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SHMultiply
Multiply two functions and determine the spherical harmonic coefficients of the resulting function.
Usage
call SHMultiply (shout
, sh1
, lmax1
, sh2
, lmax2
, precomp
, norm
, csphase
, exitstatus
)
Parameters
shout
: output, real*8, dimension (2,lmax1
+lmax2
+1,lmax1
+lmax2
+1)- The real spherical harmonic coefficients corresponding to the multiplication of
sh1
andsh2
in the space domain. sh1
: input, real*8, dimension (2,lmax1
+1,lmax1
+1)- The spherical harmonic coefficients of the first function.
lmax1
: input, integer- The maximum spherical harmonic degree used in evaluting
sh1
. sh2
: input, real*8, dimension (2,lmax2
+1,lmax2
+1)- The spherical harmonic coefficients of the second function.
lmax2
: input, integer- The maximum spherical harmonic degree used in evaluting
sh2
. precomp
: input, optional, integer, default = 0- If 1, the array of Legendre functions
plx
will be precomputed on the Gauss-Legendre quadrature nodes. norm
: input, optional, integer, default = 1- 1 (default) = Geodesy 4-pi normalized harmonics; 2 = Schmidt semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal harmonics.
csphase
: input, 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.
exitstatus
: output, optional, integer- If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.
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. If the optional parameter precomp
is set, then the array of Legendre functions plx
will be precomputed on the Gauss-Legendre quadrature nodes.
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.
See also
shexpandglq, makegridglq, shglq
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