pyTensorlab

pyTensorlab is a Python package for tensor computations and complex optimization. The packages provides the following:

• data types to represent sparse, incomplete, structured and decomposed tensors efficiently;
• tools to generate and work with these data types effectively and efficiently;
• algorithms for computing the canonical polyadic decomposition, the multilinear singular value decomposition, the Tucker decomposition or low multilinear rank approximation and the tensor-train decomposition;
• tensorization techniques relying on statistics or Hankelization;
• visualization routines;
• preconditioned Gauss-Newton type optimization methods for complex variables;
• fully typed code, which facilitates development.

pyTensorlab is a reimplementation of the Matlab toolbox Tensorlab. Currently, the feature set is not identical. The Matlab toolbox also supports block term decompositions and has a structured data fusion framework which relies on a domain specific language to easily model coupled matrix and tensor decompositions and prior knowledge. On the other hand, pyTensorlab provides basic support for the TT decomposition and a more complete set of complex Gauss-Newton type optimization algorithms.

Getting Started

To install pyTensorlab, use:

$ pip install pytensorlab

pyTensorlab requires Python 3.10 to take advantage of new typing features. NumPy, SciPy and Numba for underly the main computations. Pymanopt is used for manifold-based optimization for low multilinear rank approximation and Vedo for visualization.

As an example, the canonical polyadic decomposition of a noisy rank-3 tensor can be computed as follows:

>>> import pytensorlab as tl
>>> import numpy as np
>>> shape = (10, 11, 12)
>>> Tpd = tl.PolyadicTensor.random(shape, 3)
>>> Tn = tl.noisy(np.array(Tpd), snr=20)
>>> Tres, info = tl.cpd(Tn, nterm=3)

Citation

If you are using pyTensorlab, please consider citing:

N. Vervliet, S. Hendrikx, R. Widdershoven, N. Govindarajan, S. Sofi, L. De Lathauwer, "pyTensorlab 2025.10," Oct. 2025. Available online at www.pytensorlab.net.

Contributors

We would like to thank all contributors:

• Ayvaz, Muzaffer
• Boussé, Martijn
• De Lathauwer, Lieven
• Devogel, Andreas
• Govindarajan, Nithin
• Hendrikx, Stijn
• Iannacito, Martina
• Seeuws, Nick
• Sofi, Shakir
• Vermeylen, Charlotte
• Vervliet, Nico
• Widdershoven, Raphaël