Create 2D cylindrical maps on a flattened ellipsoid of all three vector components of the magnetic field, the magnitude of the magnetic field, and the magnetic potential.

## Usage

rad, theta, phi, total, pot = MakeMagGridDH (cilm, r0, [lmax, a, f, sampling, lmax_calc, extend])

## Returns

- rad : float, dimension(nlat, nlong)
- A 2D map of the radial component of the magnetic field that conforms to the sampling theorem of Driscoll and Healy (1994). If sampling is 1, the grid is equally sampled and is dimensioned as (n by n), where n is 2lmax+2. If sampling is 2, the grid is equally spaced and is dimensioned as (n by 2n). The first latitudinal band of the grid corresponds to 90 N, the latitudinal sampling interval is 180/n degrees, and the default behavior is to exclude the latitudinal band for 90 S. The first longitudinal band of the grid is 0 E, by default the longitudinal band for 360 E is not included, and the longitudinal sampling interval is 360/n for an equally sampled and 180/n for an equally spaced grid, respectively. If extend is 1, the longitudinal band for 360 E and the latitudinal band for 90 S will be included, which increases each of the dimensions of the grid by 1.
- theta : float, dimension(nlat, nlong)
- A 2D equally sampled or equally spaced grid of the theta component of the magnetic field.
- phi : float, dimension(nlat, nlong)
- A 2D equally sampled or equally spaced grid of the phi component of the magnetic field.
- total : float, dimension(nlat, nlong)
- A 2D equally sampled or equally spaced grid of the total magnetic field strength.
- pot : float, dimension(nlat, nlong)
- A 2D equally sampled or equally spaced grid of the magnetic potential.

## Parameters

- cilm : float, dimension (2, lmaxin+1, lmaxin+1)
- The real Schmidt semi-normalized spherical harmonic coefficients to be expanded in the space domain. The coefficients C1lm and C2lm refer to the cosine (Clm) and sine (Slm) coefficients, respectively, with Clm=cilm[0,l,m] and Slm=cilm[1,l,m]. Alternatively, C1lm and C2lm correspond to the positive and negative order coefficients, respectively. The coefficients are assumed to have units of nT.
- r0 : float
- The reference radius of the spherical harmonic coefficients.
- lmax : optional, integer, default = lamxin
- The maximum spherical harmonic degree of the coefficients cilm. This determines the number of samples of the output grids, n=2*lmax+2, and the latitudinal sampling interval, 90/(lmax+1).
- a : optional, float, default = r0
- The semi-major axis of the flattened ellipsoid on which the field is computed.
- f : optional, float, default = 0
- The flattening of the reference ellipsoid: i.e., F=(R_equator-R_pole)/R_equator.
- sampling : optional, integer, default = 2
- If 1 the output grids are equally sampled (n by n). If 2, the grids are equally spaced (n by 2n).
- lmax_calc : optional, integer, default = lmax
- The maximum spherical harmonic degree used in evaluating the functions. This must be less than or equal to lmax.
- extend : input, optional, bool, default = False
- If True, compute the longitudinal band for 360 E and the latitudinal band for 90 S. This increases each of the dimensions of the grids by 1.

## Description

MakeMagGridDH will create 2-dimensional cylindrical maps from the spherical harmonic coefficients cilm of all three components of the magnetic field, the total field strength, and the magnetic potential. The magnetic potential is given by

`V = R0 Sum_{l=1}^LMAX (R0/r)^{l+1} Sum_{m=-l}^l C_{lm} Y_{lm}`

and the magnetic field is

`B = - Grad V`

.

The coefficients are referenced to a radius r0, and the function is computed on a flattened ellipsoid with semi-major axis a (i.e., the mean equatorial radius) and flattening f.

The default is to use an input grid that is equally sampled (n by n), but this can be changed to use an equally spaced grid (n by 2n) by the optional argument sampling. The redundant longitudinal band for 360 E and the latitudinal band for 90 S are excluded by default, but these can be computed by specifying the optional argument 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.

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