This module provides routines for performing spherical harmonic expansions and the construction of grids from spherical harmonic coefficients.
Equally sampled (N×N) and equally spaced (N×2N) grids
| Function 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. |
| MakeGradientDH |
Compute the gradient of a scalar function and return grids of the two horizontal components that conform with Driscoll and Healy’s (1994) sampling theorem. |
Gauss-Legendre quadrature grids
| Function name |
Description |
| SHGLQ |
Precompute the weights and nodes 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. |
Least squares inversion
| Function name |
Description |
| shlsq |
Determine the spherical harmonic coefficients of an irregularly sampled function using a (weighted) least squares inversion, optionally with a precomputed data kernel matrix. |
| SHExpandLSQ |
Determine the spherical harmonic coefficients of an irregularly sampled function using a least squares inversion. |
| SHExpandLSQ_G |
Determine the spherical harmonic coefficients of an irregularly sampled function using a least squares inversion with a precomputed data kernel matrix. |
| SHExpandWLSQ |
Determine the spherical harmonic coefficients of an irregularly sampled function using a weighted least squares inversion. |
| SHExpandWLSQ_G |
Determine the spherical harmonic coefficients of an irregularly sampled function using a weighted least squares inversion with a precomputed data kernel matrix. |
| LSQ_G |
Compute the data kernel matrix G that is used when computing spherical harmonic coefficients by least squares inversion. |
Other routines
| Function name |
Description |
| 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 set of points. |
| MakeGridPointC |
Evaluate a complex function expressed in complex spherical harmonics at a set of points. |
| SHMultiply |
Multiply two functions and determine the spherical harmonic coefficients of the resulting function. |
| spharm |
Compute all the spherical harmonic functions up to a maximum degree and order. |
| spharm_lm |
Compute the spherical harmonic function for specific degrees l and orders m. |
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