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SHCrossPowerSpectrumDensity
Compute the cross-power spectral density of two real functions.
Usage
call SHCrossPowerSpectrumDensity (cilm1
, cilm2
, lmax
, cspectrum
)
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
andlmaxin2
. cspectrum
: output, real*8, dimension (lmax
+1)- The cross-power spectral density of the two functions.
Description
SHCrossPowerSpectrumDensity
will calculate the cross-power spectral density of two functions expressed in real 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, shcrosspower, shcrosspowerdensityl, shpowerspectrum, shpowerspectrumdensity, shcrosspowerspectrum, shadmitcorr
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