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.

Tags: