%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-09-28 13:09:40
 % @LastEditTime: 2021-09-29 19:23:58

 % sensitivies for full-scale density, using the displacements
%--------------------------
function [dcdt, dvdt] = sensitivity_mmc(U, regulated_matrix, ke1, dH, edofMat_ma, edofMat_mi, dofid, cell2global_id)

    order2 = dofid(edofMat_mi');
    nele_mi = size(edofMat_mi, 1);
    nele_ma = size(edofMat_ma, 1);

    dcdp = zeros(nele_mi, nele_ma);

    % step.1 recover micro-displacements
    for ele = 1 : nele_ma
        Re = regulated_matrix{ele};
        edof = edofMat_ma(ele, :);
        umicro = Re * U(edof); % [boundary, inner]
        
        u1 = umicro(order2); % [8,m]
        u2(1,:,:) = u1;       % [1,8,m]
        u3 = permute(u2, [2,1,3]); % [8,1,m]

        % step.2 sensitivities for micro-density
        ke2 = repmat(ke1(:), 1, nele_mi);
        ke3 = reshape(ke2, 8,8,[]);

        % step.3 sensitivities for micro-density
        dcdp(:, ele) = mtimesx(mtimesx(u2, ke3), u3); % m,1        
    end

    dc = dcdp(cell2global_id); % [globaly, globalx], change to global_order

    % step.4 sensitivities for mmc-thickness
    dcdt = zeros(nele_ma * 20, 1);
    dvdt = zeros(nele_ma * 20, 1);
    
    for ci = 1 : nele_ma * 20
        dH_i = dH{ci}; % globaly, globalx
        dcdt(ci, 1) = dH_i(:)' * dc(:);

        dvdt(ci, 1) = mean(dH_i(:));
    end

end