Compute the cross-power spectral density of two complex functions.
call SHCrossPowerSpectrumDensityC (cilm1
, cilm2
, lmax
, cspectrum
, exitstatus
)
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.
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)
.
shpowerlc, shpowerdensitylc, shcrosspowerlc, shcrosspowerdensitylc, shpowerspectrumc, shpowerspectrumdensityc, shcrosspowerspectrumc