%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-08-25 20:20:38
 % @LastEditTime: 2021-09-28 12:25:56
%--------------------------
function [regulated_matrix, dFdx] = precomputation_mmc(nele_macro, microx, rho, bezier_B, ke1, iK_mi, jK_mi, ...
    bdofs_num, dofid, edofMat_mi, dx)

    nele_micro = microx^2;
    regulated_matrix  = cell(nele_macro, 1);
    dFdx = cell(nele_macro);
    
    bezier_B = sparse(bezier_B);
    order1 = reshape(edofMat_mi', [], 1);
    
    vdofs_num = size(bezier_B, 2);

    % NOTE: Nh is ordered as 
    % 2 4
    % 1 3
    [~, dNh_ele, ~]   = shape_gradient_ele(dx/2, dx/2, 4);     
    
    for ele = 1 : nele_macro          
        rho_penal = rho{ele}(:);

        % Assemble the micro global stiffness as the order of [dofid]
        % i.e. [4-borders, inner], to be specific, [bottom, right, up, left, inner]
        % this order is determined by bezier_B
        K   = assemble_micro_k_mmc(dofid, rho_penal, microx, ke1, iK_mi, jK_mi);
        phi = build_M_simply(bdofs_num, K, bezier_B);

        Re = [bezier_B; phi]; % NOTE: current order of ndofs is as of [dofid]       
        R1 = Re(dofid(order1), :);
        R2 = reshape(R1, 8, []); % [8, nele*v]

        %% sensitivities
        dFe_gp = zeros(3, vdofs_num, nele_micro, 4);
        for gp = 1:4
            dNe_g = dNh_ele{gp}; % [3, 8]
            dFe = dNe_g * R2; % [3, nele*v]
            dF1 = reshape(dFe, 3, nele_micro, vdofs_num); % [3, nele, v]
            dFe_gp(:, :, :, gp) = permute(dF1, [1,3,2]);  % [3, v, nele]            
        end
        dFdx{ele} = dFe_gp;
        regulated_matrix{ele} = Re;    
    end   
end

% dK is dK_dx_micro
function [K] = assemble_micro_k_mmc(dofid, rho_e, microx, ke, iK, jK)
    
    new_iK = dofid(iK);
    new_jK = dofid(jK);
    
    sK = reshape(ke(:) * rho_e(:)', 64 * microx^2, 1);

    K = sparse(new_iK, new_jK, sK(:)); 
    K = (K + K') / 2;
end