spherical-harmonic-transforms.md

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Spherical harmonic transforms	spherical harmonics software package, spherical harmonic transform, legendre functions, multitaper spectral analysis, fortran, Python, gravity, magnetic field	mydoc_sidebar	spherical-harmonic-transforms.html		true

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Equally sampled (N×N) and equally spaced (N×2N) grids

Routine name	Description
SHExpandDH	Expand an equally sampled or equally spaced map into spherical harmonics using Driscoll and Healy's (1994) sampling theorem.
MakeGridDH	Create a 2D map from a set of spherical harmonic coefficients that conforms with Driscoll and Healy's (1994) sampling theorem.
SHExpandDHC	Expand an equally sampled or equally spaced complex map into complex spherical harmonics using Driscoll and Healy's (1994) sampling theorem.
MakeGridDHC	Create a 2D complex map from a set of complex spherical harmonic coefficients that conforms with Driscoll and Healy's (1994) sampling theorem.

Gauss-Legendre quadrature grids

Routine name	Description
SHGLQ	Precompute weights, nodes, and associated Legendre functions used in the GLQ-based spherical harmonics routines.
SHExpandGLQ	Expand a 2D map sampled on the Gauss-Legendre quadrature nodes into spherical harmonics.
MakeGridGLQ	Create a 2D map from a set of spherical harmonic coefficients sampled on a the Gauss-Legendre quadrature nodes.
SHExpandGLQC	Expand a 2D complex map sampled on the Gauss-Legendre quadrature nodes into complex spherical harmonics.
MakeGridGLQC	Create a 2D complex map from a set of complex spherical harmonic coefficients sampled on a the Gauss-Legendre quadrature nodes.
GLQGridCoord	Compute the latitude and longitude coordinates used in Gauss-Legendre quadrature grids.

Other routines

Routine name	Description
SHExpandLSQ	Expand a set of irregularly sampled data points into spherical harmonics using a (weighted) least squares inversion.
MakeGrid2D	Create a 2D cylindrical map with arbitrary grid spacing from a set of spherical harmonic coefficients.
MakeGridPoint	Evaluate a real function expressed in real spherical harmonics at a single point.
MakeGridPointC	Evaluate a complex function expressed in complex spherical harmonics at a single point.
SHMultiply	Multiply two functions and determine the spherical harmonic coefficients of the resulting function.