%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2020-10-29 15:04:18
 % @LastEditTime: 2021-01-11 15:54:42
%--------------------------
% node order: 4-3
%             1-2
% alldofs: alldofs num in the whole domain
% ele_nodeNum: node num in this macro-ele
function f = multi_elastic_force(lenout, alldofs, dx, F, dFdx, edofMat_ma, global_u, global_l)

    % % take one column in dF:
    % % dF here: [   0,    0;         current dF:[0, dNdx;
    % %           dNdx, dNdy];                    0, dNdy];
    % % At first, we need to transpose current dF to become dF here
    % dFdx = dFdx([1,3,2,4], :, :);
    
    eleNum_ma = size(dFdx, 2);
    f = zeros(alldofs, 1);
    jac = dx^2/4;

    for ele_ma = 1:eleNum_ma
        u = global_u{ele_ma}(:);
        l = global_l{ele_ma}(:);
        
        % as micro outer order: 4_coners, bottom, right, up, left
        fe = 0;
        for gp = 1:4
            Fe = F{gp, ele_ma};      % 4 * eleNum_mi
            P2 = PK1_fast(u, l, Fe); % 4 * eleNum_mi

            dFe = dFdx{gp, ele_ma};          % 4 * lenout * eleNum_mi
            dF1 = permute(dFe, [2,1,3]);     % l * 4 * eleNum_mi 
            dF2 = reshape(dF1, lenout, [])'; % 4m * l

            fg = P2(:)' * dF2;  % 1 * lenout
            fe = fe + fg * jac;        
        end

        % every macro ele: 4corners -> down -> right -> up -> left
        edof = edofMat_ma(ele_ma, :); 
        f(edof) = f(edof) - fe(:); % NOTE: MINUS!
    end   
end

function P = PK1(u,l,F)
    F = reshape(F, 2, 2);
    
    % Neo hookean
    JJ = log(det(F));
    Finv = inv(F)';
    PP = u*(F-Finv) + l*JJ*Finv;
    
    P = PP(:)';

    % Linear
    % I = eye(3,3);
    % PP = u*(F + F'-2*I) + l * (trace(F)-3) * I;
end