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

4.3.13 SHTSWM

1.

Function

Performs inverse Legendre transformation, which corresponds to the first half of the inverse spectral transformation, for a single specified wavenumber component.

2.

Definition

Transforms spectral data S^m_n into wave data W^m_(&phi) only for a single specified wavenumber component m=M (>0). See SHTS2W for equations of transformation.

3.

Call

SHTSWM(MM,JM,M,ISW,S,WR,WI,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)
M	(I)	Input parameter. Specifies the wavenumber to transform. (See above definition.)
ISW	(I)	Input parameter. Specifies the type of transformation. (See SHTS2W.)
S	(R)	Input parameter. Spectral data. (For length and arrangement, see SHTNML.)
WR	(R)	Output parameter. The floating-point part of Wm(&phi). An array of length 2*JM+1. (See Notes for arrangement of array.)
WI	(R)	Output parameter. The imaginary part of Wm(&phi). An array of length 2*JM+1(See Notes for arrangement of array.)
WORK	(R)	Working area initialized by SHTINT.

5.

Notes

(a)

When WR(-JM:JM) and WI(-JM:JM) are declared in advance, Re(W^m_{(&phi j）}) is stored in WR(J) and Ie(W^m_{(&phi j)}) in WI(J).

(b)

For M=0 (zonal component), use SHTSWZ.