Compute the cross-power spectral density of two real functions.

## Usage

call SHCrossPowerSpectrumDensity (cilm1, cilm2, lmax, cspectrum, exitstatus)

## Parameters

cilm1 : input, real*8, dimension (2, lmaxin1+1, lmaxin1+1)
The first function expressed in real spherical harmonics.
cilm2 : input, real*8, dimension (2, lmaxin2+1, lmaxin2+1)
The second function expressed in real spherical harmonics.
lmax : input, integer
The maximum spherical harmonic degree to calculate the cross-power spectral density. This must be less than or equal to the minimum of lmaxin1 and lmaxin2.
cspectrum : output, real*8, dimension (lmax+1)
The cross-power spectral density of the two functions.
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

SHCrossPowerSpectrumDensity will calculate the cross-power spectral density of two functions expressed in real 4-pi normalized spherical harmonics. For a given spherical harmonic degree l, this is explicitly calculated as:

cspectrum(l) = Sum_{i=1}^2 Sum_{m=0}^l cilm1(i, l+1, m+1) * cilm2(i, l+1, m+1) / (2l + 1).

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