Complex tensor for SLoopTNR

[LLLantern]

Hi, I'm new to Julia and I'm trying to learn TNRKit. I found the SLoopTNR method, as in symmetric_looptnr.jl, is applicable for real tensors but not for tensors with complex elements. So I wonder how the method can be adapted for complex tensors.

I previously used fortran 90 to implement LoopTNR with C4 and reflection symmetry for complex tensors, when the Hamiltonian symmetry is not imposed. The idea is to use a vector to store the real part and imaginary part of S tensor, respectively. That is, we first create a 1d array with size 2n, if the total number of elements in S is n. Then we fill the first n elements with the real part of S, and the last n elements with the imaginary part. This vector or 1d array is the 'x' that is to be optimized for the minimization of the error function.
But in the present case, where the tensor has some symmetry, I have no idea on how to create such a vector or 1d array.

In short, I have two questions: the first is, how to implement the SLoopTNR scheme for complex tensors? The second is, how to define such a vector as just mentioned, in the presence of Hamiltonian symmetry?

Best regards.

[Adwait-Naravane]

Hello, Sorry for the late reply. The SloopTNR implementation in TNRKit right now is a simple implementation that only works for tensors with real entries. As far as I understand, it should be easy to make it work for complex tensors by replacing the conjugates in the cost function with permutations (with added flips to compensate for the primed spaces).

[LLLantern]

Hello, Sorry for the late reply. The SloopTNR implementation in TNRKit right now is a simple implementation that only works for tensors with real entries. As far as I understand, it should be easy to make it work for complex tensors by replacing the conjugates in the cost function with permutations (with added flips to compensate for the primed spaces).

Thank you for the reply! As far as I know, the input for the error function and the corresponding gradient should be real. Does the present method support for complex input, i.e., complex rank-3 tensor and complex gradient?