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slepiancoeffs.doc
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slepiancoeffs.doc
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Determine the expansion coefficients of a function for a given set of input
Slepian functions.
Usage
-----
falpha = SlepianCoeffs(galpha, flm, nmax)
Returns
-------
falpha : float, dimension (nmax)
A vector containing the Slepian coefficients of the input function flm.
Parameters
----------
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.
flm : float, dimension (2, lmax+1, lmax+1)
The spherical harmonic coefficients of the global function to be expanded in
Slepian functions.
nmax : integer
The number of expansion coefficients to compute. This must be less than or
equal to (lmax+1)**2.
Description
-----------
SlepianCoeffs will compute the Slepian coefficients of a global input function
flm given the Slepian functions galpha. 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 Slepian coefficients
are calculated as
f_alpha = sum_{lm}^{lmax} f_lm g(alpha)_lm