logqr

logqr is a Python library designed for efficient computation of the matrix logarithm and its inverse, the matrix exponential. It provides optimized implementations for both dense and sparse matrices, leveraging linear algebra techniques to handle large-scale problems. The library is particularly useful in fields such as control theory, differential equations, and machine learning, where matrix exponentials and logarithms frequently arise.

The core functionality of logqr revolves around the QR decomposition method, which decomposes a matrix into an orthogonal matrix Q and an upper triangular matrix R. This decomposition is then used to compute the logarithm and exponential of matrices through iterative refinement. The library supports both real and complex-valued matrices, making it versatile for a range of applications.

logqr is built on top of NumPy and SciPy, ensuring compatibility with existing scientific computing workflows. It includes functions for computing the matrix logarithm (logm), matrix exponential (expm), and related operations like the square root of a matrix (sqrtm). The implementation is designed to be numerically stable, minimizing errors in computations involving large or ill-conditioned matrices.

The library is open-source and maintained by a community of developers, with contributions from researchers and engineers. It is distributed under the MIT License, allowing for widespread adoption in both academic and industrial settings. Documentation and examples are provided to assist users in integrating logqr into their projects, with a focus on clarity and performance.

For users working with high-dimensional matrices, logqr offers sparse matrix support, reducing memory usage and computational overhead. This feature is particularly beneficial in large-scale simulations or optimization problems where efficiency is critical. The library also includes utilities for handling edge cases, such as singular matrices, with appropriate warnings or fallback methods.

Overall, logqr serves as a reliable tool for numerical linear algebra, bridging the gap between theoretical formulations and practical computations in scientific research and engineering.