diffaaable 1.3.1

diffaaable is a JAX differentiable version of the AAA algorithm. The derivatives are implemented as custom Jacobian Vector products in accordance to [1]. A detailed derivation of the used matrix expressions is provided in the appendix of [2]. Under the hood diffaaable uses the AAA implementation of baryrat. Additionaly the following application specific extensions to the AAA algorithm are included:

• Adaptive: Adaptive refinement strategy (called Iterative Sample Refinement (ISR) in the corresponding paper) to minimize the number of function evaluation needed to precisely locate poles within some domain

• Vectorial: AAA algorithm acting on vector valued functions \(\mathbf{f}(z)\) as presented in [3].

• Tensor: Convenience alternative to the vector valued AAA algorithm (vectorial) accepting a tensor valued function F_k (so arbitrary dimensionality) instead of the single dimension that vectorial requires.

• Lorentz: Variant that enforces symmetric poles around the imaginary axis.

• Selective Refinement: Use a divide and conquer theme to capture many pole simultaneously and accurately, by limiting the number of poles per AAA solve. Suggested in [4].

Installation

to install diffaaable run pip install diffaaable

Usage

Please refer to the quickstart tutorial

Contributing

Feel free to open issues and/or PRs.

Citation

When using this software package for scientific work please cite the associated publication [2].

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[1]

https://arxiv.org/pdf/2403.19404

[2] (1,2)

“A framework to compute resonances arising from multiple scattering”, https://doi.org/10.1002/adts.202400989

[3]

https://doi.org/10.1093/imanum/draa098

[4]

https://doi.org/10.48550/arXiv.2405.19582