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DCL:MATH2:SHTLIB: Spherical Harmonic Functions: Explanation of Subroutines

4.3.2 SHTNML

1.

Function

Determines the storage area of the spectral data.

2.

Definition

In SHTLIB, the spectral data (S^m_n) are stored as (M+1)² independent components - S⁰_0,S⁰_1,…,S⁰_M,  Re(S¹₁),Re(S¹₂),_…,Re(S¹_M), Im(S¹₁ ),Im(S¹₂),_…,Im(S¹_M),_…,Re(S^M_M),Im(S^M_M) - in the order given (as an array with length of (MM+1)**2), based on the restrictions given in "Summary." Here, Re( ) and; Im( ) represents the floating-point and imaginary parts. This subroutine determines the storage position of Re(S^m_n ) and Im(S^m_n) within the array from the cut-off wavenumber M, the total wavenumber n of S^m_n, and the zonal wavenumber m.

3.

Call

SHTNML(MM,N,M,LR,LI)

4.

Explanation of Parameters

MM	(I)	Input parameter. Cut-off wavenumber (M).
N	(I)	Input parameter. Total wavenumber (n)
M	(I)	Input parameter. Zonal wavenumber (m)
LR	(I)	Output parameter. Storage position of Re(Smn).
LI	(I)	Output parameter. Storage position of Im(Smn).

5.

Notes

(a)

Since the Im(S⁰_n ) component does not exist, the value of LR will be returned as LI in case of M=0.