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

4.3.24 SHTLBW

1.

Function

Performs inverse Legendre transformation.

2.

Definition

The following are performed on floating-point spectral  data S^m_n (n =m,m+1,...,M) for a zonal wavenumber m (≥0).

When ISW=0, a normal inverse Legendre transformation is performed.

When ISW=1 When ISW=-1, the latitudinal derivative of the inverse Legendre transform is calculated.

When ISW=-1, the meridional derivative of the inverse Legendre transform is calculated.

3.

Call

SHTLBW(MM,JM,M,ISW,SM,WM,WORK)

4.

Explanation of Parameters

MM	(I)	Input parameter. The cut-off wavenumber (M).
JM	(I)	Input parameter. 1/2 of the NS partition number (J)
ISW	(I)	Input parameter. Specifies the type of transformation (See above definition.)
M	(I)	Input parameter. The zonal wavenumber (m) on which to perform transformation.
SM	(R)	Input parameter. Spectral data. An array of length MM-M+1. (See Notes for arrangement.)
WM	(R)	Output parameter. Wave data. An array of length (2*JM+1). (See Notes for arrangement.)
WORK	(R)	Working area initialized by SHTINT.

5.

Notes

(a)

When SM(M:MM) is declared in advance, S^m_n should be stored in SM(N). Also, when WM(-JM:JM) is declared, W^m_{(sin&phi j)} will be stored in WM(J).

(b)

Must be M≥0.