SSHT

"The SSHT code provides functionality to perform fast and exact spin spherical harmonic transforms based on the sampling theorem on the sphere derived in our paper: A novel sampling theorem on the sphere (ArXiv | DOI). In some applications, adjoint forward and inverse spherical harmonic transforms are also required (for example, when solving convex optimisation problems). We provide functionality to perform fast and exact adjoint transforms, based on the fast algorithms derived in our paper: Efficient and compressive sampling on the sphere.

Routines are provided to compute forward and inverse transforms using our optimal sampling (the MW routines). An extension of our sampling theorem to a sub-optimal but diametrically symmetric sampling, which is important for certain applications, is also provided (the MWSS routines). For the MW and MWSS routines we also provide fast algorithms to perform adjoint forward and inverse transforms.

We also provide optimal routines to perform spherical harmonic transforms using Gauss-Legendre quadrature (the GL routines), although these are slower than the MW routines.

Finally, we provide routines to perform transforms based on the quadrature of Driscoll & Healy (the DH routines). Note that we do NOT implement the fast Driscoll & Healy algorithms (which may be found in s2kit) but simply apply the quadrature rule to implement a simple algorithm based on a separation of variables, hence these routines are slower still.
All of these transforms correspond to sampling theorems on the sphere, with exact forward and inverse transforms for band-limited signals. In practice reconstruction accuracy is limited by machine precision. For all of the algorithms we find maximum reconstruction errors are of the order 10^(-10) or considerably smaller. Please set our paper for a discussion of the various algorithms implemented in the SSHT package and for a comparison of their performance.

The SSHT package contains both C and Fortran 90 implementations. The C version is recommended since it is faster (due to more efficient memory addressing) and, in addition to the MW routines, it also contains the MWSS, GL and DH routines described above. Furthermore, fast adjoint algorithms are provided in the C implementation only. The Fortran version contains the core MW routines and additional development and testing routines. Furthermore, a Matlab interface to the C implementation is provided."

http://astro-informatics.github.io/ssht/