MatlabTrack

Installation

Prerequisites

In order to get started, you'll need the following:

• MATLAB (> R2020b)
• Parallel Computing Toolbox
• C compiler

You can then extract the code into any folder, making sure to add it to the MATLAB path. This is done either manually (right click folder -> Add to Path -> Selected Folders and Subfolders), or by navigating to the MatlabTrack directory and running doPath. Additionally, for the initial installation you should run the command GetMD5 once, which will compile the required mex files.

Settings

Note that usage of this package will create a folder LocalStorage in the current working directory, in order to store cached data. The default location of this folder can be changed in Mediators/@Mediator/Mediator.m, line 61.

Getting Started

You can now start using the MatlabTrack. The cornerstone of this package are the classes @TensorNone, @TensorSymm and @Tensor6j, the first defining non-symmetric tensors, while the latter are two separate implementations of symmetric tensors.

Creating tensors

Creating non-symmetric tensors is done in the following way:

>> dims = [2 3 2];
>> t = TensorNone.Random(dims)

t = 

  TensorNone with properties:

     var: [2×3×2 double]
    dims: [2 3 2]
    legs: 3
>> t.var

ans(:,:,1) =

  -0.1924 - 0.8045i  -0.7648 + 0.8351i  -1.4224 + 0.2157i
   0.8886 + 0.6966i  -1.4023 - 0.2437i   0.4882 - 1.1658i


ans(:,:,2) =

  -0.1774 - 1.1480i   1.4193 + 0.7223i   0.1978 - 0.6669i
  -0.1961 + 0.1049i   0.2916 + 2.5855i   1.5877 + 0.1873i

This creates a three-leg tensor of dimension 2 x 3 x 2, with normally distributed pseudorandom complex numbers. For more control over the initialisation, see also TensorNone.New, TensorNone.Ones and TensorNone.Zeros.

These objects behave like tensors, and as such support the following (incomplete) list of operations:

Permutations

>> t2 = Permute(t, [2 1 3])

t2 = 

  TensorNone with properties:

     var: [3×2×2 double]
    dims: [3 2 2]
    legs: 3
>> t2.var

ans(:,:,1) =

  -0.1924 - 0.8045i   0.8886 + 0.6966i
  -0.7648 + 0.8351i  -1.4023 - 0.2437i
  -1.4224 + 0.2157i   0.4882 - 1.1658i


ans(:,:,2) =

  -0.1774 - 1.1480i  -0.1961 + 0.1049i
   1.4193 + 0.7223i   0.2916 + 2.5855i
   0.1978 - 0.6669i   1.5877 + 0.1873i

Contractions

The contraction routine uses ncon-like syntax, with arbitrary amount of tensors:

>> t1 = TensorNone.Random([2 3 2]);
>> t2 = TensorNone.Random([3 4]);
>> t3 = Contract({t1 t2}, {[-1 1 -2] [1 -3]})

t3 = 

  TensorNone with properties:

     var: [2×2×4 double]
    dims: [2 2 4]
    legs: 3
>> t4 = Contract({t1 t2 t3}, {[1 2 3] [2 -1] [1 3 -2]})

t4 = 

  TensorNone with properties:

     var: [4×4 double]
    dims: [4 4]
    legs: 2

Factorisations