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

## Usage

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

## Parameters

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

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

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