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. |
| 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
| 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. |
Least squares inversion
| Routine name | Description |
|---|---|
| SHExpandLSQ | Determine the spherical harmonic coefficients of an irregularly sampled function using a (weighted) least squares inversion. |
| LSQ_G | Compute the data kernel matrix G that is used when computing spherical harmonic coefficients by least squares inversion. |
Other routines
| Routine 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 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. |