function result_map = ff_az_vf_vec(varargin)

%% FF_AZ_VF_VEC solve infinite horizon exo shock + endo asset problem

% This program solves the infinite horizon dynamic single asset and single

% shock problem with vectorized codes.

% <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf.html

% ff_az_vf> shows looped codes. The solution is the same.

%

% The vectorization takes advantage of implicit parallization that modern

% computers have when <https://en.wikipedia.org/wiki/SIMD same instructions

% are given for different blocks of data> With vectorization, we face a

% tradeoff between memory and speed. Suppose we have many shock points and

% many states points, if we build all states and choices into one single

% matrix and compute consumption, utility, etc over that entire matrix, that

% might be more efficient than computing consumption, utility, etc by

% subset of that matrix over a loop, but there is time required for

% generating that large input matrix, and if there are too many states, a

% computer could run out of memory.

%

% The design philosophy here is that we vectorize the endogenous states and

% choices into matrixes, but do not include the exogeous states (shocks).

% The exogenous shocks remain looped. This means we can potentially have

% multiple shock variables discretized over a large number of shock states,

% and the computer would not run into memory problems. The speed gain from

% vectoring the rest of the problem conditional on shocks is very large

% compared to the pure looped version of the problem. Even if more memory

% is available, including the exogenous states in the vectorization process

% might not be speed improving.

%

% Note one key issue is whether a programming language is

% <https://en.wikipedia.org/wiki/Row-_and_column-major_order row or column

% major> depending on which, states should be rows or columns.

%

% Another programming issue is the idea of *broadcasting* vs matrix

% algebra, both are used here. Since Matlab R2016b,

% <https://blogs.mathworks.com/loren/2016/10/24/matlab-arithmetic-expands-in-r2016b/

% matrix broadcasting> has been allowed, which means the sum of a N by 1

% and 1 by M is N by M. This is unrelated to matrix algebra. Matrix array

% broadcasting is very useful because it reduces the dimensionality of our

% model input state and choice and shock vectors, offering greater code

% clarity.

%

% @param param_map container parameter container

%

% @param support_map container support container

%

% @param armt_map container container with states, choices and shocks

% grids that are inputs for grid based solution algorithm

%

% @param func_map container container with function handles for

% consumption cash-on-hand etc.

%

% @return result_map container contains policy function matrix, value

% function matrix, iteration results, and policy function, value function

% and iteration results tables.

%

% keys included in result_map:

%

% * mt_val matrix states_n by shock_n matrix of converged value function grid

% * mt_pol_a matrix states_n by shock_n matrix of converged policy function grid

% * ar_val_diff_norm array if bl_post = true it_iter_last by 1 val function

% difference between iteration

% * ar_pol_diff_norm array if bl_post = true it_iter_last by 1 policy

% function difference between iterations

% * mt_pol_perc_change matrix if bl_post = true it_iter_last by shock_n the

% proportion of grid points at which policy function changed between

% current and last iteration for each element of shock

%

% @example

%

%    % Get Default Parameters

%    it_param_set = 2;

%    [param_map, support_map] = ffs_abz_set_default_param(it_param_set);

%    % Change Keys in param_map

%    param_map('it_a_n') = 500;

%    param_map('it_z_n') = 11;

%    param_map('fl_a_max') = 100;

%    param_map('fl_w') = 1.3;

%    % Change Keys support_map

%    support_map('bl_display') = false;

%    support_map('bl_post') = true;

%    support_map('bl_display_final') = false;

%    % Call Program with external parameters that override defaults.

%    ff_az_vf_vec(param_map, support_map);

%

% @include

%

% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/paramfunc/html/ffs_az_set_default_param.html ffs_az_set_default_param>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/paramfunc/html/ffs_az_get_funcgrid.html ffs_az_get_funcgrid>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/solvepost/html/ff_az_vf_post.html ff_az_vf_post>

%

% @seealso

%

% * save loop: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf.html ff_az_vf>

% * save vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf_vec.html ff_az_vf_vec>

% * save optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf_vecsv.html ff_az_vf_vecsv>

% * save + borr loop: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf.html ff_abz_vf>

% * save + borr vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf_vec.html ff_abz_vf_vec>

% * save + borr optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf_vecsv.html ff_abz_vf_vecsv>

%

%% Default

% * it_param_set = 1: quick test

% * it_param_set = 2: benchmark run

% * it_param_set = 3: benchmark profile

% * it_param_set = 4: press publish button

it_param_set = 3;

bl_input_override = true;

[param_map, support_map] = ffs_az_set_default_param(it_param_set);

% Note: param_map and support_map can be adjusted here or outside to override defaults

% param_map('it_a_n') = 750;

% param_map('it_z_n') = 15;

[armt_map, func_map] = ffs_az_get_funcgrid(param_map, support_map, bl_input_override); % 1 for override

default_params = {param_map support_map armt_map func_map};

%% Parse Parameters 1

% if varargin only has param_map and support_map,

params_len = length(varargin);

[default_params{1:params_len}] = varargin{:};

param_map = [param_map; default_params{1}];

support_map = [support_map; default_params{2}];

if params_len >= 1 && params_len <= 2

    % If override param_map, re-generate armt and func if they are not

    % provided

    bl_input_override = true;

    [armt_map, func_map] = ffs_az_get_funcgrid(param_map, support_map, bl_input_override);

else

    % Override all

    armt_map = [armt_map; default_params{3}];

    func_map = [func_map; default_params{4}];

end

% append function name

st_func_name = 'ff_az_vf_vec';

support_map('st_profile_name_main') = [st_func_name support_map('st_profile_name_main')];

support_map('st_mat_name_main') = [st_func_name support_map('st_mat_name_main')];

support_map('st_img_name_main') = [st_func_name support_map('st_img_name_main')];

%% Parse Parameters 2

% armt_map

params_group = values(armt_map, {'ar_a', 'mt_z_trans', 'ar_z'});

[ar_a, mt_z_trans, ar_z] = params_group{:};

% func_map

params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_cons', 'f_coh'});

[f_util_log, f_util_crra, f_cons, f_coh] = params_group{:};

% param_map

params_group = values(param_map, {'it_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_nan_replace'});

[it_a_n, it_z_n, fl_crra, fl_beta, fl_nan_replace] = params_group{:};

params_group = values(param_map, {'it_maxiter_val', 'fl_tol_val', 'fl_tol_pol', 'it_tol_pol_nochange'});

[it_maxiter_val, fl_tol_val, fl_tol_pol, it_tol_pol_nochange] = params_group{:};

% support_map

params_group = values(support_map, {'bl_profile', 'st_profile_path', ...

    'st_profile_prefix', 'st_profile_name_main', 'st_profile_suffix',...

    'bl_time', 'bl_display', 'it_display_every', 'bl_post'});

[bl_profile, st_profile_path, ...

    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...

    bl_time, bl_display, it_display_every, bl_post] = params_group{:};

%% Initialize Output Matrixes

% include mt_pol_idx which we did not have in looped code

mt_val_cur = zeros(length(ar_a),length(ar_z));

mt_val = mt_val_cur - 1;

mt_pol_a = zeros(length(ar_a),length(ar_z));

mt_pol_a_cur = mt_pol_a - 1;

mt_pol_idx = zeros(length(ar_a),length(ar_z));

%% Initialize Convergence Conditions

bl_vfi_continue = true;

it_iter = 0;

ar_val_diff_norm = zeros([it_maxiter_val, 1]);

ar_pol_diff_norm = zeros([it_maxiter_val, 1]);

mt_pol_perc_change = zeros([it_maxiter_val, it_z_n]);

%% Iterate Value Function

% Loop solution with 4 nested loops

%

% # loop 1: over exogenous states

% # loop 2: over endogenous states

% # loop 3: over choices

% # loop 4: add future utility, integration--loop over future shocks

%

% Start Profile

if (bl_profile)

    close all;

    profile off;

    profile on;

end 

% Start Timer

if (bl_time) 

    tic; 

end 

% Value Function Iteration

while bl_vfi_continue 

    it_iter = it_iter + 1; 

    %% Solve Optimization Problem Current Iteration

    % Only this segment of code differs between ff_az_vf and ff_az_vf_vec

    % loop 1: over exogenous states

    % incorporating these shocks into vectorization has high memory burden

    % but insignificant speed gains. Keeping this loop allows for large

    % number of shocks without overwhelming memory

    for it_z_i = 1:length(ar_z) 

        % Current Shock

        fl_z = ar_z(it_z_i); 

        % Consumption: fl_z = 1 by 1, ar_a = 1 by N, ar_a' = N by 1

        % mt_c is N by N: matrix broadcasting, expand to matrix from arrays

        mt_c = f_cons(fl_z, ar_a, ar_a'); 

        % EVAL current utility: N by N, f_util defined earlier

        if (fl_crra == 1) 

            mt_utility = f_util_log(mt_c);

        else 

            mt_utility = f_util_crra(mt_c); 

        end 

        % f(z'|z), 1 by Z

        ar_z_trans_condi = mt_z_trans(it_z_i,:); 

        % EVAL EV((A',K'),Z'|Z) = V((A',K'),Z') x p(z'|z)', (N by Z) x (Z by 1) = N by 1

        % Note: transpose ar_z_trans_condi from 1 by Z to Z by 1

        % Note: matrix multiply not dot multiply

        mt_evzp_condi_z = mt_val_cur * ar_z_trans_condi'; 

        % EVAL add on future utility, N by N + N by 1, broadcast again

        mt_utility = mt_utility + fl_beta*mt_evzp_condi_z; 

        mt_utility(mt_c <= 0) = fl_nan_replace; 

        % Optimization: remember matlab is column major, rows must be

        % choices, columns must be states

        % <https://en.wikipedia.org/wiki/Row-_and_column-major_order COLUMN-MAJOR>

        % mt_utility is N by N, rows are choices, cols are states.

        [ar_opti_val1_z, ar_opti_idx_z] = max(mt_utility); 

        mt_val(:,it_z_i) = ar_opti_val1_z; 

        mt_pol_a(:,it_z_i) = ar_a(ar_opti_idx_z); 

        if (it_iter == (it_maxiter_val + 1)) 

            mt_pol_idx(:,it_z_i) = ar_opti_idx_z; 

        end 

    end 

    %% Check Tolerance and Continuation

    % Difference across iterations

    ar_val_diff_norm(it_iter) = norm(mt_val - mt_val_cur); 

    ar_pol_diff_norm(it_iter) = norm(mt_pol_a - mt_pol_a_cur); 

    mt_pol_perc_change(it_iter, :) = sum((mt_pol_a ~= mt_pol_a_cur))/(it_a_n); 

    % Update

    mt_val_cur = mt_val; 

    mt_pol_a_cur = mt_pol_a; 

    % Print Iteration Results

    if (bl_display && (rem(it_iter, it_display_every)==0)) 

        fprintf('VAL it_iter:%d, fl_diff:%d, fl_diff_pol:%d\n', ...

            it_iter, ar_val_diff_norm(it_iter), ar_pol_diff_norm(it_iter));

        tb_valpol_iter = array2table([mean(mt_val_cur,1); mean(mt_pol_a_cur,1); ...

            mt_val_cur(it_a_n,:); mt_pol_a_cur(it_a_n,:)]);

        tb_valpol_iter.Properties.VariableNames = strcat('z', string((1:size(mt_val_cur,2))));

        tb_valpol_iter.Properties.RowNames = {'mval', 'map', 'Hval', 'Hap'};

        disp('mval = mean(mt_val_cur,1), average value over a')

        disp('map  = mean(mt_pol_a_cur,1), average choice over a')

        disp('Hval = mt_val_cur(it_a_n,:), highest a state val')

        disp('Hap = mt_pol_a_cur(it_a_n,:), highest a state choice')

        disp(tb_valpol_iter);

    end

    % Continuation Conditions:

    % 1. if value function convergence criteria reached

    % 2. if policy function variation over iterations is less than

    % threshold

    if (it_iter == (it_maxiter_val + 1)) 

        bl_vfi_continue = false; 

    elseif ((it_iter == it_maxiter_val) || ... 

            (ar_val_diff_norm(it_iter) < fl_tol_val) || ... 

            (sum(ar_pol_diff_norm(max(1, it_iter-it_tol_pol_nochange):it_iter)) < fl_tol_pol)) 

        % Fix to max, run again to save results if needed

        it_iter_last = it_iter; 

        it_iter = it_maxiter_val; 

    end 

end 

% End Timer

if (bl_time) 

    toc; 

end 

% End Profile

if (bl_profile) 

    profile off 

    profile viewer

    st_file_name = [st_profile_prefix st_profile_name_main st_profile_suffix];

    profsave(profile('info'), strcat(st_profile_path, st_file_name));

end

%% Process Optimal Choices

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

result_map('mt_val') = mt_val;

result_map('mt_pol_a') = mt_pol_a;

result_map('mt_pol_c') = f_coh(ar_z, ar_a') - mt_pol_a

result_map('ar_st_pol_names') = ['mt_pol_a', 'mt_pol_c'];

result_map('mt_pol_idx') = mt_pol_idx;

if (bl_post)

    bl_input_override = true;

    result_map('ar_val_diff_norm') = ar_val_diff_norm(1:it_iter_last);

    result_map('ar_pol_diff_norm') = ar_pol_diff_norm(1:it_iter_last);

    result_map('mt_pol_perc_change') = mt_pol_perc_change(1:it_iter_last, :);

    result_map = ff_az_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);

end

end