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# SHTOOLS/SHTOOLS: Version 4.4

Mark Wieczorek; MMesch; Elliott Sales de Andrade; Ilya Oshchepkov; Benda Xu; Katrin Leinweber; Andrew Walker

Version 4.4

New Slepian expansion routines

• Added the new Fortran 95 functions SHRotateTapers for rotating spherical cap Slepian functions, SlepianCoeffs for expanding a function in a Slepian basis, and SlepianCoeffsToSH to convert the Slepian coefficients into spherical harmonic coefficients.
• Added two python classes Slepian and SlepianCoeffs for managing Slepian basis functions and the Slepian expansion coefficients of a function.

Legendre and spherical harmonic convenience functions

• Added 4 python convenience functions for computing Legendre and spherical harmonic functions: legendre() to compute all the legendre functions, legendre_lm() to compute the legendre function for a specified degree and order, spharm() to compute all the spherical harmonic functions, and spharm_lm() to compute the spherical harmonic functions for a specific degree and order.

Other improvements

• Added the option to perform a weighted least squares inversion in the fortran routine SHExpandLSQ, and added a python wrapped function SHExpandWLSQ().
• Added min() and max() methods to the SHGrid class, to return the minimum and maximum value of the gridded data.
• Added the property mass to the SHGravCoeffs class, which is computed by the input GM and the codata value for G.
• Add the optional parameter omega to SHGravCoeffs.geoid() to override the value provided in the class instance.
• Fixed some minor typos and usability issues, and cleaned up the python wrapper and signature files.

M. A. Wieczorek, M. Meschede, E. Sales de Andrade, I. Oshchepkov, B. Xu, and A. Walker (2018). SHTOOLS: Version 4.4, Zenodo, doi:10.5281/zenodo.592762

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