shmultiply.1

.\" Automatically generated by Pandoc 2.7.3
.\"
.TH "shmultiply" "1" "2019-09-17" "Fortran 95" "SHTOOLS 4.5"
.hy
.SH SHMultiply
.PP
Multiply two functions and determine the spherical harmonic coefficients
of the resulting function.
.SH Usage
.PP
call SHMultiply (\f[C]shout\f[R], \f[C]sh1\f[R], \f[C]lmax1\f[R],
\f[C]sh2\f[R], \f[C]lmax2\f[R], \f[C]precomp\f[R], \f[C]norm\f[R],
\f[C]csphase\f[R], \f[C]exitstatus\f[R])
.SH Parameters
.TP
.B \f[C]shout\f[R] : output, real(dp), dimension (2, \f[C]lmax1\f[R]+\f[C]lmax2\f[R]+1, \f[C]lmax1\f[R]+\f[C]lmax2\f[R]+1)
The real spherical harmonic coefficients corresponding to the
multiplication of \f[C]sh1\f[R] and \f[C]sh2\f[R] in the space domain.
.TP
.B \f[C]sh1\f[R] : input, real(dp), dimension (2, \f[C]lmax1\f[R]+1, \f[C]lmax1\f[R]+1)
The spherical harmonic coefficients of the first function.
.TP
.B \f[C]lmax1\f[R] : input, integer
The maximum spherical harmonic degree used in evaluting \f[C]sh1\f[R].
.TP
.B \f[C]sh2\f[R] : input, real(dp), dimension (2, \f[C]lmax2\f[R]+1, \f[C]lmax2\f[R]+1)
The spherical harmonic coefficients of the second function.
.TP
.B \f[C]lmax2\f[R] : input, integer
The maximum spherical harmonic degree used in evaluting \f[C]sh2\f[R].
.TP
.B \f[C]precomp\f[R] : input, optional, integer, default = 0
If 1, the array of Legendre functions \f[C]plx\f[R] will be precomputed
on the Gauss-Legendre quadrature nodes.
.TP
.B \f[C]norm\f[R] : input, optional, integer, default = 1
1 (default) = Geodesy 4-pi normalized harmonics; 2 = Schmidt
semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal
harmonics.
.TP
.B \f[C]csphase\f[R] : 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)\[ha]m to the associated Legendre functions.
.TP
.B \f[C]exitstatus\f[R] : 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.
.SH Description
.PP
\f[C]SHMultiply\f[R] will take two sets of spherical harmonic
coefficients, multiply the functions in the space domain, and expand the
resulting field in spherical harmonics using \f[C]SHExpandGLQ\f[R].
The spherical harmonic bandwidth of the resulting field is
\f[C]lmax1+lmax2\f[R], where \f[C]lmax1\f[R] and \f[C]lmax2\f[R] are the
bandwidths of the input fields.
If the optional parameter \f[C]precomp\f[R] is set, then the array of
Legendre functions \f[C]plx\f[R] will be precomputed on the
Gauss-Legendre quadrature nodes.
.PP
The employed spherical harmonic normalization and Condon-Shortley phase
convention can be set by the optional arguments \f[C]norm\f[R] and
\f[C]csphase\f[R]; if not set, the default is to use geodesy 4-pi
normalized harmonics that exclude the Condon-Shortley phase of
(-1)\[ha]m.
.SH See also
.PP
shexpandglq, makegridglq, shglq