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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Footnotes

1. https://arxiv.org/pdf/2403.19404 ↩

2. "A framework to compute resonances arising from multiple scattering", https://doi.org/10.1002/adts.202400989 ↩ ↩²

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

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