Compute the cross-power spectral density of two real functions.
Usage
call SHCrossPowerSpectrumDensity (cilm1, cilm2, lmax, cspectrum, exitstatus)
Parameters
cilm1: input, real(dp), dimension (2,lmaxin1+1,lmaxin1+1)- The first function expressed in real spherical harmonics.
cilm2: input, real(dp), dimension (2,lmaxin2+1,lmaxin2+1)- The second function expressed in real spherical harmonics.
lmax: input, integer(int32)- The maximum spherical harmonic degree to calculate the cross-power spectral density. This must be less than or equal to the minimum of
lmaxin1andlmaxin2. cspectrum: output, real(dp), dimension (lmax+1)- The cross-power spectral density of the two functions.
exitstatus: output, optional, integer(int32)- 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).
See also
shpowerl, shpowerdensityl, shcrosspowerl, shcrosspowerdensityl, shpowerspectrum, shpowerspectrumdensity, shcrosspowerspectrum, shadmitcorr
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