barytmat

A small Python library for saving and loading T-matrices in barycentric rational form (equivalent to the pole-expansion form), stored in a format compatible with the daphona T-matrix database.

Background

Electromagnetic scattering properties of particles are fully encoded in their T-matrix. The T-matrix varies smoothly with frequency, and its poles correspond to resonances of the scatterer. barytmat stores a compact pole expansion, for example computed via a matrix-valued AAA algorithm (diffaaable), as an HDF5 file that conforms to the treams/daphona data format. The expansion can then be evaluated at arbitrary frequencies without re-running the full T-matrix calculation.

The method is described in:

J. D. Fischbach et al., Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm, arXiv:2602.18414 (2026). https://doi.org/10.48550/arXiv.2602.18414

Related publications

Installation

pip install barytmat

or

uv add barytmat

Usage

import numpy as np
import barytmat

# Save a pole expansion to HDF5 (daphona-compatible)
# z_j: pole frequencies (complex), f_j: residues (matrix-valued), w_j: AAA weights
# T0: a treams.TMatrix instance that carries the basis/poltype/material metadata
barytmat.save_hdf5("my_particle.hdf5", z_j, f_j, w_j, T0,
                   description="Gold nanosphere, r=50 nm")

# Load and evaluate at arbitrary frequencies
T = barytmat.load_hdf5("my_particle.hdf5")
Ts = T(k0=np.linspace(0.9e7, 1.1e7, 50))  # array of frequencies

The saved file is a valid daphona/treams HDF5 file. The barycentric weights needed to reconstruct the rational approximation are stored in the file's description attribute so that no sidecar files are required.

Dependencies

• treams — T-matrix representation and HDF5 I/O
• diffaaable — differentiable matrix-valued AAA algorithm
• h5py, numpy