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SHTOOLS - Tools for working with spherical harmonics

Project Description


SHTOOLS is a Fortran 95 / Python library that can be used to perform spherical harmonic transforms and reconstructions, rotations of data expressed in spherical harmonics, and multitaper spectral analyses on the sphere.


  • A wide range of supported spherical harmonic functions:
  • real and complex,
  • different normalizations (Geodesy 4π, Schmidt semi-normalized, orthonormalized, unnormalized),
  • Condon-Shortley phase factor of (-1)m.
  • Selected applications and routines:
  • global spectral analysis, spherical harmonic rotations, Wigner 3j symbols,
  • localized multitaper spectral analyses, optimal window generation, spherical harmonic coupling matrices,
  • standard gravity and magnetic field calculations, computation of the geoid, finite-amplitude potential from topography.
  • Clean implementation of the spherical harmonic transforms:
  • Exact quadrature rules using either the sampling theorem of Driscoll and Healy (1994) where data are equally sampled (or spaced) in latitude and longitude, or Gauss-Legendre quadrature.
  • Accurate and fast to approximately degree 2800, corresponding to a spatial resolution higher than 4 arc minutes. Transforms and reconstructions take on the order of 1 second for bandwidths less than 600 and about 3 minutes for bandwidths close to 2800 on standard machines. The Fortran 95 routines are OpenMP compatible and OpenMP thread-safe.




sudo apt-get install libblas-dev liblapack-dev g++ gfortran libfftw3-dev tcsh


brew install fftw --with-fortran

Python Library

pip install pyshtools

Or, to install a developer version, download or clone the SHTOOLS repository, enter the SHTOOLS folder and then execute one of the following commands:

pip install .  # installs into the active python environment lib folder
pip install -v -e .  # installs into the SHTOOLS/pyshtools folder and links to the active python environment

Fortran Library

To install the Fortran 95 library, enter one of the following

make fortran
make fortran-mp  # Open-MP Fortran routines

Or, with OSX, use the brew package manager:

brew tap shtools/shtools
brew install shtools

To also install the OpenMP components, add --with-openmp to the last command.

More installation instructions and options can be found in the web documentation and GitHub wiki.


SHTOOLS can be invoked from Fortran 95, Python 2, or Python 3. The base SHTOOLS software is written in Fortran 95, and the Python library allows simple access to all fortran-compiled routines and offers helper routines as well as simple interfaces.

To get started, check out the following Python tutorial notebooks:

  • Introduction 1: Grids and Spherical Harmonic Coefficients [ipynb]
  • Introduction 2: Localization Windows and Spectral Analysis [ipynb]
  • Tutorial 1: Simple Spherical Harmonic Analyses [ipynb]
  • Tutorial 2: Localized Spectral Analysis on the Sphere [ipynb]
  • Tutorial 3: The SHTOOLS Class Interface [ipynb]
  • Tutorial 4: Spherical Harmonic Normalizations and Parseval’s theorem [ipynb]
  • Tutorial 5: Multitaper Spectral Analysis Class Interface [ipynb]
  • Tutorial 6: 3D Spherical Harmonic Plots [ipynb]

You can keep up to date by following SHTOOLS on Twitter.


SHTOOLS is open source (revised BSD license) and makes use of the freely available Fourier transform package FFTW and the linear algebra packages LAPACK and BLAS.


Wieczorek, M. A., M. Meschede, I. Oshchepkov, E. Sales de Andrade (2016). SHTOOLS: Version 3.4. Zenodo. doi:10.5281/zenodo.61180.

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File Name & Checksum SHA256 Checksum Help Version File Type Upload Date
pyshtools-4.0.tar.gz (18.5 MB) Copy SHA256 Checksum SHA256 Source Dec 16, 2016

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