MATLAB: Looking for a more elegant (less process-time consuming) code that obviates the external for loops.

for loopMATLAB

    L = zeros(Nz1,Ny);
    for z1 = 1:Nz1
        for y1 = 1:Ny
            AA6 = 0;
            for z2 = 1:Nz2
                AA5 = 0;
                for z3 = 1:Nz3
                    AA4 = 0;
                    for t1 = 1:Nt1
                        AA3 = 0;
                        for t2 = 1:Nt2
                            AA2 = 0;
                            for t3 = 1:Nt3
                                AA1 = 0;
                                for x = 1:Nx
                                    S1 = (M(x,y1,z2,z3) .* log(M(x,y1,z2,z3) ./ N(x,t1,t2,t3)));
                                    S1(isnan(S1)) = 0;
                                    AA0 = H(z2,z3,y1) .* A(t1,z1) .* B(t2,z2) .* C(t3,z3) .* S1;
                                    AA1 = AA1 + AA0;
                                end
                                AA2 = AA2 + AA1;
                            end
                            AA3 = AA3 + AA2;
                        end
                        AA4 = AA4 + AA3;
                    end
                    AA5 = AA5 + AA4;
                end
                AA6 = AA6 + AA5;
            end
            L(z1,y1) = AA6;
        end
    end

Best Answer

    % order everything as 8D array as following
    %              (x,y1,z1,z2,z3,t1,t2,t3)
    MM = permute(M,[1  2  5  3  4  6  7  8]);
    NN = permute(N,[1  5  6  7  8  2  3  4]);
    HH = permute(H,[4  3  5  1  2  6  7  8]);
    AA = permute(A,[3  4  2  5  6  1  7  8]);
    BB = permute(B,[3  4  5  2  6  7  1  8]);
    CC = permute(C,[3  4  5  6  2  7  8  1]);
    S1 = MM.* log(MM./NN);
    S1(isnan(S1)) = 0;
    AAA = HH .* AA .* BB .* CC .* S1;
    AAA = permute(AAA,[3 2 1 4 5 6 7 8]);
    L = sum(reshape(AAA,size(AAA,1),size(AAA,2),[]),3);
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