SHTns.jl

A Julia wrapper around the SHTns spherical harmonic transform library.

Warning

This is WORK IN PROGRESS and will certainly have BREAKING changes.

Installation

import Pkg; Pkg.add("SHTns")

Example usage

using SHTns

cfg = SHTnsCfg(64) #define configuration

θ,ϕ = SHTns.grid(cfg) #get (co-)latitude and longitude
d = @. 0.3*sin(ϕ') * sin(θ) #create some spatial data (0.3 Y₁¹)

q = SHTns.analys(cfg,d) #transform to spectral space
q[SHTns.LM(cfg, 1,1)] ≈ 0.3*sqrt(2π/3)*im #true

d2 = SHTns.synth(cfg,q) #transform back to spatial space
d2 ≈ d #true

Or we can do the same on a CUDA-enabled GPU!

using CUDA

cfg_gpu = SHTnsCfg(64; shtype=SHTns.QuickInit(;gpu=true))

d_gpu = CuArray(d)

q_gpu = SHTns.analys(cfg_gpu,d_gpu)
Array(q_gpu)[SHTns.LM(cfg, 1,1)] ≈ 0.3*sqrt(2π/3)*im

d2_gpu = SHTns.synth(cfg_gpu,q_gpu)
(d_gpu ≈ d2_gpu) && (Array(d2_gpu) ≈ d) #true

License

SHTns.jl is distributed under the GPL-3.0 license in agreement with the CeCILL license of SHTns.

Copyright (c) 2010-2021 Centre National de la Recherche Scientifique. written by Nathanael Schaeffer (CNRS, ISTerre, Grenoble, France). SHTns is distributed under the open source CeCILL License (GPL compatible) located in the LICENSE file.

Citation

The SHTns guidelines read:

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

• If you use SHTns for research work, please cite this paper:

    @article {shtns,
      author = {Schaeffer, Nathanael},
      title = {Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations},
      journal = {Geochemistry, Geophysics, Geosystems},
      doi = {10.1002/ggge.20071}, volume = {14}, number = {3}, pages = {751--758},
      year = {2013},
    }
  

  If you use Ishioka's recurrence (the default since SHTns v3.4), you may also want to cite his paper:

    @article {ishioka2018,
      author={Ishioka, Keiichi},
      title={A New Recurrence Formula for Efficient Computation of Spherical Harmonic Transform},
      journal={Journal of the Meteorological Society of Japan},
      doi = {10.2151/jmsj.2018-019}, volume={96}, number={2}, pages={241--249},
      year={2018},
    }