Calculate the admittance and correlation spectra of two real functions.
call SHAdmitCorr (gilm
, tilm
, lmax
, admit
, corr
, admit_error
, exitstatus
)
gilm
: input, real(dp), dimension (2, lmaxg
+1, lmaxg
+1)
: The real spherical harmonic coefficients of the function G
.
tilm
: input, real(dp), dimension (2, lmaxt
+1, lmaxt
+1)
: The real spherical harmonic coefficients of the function T
.
lmax
: input, integer(int32)
: The maximum spherical harmonic degree that will be calculated for the admittance and correlation spectra. This must be less than or equal to the minimum of lmaxg
and lmaxt
.
admit
: output, real(dp), dimension (lmax
+1)
: The admittance function, which is equal to Sgt/Stt
.
corr
: output, real(dp), dimension (lmax
+1)
: The degree correlation function, which is equal to Sgt/sqrt(Sgg Stt)
.
admit_error
: output, optional, real(dp), dimension (lmax
+1)
: The uncertainty of the admittance function, assuming that gilm
and tilm
are related by a linear isotropic transfer function, and that the lack of correlation is a result of uncorrelated noise.
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.
SHAdmitCorr
will calculate the admittance and correlation spectra associated with two real functions expressed in real spherical harmonics. The admittance is defined as Sgt/Stt
, where Sgt
is the cross-power spectrum of two functions G
and T
. The degree-correlation spectrum is defined as Sgt/sqrt(Sgg Stt)
, which can possess values between -1 and 1.
If the optional argument admit_error
is specified, then the error of the admittance will be calculated by assuming that G
and T
are related by a linear isotropic transfer function: Gilm = Ql Tilm + Nilm
, where N
is noise that is uncorrelated with the topography. It is important to note that the relationship between two fields is often not described by such an isotropic expression.