Calculate the admittance and correlation spectra of two real functions.

## Usage

admit, error, corr = SHAdmitCorr (gilm, tilm, [lmax])

## Returns

admit : float, dimension (lmax+1)
The admittance function, which is equal to Sgt/Stt.
error : float, dimension (lmax+1)
The uncertainty of the admittance function, assuming that gilm and tilm are related by a linear isotropic transfer function, and that the lack of correlation is a result of uncorrelated noise.
corr : float, dimension (lmax+1)
The degree correlation function, which is equal to Sgt/sqrt(Sgg Stt).

## Parameters

gilm : float, dimension (2, lmaxg+1, lmaxg+1)
The real spherical harmonic coefficients of the function G.
tilm : float, dimension (2, lmaxt+1, lmaxt+1)
The real spherical harmonic coefficients of the function T.
lmax : optional, integer, default = min(lmaxg, lmaxt)
The maximum spherical harmonic degree that will be calculated for the admittance and correlation spectra. This must be less than or equal to the minimum of lmaxg and lmaxt.

## Description

SHAdmitCorr will calculate the admittance, admittance error, and correlation spectra associated with two real functions expressed in real spherical harmonics. The admittance is defined as Sgt/Stt, where Sgt is the cross-power spectrum of two functions G and T. The degree-correlation spectrum is defined as Sgt/sqrt(Sgg Stt), which can possess values between -1 and 1. The error of the admittance is calculated assuming that G and T are related by a linear isotropic transfer function: Gilm = Ql Tilm + Nilm, where N is noise that is uncorrelated with the topography. It is important to note that the relationship between two fields is often not described by such an isotropic expression.