## 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. |

## 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. |