Fast evaluation of spherical harmonics with sphericart
- URL: http://arxiv.org/abs/2302.08381v2
- Date: Sun, 30 Apr 2023 19:22:26 GMT
- Title: Fast evaluation of spherical harmonics with sphericart
- Authors: Filippo Bigi, Guillaume Fraux, Nicholas J. Browning, Michele Ceriotti
- Abstract summary: We present an elegant algorithm for the evaluation of the real-valued spherical harmonics.
We implement this algorithm in sphericart, a fast C++ library which also provides C bindings, a Python API, and a PyTorch implementation that includes a GPU kernel.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis
to expand functions on a sphere, and they are used routinely in physical and
theoretical chemistry as well as in different fields of science and technology,
from geology and atmospheric sciences to signal processing and computer
graphics. More recently, they have become a key component of rotationally
equivariant models in geometric machine learning, including applications to
atomic-scale modeling of molecules and materials. We present an elegant and
efficient algorithm for the evaluation of the real-valued spherical harmonics.
Our construction features many of the desirable properties of existing schemes
and allows to compute Cartesian derivatives in a numerically stable and
computationally efficient manner. To facilitate usage, we implement this
algorithm in sphericart, a fast C++ library which also provides C bindings, a
Python API, and a PyTorch implementation that includes a GPU kernel.
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