function [ar_a_grid_ceil_principle, ar_a_grid_ceil_wthr, ...

    ar_a_grid_floor_principle, ar_a_grid_floor_wthr] = ffs_for_br_block_match(varargin)

%% FFS_FOR_BR_BLOCK_MATCH formal borrowing blocks

% Find Value just below or above each element of *ar_a* from *ar_forbrblk*.

% a vector of grid points, find for each element of ar_a the element of

% ar_forbrblk that is just above or just below.

%

% # _ar_a_: $a'_i$ where $i \in (1,...,N)$

% # _ar_forbrblk_: $grid_j$ where $j\in (1,...,M)$

%

% $$ForCEIL_i = argmin_{j}(ForGrid_j - a'_i | grid_j > a'_i)$$

%

% $ForCEIL_i$ is the level of formal borrowing if joint formal + informal

% borrowing is chosen.

%

% $$ForFLOOR_i = argmax_{j}(ForGrid_j - a'_i | grid_j <= a'_i)$$

%

% $ForFLOOR_i$ is the level of formal borrowing if joint formal borrowing +

% informal savings is chosen.

%

% @param ar_a boolean N by 1 single formal borrowing levels, could include

% interest rate or principle only depending on _bl_b_is_principle_

%

% @param ar_forbrblk 1 by M array array of formal borrowing grid points.

% This always is just the formal borrowing levels principles only without

% interest rate.

%

% @param ar_forbrblk_r array interest rates associated with equal-length

% _ar_forbrblk_.

%

% @param bl_b_is_principle boolean solving with aggregate savings as

% savings + debt principles + interests, or just principles no interests.

% if true, principels only, no interests. Specifically: 

%

% * bl_b_is_principle = false: this means that the asset choices include

% both principle and interest rate. For here, that means _ar_a_ vector

% elements include both principle and interest rate, but the _ar_forbrblk_

% vector always only include principles. So when matching, need to

% translate _ar_forbrblk_ by appending interest rates on. 

% * bl_b_is_principle = false for *abz*, bl_b_is_principle = true for

% *ipwkbz*.

%

% @return ar_a_grid_ceil_principle array N by 1 Solution to:

%

% $$min_{j}(ForGrid_j - a'_i | grid_j > a'_i)$$

%

% @return ar_a_grid_ceil_wthr array _ar_a_grid_ceil_principle_ with

% interest rates specified to each borrowing formal level added

%

% @return ar_a_grid_floor_principle array N by 1 element of the *ar_forbrblk* vector that are

% the elements right above each eelemnt of ar_a. Solution to:

%

% $$max_{j}(ForGrid_j - a'_i | grid_j <= a'_i)$$

%

% @return ar_a_grid_floor_principle array _ar_a_grid_floor_principle_ with

% interest rates specified to each borrowing formal level added

%

% @example

%

%   [ar_a_grid_ceil, ar_a_grid_floor] = ...

%        ffs_for_br_block_match(ar_a, ar_forbrblk, ar_forbrblk_r, bl_b_is_principle);

%

% @seealso

%

% * Formal Borrowing Grid: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_for_br_block_gen.html ffs_for_br_block_gen>

% * Informal Interest Rates: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_r_inf.html ffs_r_inf>

% * Match Borrowing to Formal Grid: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_for_br_block_match.html ffs_for_br_block_match>

% * Optimize Formal and Informal, Borrowing and Savings Joint Choices: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_fibs_min_c_cost.html ffs_fibs_min_c_cost>

% * Bridge Loan: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_fibs_inf_bridge.html ffs_fibs_inf_bridge>

% * Overall Optimization: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_fibs_min_c_cost_bridge.html ffs_fibs_min_c_cost_bridge>

% * Discrete Choices: <https://fanwangecon.github.io/CodeDynaAsset/m_fibs/paramfunc_fibs/html/ffs_fibs_identify_discrete.html ffs_fibs_identify_discrete>

%

%% Default

% array of a choices

% ar_a could be principles + interests, or principles only

ar_a = -sort(rand([10,1])*20); 

% use defaults from block gen

[ar_forbrblk, ar_forbrblk_r] = ffs_for_br_block_gen(); 

% if bl_b_is_principle is true, b is principles only, no interests.

% bl_b_is_principle = false is the case for models like *abz* without

% interpolation over cash-on-hand

bl_b_is_principle = true; 

% Display

bl_display_brblockmatch = false; 

default_params = {ar_a ar_forbrblk ar_forbrblk_r bl_b_is_principle bl_display_brblockmatch}; 

%% Parse Parameters

% numvarargs is the number of varagin inputted

[default_params{1:length(varargin)}] = varargin{:}; 

[ar_a, ar_forbrblk, ar_forbrblk_r, bl_b_is_principle, bl_display_brblockmatch] = default_params{:}; 

%% Adjust Inputs t

% if bl_b_is_principle, then principle, with the assumption that

% ar_forbrblk. If bl_b_is_principle is false, that means the ar_a vector is

% principle and interest rates. Hence, need to convert ar_forbrblk which

% are principles to interests plus principles to be on the same scale as

% ar_a.

if (bl_b_is_principle) 

    ar_forbrblk_use = ar_forbrblk;

else 

    ar_forbrblk_use = ar_forbrblk.*(1+ar_forbrblk_r); 

end 

%% Show Details Step by Step

if (bl_display_brblockmatch) 

    % show borrowing array

    disp('ar_a')

    disp(ar_a)

    % show borrowing formal blocks/grids

    disp('ar_forbrblk_use and ar_forbrblk');

    disp([ar_forbrblk_use;ar_forbrblk]');

    % all combination division

    disp('mt_a_dvd_grid = (ar_a./ar_forbrblk_use)');

    mt_a_dvd_grid = (ar_a./ar_forbrblk_use);

    % ceiling for each

    disp('(mt_a_dvd_grid >= 1)');

    (mt_a_dvd_grid >= 1)

    % If ceiling exists and cloest ceiling index

    % min_{j}( ar_forbrblk[j] - ar_a[i] | ar_forbrblk[j] > ar_a[i])

    disp('[~, ar_max_a_on_grid_idx] = max((mt_a_dvd_grid >= 1),[], 2)');

    [~, ar_max_a_on_grid_idx] = max((mt_a_dvd_grid >= 1),[], 2)

    % ar_forbrblk[argmin_{j}( ar_forbrblk[j] - ar_a[i] | ar_forbrblk[j] > ar_a[i])]

    disp('ar_a_grid_ceil = ar_forbrblk_use(ar_max_a_on_grid_idx)');

    ar_a_grid_ceil = ar_forbrblk_use(ar_max_a_on_grid_idx)

    % ar_a_grid_ceil(ar_max_a_on_grid_idx == 1) = ar_forbrblk(0)

    % now floor, just one index less

    disp('ar_a_grid_floor = ar_forbrblk_use(max(ar_max_a_on_grid_idx - 1, 1))');

    ar_a_grid_floor = ar_forbrblk_use(max(ar_max_a_on_grid_idx - 1, 1))

    % ar_a_grid_floor(ar_max_a_on_grid_idx == 1) =

    % Dispaly

    tab_matched_grid = table(ar_a, ar_a_grid_floor', ar_a_grid_ceil');

    tab_matched_grid.Properties.VariableNames = {'ar_a','ar_a_grid_floor','ar_a_grid_ceil'};

    disp('ar_a_grid_floor: for borrow + for save');

    disp('ar_a_grid_ceil: for + inf borrow');

    disp(tab_matched_grid);

end

%% Standard Quicker Solve

% Get Index

[~, ar_max_a_on_grid_idx] = max(((ar_a./ar_forbrblk_use) >= 1),[], 2); 

% Get Values

if (bl_b_is_principle) 

    % Borrowing borrowing points, following formal grids, but add interests

    ar_a_grid_ceil_wthr = ...

        (ar_forbrblk_use(ar_max_a_on_grid_idx).*(1+ar_forbrblk_r(ar_max_a_on_grid_idx)))';

    ar_a_grid_floor_wthr = ...

        (ar_forbrblk_use(max(ar_max_a_on_grid_idx - 1, 1)).*(1+ar_forbrblk_r(max(ar_max_a_on_grid_idx - 1, 1))))';

    % Principles only, note ar_forbrblk_use = ar_forbrblk

    ar_a_grid_ceil_principle = ar_forbrblk_use(ar_max_a_on_grid_idx)';

    ar_a_grid_floor_principle = ar_forbrblk_use(max(ar_max_a_on_grid_idx - 1, 1))';

else 

    % Borrowing borrowing points, following formal grids, but add interests

    ar_a_grid_ceil_wthr = ar_forbrblk_use(ar_max_a_on_grid_idx)'; 

    ar_a_grid_floor_wthr = ar_forbrblk_use(max(ar_max_a_on_grid_idx - 1, 1))'; 

    % Principles only

    ar_a_grid_ceil_principle = ar_forbrblk(ar_max_a_on_grid_idx)'; 

    ar_a_grid_floor_principle = ar_forbrblk(max(ar_max_a_on_grid_idx - 1, 1))'; 

end 

%% Display

if (bl_display_brblockmatch) 

    disp('ar_a_grid_ceil_principle');

    disp(ar_a_grid_ceil_principle);

    disp('ar_a_grid_ceil_wthr');

    disp(ar_a_grid_ceil_wthr);

    disp('ar_a_grid_floor_principle');

    disp(ar_a_grid_floor_principle);

    disp('ar_a_grid_floor_wthr');

    disp(ar_a_grid_floor_wthr);

end

end