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TensorLy is a Python library that aims at making tensor learning simple and accessible. It allows to easily perform tensor decomposition, tensor learning and tensor algebra. Its backend system allows to seamlessly perform computation with NumPy, MXNet, PyTorch, TensorFlow or CuPy, and run methods at scale on CPU or GPU.

Installing TensorLy

The only pre-requisite is to have Python 3 installed. The easiest way is via the Anaconda distribution.

With pip (recommended) With conda
pip install -U tensorly
conda install -c tensorly tensorly
Development (from git)
# clone the repository
git clone
cd tensorly
# Install in editable mode with `-e` or, equivalently, `--editable`
pip install -e .

Note: TensorLy depends on NumPy by default. If you want to use the MXNet or PyTorch backends, you will need to install these packages separately.

For detailed instruction, please see the documentation.

Running the tests

Testing and documentation are an essential part of this package and all functions come with uni-tests and documentation.

The tests are ran using the pytest package (though you can also use nose). First install pytest:

pip install pytest

Then to run the test, simply run, in the terminal:

pytest -v tensorly

Alternatively, you can specify for which backend you wish to run the tests:

TENSORLY_BACKEND='numpy' pytest -v tensorly


Create a small third order tensor of size 3 x 4 x 2 and perform simple operations on it:

import tensorly as tl
import numpy as np

tensor = tl.tensor(np.arange(24).reshape((3, 4, 2)), dtype=tl.float64)
unfolded = tl.unfold(tensor, mode=0)
tl.fold(unfolded, mode=0, shape=tensor.shape)

Applying tensor decomposition is easy:

from tensorly.decomposition import tucker
# Apply Tucker decomposition
tucker_tensor = tucker(tensor, rank=[2, 2, 2])
# Reconstruct the full tensor from the decomposed form

You can change the backend to perform computation with a different framework. Note that using MXNet, PyTorch, TensorFlow or CuPy requires to have installed them first. For instance, after setting the backend to PyTorch, all the computation is done by PyTorch, and tensors can be created on GPU:

tl.set_backend('pytorch') # Or 'mxnet', 'numpy', 'tensorflow' or 'cupy'
tensor = tl.tensor(np.arange(24).reshape((3, 4, 2)), device='cuda:0')
type(tensor) # torch.Tensor

For more information on getting started, checkout the user-guide and for a detailed reference of the functions and their documentation, refer to the API

If you see a bug, open an issue, or better yet, a pull-request!


If you use TensorLy in an academic paper, please cite [1]:

  author  = {Jean Kossaifi and Yannis Panagakis and Anima Anandkumar and Maja Pantic},
  title   = {TensorLy: Tensor Learning in Python},
  journal = {Journal of Machine Learning Research},
  year    = {2019},
  volume  = {20},
  number  = {26},
  pages   = {1-6},
  url     = {}
[1]Jean Kossaifi, Yannis Panagakis, Anima Anandkumar and Maja Pantic, TensorLy: Tensor Learning in Python, Journal of Machine Learning Research (JMLR), 2019, volume 20, number 26.
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