SHGLQ (Fortran)

Precompute weights, nodes, and associated Legendre functions used in the Gauss-Legendre quadrature based spherical harmonics routines.

Usage

call SHGLQ (lmax, zero, w, plx, norm, csphase, cnorm, exitstatus)

Parameters

lmax : input, integer(int32)

The maximum spherical harmonic degree of the coefficients to be calculated in the Gauss-Legendre quadrature based spherical harmonic transform routines.

zero : output, real(dp), dimension (lmax+1)

The nodes used in the Gauss-Legendre quadrature over latitude, determined from a call to PreGLQ.

w : output, real(dp), dimension (lmax+1)

The weights used in the Gauss-Legendre quadrature over latitude, determined from a call to PreGLQ.

plx : output, optional, real(dp), dimension (lmax+1, (lmax+1)*(lmax+2)/2)

An array of the associated Legendre functions calculated at the nodes used in the Gauss-Legendre quadrature.

norm : input, optional, integer(int32), default = 1

1 (default) = Geodesy 4-pi normalized harmonics; 2 = Schmidt semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal harmonics.

csphase : input, optional, integer(int32), 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.

cnorm : input, optional, integer(int32), default = 0

If 0 (default), the real normalization of the associated Legendre functions will be used. If 1, the complex normalization of the associated Legendre functions will be used.

exitstatus : output, optional, integer(int32)

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

SHGLQ will calculate the weights and zeros used in the Gauss-Legendre quadrature based spherical harmonic routines SHExpandGLQ, MakeGridGLQ, SHExpandGLQC, and MakeGridGLQC. Optionally, an array of the associated Legendre functions evaluated on the quadrature nodes can be computed as well. If the complex routines are to be used, the optional parameter cnorm must be set equal to 1.

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, shexpandglqc, makegridglqc, glqgridcoord, preglq