%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2020-10-29 15:04:15
 % @LastEditTime: 2021-03-13 16:28:28
%--------------------------

% obj and sensitivies
function [Q, dQ] = homogenization(KE0, KE1, edofMat, U, lx, ly, Emin, E0, xPhys)  
% function [Q,dQ] = homogenization(KE, edofMat, U, lx, ly, Emin, E0, xPhys)  
    qe = cell(3, 3);
    Q = zeros(3, 3);
    dQ = cell(3, 3);
    
    [nely, nelx] = size(xPhys);

    for i = 1:3

        for j = 1:3
            U1 = U(:, i);
            U2 = U(:, j);
            
            for ii = 1:nelx
                for jj = 1:nely       
                    ele = jj + (ii-1)*nely;
                    if xPhys(jj,ii)==1
                        KE = KE1;
                    else
                        KE = KE0;
                    end
                end
            end

            % these three are all col vec
            qe{i, j} = sum((U1(edofMat) * KE) .* U2(edofMat), 2) / (lx * ly); 
            Q(i, j) = sum(qe{i, j});

            % qe{i, j} = sum((U1(edofMat) * KE) .* U2(edofMat), 2) / (lx * ly); 
            % Q(i, j) = sum((Emin + xPhys(:) * (E0 - Emin)) .* qe{i, j}); 
            
            % dQ{i, j} = penal * (E0 - Emin) * xPhys.^(penal - 1) .* qe{i, j}; 
        end

    end
end