pymakemaggriddh.1

.\" Automatically generated by Pandoc 2.0.3
.\"
.TH "pymakemaggriddh" "1" "2016\-12\-15" "Python" "SHTOOLS 4.1"
.hy
.SH MakeMagGridDH
.PP
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.
.SH Usage
.PP
\f[C]rad\f[], \f[C]theta\f[], \f[C]phi\f[], \f[C]total\f[] =
MakeMagGridDH (\f[C]cilm\f[], \f[C]r0\f[], [\f[C]lmax\f[], \f[C]a\f[],
\f[C]f\f[], \f[C]sampling\f[], \f[C]lmaxcalc\f[]])
.SH Returns
.TP
.B \f[C]rad\f[] : float, dimension(2*\f[C]lmax\f[]+2, \f[C]sampling\f[]*(2*\f[C]lmax\f[]+2))
A 2D equally sampled (\f[C]n\f[] by \f[C]n\f[]) or equally spaced
(\f[C]n\f[] by 2\f[C]n\f[]) grid of the radial component of the magnetic
field corresponding to the input spherical harmonic coefficients
\f[C]cilm\f[].
The first latitudinal band corresponds to 90 N, the latitudinal band for
90 S is not included, and the latitudinal sampling interval is
180/\f[C]n\f[] degrees.
The first longitudinal band is 0 E, the longitudinal band for 360 E is
not included, and the longitudinal sampling interval is 360/\f[C]n\f[]
for an equally sampled and 180/\f[C]n\f[] for an equally spaced grid,
respectively.
.RS
.RE
.TP
.B \f[C]theta\f[] : float, dimension(2*\f[C]lmax\f[]+2, \f[C]sampling\f[]*(2*\f[C]lmax\f[]+2))
A 2D equally sampled or equally spaced grid of the theta component of
the magnetic field.
.RS
.RE
.TP
.B \f[C]phi\f[] : float, dimension(2*\f[C]lmax\f[]+2, \f[C]sampling\f[]*(2*\f[C]lmax\f[]+2))
A 2D equally sampled or equally spaced grid of the phi component of the
magnetic field.
.RS
.RE
.TP
.B \f[C]total\f[] : float, dimension(2*\f[C]lmax\f[]+2, \f[C]sampling\f[]*(2*\f[C]lmax\f[]+2))
A 2D equally sampled or equally spaced grid of the total magnetic field
strength.
.RS
.RE
.SH Parameters
.TP
.B \f[C]cilm\f[] : float, dimension (2, \f[C]lmaxin\f[]+1, \f[C]lmaxin\f[]+1)
The real Schmidt semi\-normalized spherical harmonic coefficients to be
expanded in the space domain.
The coefficients \f[C]C1lm\f[] and \f[C]C2lm\f[] refer to the cosine
(\f[C]Clm\f[]) and sine (\f[C]Slm\f[]) coefficients, respectively, with
\f[C]Clm=cilm[0,l,m]\f[] and \f[C]Slm=cilm[1,l,m]\f[].
Alternatively, \f[C]C1lm\f[] and \f[C]C2lm\f[] correspond to the
positive and negative order coefficients, respectively.
.RS
.RE
.TP
.B \f[C]r0\f[] : float
The reference radius of the spherical harmonic coefficients.
.RS
.RE
.TP
.B \f[C]lmax\f[] : optional, integer, default = \f[C]lamxin\f[]
The maximum spherical harmonic degree of the coefficients \f[C]cilm\f[].
This determines the number of samples of the output grids,
\f[C]n=2*lmax+2\f[], and the latitudinal sampling interval,
\f[C]90/(lmax+1)\f[].
.RS
.RE
.TP
.B \f[C]a\f[] : optional, float, default = \f[C]r0\f[]
The semi\-major axis of the flattened ellipsoid on which the field is
computed.
.RS
.RE
.TP
.B \f[C]f\f[] : optional, float, default = 0
The flattening of the reference ellipsoid: i.e.,
\f[C]F=(R_equator\-R_pole)/R_equator\f[].
.RS
.RE
.TP
.B \f[C]sampling\f[] : optional, integer, default = 2
If 1 the output grids are equally sampled (\f[C]n\f[] by \f[C]n\f[]).
If 2, the grids are equally spaced (\f[C]n\f[] by 2\f[C]n\f[]).
.RS
.RE
.TP
.B \f[C]lmaxcalc\f[] : optional, integer, default = \f[C]lmax\f[]
The maximum spherical harmonic degree used in evaluating the functions.
This must be less than or equal to \f[C]lmax\f[].
.RS
.RE
.SH Description
.PP
\f[C]MakeMagGridDH\f[] will create 2\-dimensional cylindrical maps from
the spherical harmonic coefficients \f[C]cilm\f[] of all three
components of the magnetic field, the total field strength, and the
magnetic potential.
The magnetic potential is given by
.PP
\f[C]V\ =\ R0\ Sum_{l=1}^LMAX\ (R0/r)^{l+1}\ Sum_{m=\-l}^l\ C_{lm}\ Y_{lm}\f[]
.PP
and the magnetic field is
.PP
\f[C]B\ =\ \-\ Grad\ V\f[].
.PP
The coefficients are referenced to a radius \f[C]r0\f[], and the
function is computed on a flattened ellipsoid with semi\-major axis
\f[C]a\f[] (i.e., the mean equatorial radius) and flattening \f[C]f\f[].
.PP
The default is to calculate grids for use in the Driscoll and Healy
routines that are equally sampled (\f[C]n\f[] by \f[C]n\f[]), but this
can be changed to calculate equally spaced grids (\f[C]n\f[] by
2\f[C]n\f[]) by setting the optional argument \f[C]sampling\f[] to 2.
The input value of \f[C]lmax\f[] determines the number of samples,
\f[C]n=2lmax+2\f[], and the latitudinal sampling interval,
\f[C]90/(lmax+1)\f[].
The first latitudinal band of the grid corresponds to 90 N, the
latitudinal band for 90 S is not calculated, and the latitudinal
sampling interval is 180/\f[C]n\f[] degrees.
The first longitudinal band is 0 E, the longitudinal band for 360 E is
not calculated, and the longitudinal sampling interval is 360/\f[C]n\f[]
for equally sampled and 180/\f[C]n\f[] for equally spaced grids,
respectively.