SHTns

"SHTns is a high performance library for Spherical Harmonic Transform written in C, aimed at numerical simulation (fluid flows, mhd, ...) in spherical geometries.

Features:

• blazingly fast.
• both scalar and vector transforms.
• backward and forward (synthesis and analysis) functions.
• flexible truncation (degree, order, azimuthal periodicity).
• spatial data can be stored in latitude-major or longitude-major arrays.
• various conventions (normalization and Condon-Shortley phase).
• can be used from Fortran, c/c++, and Python programs.
• highly efficient Gauss algorithm working with Gauss nodes (based on Gauss-Legendre quadrature).
• support for SSE2, SSE3, AVX, AVX2 vectorization, as well as Xeon Phi and Blue Gene/Q.
• parallel transforms with OpenMP.
• synthesis (inverse transform) at any coordinate (not constrained to a grid).
• on-the-fly transforms : saving memory and bandwidth, they are even faster on modern architectures.
• accurate up to spherical harmonic degree l=16383 (at least).
• rotation functions to rotate spherical harmonics.
• special spectral operator functions that do not require a transform (multiply by cos(theta)...).
• scalar transforms and rotations for complex spatial fields.
• SHT at fixed m (without fft, aka Legendre transform - beta).

Documentation:

On-line doc is available: http://users.isterre.fr/nschaeff/SHTns/

You can build it locally: Run make docs to generate documentation (requires doxygen). Then browse the html documentation starting with doc/html/index.html

A related research paper has been published: Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations, also available from arXiv.

https://bitbucket.org/nschaeff/shtns