DHaj (Fortran)

Compute the latitudinal weights used in the Driscoll and Healy (1994) spherical harmonic transform.

Usage

call DHaj (n, aj, exitstatus)

Parameters

n : input, integer(int32)

The number of samples in latitude used in the spherical harmonic transform. This must be even.

aj : output, real(dp), dimension (n) or (n+1)

The latitudinal weights used in the spherical harmonic transform.

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

If 1, include the latitudinal band for 90 S, which increases the dimension of aj by 1.

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

DHaj will calculate the latitudinal weights used in the spherical harmonic transform of Driscoll and Healy (1994; equation 9). The number of samples n must be even, and the transform and its inverse are implemented as SHExpandDH and MakeGridDH, respectively. It is noted that the first element, corresponding to the north pole, is always zero. The element corresponding to the south pole is not included by default, but can be returned by specifying extend.

Reference

Driscoll, J.R. and D.M. Healy, Computing Fourier transforms and convolutions on the 2-sphere, Adv. Appl. Math., 15, 202-250, 1994.

See also

shexpanddh, makegriddh, shexpanddhc, makegriddhc