SHrtoc()

Convert real spherical harmonics to complex form.

Usage

ccilm = SHrtoc (rcilm, [lmax, convention, switchcs])

Returns

ccilm : float, dimension (2, lmax+1, lmax+1)

The output complex spherical harmonic coefficients. ccilm[0,:,:] and ccilm[1,:,:] correspond to the real and complex part of the coefficients, respectively. Only the positive angular orders are output; the negative orders can be calculated from the relation C_{l-m}=(-1)^m C_{lm}^*.

Parameters

rcilm : float, dimension (2, lmaxin+1, lmaxin+1)

The input real spherical harmonic coefficients. rcilm[0,:,:] and rcilm[1,:,:] correspond to the cosine and sine terms, respectively.

lmax : optional, integer, default = lmaxin

The maximum degree of the output coefficients.

convention : optional, integer, default = 1

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

swtichcs : optional, integer default = 0

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.

Description

SHrtoc will convert real spherical harmonics to complex form. 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.