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shmultiply.doc
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shmultiply.doc
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Multiply two functions and determine the spherical harmonic coefficients of the
resulting function.
Usage
-----
shout = SHMultiply (sh1, sh2, [lmax1, lmax2, norm, csphase])
Returns
-------
shout : float, dimension (2, lmax1+lmax2+1, lmax1+lmax2+1)
The real spherical harmonic coefficients corresponding to the multiplication
of sh1 and sh2 in the space domain.
Parameters
----------
sh1 : float, dimension (2, lmax1in+1, lmax1in+1)
The spherical harmonic coefficients of the first function.
sh2 : float, dimension (2, lmax2in+1, lmax2in+1)
The spherical harmonic coefficients of the second function.
lmax1 : integer, optional, default = lmax1in
The maximum spherical harmonic degree used in evaluting sh1.
lmax2 : integer, optional, default = lmax2in
The maximum spherical harmonic degree used in evaluting sh2.
norm : optional, integer, default = 1
1 (default) = Geodesy 4-pi normalized harmonics; 2 = Schmidt semi-normalized
harmonics; 3 = unnormalized harmonics; 4 = orthonormal harmonics.
csphase : optional, integer, default = 1
1 (default) = do not apply the Condon-Shortley phase factor to the
associated Legendre functions; -1 = append the Condon-Shortley phase factor
of (-1)^m to the associated Legendre functions.
Description
-----------
SHMultiply will take two sets of spherical harmonic coefficients, multiply the
functions in the space domain, and expand the resulting field in spherical
harmonics using SHExpandGLQ. The spherical harmonic bandwidth of the resulting
field is lmax1+lmax2, where lmax1 and lmax2 are the bandwidths of the input
fields.
The employed spherical harmonic normalization and Condon-Shortley phase
convention can be set by the optional arguments norm and csphase; if not set,
the default is to use geodesy 4-pi normalized harmonics that exclude the Condon-
Shortley phase of (-1)^m.