Compute the cross-power spectral density of two real functions.
call SHCrossPowerSpectrumDensity (cilm1
, cilm2
, lmax
, cspectrum
, exitstatus
)
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
and lmaxin2
.
cspectrum
: output, real*8, dimension (lmax
+1)
: The cross-power spectral density of the two 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.
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)
.
shpowerl, shpowerdensityl, shcrosspowerl, shcrosspowerdensityl, shpowerspectrum, shpowerspectrumdensity, shcrosspowerspectrum, shadmitcorr