TensorToolbox 0.3.3

Tools for the decomposition of tensors

The Tensor Toolbox provides functionalities for the decomposition of tensors in tensor-train format [1] and spectral tensor-train format [2].

The toolbox provides the following tools:

• TT-svd

• TT-cross

• TT-dmrg

• TT-vectors

• TT-matrices

• Quatics TT-vectors/matrices (cross and dmrg)

• TT-integration

• Basic operations in TT format

• Multi-linear algebra in TT format (Steepest descent, CG and GMRES)

• STT-construction

• STT-projection/interpolation

• STT for single quantities and for fields

Installation

For everything to go smooth, I suggest that you first install some dependencies separately: numpy, scipy, matplotlib can be installed by:

$ pip install numpy scipy matplotlib

If you need MPI support in the TensorToolbox, you need to have an MPI back-end installed on your machine and add the right path on the $LD_LIBRARY_PATH, so that mpi4py can link to it. You should install mpi4py manually by

$ pip install mpi4py

When everything is set, you can install the TensorToolbox using:

$ pip install TensorToolbox

Some users might want to install the toolbox without MPI support. This is possible, but not through the pip command:

$ pip install –download=”/pth/to/downloaded/files” TensorToolbox

$ cd /pth/to/downloaded/files

$ tar xzf TensorToolbox-x.x.x.tar.gz

$ cd TensorToolbox-x.x.x

$ python setup.py install –without-mpi4py

Test Installation

You can test whether all the functionalities work by running the unit tests.

>>> import TensorToolbox
>>> TensorToolbox.RunUnitTests(maxprocs=None)

where maxprocs defines the number of processors to be used if MPI support is activated. Be patient. The number of unit tests grows with the number of functionalities implemented in the software.

Examples

Examples can be found inside the package. To find them, download the source:

$ pip install –download=”/pth/to/downloaded/files” TensorToolbox

$ cd /pth/to/downloaded/files

$ tar xzf TensorToolbox-x.x.x.tar.gz

$ cd TensorToolbox-x.x.x

$ cd Examples

References

[1] Oseledets, I. (2011). Tensor-train decomposition. SIAM Journal on Scientific Computing, 33(5), 2295–2317. Retrieved from http://epubs.siam.org/doi/pdf/10.1137/090752286

[2] Bigoni, D. and Marzouk, Y.M. and Engsig-Karup, A.P. (2014) Spectral tensor-train decomposition. (Submitted) ArXiv: http://arxiv.org/abs/1405.5713