covmats 0.2.1

A python impementation of covariance matrices.

covmats

🐍 Covariance matrices representation.

The complete and up to date documentation can be found here: https://covmats.readthedocs.io.

🎯 Motivations

Calculations involving covariance matrices (e.g. linear algebra, data whitening, multivariate normal function evaluation) are often performed more efficiently using a decomposition of the covariance matrix instead of the covariance matrix itself. For large scale application, a dense covariance matrix would not even fit in memory and one must rely on low-rank approxiations. This package allows the user to construct an object representing a covariance matrix using any of several decompositions/approximations and perform calculations using a common interface.

The common interface CovarianceMatrix can be seen as a extension of the class scipy.stats.Covariance as it inherits from it (thus making it compatible with all scipy.stats functions and classes) and dope it with LinearOperator capabilities.

The package is used in large-scale inversion packages such as pypcga, pyesmda and pyrtid.

🚀 Quick start

To install covmats, the easiest way is through pip:

pip install covmats

Or alternatively using conda

conda install covmats

You might also clone the repository and install from source

pip install -e .

Once the installation is done, covmats is straighforward to use and proposes the following full-rank covariance representations:

• CovViaDiagonal

• CovViaCholesky

• CovViaSparseCholesky

• CovViaPrecisionCholesky

• CovViaSparsePrecisionCholesky

It also provides low-rank approximations suitable for large scale problems:

• CovViaEigenFactorization

• CovViaEnsemble

Let’s start by importing numpy, scipy and covmats for the tests and define a random number generator seed for reproducibility:

import numpy as np
import scipy as sp
import covmats

rng_seed = 2026

First example with a diagonal covariance matrix

In the following, we define a (3 x 3) covariance matrix defining only its diagonal (i.e., all elements of the random vectors are independent). Using scipy, it is possible to compute the pdf.

d = [1, 2, 3]
A33 = np.diag(d)  # a diagonal covariance matrix
x = [4, -2, 5]  # a point of interest
dist = sp.stats.multivariate_normal(mean=[0, 0, 0], cov=A33)
dist.pdf(x)

np.float64(4.9595685102808205e-08)

It is possible to obtain a dense representation in a straighforward manner:

cov_diag33 = covmats.CovViaDiagonal(d)
dist = sp.stats.multivariate_normal(mean=[0, 0, 0], cov=cov_diag33)
dist.pdf(x)

np.float64(4.9595685102808205e-08)

It is compatible with the stats API from scipy since the base class inherit from Covariance.

🏗️ Complete example with supporting paper coming Q1 2026.

🔑 License

This project is released under the BSD 3-Clause License.

Copyright (c) 2026, Antoine COLLET. All rights reserved.

For more details, see the LICENSE file included in this repository.

⚠️ Disclaimer

This software is provided “as is”, without warranty of any kind, express or implied, including but not limited to the warranties of merchantability, fitness for a particular purpose, or non-infringement. In no event shall the authors or copyright holders be liable for any claim, damages, or other liability, whether in an action of contract, tort, or otherwise, arising from, out of, or in connection with the software or the use or other dealings in the software.

By using this software, you agree to accept full responsibility for any consequences, and you waive any claims against the authors or contributors.

📧 Contact

For questions, suggestions, or contributions, you can reach out via:

• Email: [e-mail]

• GitHub: https://github.com/antoinecollet5/covmats

We welcome contributions!

📚 References

TODO

• Free software: SPDX-License-Identifier: BSD-3-Clause