Calculate the theoretical variance of the power of a function expanded in spherical-cap Slepian functions for a given spherical harmonic degree.
Usage
variance = SHSlepianVar (l, galpha, galpha_order, sff, [kmax])
Returns
- variance : float
- The theoretical variance of the spectral estimate for degree l.
Parameters
- l : integer
- The spherical harmonic degree used to calculate the theoretical variance.
- galpha : float, dimension (lmaxin+1, kmaxin)
- A matrix of spherical-cap Slepian functions obtained from SHReturnTapers or SHReturnTapersM.
- galpha_order : integer, dimension (kmaxin)
- The angular order of the Slepian functions in galpha.
- sff : float, dimension (lmaxin+1)
- The global power spectrum of the function.
- kmax : optional, integer, default = kmaxin
- The maximum number of Slepian functions to use when calculating the variance.
Description
SHSlepianVar will compute the theoretical variance of the power of a function expanded in spherical-cap Slepian functions for a given spherical harmonic degree. This routine takes as input the spherical harmonic coefficients of the spherical-cap Slepian functions as obtained by a call to SHReturnTapers, and only the first kmax Slepian functions in the matrix galpha are used to compute the variance.
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