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.
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