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SHctor

SHctor -

Convert complex spherical harmonics to real form.

SYNOPSIS

SUBROUTINE SHctor (

CCILM, RCILM, DEGMAX, CONVENTION, SWITCHCS )

    REAL*8

    CCILM(2, *, *), RCILM(2, *, *)

    INTEGER, OPTIONAL

    DEGMAX, CONVENTION, SWITCHCS

DESCRIPTION

SHctor will convert complex spherical harmonics of a real function to real form. By default, the dimension of the output array is the minimum of RCILM(1,*,*) and CCILM(1,*,*), though this can be changed by specifying the optional parameter DEGMAX. The normalization of the input and output coefficients are by default the same, but if the optional argument CONVENTION is set to 2, this routine will convert from geodesy 4-pi normalized coefficients to orthonormalized coefficients. The Condon-Shortley phase convention between the input an output coefficients can be modified by the optional argument SWITCHCS.

ARGUMENTS

CCILM

(input) REAL*8, DIMENSION (2, *, *)

The input complex spherical harmonic coefficients. CCILM(1, *, *) and CCILM(2, *, *) correspond to the real and complex part of the coefficients, respectively. Only the positive angular orders are input; the negative orders are assumed to satisfy the relation C_{l-m} = (-1)^m C_{lm}^*.

RCILM

(output) REAL*8, DIMENSION (2, *, *)

The output real spherical harmonic coefficients. RCILM(1, *, *) and RCILM(2, *, *) correspond to the COS and SIN terms, respectively.

DEGMAX

(input) INTEGER, OPTIONAL

The maximum degree of the output coefficients. By default, the dimension of the output coefficients will be the smallest of RCILM and CCILM.

CONVENTION

(input) INTEGER, OPTIONAL

If 1 (default), the input and output coefficients will have the same normalization. If 2, orthonormalized coefficients will be converted to real geodesy 4-pi form.

SWTICHCS

(input) INTEGER, OPTIONAL

If 0 (default), the input and output coefficients will possess the same Condon-Shortley phase convention. If 1, the input coefficients will first be multiplied by (-1)^m.

SEE ALSO

shrtoc(1), shcilmtocindex(1), shcindextocilm(1)

http://shtools.ipgp.fr/

COPYRIGHT AND LICENSE

Copyright 2012 by Mark Wieczorek <wieczor@ipgp.fr>.

This is free software; you can distribute and modify it under the terms of the revised BSD license.