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SHCrossPowerSpectrumDensityC

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

Usage

call SHCrossPowerSpectrumDensityC (cilm1, cilm2, lmax, cspectrum)

Parameters

cilm1 : input, complex*16, dimension (2, lmaxin1+1, lmaxin1+1)
The complex spherical harmonics of the first complex function.
cilm2 : input, complex*16, 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*16, dimension (lmax+1)
The cross-power spectral density of the two complex functions.

Description

SHCrossPowerSpectrumDensityC will calculate the cross-power spectral density of two complex functions expressed in complex 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).

See also

shpowerlc, shpowerdensitylc, shcrosspowerlc, shcrosspowerdensitylc, shpowerspectrumc, shpowerspectrumdensityc, shcrosspowerspectrumc

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