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

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Contents

function [armt_map, func_map] = ffs_akz_get_funcgrid(varargin)

FFS_AKZ_GET_FUNCGRID get funcs, params, states choices shocks grids

Centralized gateway for retrieving parameters, and solution grids and functions.

This function services both m_akz as well as m_akbz functions. This means that the function here support solving both the borrowing as well as the savings problems.

Note that while we have several versions of algorithms, one version requires interpolation, so there are several matrixes and vectors below that are specifically for that. These interpolation related matrixes and arrays are not used when we solve the wkz or akz problem, but are used when we solve the iwkz problem.

For the ikwz problem, we have two cash-on-hand matrixes: mt_coh_wkb

Note that in the m_abz problem's funcgrid function, we also called ffs_abz_gen_borrsave_grid function, which generates borrowing grid depending on if default is allowed or not. In the problem here, the situation is more complicated, because now the maximum borrowing level is a function of the risky investment choice when default is not allowed. We impose a exogenous borrowing bound here.

@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. keys included in armt_map are described below for each group of vectors when they are stored into armt_map.

@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_akz_set_default_param(it_param_set); [armt_map, func_map] =
  ffs_akz_get_funcgrid(param_map, support_map, bl_input_override);

@include

* ffs_akz_set_functions * ffto_gen_tauchen_jhl * fft_gen_grid_loglin

Default

if (~isempty(varargin))
    % override when called from outside
    [param_map, support_map] = varargin{:};
else
    % default internal run
    [param_map, support_map] = ffs_akz_set_default_param();
    support_map('bl_graph_funcgrids') = true;
    support_map('bl_display_funcgrids') = true;
    default_maps = {param_map, support_map};

    % Run Default with Borrowing
    param_map('fl_b_bd') = -20;

    % 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

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, {'fl_b_bd', 'fl_w_max', 'it_w_n', 'fl_coh_interp_grid_gap'});
[fl_b_bd, fl_w_max, it_w_n, fl_coh_interp_grid_gap] = params_group{:};

params_group = values(param_map, {'fl_k_min', 'it_ak_n'});
[fl_k_min, it_ak_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_display_funcgrids'});
[bl_graph_funcgrids, bl_display_funcgrids] = params_group{:};

Get Asset and Choice Grid

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. See ffs_akz_set_default_param for details.

fl_w_min = param_map('fl_b_bd');
fl_k_max = (param_map('fl_w_max') - param_map('fl_b_bd'));

ar_w = linspace(fl_w_min, fl_w_max, it_w_n);
ar_k = linspace(fl_k_min, fl_k_max, it_ak_n);

mt_a = ar_w - ar_k';
mt_k = ar_w - mt_a;

mt_bl_constrained = (mt_a < fl_b_bd); % this generates NAN, some NAN have -Inf Util
mt_a_wth_na = mt_a;
mt_k_wth_na = mt_k;
mt_a_wth_na(mt_bl_constrained) = nan;
mt_k_wth_na(mt_bl_constrained) = nan;

ar_a_mw_wth_na = mt_a_wth_na(:);
ar_k_mw_wth_na = mt_k_wth_na(:);

ar_a_meshk = ar_a_mw_wth_na(~isnan(ar_a_mw_wth_na));
ar_k_mesha = ar_k_mw_wth_na(~isnan(ar_k_mw_wth_na));

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_akz_set_functions(fl_crra, fl_c_min, 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 = f_coh(ar_z, ar_a_meshk, ar_k_mesha);
mt_z_mesh_coh_wkb = repmat(ar_z, [size(mt_coh_wkb,1),1]);

if (bl_display_funcgrids)

    % Generate Aggregate Variables
    ar_aplusk_mesh = ar_a_meshk + ar_k_mesha;

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

    % Label Table Variables
    tab_ak_choices.Properties.VariableDescriptions{'ar_aplusk_mesh'} = ...
        '*ar_aplusk_mesh*: ar_aplusk_mesh = ar_a_meshk + ar_k_mesha;';
    tab_ak_choices.Properties.VariableDescriptions{'ar_k_mesha'} = ...
        '*ar_k_mesha*:';
    tab_ak_choices.Properties.VariableDescriptions{'ar_a_meshk'} = ...
        '*ar_a_meshk*:';

    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)*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');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_coh_wkb));
    disp(head(array2table(mt_coh_wkb), it_rows_toshow));
    disp(tail(array2table(mt_coh_wkb), it_rows_toshow));

end
*ar_aplusk_mesh*: ar_aplusk_mesh = ar_a_meshk + ar_k_mesha;
*ar_k_mesha*:
*ar_a_meshk*:
----------------------------------------
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tab_ak_choices
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        1275           3

    tab_ak_choices1    tab_ak_choices2    tab_ak_choices3
    ar_aplusk_mesh       ar_k_mesha         ar_a_meshk   
    _______________    _______________    _______________

           -20                  0                -20     
       -18.571                  0            -18.571     
       -18.571             1.4286                -20     
       -17.143                  0            -17.143     
       -17.143             1.4286            -18.571     
       -17.143             2.8571                -20     
       -15.714                  0            -15.714     
       -15.714             1.4286            -17.143     
       -15.714             2.8571            -18.571     
       -15.714             4.2857                -20     
       -14.286                  0            -14.286     
       -14.286             1.4286            -15.714     
       -14.286             2.8571            -17.143     
       -14.286             4.2857            -18.571     
       -14.286             5.7143                -20     
       -12.857                  0            -12.857     
       -12.857             1.4286            -14.286     
       -12.857             2.8571            -15.714     
       -12.857             4.2857            -17.143     
       -12.857             5.7143            -18.571     
       -12.857             7.1429                -20     
       -11.429                  0            -11.429     
       -11.429             1.4286            -12.857     
       -11.429             2.8571            -14.286     
       -11.429             4.2857            -15.714     
       -11.429             5.7143            -17.143     
       -11.429             7.1429            -18.571     
       -11.429             8.5714                -20     
           -10                  0                -10     
           -10             1.4286            -11.429     
           -10             2.8571            -12.857     
           -10             4.2857            -14.286     
           -10             5.7143            -15.714     
           -10             7.1429            -17.143     
           -10             8.5714            -18.571     
           -10                 10                -20     
       -8.5714                  0            -8.5714     
       -8.5714             1.4286                -10     
       -8.5714             2.8571            -11.429     
       -8.5714             4.2857            -12.857     
       -8.5714             5.7143            -14.286     
       -8.5714             7.1429            -15.714     
       -8.5714             8.5714            -17.143     
       -8.5714                 10            -18.571     
       -8.5714             11.429                -20     
       -7.1429                  0            -7.1429     
       -7.1429             1.4286            -8.5714     
       -7.1429             2.8571                -10     
       -7.1429             4.2857            -11.429     
       -7.1429             5.7143            -12.857     
       -7.1429             7.1429            -14.286     
       -7.1429             8.5714            -15.714     
       -7.1429                 10            -17.143     
       -7.1429             11.429            -18.571     
       -7.1429             12.857                -20     
       -5.7143                  0            -5.7143     
       -5.7143             1.4286            -7.1429     
       -5.7143             2.8571            -8.5714     
       -5.7143             4.2857                -10     
       -5.7143             5.7143            -11.429     
       -5.7143             7.1429            -12.857     
       -5.7143             8.5714            -14.286     
       -5.7143                 10            -15.714     
       -5.7143             11.429            -17.143     
       -5.7143             12.857            -18.571     
       -5.7143             14.286                -20     
       -4.2857                  0            -4.2857     
       -4.2857             1.4286            -5.7143     
       -4.2857             2.8571            -7.1429     
       -4.2857             4.2857            -8.5714     
       -4.2857             5.7143                -10     
       -4.2857             7.1429            -11.429     
       -4.2857             8.5714            -12.857     
       -4.2857                 10            -14.286     
       -4.2857             11.429            -15.714     
       -4.2857             12.857            -17.143     
       -4.2857             14.286            -18.571     
       -4.2857             15.714                -20     
       -2.8571                  0            -2.8571     
       -2.8571             1.4286            -4.2857     
       -2.8571             2.8571            -5.7143     
       -2.8571             4.2857            -7.1429     
       -2.8571             5.7143            -8.5714     
       -2.8571             7.1429                -10     
       -2.8571             8.5714            -11.429     
       -2.8571                 10            -12.857     
       -2.8571             11.429            -14.286     
       -2.8571             12.857            -15.714     
       -2.8571             14.286            -17.143     
       -2.8571             15.714            -18.571     
       -2.8571             17.143                -20     
       -1.4286                  0            -1.4286     
       -1.4286             1.4286            -2.8571     
       -1.4286             2.8571            -4.2857     
       -1.4286             4.2857            -5.7143     
       -1.4286             5.7143            -7.1429     
       -1.4286             7.1429            -8.5714     
       -1.4286             8.5714                -10     
       -1.4286                 10            -11.429     
       -1.4286             11.429            -12.857     

    tab_ak_choices1    tab_ak_choices2    tab_ak_choices3
    ar_aplusk_mesh       ar_k_mesha         ar_a_meshk   
    _______________    _______________    _______________

        47.143             67.143                -20     
        48.571                  0             48.571     
        48.571             1.4286             47.143     
        48.571             2.8571             45.714     
        48.571             4.2857             44.286     
        48.571             5.7143             42.857     
        48.571             7.1429             41.429     
        48.571             8.5714                 40     
        48.571                 10             38.571     
        48.571             11.429             37.143     
        48.571             12.857             35.714     
        48.571             14.286             34.286     
        48.571             15.714             32.857     
        48.571             17.143             31.429     
        48.571             18.571                 30     
        48.571                 20             28.571     
        48.571             21.429             27.143     
        48.571             22.857             25.714     
        48.571             24.286             24.286     
        48.571             25.714             22.857     
        48.571             27.143             21.429     
        48.571             28.571                 20     
        48.571                 30             18.571     
        48.571             31.429             17.143     
        48.571             32.857             15.714     
        48.571             34.286             14.286     
        48.571             35.714             12.857     
        48.571             37.143             11.429     
        48.571             38.571                 10     
        48.571                 40             8.5714     
        48.571             41.429             7.1429     
        48.571             42.857             5.7143     
        48.571             44.286             4.2857     
        48.571             45.714             2.8571     
        48.571             47.143             1.4286     
        48.571             48.571                  0     
        48.571                 50            -1.4286     
        48.571             51.429            -2.8571     
        48.571             52.857            -4.2857     
        48.571             54.286            -5.7143     
        48.571             55.714            -7.1429     
        48.571             57.143            -8.5714     
        48.571             58.571                -10     
        48.571                 60            -11.429     
        48.571             61.429            -12.857     
        48.571             62.857            -14.286     
        48.571             64.286            -15.714     
        48.571             65.714            -17.143     
        48.571             67.143            -18.571     
        48.571             68.571                -20     
            50                  0                 50     
            50             1.4286             48.571     
            50             2.8571             47.143     
            50             4.2857             45.714     
            50             5.7143             44.286     
            50             7.1429             42.857     
            50             8.5714             41.429     
            50                 10                 40     
            50             11.429             38.571     
            50             12.857             37.143     
            50             14.286             35.714     
            50             15.714             34.286     
            50             17.143             32.857     
            50             18.571             31.429     
            50                 20                 30     
            50             21.429             28.571     
            50             22.857             27.143     
            50             24.286             25.714     
            50             25.714             24.286     
            50             27.143             22.857     
            50             28.571             21.429     
            50                 30                 20     
            50             31.429             18.571     
            50             32.857             17.143     
            50             34.286             15.714     
            50             35.714             14.286     
            50             37.143             12.857     
            50             38.571             11.429     
            50                 40                 10     
            50             41.429             8.5714     
            50             42.857             7.1429     
            50             44.286             5.7143     
            50             45.714             4.2857     
            50             47.143             2.8571     
            50             48.571             1.4286     
            50                 50                  0     
            50             51.429            -1.4286     
            50             52.857            -2.8571     
            50             54.286            -4.2857     
            50             55.714            -5.7143     
            50             57.143            -7.1429     
            50             58.571            -8.5714     
            50                 60                -10     
            50             61.429            -11.429     
            50             62.857            -12.857     
            50             64.286            -14.286     
            50             65.714            -15.714     
            50             67.143            -17.143     
            50             68.571            -18.571     
            50                 70                -20     

----------------------------------------
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mt_coh_wkb
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        1275          15

    mt_coh_wkb1    mt_coh_wkb2    mt_coh_wkb3    mt_coh_wkb4    mt_coh_wkb5    mt_coh_wkb6    mt_coh_wkb7    mt_coh_wkb8    mt_coh_wkb9    mt_coh_wkb10    mt_coh_wkb11    mt_coh_wkb12    mt_coh_wkb13    mt_coh_wkb14    mt_coh_wkb15
    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ____________    ____________    ____________    ____________    ____________    ____________

      -20.056        -20.056        -20.056        -20.056        -20.056        -20.056         -20.056        -20.056       -20.056         -20.056         -20.056         -20.056         -20.056         -20.056         -20.056  
      -18.592        -18.592        -18.592        -18.592        -18.592        -18.592         -18.592        -18.592       -18.592         -18.592         -18.592         -18.592         -18.592         -18.592         -18.592  
      -18.347        -18.286        -18.216        -18.136        -18.043        -17.935         -17.811        -17.668       -17.503         -17.313         -17.094         -16.841         -16.549         -16.212         -15.823  
      -17.128        -17.128        -17.128        -17.128        -17.128        -17.128         -17.128        -17.128       -17.128         -17.128         -17.128         -17.128         -17.128         -17.128         -17.128  
      -16.883        -16.822        -16.752        -16.671        -16.578        -16.471         -16.347        -16.204       -16.039         -15.849          -15.63         -15.376         -15.084         -14.748         -14.359  
      -16.921        -16.843        -16.753         -16.65         -16.53        -16.392         -16.233         -16.05       -15.838         -15.594         -15.312         -14.988         -14.613          -14.18         -13.682  
      -15.663        -15.663        -15.663        -15.663        -15.663        -15.663         -15.663        -15.663       -15.663         -15.663         -15.663         -15.663         -15.663         -15.663         -15.663  
      -15.418        -15.358        -15.288        -15.207        -15.114        -15.007         -14.883         -14.74       -14.575         -14.385         -14.165         -13.912          -13.62         -13.283         -12.895  
      -15.457        -15.379        -15.289        -15.185        -15.066        -14.928         -14.769        -14.585       -14.374          -14.13         -13.848         -13.523         -13.148         -12.716         -12.218  
      -15.527        -15.437        -15.333        -15.213        -15.075        -14.915         -14.731        -14.519       -14.274         -13.991         -13.666          -13.29         -12.856         -12.356         -11.779  
      -14.199        -14.199        -14.199        -14.199        -14.199        -14.199         -14.199        -14.199       -14.199         -14.199         -14.199         -14.199         -14.199         -14.199         -14.199  
      -13.954        -13.894        -13.824        -13.743         -13.65        -13.542         -13.418        -13.275       -13.111          -12.92         -12.701         -12.448         -12.156         -11.819          -11.43  
      -13.992        -13.914        -13.825        -13.721        -13.601        -13.464         -13.305        -13.121        -12.91         -12.665         -12.384         -12.059         -11.684         -11.252         -10.753  
      -14.063        -13.972        -13.869        -13.749         -13.61        -13.451         -13.267        -13.055        -12.81         -12.527         -12.201         -11.825         -11.392         -10.892         -10.315  
      -14.149        -14.049        -13.933          -13.8        -13.647         -13.47         -13.266        -13.031       -12.759         -12.446         -12.084         -11.667         -11.186         -10.632         -9.9915  
      -12.735        -12.735        -12.735        -12.735        -12.735        -12.735         -12.735        -12.735       -12.735         -12.735         -12.735         -12.735         -12.735         -12.735         -12.735  
       -12.49        -12.429        -12.359        -12.279        -12.185        -12.078         -11.954        -11.811       -11.646         -11.456         -11.237         -10.984         -10.692         -10.355         -9.9662  
      -12.528         -12.45         -12.36        -12.257        -12.137        -11.999          -11.84        -11.657       -11.445         -11.201         -10.919         -10.595          -10.22         -9.7876         -9.2889  
      -12.598        -12.508        -12.404        -12.284        -12.146        -11.987         -11.803         -11.59       -11.345         -11.063         -10.737         -10.361         -9.9275         -9.4273         -8.8502  
      -12.684        -12.584        -12.469        -12.336        -12.183        -12.006         -11.802        -11.566       -11.295         -10.981          -10.62         -10.203         -9.7221         -9.1672         -8.5272  
       -12.78        -12.672        -12.547        -12.403        -12.236        -12.045         -11.823        -11.568       -11.274         -10.934         -10.543         -10.091         -9.5698         -8.9686         -8.2751  
      -11.271        -11.271        -11.271        -11.271        -11.271        -11.271         -11.271        -11.271       -11.271         -11.271         -11.271         -11.271         -11.271         -11.271         -11.271  
      -11.026        -10.965        -10.895        -10.814        -10.721        -10.614          -10.49        -10.347       -10.182         -9.9918         -9.7724         -9.5193         -9.2273         -8.8904         -8.5019  
      -11.064        -10.986        -10.896        -10.792        -10.673        -10.535         -10.376        -10.193       -9.9809         -9.7368         -9.4552         -9.1304         -8.7556         -8.3233         -7.8247  
      -11.134        -11.044         -10.94         -10.82        -10.682        -10.522         -10.338        -10.126       -9.8811         -9.5986         -9.2728         -8.8968         -8.4632          -7.963         -7.3859  
       -11.22         -11.12        -11.005        -10.872        -10.718        -10.542         -10.337        -10.102       -9.8304         -9.5171         -9.1556         -8.7387         -8.2578          -7.703         -7.0629  
      -11.316        -11.207        -11.082        -10.938        -10.772         -10.58         -10.359        -10.104       -9.8097         -9.4702         -9.0785         -8.6267         -8.1056         -7.5043         -6.8108  
      -11.418        -11.302        -11.169        -11.015        -10.837        -10.633         -10.396        -10.124       -9.8097         -9.4472          -9.029         -8.5465           -7.99          -7.348         -6.6074  
      -9.8064        -9.8064        -9.8064        -9.8064        -9.8064        -9.8064         -9.8064        -9.8064       -9.8064         -9.8064         -9.8064         -9.8064         -9.8064         -9.8064         -9.8064  
      -9.5613        -9.5007        -9.4307          -9.35        -9.2569        -9.1495         -9.0255        -8.8826       -8.7177         -8.5275         -8.3081          -8.055          -7.763         -7.4262         -7.0376  
      -9.5994        -9.5215        -9.4317        -9.3281        -9.2086        -9.0708         -8.9117        -8.7283       -8.5167         -8.2725         -7.9909         -7.6661         -7.2913          -6.859         -6.3604  
      -9.6697        -9.5796        -9.4757        -9.3558        -9.2175         -9.058          -8.874        -8.6617       -8.4168         -8.1343         -7.8085         -7.4326         -6.9989         -6.4987         -5.9217  
      -9.7557        -9.6558        -9.5405        -9.4076        -9.2542        -9.0773         -8.8731        -8.6377       -8.3661         -8.0528         -7.6914         -7.2744         -6.7935         -6.2387         -5.5987  
      -9.8513         -9.743        -9.6181         -9.474        -9.3078        -9.1161         -8.8949        -8.6398       -8.3454         -8.0059         -7.6143         -7.1625         -6.6413         -6.0401         -5.3465  
      -9.9534        -9.8378        -9.7045        -9.5506        -9.3731        -9.1684         -8.9322        -8.6597       -8.3455         -7.9829         -7.5647         -7.0822         -6.5257         -5.8837         -5.1431  
       -10.06        -9.9383        -9.7973        -9.6346         -9.447        -9.2306          -8.981         -8.693       -8.3607         -7.9775         -7.5354         -7.0254         -6.4371         -5.7585         -4.9756  
      -8.3421        -8.3421        -8.3421        -8.3421        -8.3421        -8.3421         -8.3421        -8.3421       -8.3421         -8.3421         -8.3421         -8.3421         -8.3421         -8.3421         -8.3421  
      -8.0971        -8.0364        -7.9664        -7.8857        -7.7926        -7.6852         -7.5613        -7.4183       -7.2534         -7.0632         -6.8438         -6.5907         -6.2987         -5.9619         -5.5733  
      -8.1351        -8.0573        -7.9674        -7.8638        -7.7443        -7.6065         -7.4474         -7.264       -7.0524         -6.8083         -6.5266         -6.2018          -5.827         -5.3948         -4.8961  
      -8.2054        -8.1153        -8.0114        -7.8915        -7.7533        -7.5937         -7.4097        -7.1974       -6.9525         -6.6701         -6.3442         -5.9683         -5.5346         -5.0344         -4.4574  
      -8.2914        -8.1915        -8.0762        -7.9433        -7.7899         -7.613         -7.4089        -7.1734       -6.9018         -6.5885         -6.2271         -5.8101         -5.3292         -4.7744         -4.1344  
       -8.387        -8.2787        -8.1538        -8.0097        -7.8435        -7.6518         -7.4306        -7.1755       -6.8812         -6.5416           -6.15         -5.6982          -5.177         -4.5758         -3.8822  
      -8.4892        -8.3735        -8.2402        -8.0863        -7.9088        -7.7041         -7.4679        -7.1955       -6.8812         -6.5186         -6.1004         -5.6179         -5.0614         -4.4194         -3.6788  
      -8.5962         -8.474         -8.333        -8.1704        -7.9827        -7.7663         -7.5167        -7.2287       -6.8964         -6.5132         -6.0711         -5.5611         -4.9728         -4.2942         -3.5113  
       -8.707        -8.5788        -8.4308        -8.2602        -8.0633        -7.8363         -7.5743        -7.2721       -6.9236         -6.5214         -6.0576         -5.5225         -4.9052         -4.1932         -3.3717  
      -6.8778        -6.8778        -6.8778        -6.8778        -6.8778        -6.8778         -6.8778        -6.8778       -6.8778         -6.8778         -6.8778         -6.8778         -6.8778         -6.8778         -6.8778  
      -6.6328        -6.5721        -6.5021        -6.4214        -6.3283        -6.2209          -6.097         -5.954       -5.7891         -5.5989         -5.3795         -5.1264         -4.8344         -4.4976          -4.109  
      -6.6708         -6.593        -6.5032        -6.3996        -6.2801        -6.1422         -5.9832        -5.7997       -5.5881          -5.344         -5.0624         -4.7375         -4.3628         -3.9305         -3.4318  
      -6.7411        -6.6511        -6.5471        -6.4273         -6.289        -6.1294         -5.9454        -5.7331       -5.4883         -5.2058         -4.8799          -4.504         -4.0704         -3.5701         -2.9931  
      -6.8271        -6.7272         -6.612         -6.479        -6.3256        -6.1487         -5.9446        -5.7091       -5.4375         -5.1242         -4.7628         -4.3459         -3.8649         -3.3101         -2.6701  
      -6.9227        -6.8144        -6.6895        -6.5454        -6.3792        -6.1875         -5.9663        -5.7112       -5.4169         -5.0773         -4.6857         -4.2339         -3.7127         -3.1115         -2.4179  
      -7.0249        -6.9093        -6.7759         -6.622        -6.4445        -6.2398         -6.0036        -5.7312       -5.4169         -5.0543         -4.6361         -4.1537         -3.5971         -2.9551         -2.2145  
      -7.1319        -7.0097        -6.8687        -6.7061        -6.5185         -6.302         -6.0524        -5.7644       -5.4322         -5.0489         -4.6068         -4.0969         -3.5086         -2.8299         -2.0471  
      -7.2427        -7.1145        -6.9666        -6.7959        -6.5991         -6.372           -6.11        -5.8078       -5.4593         -5.0572         -4.5933         -4.0582         -3.4409         -2.7289         -1.9075  
      -7.3565        -7.2228        -7.0684        -6.8904         -6.685        -6.4481         -6.1748        -5.8595       -5.4958         -5.0763         -4.5924         -4.0341         -3.3901         -2.6472         -1.7902  
      -5.4135        -5.4135        -5.4135        -5.4135        -5.4135        -5.4135         -5.4135        -5.4135       -5.4135         -5.4135         -5.4135         -5.4135         -5.4135         -5.4135         -5.4135  
      -5.1685        -5.1078        -5.0379        -4.9571         -4.864        -4.7566         -4.6327        -4.4898       -4.3249         -4.1347         -3.9152         -3.6621         -3.3701         -3.0333         -2.6448  
      -5.2065        -5.1287        -5.0389        -4.9353        -4.8158        -4.6779         -4.5189        -4.3354       -4.1238         -3.8797         -3.5981         -3.2732         -2.8985         -2.4662         -1.9675  
      -5.2769        -5.1868        -5.0828         -4.963        -4.8247        -4.6652         -4.4811        -4.2688        -4.024         -3.7415         -3.4156         -3.0397         -2.6061         -2.1058         -1.5288  
      -5.3628        -5.2629        -5.1477        -5.0147        -4.8613        -4.6844         -4.4803        -4.2448       -3.9732         -3.6599         -3.2985         -2.8816         -2.4006         -1.8458         -1.2058  
      -5.4584        -5.3501        -5.2252        -5.0812         -4.915        -4.7232          -4.502        -4.2469       -3.9526         -3.6131         -3.2214         -2.7696         -2.2484         -1.6472        -0.95366  
      -5.5606         -5.445        -5.3116        -5.1577        -4.9803        -4.7755         -4.5393        -4.2669       -3.9526           -3.59         -3.1718         -2.6894         -2.1328         -1.4908        -0.75023  
      -5.6676        -5.5454        -5.4044        -5.2418        -5.0542        -4.8378         -4.5881        -4.3001       -3.9679         -3.5846         -3.1425         -2.6326         -2.0443         -1.3656        -0.58278  
      -5.7784        -5.6502        -5.5023        -5.3316        -5.1348        -4.9077         -4.6457        -4.3436        -3.995         -3.5929          -3.129         -2.5939         -1.9766         -1.2646        -0.44318  
      -5.8923        -5.7585        -5.6041        -5.4261        -5.2207        -4.9838         -4.7105        -4.3952       -4.0316          -3.612         -3.1281         -2.5698         -1.9258         -1.1829        -0.32592  
      -6.0086        -5.8696        -5.7093        -5.5244        -5.3111         -5.065         -4.7811        -4.4537        -4.076         -3.6402         -3.1375         -2.5577         -1.8888         -1.1172        -0.22705  
      -3.9492        -3.9492        -3.9492        -3.9492        -3.9492        -3.9492         -3.9492        -3.9492       -3.9492         -3.9492         -3.9492         -3.9492         -3.9492         -3.9492         -3.9492  
      -3.7042        -3.6435        -3.5736        -3.4928        -3.3997        -3.2923         -3.1684        -3.0255       -2.8606         -2.6704         -2.4509         -2.1978         -1.9058          -1.569         -1.1805  
      -3.7422        -3.6644        -3.5746         -3.471        -3.3515        -3.2136         -3.0546        -2.8711       -2.6595         -2.4154         -2.1338         -1.8089         -1.4342         -1.0019        -0.50323  
      -3.8126        -3.7225        -3.6186        -3.4987        -3.3604        -3.2009         -3.0168        -2.8046       -2.5597         -2.2772         -1.9513         -1.5754         -1.1418        -0.64156       -0.064512  
      -3.8986        -3.7986        -3.6834        -3.5504         -3.397        -3.2201          -3.016        -2.7806        -2.509         -2.1956         -1.8342         -1.4173        -0.93634        -0.38153         0.25848  
      -3.9941        -3.8859         -3.761        -3.6169        -3.4507        -3.2589         -3.0378        -2.7826       -2.4883         -2.1488         -1.7571         -1.3053        -0.78413        -0.18292         0.51063  
      -4.0963        -3.9807        -3.8473        -3.6935         -3.516        -3.3112          -3.075        -2.8026       -2.4883         -2.1258         -1.7075         -1.2251        -0.66854        -0.02654         0.71405  
      -4.2033        -4.0811        -3.9401        -3.7775        -3.5899        -3.3735         -3.1238        -2.8358       -2.5036         -2.1204         -1.6783         -1.1683        -0.57998        0.098655         0.88151  
      -4.3141        -4.1859         -4.038        -3.8673        -3.6705        -3.4434         -3.1815        -2.8793       -2.5307         -2.1286         -1.6647         -1.1296        -0.51236          0.1997          1.0211  
       -4.428        -4.2942        -4.1399        -3.9618        -3.7564        -3.5195         -3.2462         -2.931       -2.5673         -2.1477         -1.6638         -1.1055        -0.46152         0.28138          1.1384  
      -4.5443        -4.4053         -4.245        -4.0601        -3.8468        -3.6007         -3.3169        -2.9894       -2.6117         -2.1759         -1.6733         -1.0934         -0.4245         0.34712          1.2372  
      -4.6627        -4.5189         -4.353        -4.1616        -3.9409        -3.6862         -3.3924        -3.0535       -2.6626         -2.2117         -1.6914         -1.0914         -0.3991         0.39945          1.3206  
      -2.4849        -2.4849        -2.4849        -2.4849        -2.4849        -2.4849         -2.4849        -2.4849       -2.4849         -2.4849         -2.4849         -2.4849         -2.4849         -2.4849         -2.4849  
      -2.2399        -2.1793        -2.1093        -2.0286        -1.9354         -1.828         -1.7041        -1.5612       -1.3963         -1.2061        -0.98666        -0.73354        -0.44156        -0.10473         0.28381  
       -2.278        -2.2001        -2.1103        -2.0067        -1.8872        -1.7493         -1.5903        -1.4069       -1.1952        -0.95111         -0.6695        -0.34464        0.030098         0.46239         0.96106  
      -2.3483        -2.2582        -2.1543        -2.0344        -1.8961        -1.7366         -1.5526        -1.3403       -1.0954        -0.81291        -0.48704        -0.11113          0.3225         0.82273          1.3998  
      -2.4343        -2.3344        -2.2191        -2.0861        -1.9328        -1.7558         -1.5517        -1.3163       -1.0447        -0.73136        -0.36993        0.046995         0.52795          1.0828          1.7228  
      -2.5298        -2.4216        -2.2967        -2.1526        -1.9864        -1.7946         -1.5735        -1.3183        -1.024        -0.68449        -0.29283         0.15897         0.68015          1.2814          1.9749  
       -2.632        -2.5164         -2.383        -2.2292        -2.0517        -1.8469         -1.6108        -1.3383        -1.024        -0.66147        -0.24325          0.2392         0.79574          1.4377          2.1783  
      -2.7391        -2.6168        -2.4759        -2.3132        -2.1256        -1.9092         -1.6595        -1.3715       -1.0393        -0.65607        -0.21398         0.29601          0.8843          1.5629          2.3458  
      -2.8499        -2.7216        -2.5737        -2.4031        -2.2062        -1.9791         -1.7172         -1.415       -1.0664         -0.6643        -0.20043         0.33466         0.95193           1.664          2.4854  
      -2.9637        -2.8299        -2.6756        -2.4975        -2.2922        -2.0552         -1.7819        -1.4667        -1.103        -0.68346        -0.19951         0.35876          1.0028          1.7457          2.6027  
        -3.08         -2.941        -2.7807        -2.5958        -2.3825        -2.1364         -1.8526        -1.5251       -1.1474        -0.71163        -0.20897         0.37089          1.0398          1.8114          2.7015  
      -3.1984        -3.0546        -2.8887        -2.6973        -2.4766        -2.2219         -1.9281        -1.5893       -1.1983        -0.74737        -0.22716         0.37293          1.0652          1.8637          2.7849  
      -3.3186        -3.1702        -2.9991        -2.8016        -2.5738         -2.311         -2.0079        -1.6583       -1.2549        -0.78958        -0.25282         0.36637          1.0807          1.9046          2.8551  
      -1.0206        -1.0206        -1.0206        -1.0206        -1.0206        -1.0206         -1.0206        -1.0206       -1.0206         -1.0206         -1.0206         -1.0206         -1.0206         -1.0206         -1.0206  
     -0.77563       -0.71497         -0.645       -0.56428       -0.47116       -0.36374        -0.23983      -0.096894      0.067995         0.25821         0.47763         0.73074          1.0227          1.3596          1.7481  
     -0.81367       -0.73582       -0.64601       -0.54242       -0.42291       -0.28505        -0.12602       0.057433       0.26906         0.51318         0.79479          1.1196          1.4944          1.9267          2.4253  
       -0.884       -0.79391       -0.68999       -0.57011       -0.43182        -0.2723       -0.088275        0.12401       0.36889         0.65138         0.97724          1.3532          1.7868           2.287          2.8641  
     -0.96999       -0.87007       -0.75481       -0.62185       -0.46847       -0.29154       -0.087433        0.14801       0.41962         0.73293          1.0944          1.5113          1.9922           2.547          3.1871  
      -1.0656       -0.95729       -0.83239        -0.6883       -0.52209       -0.33036        -0.10919        0.14595       0.44028          0.7798          1.1715          1.6233          2.1444          2.7457          3.4392  
      -1.1677        -1.0521       -0.91874       -0.76488        -0.5874       -0.38266        -0.14648        0.12597       0.44026         0.80281           1.221          1.7035            2.26           2.902          3.6426  
      -1.2748        -1.1526        -1.0116       -0.84893       -0.66132        -0.4449        -0.19524       0.092758       0.42498         0.80822          1.2503          1.7603          2.3486          3.0272          3.8101  
      -1.3856        -1.2573        -1.1094       -0.93877       -0.74191       -0.51483        -0.25288       0.049295       0.39788         0.79999          1.2639          1.7989          2.4162          3.1283          3.9497  

    mt_coh_wkb1    mt_coh_wkb2    mt_coh_wkb3    mt_coh_wkb4    mt_coh_wkb5    mt_coh_wkb6    mt_coh_wkb7    mt_coh_wkb8    mt_coh_wkb9    mt_coh_wkb10    mt_coh_wkb11    mt_coh_wkb12    mt_coh_wkb13    mt_coh_wkb14    mt_coh_wkb15
    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ____________    ____________    ____________    ____________    ____________    ____________

      43.295         43.537         43.817          44.14         44.512         44.942         45.437         46.009         46.668          47.429          48.307          49.319          50.486          51.833          53.387   
      50.229         50.229         50.229         50.229         50.229         50.229         50.229         50.229         50.229          50.229          50.229          50.229          50.229          50.229          50.229   
      50.474         50.535         50.605         50.686         50.779         50.886          51.01         51.153         51.318          51.508          51.728          51.981          52.273           52.61          52.998   
      50.436         50.514         50.604         50.708         50.827         50.965         51.124         51.307         51.519          51.763          52.045           52.37          52.744          53.177          53.675   
      50.366         50.456          50.56          50.68         50.818         50.978         51.162         51.374         51.619          51.901          52.227          52.603          53.037          53.537          54.114   
       50.28          50.38         50.495         50.628         50.782         50.958         51.163         51.398          51.67          51.983          52.344          52.761          53.242          53.797          54.437   
      50.184         50.293         50.418         50.562         50.728          50.92         51.141         51.396          51.69           52.03          52.421          52.873          53.394          53.996          54.689   
      50.082         50.198         50.331         50.485         50.663         50.867         51.104         51.376          51.69          52.053          52.471          52.953           53.51          54.152          54.893   
      49.975         50.097         50.238         50.401         50.589         50.805         51.055         51.343         51.675          52.058            52.5           53.01          53.599          54.277           55.06   
      49.864         49.993         50.141         50.311         50.508         50.735         50.997         51.299         51.648           52.05          52.514          53.049          53.666          54.378            55.2   
      49.751         49.884         50.039         50.217         50.422         50.659         50.932         51.248         51.611          52.031          52.515          53.073          53.717           54.46          55.317   
      49.634         49.773         49.934         50.118         50.332         50.578         50.862         51.189         51.567          52.003          52.505          53.085          53.754          54.526          55.416   
      49.516          49.66         49.826         50.017         50.238         50.492         50.786         51.125         51.516          51.967          52.487          53.087          53.779          54.578          55.499   
      49.396         49.544         49.715         49.913          50.14         50.403         50.706         51.056         51.459          51.925          52.461          53.081          53.795          54.619          55.569   
      49.274         49.427         49.603         49.806         50.041         50.311         50.623         50.983         51.398          51.877          52.429          53.067          53.802           54.65          55.628   
      49.151         49.308         49.489         49.697         49.938         50.216         50.536         50.906         51.332          51.824          52.392          53.046          53.801          54.672          55.677   
      49.026         49.187         49.373         49.587         49.834         50.118         50.447         50.826         51.263          51.767          52.349           53.02          53.794          54.687          55.717   
      48.901         49.066         49.256         49.475         49.727         50.019         50.355         50.743          51.19          51.706          52.301          52.988           53.78          54.694          55.749   
      48.775         48.943         49.137         49.361         49.619         49.917         50.261         50.657         51.114          51.642           52.25          52.952          53.762          54.696          55.773   
      48.648         48.819         49.017         49.246         49.509         49.813         50.164         50.569         51.036          51.574          52.195          52.912          53.738          54.692          55.792   
       48.52         48.695         48.897          49.13         49.398         49.708         50.066         50.479         50.955          51.504          52.137          52.867           53.71          54.682          55.804   
      48.391         48.569         48.775         49.012         49.286         49.602         49.966         50.386         50.871           51.43          52.076           52.82          53.678          54.669          55.811   
      48.261         48.443         48.652         48.894         49.172         49.494         49.865         50.292         50.786          51.355          52.011          52.769          53.642           54.65          55.813   
      48.131         48.316         48.529         48.774         49.058         49.385         49.762         50.197         50.698          51.277          51.945          52.715          53.603          54.628           55.81   
      48.001         48.188         48.405         48.654         48.942         49.274         49.657         50.099         50.609          51.197          51.876          52.658          53.561          54.602          55.804   
       47.87          48.06          48.28         48.533         48.825         49.163         49.552         50.001         50.518          51.115          51.804          52.599          53.516          54.573          55.793   
      47.738         47.931         48.154         48.411         48.708          49.05         49.445           49.9         50.426          51.032          51.731          52.537          53.468          54.541          55.779   
      47.606         47.802         48.028         48.289          48.59         48.937         49.337         49.799         50.332          50.947          51.656          52.473          53.417          54.505          55.761   
      47.473         47.672         47.901         48.166         48.471         48.822         49.228         49.697         50.237           50.86          51.578          52.408          53.364          54.467           55.74   
       47.34         47.542         47.774         48.042         48.351         48.707         49.118         49.593          50.14          50.771            51.5           52.34          53.309          54.426          55.716   
      47.207         47.411         47.646         47.917          48.23         48.591         49.008         49.488         50.042          50.682          51.419           52.27          53.251          54.383          55.689   
      47.073          47.28         47.518         47.792         48.109         48.475         48.896         49.382         49.943          50.591          51.337          52.198          53.192          54.338           55.66   
      46.939         47.148         47.389         47.667         47.987         48.357         48.784         49.276         49.844          50.498          51.254          52.125           53.13           54.29          55.627   
      46.805         47.016          47.26         47.541         47.865         48.239         48.671         49.168         49.743          50.405          51.169           52.05          53.067           54.24          55.593   
       46.67         46.884          47.13         47.414         47.742          48.12         48.557          49.06         49.641           50.31          51.083          51.974          53.002          54.188          55.556   
      46.535         46.751             47         47.287         47.619         48.001         48.442         48.951         49.538          50.215          50.996          51.896          52.936          54.134          55.517   
        46.4         46.618          46.87          47.16         47.495         47.881         48.327         48.841         49.434          50.118          50.907          51.817          52.868          54.079          55.476   
      46.264         46.485         46.739         47.032         47.371         47.761         48.211          48.73         49.329           50.02          50.818          51.737          52.798          54.022          55.433   
      46.129         46.351         46.608         46.904         47.246          47.64         48.095         48.619         49.224          49.922          50.727          51.656          52.727          53.963          55.388   
      45.993         46.217         46.477         46.776         47.121         47.518         47.977         48.507         49.118          49.822          50.635          51.573          52.655          53.902          55.342   
      45.856         46.083         46.345         46.647         46.995         47.397          47.86         48.394         49.011          49.722          50.543          51.489          52.581           53.84          55.293   
       45.72         45.949         46.213         46.517         46.869         47.274         47.742         48.281         48.903          49.621          50.449          51.404          52.506          53.777          55.243   
      45.583         45.814         46.081         46.388         46.742         47.151         47.623         48.167         48.795          49.519          50.355          51.318           52.43          53.712          55.191   
      45.446         45.679         45.948         46.258         46.616         47.028         47.504         48.053         48.686          49.417          50.259          51.231          52.353          53.646          55.138   
      45.309         45.544         45.815         46.128         46.488         46.904         47.384         47.938         48.577          49.313          50.163          51.143          52.274          53.579          55.084   
      45.172         45.409         45.682         45.997         46.361          46.78         47.264         47.823         48.466          49.209          50.066          51.055          52.195           53.51          55.028   
      45.034         45.273         45.549         45.867         46.233         46.656         47.144         47.707         48.356          49.105          49.968          50.965          52.114          53.441           54.97   
      44.897         45.138         45.415         45.736         46.105         46.531         47.023          47.59         48.244          48.999           49.87          50.874          52.033           53.37          54.911   
      44.759         45.002         45.281         45.604         45.977         46.406         46.902         47.473         48.133          48.893          49.771          50.783          51.951          53.298          54.851   
      44.621         44.865         45.147         45.473         45.848         46.281          46.78         47.356          48.02          48.787          49.671          50.691          51.867          53.225           54.79   
      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         51.999         52.069          52.15         52.243         52.351         52.474         52.617         52.782          52.972          53.192          53.445          53.737          54.074          54.462   
      51.901         51.978         52.068         52.172         52.291         52.429         52.588         52.772         52.983          53.227          53.509          53.834          54.209          54.641           55.14   
       51.83          51.92         52.024         52.144         52.282         52.442         52.626         52.838         53.083          53.366          53.692          54.067          54.501          55.001          55.578   
      51.744         51.844         51.959         52.092         52.246         52.423         52.627         52.862         53.134          53.447          53.809          54.226          54.707          55.261          55.901   
      51.649         51.757         51.882         52.026         52.192         52.384         52.605          52.86         53.155          53.494          53.886          54.338          54.859           55.46          56.153   
      51.547         51.662         51.796         51.949         52.127         52.332         52.568          52.84         53.155          53.517          53.935          54.418          54.974          55.616          56.357   
       51.44         51.562         51.703         51.865         52.053         52.269         52.519         52.807         53.139          53.523          53.965          54.475          55.063          55.742          56.524   
      51.329         51.457         51.605         51.776         51.972         52.199         52.461         52.764         53.112          53.514          53.978          54.513          55.131          55.843          56.664   
      51.215         51.349         51.503         51.681         51.886         52.123         52.397         52.712         53.076          53.495          53.979          54.537          55.181          55.924          56.781   
      51.099         51.238         51.398         51.583         51.796         52.042         52.326         52.653         53.031          53.467           53.97          54.549          55.218           55.99           56.88   
       50.98         51.124          51.29         51.481         51.702         51.957          52.25         52.589          52.98          53.431          53.951          54.552          55.244          56.042          56.963   
       50.86         51.008          51.18         51.377         51.605         51.868         52.171          52.52         52.924          53.389          53.926          54.545          55.259          56.083          57.034   
      50.738         50.891         51.067          51.27         51.505         51.775         52.087         52.447         52.862          53.341          53.894          54.531          55.266          56.114          57.092   
      50.615         50.772         50.953         51.162         51.402          51.68         52.001          52.37         52.797          53.288          53.856           54.51          55.265          56.136          57.141   
      50.491         50.652         50.837         51.051         51.298         51.583         51.911          52.29         52.727          53.231          53.813          54.484          55.258          56.151          57.181   
      50.365          50.53          50.72         50.939         51.191         51.483         51.819         52.207         52.654           53.17          53.766          54.452          55.245          56.159          57.213   
      50.239         50.407         50.601         50.825         51.083         51.381         51.725         52.121         52.578          53.106          53.714          54.416          55.226           56.16          57.238   
      50.112         50.284         50.482          50.71         50.974         51.278         51.629         52.033           52.5          53.038          53.659          54.376          55.202          56.156          57.256   
      49.984         50.159         50.361         50.594         50.863         51.173          51.53         51.943         52.419          52.968          53.601          54.332          55.175          56.147          57.268   
      49.855         50.033         50.239         50.476          50.75         51.066          51.43         51.851         52.335          52.895           53.54          54.284          55.142          56.133          57.275   
      49.726         49.907         50.117         50.358         50.637         50.958         51.329         51.757          52.25          52.819          53.476          54.233          55.107          56.115          57.277   
      49.596          49.78         49.993         50.239         50.522         50.849         51.226         51.661         52.163          52.741          53.409          54.179          55.068          56.092          57.275   
      49.465         49.653         49.869         50.118         50.406         50.738         51.122         51.564         52.073          52.661           53.34          54.122          55.025          56.067          57.268   
      49.334         49.524         49.744         49.997          50.29         50.627         51.016         51.465         51.982           52.58          53.269          54.063           54.98          56.037          57.257   
      49.202         49.395         49.618         49.876         50.172         50.514         50.909         51.365          51.89          52.496          53.195          54.002          54.932          56.005          57.243   
       49.07         49.266         49.492         49.753         50.054         50.401         50.801         51.263         51.796          52.411           53.12          53.938          54.881           55.97          57.225   
      48.938         49.136         49.365          49.63         49.935         50.287         50.693         51.161         51.701          52.324          53.043          53.872          54.828          55.932          57.204   
      48.805         49.006         49.238         49.506         49.815         50.172         50.583         51.057         51.604          52.236          52.964          53.804          54.773          55.891           57.18   
      48.671         48.875          49.11         49.382         49.695         50.056         50.472         50.952         51.507          52.146          52.883          53.734          54.715          55.848          57.153   
      48.538         48.744         48.982         49.257         49.573         49.939          50.36         50.847         51.408          52.055          52.801          53.663          54.656          55.802          57.124   
      48.404         48.612         48.853         49.131         49.452         49.821         50.248          50.74         51.308          51.963          52.718          53.589          54.595          55.754          57.092   
      48.269          48.48         48.724         49.005         49.329         49.703         50.135         50.633         51.207          51.869          52.633          53.515          54.531          55.704          57.057   
      48.134         48.348         48.594         48.879         49.207         49.585         50.021         50.524         51.105          51.775          52.547          53.438          54.466          55.652           57.02   
      47.999         48.215         48.464         48.752         49.083         49.465         49.906         50.415         51.002          51.679           52.46          53.361            54.4          55.599          56.982   
      47.864         48.082         48.334         48.624         48.959         49.346         49.791         50.305         50.898          51.582          52.371          53.282          54.332          55.543          56.941   
      47.729         47.949         48.203         48.497         48.835         49.225         49.675         50.195         50.794          51.485          52.282          53.201          54.262          55.486          56.898   
      47.593         47.816         48.072         48.368          48.71         49.104         49.559         50.083         50.688          51.386          52.191           53.12          54.191          55.427          56.853   
      47.457         47.682         47.941          48.24         48.585         48.983         49.442         49.971         50.582          51.287            52.1          53.037          54.119          55.367          56.806   
      47.321         47.547         47.809         48.111         48.459         48.861         49.324         49.859         50.475          51.186          52.007          52.953          54.045          55.305          56.758   
      47.184         47.413         47.677         47.982         48.333         48.738         49.206         49.745         50.368          51.085          51.913          52.868           53.97          55.241          56.707   
      47.048         47.278         47.545         47.852         48.207         48.616         49.087         49.632         50.259          50.983          51.819          52.783          53.894          55.177          56.656   
      46.911         47.144         47.412         47.722          48.08         48.492         48.968         49.517          50.15          50.881          51.724          52.696          53.817           55.11          56.603   
      46.774         47.008         47.279         47.592         47.953         48.369         48.849         49.402         50.041          50.778          51.627          52.608          53.739          55.043          56.548   
      46.636         46.873         47.146         47.462         47.825         48.245         48.729         49.287         49.931          50.674           51.53          52.519          53.659          54.975          56.492   
      46.499         46.738         47.013         47.331         47.697          48.12         48.608         49.171          49.82          50.569          51.433          52.429          53.579          54.905          56.434   
      46.361         46.602         46.879           47.2         47.569         47.996         48.487         49.054         49.709          50.464          51.334          52.339          53.497          54.834          56.376   
      46.223         46.466         46.746         47.069         47.441          47.87         48.366         48.938         49.597          50.358          51.235          52.247          53.415          54.762          56.316   
      46.085          46.33         46.612         46.937         47.312         47.745         48.244          48.82         49.485          50.251          51.135          52.155          53.332          54.689          56.255   
      45.947         46.193         46.477         46.805         47.183         47.619         48.122         48.702         49.372          50.144          51.035          52.062          53.248          54.615          56.192   

IWKZ 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));
fl_min_mt_coh = min(min(mt_coh_wkb));
it_coh_interp_n = (fl_max_mt_coh-fl_min_mt_coh)/(fl_coh_interp_grid_gap);
ar_interp_coh_grid = linspace(fl_min_mt_coh, fl_max_mt_coh, it_coh_interp_n);
[mt_interp_coh_grid_mesh_z, mt_z_mesh_coh_interp_grid] = ndgrid(ar_interp_coh_grid, ar_z);

IWKZ 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)) - 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);

Store

armt_map = containers.Map('KeyType','char', 'ValueType','any');
armt_map('ar_w') = ar_w;
armt_map('ar_k') = ar_k;
armt_map('mt_z_trans') = mt_z_trans;
armt_map('ar_stationary') = ar_stationary;
armt_map('ar_z') = ar_z;
armt_map('mt_k_wth_na') = mt_k_wth_na;
armt_map('ar_a_mw_wth_na') = ar_a_mw_wth_na;
armt_map('ar_k_mw_wth_na') = ar_k_mw_wth_na;
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;
armt_map('mt_z_mesh_coh_wkb') = mt_z_mesh_coh_wkb;
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;

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

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

    chart = plot(mt_a_wth_na, mt_k_wth_na, 'blue');

    clr = jet(numel(chart));
    for m = 1:numel(chart)
       set(chart(m),'Color',clr(m,:))
    end
    if (length(ar_w) <= 100)
        scatter(ar_a_meshk, ar_k_mesha, 5, 'filled');
    end
    xline(0);
    yline(0);

    title('Choice Grids Conditional on k+a=w')
    ylabel('Capital Choice')
    xlabel({'Borrowing or Saving'})
    legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
    legendCell = cellstr(num2str(ar_w', 'k+a=%3.2f'));
    legend(chart(legend2plot), legendCell(legend2plot), 'Location','northeast');

    grid on;

Graph 2: coh by shock

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

    title('Cash-on-Hand given w(k+b),k,z');
    ylabel('Cash-on-Hand');
    xlabel({'Index of Cash-on-Hand Discrete Point'...
        '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'));
    legend(chart(legend2plot), legendCell(legend2plot), 'Location','southeast');

    grid on;

Graph 3: coh by index

    figure('PaperPosition', [0 0 7 3.5]);
    ar_coh_kpzgrid_unique = unique(sort(mt_coh_wkb(:)));
    scatter(1:length(ar_coh_kpzgrid_unique), ar_coh_kpzgrid_unique);
    title('Cash-on-Hand given w(k+b),k,z');
    ylabel('Cash-on-Hand');
    xlabel({'Index of Cash-on-Hand Discrete Point'});
    grid on;

Graph 4: coh by coh

    figure('PaperPosition', [0 0 7 3.5]);
    ar_coh_kpzgrid_unique = unique(sort(mt_coh_wkb(:)));
    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');
    xlabel({'Cash-on-Hand'});
    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');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(ar_w));
    disp(ar_w);

    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_wth_na');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_a_wth_na));
    disp(head(array2table(mt_a_wth_na), 10));
    disp(tail(array2table(mt_a_wth_na), 10));

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

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_a_meshk and ar_k_mesha');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    summary(array2table(ar_a_meshk));
    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
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
     1    50

  Columns 1 through 7

  -20.0000  -18.5714  -17.1429  -15.7143  -14.2857  -12.8571  -11.4286

  Columns 8 through 14

  -10.0000   -8.5714   -7.1429   -5.7143   -4.2857   -2.8571   -1.4286

  Columns 15 through 21

         0    1.4286    2.8571    4.2857    5.7143    7.1429    8.5714

  Columns 22 through 28

   10.0000   11.4286   12.8571   14.2857   15.7143   17.1429   18.5714

  Columns 29 through 35

   20.0000   21.4286   22.8571   24.2857   25.7143   27.1429   28.5714

  Columns 36 through 42

   30.0000   31.4286   32.8571   34.2857   35.7143   37.1429   38.5714

  Columns 43 through 49

   40.0000   41.4286   42.8571   44.2857   45.7143   47.1429   48.5714

  Column 50

   50.0000

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_z_trans
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    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 

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_interp_coh_grid
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Variables:

    Var1: 773×1 double

        Values:

            Min       -20.056
            Median      18.61
            Max        57.277

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_interp_c_grid
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Variables:

    Var1: 772762×1 double

        Values:

            Min        0.001
            Median    38.639
            Max       77.277

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_interp_coh_grid_mesh_z
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
   773    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
    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________

             -20.056                       -20.056                       -20.056                       -20.056                       -20.056                       -20.056                       -20.056                       -20.056                       -20.056                        -20.056                        -20.056                        -20.056                        -20.056                        -20.056                        -20.056          
             -19.956                       -19.956                       -19.956                       -19.956                       -19.956                       -19.956                       -19.956                       -19.956                       -19.956                        -19.956                        -19.956                        -19.956                        -19.956                        -19.956                        -19.956          
             -19.856                       -19.856                       -19.856                       -19.856                       -19.856                       -19.856                       -19.856                       -19.856                       -19.856                        -19.856                        -19.856                        -19.856                        -19.856                        -19.856                        -19.856          
             -19.756                       -19.756                       -19.756                       -19.756                       -19.756                       -19.756                       -19.756                       -19.756                       -19.756                        -19.756                        -19.756                        -19.756                        -19.756                        -19.756                        -19.756          
             -19.656                       -19.656                       -19.656                       -19.656                       -19.656                       -19.656                       -19.656                       -19.656                       -19.656                        -19.656                        -19.656                        -19.656                        -19.656                        -19.656                        -19.656          
             -19.555                       -19.555                       -19.555                       -19.555                       -19.555                       -19.555                       -19.555                       -19.555                       -19.555                        -19.555                        -19.555                        -19.555                        -19.555                        -19.555                        -19.555          
             -19.455                       -19.455                       -19.455                       -19.455                       -19.455                       -19.455                       -19.455                       -19.455                       -19.455                        -19.455                        -19.455                        -19.455                        -19.455                        -19.455                        -19.455          
             -19.355                       -19.355                       -19.355                       -19.355                       -19.355                       -19.355                       -19.355                       -19.355                       -19.355                        -19.355                        -19.355                        -19.355                        -19.355                        -19.355                        -19.355          
             -19.255                       -19.255                       -19.255                       -19.255                       -19.255                       -19.255                       -19.255                       -19.255                       -19.255                        -19.255                        -19.255                        -19.255                        -19.255                        -19.255                        -19.255          
             -19.155                       -19.155                       -19.155                       -19.155                       -19.155                       -19.155                       -19.155                       -19.155                       -19.155                        -19.155                        -19.155                        -19.155                        -19.155                        -19.155                        -19.155          

    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
    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    __________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________    ___________________________

              56.376                        56.376                        56.376                        56.376                        56.376                        56.376                        56.376                        56.376                        56.376                        56.376                         56.376                         56.376                         56.376                         56.376                         56.376           
              56.476                        56.476                        56.476                        56.476                        56.476                        56.476                        56.476                        56.476                        56.476                        56.476                         56.476                         56.476                         56.476                         56.476                         56.476           
              56.576                        56.576                        56.576                        56.576                        56.576                        56.576                        56.576                        56.576                        56.576                        56.576                         56.576                         56.576                         56.576                         56.576                         56.576           
              56.676                        56.676                        56.676                        56.676                        56.676                        56.676                        56.676                        56.676                        56.676                        56.676                         56.676                         56.676                         56.676                         56.676                         56.676           
              56.776                        56.776                        56.776                        56.776                        56.776                        56.776                        56.776                        56.776                        56.776                        56.776                         56.776                         56.776                         56.776                         56.776                         56.776           
              56.877                        56.877                        56.877                        56.877                        56.877                        56.877                        56.877                        56.877                        56.877                        56.877                         56.877                         56.877                         56.877                         56.877                         56.877           
              56.977                        56.977                        56.977                        56.977                        56.977                        56.977                        56.977                        56.977                        56.977                        56.977                         56.977                         56.977                         56.977                         56.977                         56.977           
              57.077                        57.077                        57.077                        57.077                        57.077                        57.077                        57.077                        57.077                        57.077                        57.077                         57.077                         57.077                         57.077                         57.077                         57.077           
              57.177                        57.177                        57.177                        57.177                        57.177                        57.177                        57.177                        57.177                        57.177                        57.177                         57.177                         57.177                         57.177                         57.177                         57.177           
              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_wth_na
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    50    50

    mt_a_wth_na1    mt_a_wth_na2    mt_a_wth_na3    mt_a_wth_na4    mt_a_wth_na5    mt_a_wth_na6    mt_a_wth_na7    mt_a_wth_na8    mt_a_wth_na9    mt_a_wth_na10    mt_a_wth_na11    mt_a_wth_na12    mt_a_wth_na13    mt_a_wth_na14    mt_a_wth_na15    mt_a_wth_na16    mt_a_wth_na17    mt_a_wth_na18    mt_a_wth_na19    mt_a_wth_na20    mt_a_wth_na21    mt_a_wth_na22    mt_a_wth_na23    mt_a_wth_na24    mt_a_wth_na25    mt_a_wth_na26    mt_a_wth_na27    mt_a_wth_na28    mt_a_wth_na29    mt_a_wth_na30    mt_a_wth_na31    mt_a_wth_na32    mt_a_wth_na33    mt_a_wth_na34    mt_a_wth_na35    mt_a_wth_na36    mt_a_wth_na37    mt_a_wth_na38    mt_a_wth_na39    mt_a_wth_na40    mt_a_wth_na41    mt_a_wth_na42    mt_a_wth_na43    mt_a_wth_na44    mt_a_wth_na45    mt_a_wth_na46    mt_a_wth_na47    mt_a_wth_na48    mt_a_wth_na49    mt_a_wth_na50
    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________

        -20           -18.571         -17.143         -15.714         -14.286         -12.857         -11.429             -10         -8.5714          -7.1429          -5.7143          -4.2857          -2.8571          -1.4286                0             1.4286          2.8571            4.2857          5.7143            7.1429          8.5714              10             11.429           12.857        14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40           41.429           42.857           44.286           45.714           47.143           48.571               50    
        NaN               -20         -18.571         -17.143         -15.714         -14.286         -12.857         -11.429             -10          -8.5714          -7.1429          -5.7143          -4.2857          -2.8571          -1.4286        -1.5543e-15          1.4286            2.8571          4.2857            5.7143          7.1429          8.5714                 10           11.429        12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40           41.429           42.857           44.286           45.714           47.143           48.571    
        NaN               NaN             -20         -18.571         -17.143         -15.714         -14.286         -12.857         -11.429              -10          -8.5714          -7.1429          -5.7143          -4.2857          -2.8571            -1.4286      4.4409e-16            1.4286          2.8571            4.2857          5.7143          7.1429             8.5714               10        11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40           41.429           42.857           44.286           45.714           47.143    
        NaN               NaN             NaN             -20         -18.571         -17.143         -15.714         -14.286         -12.857          -11.429              -10          -8.5714          -7.1429          -5.7143          -4.2857            -2.8571         -1.4286       -8.8818e-16          1.4286            2.8571          4.2857          5.7143             7.1429           8.5714            10           11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40           41.429           42.857           44.286           45.714    
        NaN               NaN             NaN             NaN             -20         -18.571         -17.143         -15.714         -14.286          -12.857          -11.429              -10          -8.5714          -7.1429          -5.7143            -4.2857         -2.8571           -1.4286      8.8818e-16            1.4286          2.8571          4.2857             5.7143           7.1429        8.5714               10           11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40           41.429           42.857           44.286    
        NaN               NaN             NaN             NaN             NaN             -20         -18.571         -17.143         -15.714          -14.286          -12.857          -11.429              -10          -8.5714          -7.1429            -5.7143         -4.2857           -2.8571         -1.4286       -8.8818e-16          1.4286          2.8571             4.2857           5.7143        7.1429           8.5714               10           11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40           41.429           42.857    
        NaN               NaN             NaN             NaN             NaN             NaN             -20         -18.571         -17.143          -15.714          -14.286          -12.857          -11.429              -10          -8.5714            -7.1429         -5.7143           -4.2857         -2.8571           -1.4286      1.7764e-15          1.4286             2.8571           4.2857        5.7143           7.1429           8.5714               10           11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40           41.429    
        NaN               NaN             NaN             NaN             NaN             NaN             NaN             -20         -18.571          -17.143          -15.714          -14.286          -12.857          -11.429              -10            -8.5714         -7.1429           -5.7143         -4.2857           -2.8571         -1.4286               0             1.4286           2.8571        4.2857           5.7143           7.1429           8.5714               10           11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571               40    
        NaN               NaN             NaN             NaN             NaN             NaN             NaN             NaN             -20          -18.571          -17.143          -15.714          -14.286          -12.857          -11.429                -10         -8.5714           -7.1429         -5.7143           -4.2857         -2.8571         -1.4286        -1.7764e-15           1.4286        2.8571           4.2857           5.7143           7.1429           8.5714               10           11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143           38.571    
        NaN               NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              -20          -18.571          -17.143          -15.714          -14.286          -12.857            -11.429             -10           -8.5714         -7.1429           -5.7143         -4.2857         -2.8571            -1.4286      -3.5527e-15        1.4286           2.8571           4.2857           5.7143           7.1429           8.5714               10           11.429           12.857           14.286           15.714           17.143           18.571               20           21.429           22.857           24.286           25.714           27.143           28.571               30           31.429           32.857           34.286           35.714           37.143    

    mt_a_wth_na1    mt_a_wth_na2    mt_a_wth_na3    mt_a_wth_na4    mt_a_wth_na5    mt_a_wth_na6    mt_a_wth_na7    mt_a_wth_na8    mt_a_wth_na9    mt_a_wth_na10    mt_a_wth_na11    mt_a_wth_na12    mt_a_wth_na13    mt_a_wth_na14    mt_a_wth_na15    mt_a_wth_na16    mt_a_wth_na17    mt_a_wth_na18    mt_a_wth_na19    mt_a_wth_na20    mt_a_wth_na21    mt_a_wth_na22    mt_a_wth_na23    mt_a_wth_na24    mt_a_wth_na25    mt_a_wth_na26    mt_a_wth_na27    mt_a_wth_na28    mt_a_wth_na29    mt_a_wth_na30    mt_a_wth_na31    mt_a_wth_na32    mt_a_wth_na33    mt_a_wth_na34    mt_a_wth_na35    mt_a_wth_na36    mt_a_wth_na37    mt_a_wth_na38    mt_a_wth_na39    mt_a_wth_na40    mt_a_wth_na41    mt_a_wth_na42    mt_a_wth_na43    mt_a_wth_na44    mt_a_wth_na45    mt_a_wth_na46    mt_a_wth_na47    mt_a_wth_na48    mt_a_wth_na49    mt_a_wth_na50
    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________

        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              -20            -18.571          -17.143          -15.714          -14.286          -12.857          -11.429              -10          -8.5714          -7.1429   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                -20          -18.571          -17.143          -15.714          -14.286          -12.857          -11.429              -10          -8.5714   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              -20          -18.571          -17.143          -15.714          -14.286          -12.857          -11.429              -10   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              NaN              -20          -18.571          -17.143          -15.714          -14.286          -12.857          -11.429   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              NaN              NaN              -20          -18.571          -17.143          -15.714          -14.286          -12.857   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              NaN              NaN              NaN              -20          -18.571          -17.143          -15.714          -14.286   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              NaN              NaN              NaN              NaN              -20          -18.571          -17.143          -15.714   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              NaN              NaN              NaN              NaN              NaN              -20          -18.571          -17.143   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              NaN              NaN              NaN              NaN              NaN              NaN              -20          -18.571   
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN                NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              -20   

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_k_wth_na
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    50    50

    mt_k_wth_na1    mt_k_wth_na2    mt_k_wth_na3    mt_k_wth_na4    mt_k_wth_na5    mt_k_wth_na6    mt_k_wth_na7    mt_k_wth_na8    mt_k_wth_na9    mt_k_wth_na10    mt_k_wth_na11    mt_k_wth_na12    mt_k_wth_na13    mt_k_wth_na14    mt_k_wth_na15    mt_k_wth_na16    mt_k_wth_na17    mt_k_wth_na18    mt_k_wth_na19    mt_k_wth_na20    mt_k_wth_na21    mt_k_wth_na22    mt_k_wth_na23    mt_k_wth_na24    mt_k_wth_na25    mt_k_wth_na26    mt_k_wth_na27    mt_k_wth_na28    mt_k_wth_na29    mt_k_wth_na30    mt_k_wth_na31    mt_k_wth_na32    mt_k_wth_na33    mt_k_wth_na34    mt_k_wth_na35    mt_k_wth_na36    mt_k_wth_na37    mt_k_wth_na38    mt_k_wth_na39    mt_k_wth_na40    mt_k_wth_na41    mt_k_wth_na42    mt_k_wth_na43    mt_k_wth_na44    mt_k_wth_na45    mt_k_wth_na46    mt_k_wth_na47    mt_k_wth_na48    mt_k_wth_na49    mt_k_wth_na50
    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________

          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                0                0                0                0                0                0                0                0                0                0                0                0                0                0                0                0                0                0                0                0                0    
        NaN            1.4286          1.4286          1.4286          1.4286          1.4286          1.4286          1.4286          1.4286          1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286           1.4286    
        NaN               NaN          2.8571          2.8571          2.8571          2.8571          2.8571          2.8571          2.8571          2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571           2.8571    
        NaN               NaN             NaN          4.2857          4.2857          4.2857          4.2857          4.2857          4.2857          4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857           4.2857    
        NaN               NaN             NaN             NaN          5.7143          5.7143          5.7143          5.7143          5.7143          5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143           5.7143    
        NaN               NaN             NaN             NaN             NaN          7.1429          7.1429          7.1429          7.1429          7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429           7.1429    
        NaN               NaN             NaN             NaN             NaN             NaN          8.5714          8.5714          8.5714          8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714           8.5714    
        NaN               NaN             NaN             NaN             NaN             NaN             NaN              10              10              10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10               10    
        NaN               NaN             NaN             NaN             NaN             NaN             NaN             NaN          11.429          11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429           11.429    
        NaN               NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN          12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857           12.857    

    mt_k_wth_na1    mt_k_wth_na2    mt_k_wth_na3    mt_k_wth_na4    mt_k_wth_na5    mt_k_wth_na6    mt_k_wth_na7    mt_k_wth_na8    mt_k_wth_na9    mt_k_wth_na10    mt_k_wth_na11    mt_k_wth_na12    mt_k_wth_na13    mt_k_wth_na14    mt_k_wth_na15    mt_k_wth_na16    mt_k_wth_na17    mt_k_wth_na18    mt_k_wth_na19    mt_k_wth_na20    mt_k_wth_na21    mt_k_wth_na22    mt_k_wth_na23    mt_k_wth_na24    mt_k_wth_na25    mt_k_wth_na26    mt_k_wth_na27    mt_k_wth_na28    mt_k_wth_na29    mt_k_wth_na30    mt_k_wth_na31    mt_k_wth_na32    mt_k_wth_na33    mt_k_wth_na34    mt_k_wth_na35    mt_k_wth_na36    mt_k_wth_na37    mt_k_wth_na38    mt_k_wth_na39    mt_k_wth_na40    mt_k_wth_na41    mt_k_wth_na42    mt_k_wth_na43    mt_k_wth_na44    mt_k_wth_na45    mt_k_wth_na46    mt_k_wth_na47    mt_k_wth_na48    mt_k_wth_na49    mt_k_wth_na50
    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________    _____________

        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN            57.143           57.143           57.143           57.143           57.143           57.143           57.143           57.143           57.143           57.143    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN           58.571           58.571           58.571           58.571           58.571           58.571           58.571           58.571           58.571    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN               60               60               60               60               60               60               60               60    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN              NaN           61.429           61.429           61.429           61.429           61.429           61.429           61.429    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN              NaN              NaN           62.857           62.857           62.857           62.857           62.857           62.857    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN              NaN              NaN              NaN           64.286           64.286           64.286           64.286           64.286    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN              NaN              NaN              NaN              NaN           65.714           65.714           65.714           65.714    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN              NaN              NaN              NaN              NaN              NaN           67.143           67.143           67.143    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN           68.571           68.571    
        NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN             NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN              NaN               70    

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_a_meshk and ar_k_mesha
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Variables:

    ar_a_meshk: 1275×1 double

        Values:

            Min               -20 
            Median     8.8818e-16 
            Max                50 


Variables:

    ar_k_mesha: 1275×1 double

        Values:

            Min             0     
            Median         20     
            Max            70     

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).*(f_coh(z,b,k)>0)+fl_c_min.*(f_coh(z,b,k)<=0))
end
ans = 

  Map with properties:

        Count: 17
      KeyType: char
    ValueType: any