hello , i need help

[XDongiang]

when i write my code i meet a problem it puzzled me
the function is :

// definition of G_{mu,nu}
Tensor<double, 4, 4> metric()
{
    Tensor<double, 4, 4> G = {{-1., 0., 0., 0.},
                              {0., -1., 0., 0.},
                              {0., 0., -1., 0.},
                              {0., 0., 0., 1.}};
    return G;
}
Tensor<double, 4> phif222(const Tensor<double, 4>& psi2s,
                          const Tensor<double, 4>& phi,
                          const Tensor<double, 4>& f2,
                          const Tensor<double, 4>& kp,
                          const Tensor<double, 4>& km,
                          const Tensor<double, 4>& pip,
                          const Tensor<double, 4>& pim)
{
    enum { mu, a, b, r, delta, sigma, nu, lamda };
    Tensor<double, 4, 4, 4, 4> leci = leci_four();
    Tensor<double, 4, 4>       G    = metric();
    Tensor<double, 4, 4, 4, 4> leci_1 =
        einsum<Index<mu, a, b, r>, Index<mu, nu>>(leci, G);
    Tensor<double, 4, 4, 4, 4> leci_2 =
        einsum<Index<mu, a, b, r>, Index<a, nu>>(leci_1, G);
    Tensor<double, 4, 4, 4, 4> leci_3 =
        einsum<Index<mu, a, b, r>, Index<b, nu>>(leci_2, G);
    Tensor<double, 4, 4, 4, 4> leci_4 =
        einsum<Index<mu, a, b, r>, Index<r, nu>>(leci_3, G);
    ////////////////////// T^{(2)}
    Tensor<double, 4, 4> T2  = TT2(psi2s, phi, f2);
    Tensor<double, 4, 4> T2_ = einsum<Index<mu, nu>, Index<nu, delta>>(T2, G);
    ////////////////////// t^{(2)}
    Tensor<double, 4, 4> t2  = TT2(f2, pip, pim);
    Tensor<double, 4, 4> t2_ = einsum<Index<mu, nu>, Index<nu, delta>>(t2, G);
    ////////////////////// t^{(1)}
    Tensor<double, 4> t1  = TT1(phi, kp, km);
    Tensor<double, 4> t1_ = einsum<Index<nu>, Index<nu, mu>>(t1, G);
    ////////////////////// p_{psi}_alph
    Tensor<double, 4> psi2s_ = einsum<Index<mu>, Index<mu, nu>>(psi2s, G);
    ////////////////////////////////////////////////////////////////////
    auto first_1 = einsum<Index<mu, a, b, r>, Index<a>>(leci_4, psi2s_);
    auto first_2 = einsum<Index<mu, b, r>, Index<a, b>>(first_1, T2_);
    auto second_1 =
        einsum<Index<mu, delta, r>, Index<r, lamda, sigma, nu>>(first_1, leci);
    auto second_2 = einsum<Index<mu, delta, r>, Index<delta, lamda, sigma, nu>>(
        first_1, leci);
    auto third_1 =
        einsum<Index<mu, delta, lamda, sigma, nu>, Index<lamda, delta>>(
            second_1, t2_);
    auto third_2 =
        einsum<Index<mu, r, lamda, sigma, nu>, Index<lamda, r>>(second_2, t2_);
    Tensor<double, 4, 4, 4> add = third_1 + third_2;
    print(add);
    auto result  = einsum<Index<mu, sigma, nu>, Index<sigma>>(add, psi2s);
    auto result_ = einsum<Index<mu, nu>, Index<nu>>(result, t1_);
    return result_;
}

it is my code , i do not konw how to write the function use einsum , do i right in up code ?
can you help me , how to write so many term to einsum

[XDongiang]

and the leci_four is

// definition of epsilon_{mu,nu}, the whole anti-symmetric tensor
Tensor<double, 4, 4, 4, 4> leci_four()
{
    Tensor<double, 4, 4, 4, 4> leci;
    leci.zeros();
    leci(0, 1, 2, 3) = 1.;
    leci(0, 1, 3, 2) = -1.;
    leci(0, 3, 1, 2) = 1.;
    leci(3, 0, 1, 2) = -1.;
    leci(3, 0, 2, 1) = 1.;
    leci(0, 3, 2, 1) = -1.;
    leci(0, 2, 3, 1) = 1.;
    leci(0, 2, 1, 3) = -1.;
    leci(2, 0, 1, 3) = 1.;
    leci(2, 0, 3, 1) = -1.;
    leci(2, 3, 0, 1) = 1.;
    leci(3, 2, 0, 1) = -1.;
    leci(3, 2, 1, 0) = 1.;
    leci(2, 3, 1, 0) = -1.;
    leci(2, 1, 3, 0) = 1.;
    leci(2, 1, 0, 3) = -1.;
    leci(1, 2, 0, 3) = 1.;
    leci(1, 2, 3, 0) = -1.;
    leci(1, 3, 2, 0) = 1.;
    leci(3, 1, 2, 0) = -1.;
    leci(3, 1, 0, 2) = 1.;
    leci(1, 3, 0, 2) = -1.;
    leci(1, 0, 3, 2) = 1.;
    leci(1, 0, 2, 3) = -1.;
    return leci;
}

i think it may have symmetry

[romeric]

What are the functions TT1 and TT2 and how does your main function that calls the function phif222 look like?

And what is the problem exactly? Does it not compile, or does it crash or do you get incorrect results?

[XDongiang]

sorry , my exactly question is : how to use einsum to calculate the function

how to determine the index order ? and

[XDongiang]

i have solve my problem . and i thank if can determin the index of output , it will more easy to use the einsum . now i must to control the order of input to control the index of output .