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

## Usage

call SlepianCoeffsToSH(flm, falpha, galpha, lmax, nmax, exitstatus)

## Parameters

flm : output, real*8, dimension (2, lmax+1, lmax+1)
The spherical harmonic coefficients of the global function.
falpha : input, real*8, dimension (nmax)
A vector containing the Slepian coefficients of the function.
galpha : input, real*8, dimension ((lmax+1)**2, nmax)
An array containing the spherical harmonic coefficients of the Slepian functions. Each column corresponds to a single function of which the spherical harmonic coefficients can be unpacked with SHVectorToCilm.
lmax : input, integer
The spherical harmonic bandwidth of the Slepian functions.
nmax : input, integer
The number of expansion coefficients to compute.
exitstatus : output, optional, integer
If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.

## 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