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

4.3.8 SHTW2S

1.
Function
Performs the forward Legendre transformation, which corresponds to the latter half of the forward spectral transformation.

2.
Definition
When ISW=0, the normal forward Legendre transformation is performed.

(4.29)



When ISW=1, the longitudinal derivative of the forward Legendre transform is calculated.

(4.30)


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

(4.31)

3.
Call
SHTW2S(MM,JM,ISW,W,S,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.)
W (R) Input parameter. Wave data. (For length and arrangement, see SHTS2W.
S (R) Output parameter. Spectral data. (For length and arrangement, see SHTNML.)
WORK (R) Working area initialized by SHTINT.

5.
Notes
(a)
When ISW=0 and the wave data W has been created by SHTS2W with the condition of ISW=0, the above integral will be free of aliasing and can be exactly evaluated.
(b)
When ISW=¡Þ1 and the wave data W has been created by SHTS2W with the condition of ISW=¡Þ1, the above integral will be free of aliasing and can be exactly evaluated.