%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-03-31 20:20:38
 % @LastEditTime: 2021-06-16 19:15:15
%--------------------------
function [regulated_matrix, dFdx, B, NH] = precomputation_3mat(eleNum_ma, microx, rho, bezier_B, ke0, ke1, ke2, iK_mi, jK_mi, ...
    bdofs_num, dofid, edofMat_mi, dx, nelx, nely)

    eleNum_mi = microx^2;
    regulated_matrix  = cell(eleNum_ma, 1);
    B    = cell(eleNum_ma, 1);
    dFdx = cell(4, eleNum_ma);
    
    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, ~, Nh]   = shape_gradient_ele(dx/2, dx/2, 4);     
    
    lx = dx * microx;
    NH = cell(eleNum_ma, 1);
        
    for ele = 1 : eleNum_ma          
        material = 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  = multi_assemble_k3(dofid, material, ke0, ke1, ke2, iK_mi, jK_mi);        
        Me = build_M_simply(bdofs_num, K, bezier_B);

        % [ndofs, v+p]. 
        Re = [bezier_B; Me]; % NOTE: current order of ndofs is as of [dofid]       
%         R1 = Re(dofid(order1), :);
%         R2 = reshape(R1, 8, []); % [8, nele*v]
        
%         for gp = 1:4
%             dNe_g = dNh_ele{gp};
%             dFe = dNe_g * R2; % [4, nele*v]
%             dF1 = reshape(dFe, 4, eleNum_mi, vdofs_num);
%             dFe = permute(dF1, [1,3,2]);
%             dFdx{gp, ele} = dFe;
%         end
        regulated_matrix{ele} = Re;    
        
        %% surface of NH
        R3 = Re(dofid, :);
        NHe = NH_alpha(microx, edofMat_mi, vdofs_num/2, Nh, R3);
        NH{ele, 1} = NHe;
    end   

    plot_NH_bezier(1, 1, lx, microx, nelx, nely, 2, NH);
    
end

%% utils
function K = multi_assemble_k3(dofid, material, ke0, ke1, ke2, iK, jK)

    microx = size(material, 1);
    sK = zeros(64, microx^2);

    for i = 1 : microx^2
        if material(i)==1
            sK(:, i) = ke1(:);
        elseif material(i)==2
            sK(:, i) = ke2(:);
        else
            sK(:, i) = ke0(:);
        end
    end
    
    new_iK = dofid(iK);
    new_jK = dofid(jK);

    % sK = reshape(ke(:) * (emin + material(:)' * (e0 - emin)), 64*microx^2, 1);
    K = sparse(new_iK, new_jK, sK(:)); 
    K = (K + K') / 2;
end