Adding optimization option for Cross-Interpolation

[WebKooH]

In the original paper by Sergei Goreinov, Ivan Oseledets, D. Savostyanov, E. Tyrtyshnikov, and Nickolai Zamarashkin "How to find a good submatrix" where maxvol routine was originally proposed, they stated that this method can help with finding not only submatrix with maximum volume in order to interpolate, but also with maximum element of the whole matrix(tensor), because of such submatrices often contain big elements(if not maximum). TT-Toolbox by Oseledets, on which you may base, have that optimization option implemented.

So i thought it may be useful to add same option here, in your lib. Especially when torchTT has much simplier installation, GPU and Torch compatibility and stuff, I'd prefer to use your lib instead of ttpy.

As i understood, all that is needed to implement such option is to when you do another maxvol procedure just update some Global-Maximum variable if needed with some bigger value from submatrix(if its bigger than Global_Maximum). Maybe this should be done not every iteration or maybe there're some other heuristics, better to check original papers. Anyways, it shouldn't be that hard especially when you already have cross-interpolation implemented.

Also, it seems that you've finally added DMRG to you lib, since I contacted you a year ago. Really can't wait to try it.
Please, contact me on email, because i no longer have @terraquantum.swiss mailbox.

Kuhmistrov Daniil, [email protected]