Calculate the theoretical variance of the power of a function expanded in spherical-cap Slepian functions for a given spherical harmonic degree.
Usage
call SHSlepianVar (l, galpha, galpha_order, lmax, kmax, sff, variance, exitstatus)
Parameters
l: input, integer(int32)- The spherical harmonic degree used to calculate the theoretical variance.
galpha: input, real(dp), dimension (lmax+1,kmax)- A matrix of spherical-cap Slepian functions obtained from
SHReturnTapersorSHReturnTapersM. galpha_order: input, integer(int32), dimension (kmax)- The angular orders of the spherical-cap Slepian functions in
galpha. lmax: input, integer(int32)- The spherical harmonic bandwidth of the Slepian functions.
kmax: input, integer(int32)- The maximum number of Slepian functions to use when calculating the variance.
sff: input, real(dp), dimension (lmax+1)- The global power spectrum of the function.
variance: output, real(dp)- The theoretical variance of the spectral estimate for degree
l. 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
SHSlepianVar will compute the theoretical variance of the power of a function expanded in spherical-cap Slepian functions for a given spherical harmonic degree. This routine takes as input the spherical harmonic coefficients of the spherical-cap Slepian functions as obtained by a call to SHReturnTapers, and only the first KMAX Slepian functions in the matrix GALPHA are used to compute the variance.
See also
shreturntapers, shreturntapersm, slepiancoeffs, slepiancoeffstosh, shscouplingmatrixcap
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