diffaaable 1.5.0

diffaaable is a JAX differentiable version of the AAA algorithm. The derivatives are implemented as custom Jacobian-vector products (JVPs) following 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. Additionally 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 evaluations needed to precisely locate poles within some domain
• Vectorial: AAA algorithm acting on vector valued functions $\mathbf{f}(z)$ as presented in ³.
• Tensor: Like Vectorial, but accepts tensor-valued functions $\mathbf{F}(z)$ of arbitrary shape, e.g. to obtain a joint pole-expansion of a T-matrix ⁴. Preferred over Vectorial.
• Lorentz: Variant that enforces symmetric poles around the imaginary axis.
• Selective Refinement: Use a divide-and-conquer scheme to capture many poles simultaneously and accurately, by limiting the number of poles per AAA solve. Suggested in ⁵.

Installation

to install diffaaable run pip install diffaaable

Usage

Please refer to the quickstart tutorial

Contributing

Feel free to open issues and/or PRs.

User facing changes are recorded with towncrier: add a one-line fragment to .changelog.d/, named <PR number>.<type>.md (or +<name>.<type>.md without a PR), where <type> is one of added, changed, performance, fixed, deprecated, removed or security, e.g. towncrier create -c "Faster set_aaa." +faster-set-aaa.performance.md.

Citation

When using this software package for scientific work please cite the associated publication ². When using the tensor-valued AAA (tensor_aaa), e.g. for pole-expansions of T-matrices, please also cite ⁴.

+++

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. "Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm", ACS Photonics 13, 5291 (2026), https://doi.org/10.1021/acsphotonics.6c00436 ↩ ↩²

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