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

4.3.4 SHTS2W

1.

Function

Performs the inverse Legendre transformation, which corresponds to the first half of the inverse spectral transformation.

2.

Definition

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

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

SHTS2W(MM,JM,ISW,S,W,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.)
S	(R)	Input parameter. Spectral data. (For length and arrangement, see SHTNML.)
W	(R)	Output parameter. Wave data.
		An array of length (2*JM+1)*(2*MM+1). (See Notes below for arrangement of array.)
WORK	(R)	Working area initialized by SHTINT.

5.

Notes

(a)

When W(-JM:JM,-MM:MM) is declared in advance, Re(W^m_{(&phi j)}) will be stored in W(J,M) (M>0), Im(W^m_{(&phi j)})  in  W(J,-M) (M>0), and (W^０_{(&phi j)}) in W(J,0).