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

4.3.19 SHTSWZ

1.

Function

Performs inverse Legendre transformation, which corresponds to the first half of the inverse spectral transformation, over a specified wavenumber interval on a single specified meridian circle.

2.

Definition

Transforms spectral data S^m_n into wave data W^m_(&phi) on a single specified meridian circle &phi j over a specified wavenumber interval of M1≤|m| ≤M2. See SHTS2W for equations used in the transformation.

3.

Call

SHTSWJ(MM,JM,ISW,J,M1,M2,S,WJ,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 SHTS2W.)
J	(I)	Input parameter. Specifies the meridian circle on which to perform transformation. (See Notes.)
M1	(I)	Input parameter. The minimum value in the wavenumber interval for transformation. (See above definition.)
M2	(I)	Input parameter. The maximum value in the wavenumber interval for transformation. (See above definition.)
S	(R)	Input parameter. Spectral data. (For length and arrangement, see SHTNML.)
WJ	(R)	Output parameter. Stores Wm(&phi j）. An array of length 2*MM+1. (See Notes for arrangement.)
WORK	(R)	Working area initialized by SHTINT.

5.

Notes

(a)

When WJ(-MM:MM) is declared in advance, Re(W^m_{(&phi j)}) will be stored in WJ(M) (M>0), Im(W^m_{(&phi j)}) in WJ(-M) (M>0), and W⁰_{(&ohi j)} in WJ(0). (j=J).

(b)

Zero is substituted into WJ(M) (|M|<M1, |M|>M2), outside the range of the specified interval.