16757
    ar_w_level                         7     7        1            27      21.826      16.971        -4.67         50
    ar_w_perc                          8     8        1            25         0.5     0.30666            0          1
    ar_z                               9     9        1            15      1.1347     0.69878      0.34741      2.567
    mt_coh_wkb                        10    11     1215            15      23.842      17.113        -4.67     57.277
    mt_interp_coh_grid_mesh_w_perc    11    12       25            30      25.427      18.814        -4.67     57.277
    mt_interp_coh_grid_mesh_z         12    13       30            15      25.427      18.823        -4.67     57.277
    mt_k                              13    14       45            27      13.248      12.441            0      54.67
    mt_w_by_interp_coh_interp_grid    14    15       25            30      10.378      14.224        -4.67     57.277
    mt_z_mesh_coh_interp_grid         15    16       30            15      1.1347     0.67583      0.34741      2.567
    mt_z_mesh_coh_wkb                 16    17     1215            15      1.1347      0.6751      0.34741      2.567
    mt_z_trans                        17    18       15            15    0.066667    0.095337            0    0.27902

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Scalars in Container and Sizes and Basic Statistics
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                   i    idx    value
                   _    ___    _____

    it_ameshk_n    1    10     1215 

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Begin: Show all key and value pairs from container
CONTAINER NAME: FUNC_MAP
----------------------------------------
  Map with properties:

        Count: 7
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = f_coh ; val = @(z,b,k)(f_prod(z,k)+k*(1-fl_delta)+fl_w+b.*(1+fl_r_save).*(b>0)+b.*(1+fl_r_borr).*(b<=0))
pos = 2 ; key = f_cons ; val = @(coh,bprime,kprime)(coh-kprime-bprime)
pos = 3 ; key = f_inc ; val = @(z,b,k)(f_prod(z,k)-(fl_delta)*k+fl_w+b.*(fl_r_save).*(b>0)+b.*(fl_r_borr).*(b<=0))
pos = 4 ; key = f_prod ; val = @(z,k)((fl_Amean.*(z)).*(k.^(fl_alpha)))
pos = 5 ; key = f_util_crra ; val = @(c)(((c).^(1-fl_crra)-1)./(1-fl_crra))
pos = 6 ; key = f_util_log ; val = @(c)log(c)
pos = 7 ; key = f_util_standin ; val = @(z,b,k)f_util_log((f_coh(z,b,k)-fl_b_bd).*((f_coh(z,b,k)-fl_b_bd)>fl_c_min)+fl_c_min.*((f_coh(z,b,k)-fl_b_bd)<=fl_c_min))
----------------------------------------
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Scalars in Container and Sizes and Basic Statistics
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                      i    idx    xFunction
                      _    ___    _________

    f_coh             1     1         1    
    f_cons            2     2         2    
    f_inc             3     3         3    
    f_prod            4     4         4    
    f_util_crra       5     5         5    
    f_util_log        6     6         6    
    f_util_standin    7     7         7    

end
ans = 

  Map with properties:

        Count: 18
      KeyType: char
    ValueType: any