# 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](https://www.tensorlab.net). 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:
```console
$ 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:
```python
>>> 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. Hendrickx, R. Widdershoven, N. Govindarajan, S. Sofi, L. De Lathauwer,
_"pyTensorlab 2025.10,"_ Oct. 2025. Available online at
[www.pytensorlab.net](https://www.pytensorlab.net).
## Contributors
We would like to thank all contributors:
- Ayvaz, Muzaffer
- Boussé, Martijn
- De Lathauwer, Lieven
- Devogel, Andreas
- Govindarajan, Nithin
- Hendrickx, Stijn
- Iannacito, Martina
- Seeuws, Nick
- Sofi, Shakir
- Vermeylen, Charlotte
- Vervliet, Nico
- Widdershoven, Raphaël
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