ttclass.m

Creates an object of a tensor train class. A tensor train is a type of un-opened Kronecker product that behaves as a matrix or a vector of a very large dimension, but takes a reasonable amount of memory to store. See https://doi.org/10.1137/090752286 for further informa- tion.

Syntax

    tt=ttclass(coeff,kronterms,tolerance)

Parameters

    coeff     - coefficient in front of the spin operator,
                usually the interaction magnitude

    kronterms - column cell array of matrices whose Krone-
                cker product makes up the spin operator

    tolerance - maximum deviation in the 2-norm between the
                TT representation and the flat matrix repre-
                sentation that the TT format is allowed to
                introduce

Outputs

    tt - tensor train object

Examples

Creating an un-opened Kronecker product of a 5x5 and a 7x7 matrices:

    >> a=ttclass(1,{rand(5);rand(7)},0)

    a = 

      35×35 ttclass array with properties:

             coeff: 1
             cores: {2×1 cell}
         tolerance: 0
        debuglevel: 0

Notes

1. If multiple columns are supplied in kronterms, multiple coeffi-

  cients are given in coeff, and multiple tolerances are given in
  tolerance, the resulting tensor train is assumed to be the sum
  of the individual tensor trains specified in different columns.

2. Tensor trains are exotic and capricious structures, do not use

  them unless you know what you are doing.

See also

polyadic.m, ttclass/mtimes.m, ttclass/kron.m, ttclass/full.m, Tensor_train_module

Version 2.4, authors: Dmitry Savostyanov, Ilya Kuprov