Convert a function expressed in Slepian coefficients to spherical harmonic coefficients.

Usage

flm = SlepianCoeffsToSH(falpha, galpha, nmax)

Returns

flm :float, dimension (2, lmax+1, lmax+1)
The spherical harmonic coefficients of the global function.

Parameters

falpha :float, dimension (nmax)
A vector containing the Slepian coefficients of the function.
galpha : float, dimension ((lmax+1)**2, nmax)
An array containing the spherical harmonic coefficients of the Slepian functions, where lmax is the spherical harmonic bandwidth of the functions. Each column corresponds to a single function of which the spherical harmonic coefficients can be unpacked with SHVectorToCilm.
nmax : input, integer
The number of expansion coefficients to compute. This must be less than or equal to (lmax+1)**2.

Description

SlepianCoeffsToSH will compute the spherical harmonic coefficients of a global function flm given the Slepian functions galpha and the corresponding Slepian coefficients falpha. The Slepian functions are determined by a call to either (1) SHReturnTapers and then SHRotateTapers, or (2) SHReturnTapersMap. Each row of galpha contains the (lmax+1)**2 spherical harmonic coefficients of a Slepian function that can be unpacked using SHVectorToCilm. The Slepian functions must be normalized to have unit power (that is the sum of the coefficients squared is 1), and the spherical harmonic coefficients are calculated as

f_lm = sum_{alpha}^{nmax} f_alpha g(alpha)_lm

See also

slepiancoeffst, shslepianvar, shreturntapers, shreturntapersmap, shrotatetapers, shvectortocilm, shscouplingmatrix, shscouplingmatrixcap, shmtcouplingmatrix

Tags: python
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