Convert a function expressed in Slepian coefficients to spherical harmonic coefficients.
flm
= SlepianCoeffsToSH(falpha
, galpha
, nmax
)
flm
:float, dimension (2, lmax
+1, lmax
+1)
: The spherical harmonic coefficients of the global function.
falpha
:float, dimension (nmax
)
: A vector containing the Slepian coefficients of the function.
galpha
: float, dimension ((lmax
+1)**2, nmax
)
: An array containing the spherical harmonic coefficients of the Slepian functions, where lmax
is the spherical harmonic bandwidth of the functions. Each column corresponds to a single function of which the spherical harmonic coefficients can be unpacked with SHVectorToCilm
.
nmax
: input, integer
: The number of expansion coefficients to compute. This must be less than or equal to (lmax
+1)**2.
SlepianCoeffsToSH
will compute the spherical harmonic coefficients of a global function flm
given the Slepian functions galpha
and the corresponding Slepian coefficients falpha
. The Slepian functions are determined by a call to either (1) SHReturnTapers
and then SHRotateTapers
, or (2) SHReturnTapersMap
. Each row of galpha
contains the (lmax
+1)**2 spherical harmonic coefficients of a Slepian function that can be unpacked using SHVectorToCilm
. The Slepian functions must be normalized to have unit power (that is the sum of the coefficients squared is 1), and the spherical harmonic coefficients are calculated as
f_lm = sum_{alpha}^{nmax} f_alpha g(alpha)_lm
slepiancoeffst, shslepianvar, shreturntapers, shreturntapersmap, shrotatetapers, shvectortocilm, shscouplingmatrix, shscouplingmatrixcap, shmtcouplingmatrix