Spherical harmonic transforms in MATLAB

This repository provides a unified MATLAB interface to various spherical harmonic transform libraries.

sht_plan(deg, n, backend) creates a plan for a spherical harmonic transform using all spherical harmonics up to degree deg and an n x n grid in latitude and longitude. Transforms between spherical harmonic coefficients and values on the grid are done by the backend specified by backend. Currently, backend may be:

• 'fasttransforms' - Mikael Slevinsky's FastTransforms library. (https://github.com/MikaelSlevinsky/FastTransforms)
• 'fmm3d' - The Flatiron Institute's FMM3D library. (https://github.com/flatironinstitute/FMM3D)
• 'shtns' - Nathanael Schaeffer's SHTns library. (https://bitbucket.org/nschaeff/shtns)

Each backend uses a different set of grid points on the sphere. The exact grid points used by a plan are stored in plan.grid.lat (for latitudinal grid points) and plan.grid.lon (for longitudinal grid points).

sht_plan([lmax mmax], [nlat nlon], backend) uses spherical harmonics with degree 0 ≤ l ≤ lmax and order |m| ≤ mmax and an nlat x nlon grid in latitude and longitude.

Example

deg = 20;
n = 200;
c = randn((deg+1)^2, 1);
plan = sht_plan(deg, n, 'shtns');
V = plan.coeffs2vals(c);
d = plan.vals2coeffs(V);