SynthesisSphericalHarmonicsMatrix
This program builds a linear operator matrix for spherical harmonic analysis or synthesis based on the points defined in grid. Depending on the chosen type (synthesis, quadrature, or leastSquares), the resulting matrix can be used to:
- synthesis: Map spherical harmonic coefficients to values on a grid,
- quadrature: Integrate grid-based functionals into spherical harmonic coefficients by a simple quadrature formula,
- leastSquares: Estimate coefficients from grid data via a least squares approach.
he spherical harmonic degree range is constrained by minDegree and maxDegree, and the ordering of the coefficients is given by numbering. The reference gravitational constant is GM, and the reference radius is R.
The computed matrix is written to outputfileMatrix with dimensions (number of grid points) $\times$ (number of spherical harmonic coefficients). For type = leastSquares, the program applies a QR-based pseudo-inverse so that the output matrix can directly form the normal-equation building blocks for a blockwise least-squares solution in spherical harmonic space.
See also Gravityfield2GriddedData, GriddedData2PotentialCoefficients, Gravityfield2SphericalHarmonicsVector, and MatrixCalculate for additional tools to convert between grids and spherical harmonics.
| Name | Type | Annotation |
|---|---|---|
outputfileMatrix | filename | |
grid | grid | |
kernel | kernel | |
minDegree | uint | |
maxDegree | uint | |
GM | double | Geocentric gravitational constant |
R | double | reference radius |
numbering | sphericalHarmonicsNumbering | numbering scheme of sh coefficients |
type | choice | |
synthesis | synthesize spherical harmonics on a grid | |
quadrature | calculate spherical harmonics from grid | |
leastSquares | estimated spherical harmonics from grid |