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procedure: dsl2gse
Purpose: THEMIS coordinate transformations
DSL<-->GSE;
interpolates, right ascension, declination
updates coord_sys atribute of output tplot variable.
inputs
name_thx_xxx_in ... data in the input coordinate system (t-plot variable name)
name_thx_spinras ... right ascension (t-plot variable name)
name_thx_spindec ... declination (t-plot variable name)
name_thx_xxx_out ... name for output (t-plot variable name)
keywords:
TRANSFORMATIONS
/GSE2DSL inverse transformation
/IGNORE_DLIMITS if the specified from coord is different from the
coord system labeled in the dlimits structure of the tplot variable
setting this keyword prevents an error
Example:
dsl2gse('tha_fgl_dsl','tha_spinras','tha_spindec','tha_fglc_gse')
expects attitude in GEI (tha_spinras,tha_spindec)
dsl2gse('tha_fglc_gse','tha_spinras','tha_spindec','tha_fgl_dsl',/GSE2DSL)
expects attitude in GEI (tha_spinras,tha_spindec)
Notes: under construction!! will run faster in the near future!!
Written by Hannes Schwarzl
$LastChangedBy: pcruce $
$LastChangedDate: 2013-07-29 10:24:04 -0700 (Mon, 29 Jul 2013) $
$LastChangedRevision: 12735 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/projects/themis/state/cotrans/dsl2gse.pro $
(See projects/themis/state/cotrans/dsl2gse.pro)
procedure: gse2sse
Purpose: Coordinate transformation between GSE & SSE coordinates(and the inverse)
SSE is defined as:
X: Moon->Sun Line
Y: Ecliptic North cross X
Z: X cross Y
GSE is defined as:
X: Earth Sun Line(naturally in the ecliptic plane)
Y: Z x X
Z: Ecliptic North
inputs:
name_in:
Name of input tplot variable to be transformed or an array of data [t,x,y,z]
name_sun_pos:
Name of the solar position tplot variable in GEI coordinates
or as an array of data [t,x,y,z]
name_lun_pos:
Name of the lunar position tplot variable in GEI coordinates
or as an array of data [t,x,y,z]
name_out:
Name that the rotated variable should take.
keywords:
/SSE2GSE inverse transformation
/IGNORE_DLIMITS: Dlimits normally used to determine if coordinate
system is correct, to decide if position needs offset, or to
stop incorrect transforms. This option will stop this behavior.
This keyword is only used with tplot variables and ignored if
array data is input
/ROTATION_ONLY: Set this flag when to only do the rotation, and not
the translation from geocentric to selenocentric coordinates.
That is used for sse2sel transform when creating the sel rotation
matrix
Examples:
gse2sse,'tha_state_pos','slp_sun_pos_gse','slp_lun_pos_gse','tha_state_pos_sse'
gse2sse,'tha_state_pos_sse','slp_sun_pos_gse','slp_lun_pos_gse','tha_state_pos_gse',/sse2gse,/ignore_dlimits
OR (with vector data [t,x,y,z]
gse2sse, pos_gse,sun_gse,lun_pos,pos_sse
gse2sse,pos_sse,sun_gse,lun_pos,pos_gse,/sse2gse
Notes:
#1 SSE coordinate Z-axis is generally not exactly parallel to ecliptic north,
as the moon will not always be in the ecliptic plane, and thus the moon->sun line
will not always lie in the ecliptic plane.
#2 If dlimit-labeled position passed in without /ignore_dlimits,
input will be offset to account for relative position of frames of reference.
#3 If dlimit-labeled velocity passed in without /ignore_dlimits,
input will be offset to account for relative motion of frames of reference
#4 If dlimit-labeled acceleration passed in without /ignore_dlimits,
warning will be raise, but offset will not be applied automatically
#5 Uses tvector_rotate, and sse_matrix_make to perform the rotation.
tvector_rotate will also interpolate the rotation matrix onto the time-grid of the input.
Interpolation done using quaterions and the spherical linear interpolation algorithm (SLERP)
#6 dlimits are automatically ignored if vector data is input
Written by Jenni Kissinger and Patrick Cruce
$LastChangedBy: jwl $
$LastChangedDate: 2023-04-12 11:20:40 -0700 (Wed, 12 Apr 2023) $
$LastChangedRevision: 31739 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/projects/themis/state/cotrans/gse2sse.pro $
(See projects/themis/state/cotrans/gse2sse.pro)
procedure: sse2sel
Purpose: Coordinate transformation between SSE & SEL coordinates(and the inverse)
SSE is defined as:
X: Moon->Sun Line
Y: Ecliptic North cross X
Z: X cross Y
SEL is defined as:
X: TBD
Y: TBD
Z: TBD
inputs:
name_in:
Name of input tplot variable to be transformed
or as an array of data [t,x,y,z]
name_sun_pos:
Name of the sun position tplot variable in GEI coordinates
or as an array of data [t,x,y,z]
name_moon_pos:
Name of the moon position tplot variable in GEI coordinates
or as an array of data [t,x,y,z]
name_lun_att_x:
Name of the SEL X-axis tplot variable in GEI coordinates
or as an array of data [t,x,y,z]
name_lun_att_z:
Name of the SEL Z-axis tplot variable in GEI coordinates
or as an array of data [t,x,y,z]
name_out:
Name that the rotated variable should take.
keywords:
/SEL2SSE inverse transformation
/IGNORE_DLIMITS: Dlimits normally used to determine if coordinate
system is correct, to decide if position needs offset, or to
stop incorrect transforms. This option will stop this behavior.
This keyword is only used with tplot variables and ignored if
array data is input
Examples:
sse2sel,'tha_state_pos_sse','slp_sun_pos','slp_lun_pos','slp_lun_att_x','slp_lun_att_z','tha_state_pos_sel'
sse2sel,'tha_state_pos_sel','slp_sun_pos','slp_moon_pos','slp_lun_att_x','slp_lun_att_z','tha_state_pos_sse',/sel2sse,/ignore_dlimits
Or for vector data
sse2sel,pos_sse,sun_pos,lun_pos,lun_att_x,lun_att_z,pos_sel
sse2sel,pos_sel,sun_pos,lun_pos,lun_att_x,lun_att_z,pos_sse, /sel2sse
Notes:
#1 Uses tvector_rotate, and sse_matrix_make to perform the rotation.
tvector_rotate will also interpolate the rotation matrix onto the time-grid of the input.
Interpolation done using quaterions and the spherical linear interpolation algorithm (SLERP)
#2 If vector data is input the IGNORE_LIMITS keyword is not used.
Adapted from gse2sse, written by Jenni Kissinger and Patrick Cruce
$LastChangedBy: jwl $
$LastChangedDate: 2012-06-04 10:25:21 -0700 (Mon, 04 Jun 2012) $
$LastChangedRevision: 10492 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/projects/themis/state/cotrans/sse2sel.pro $
(See projects/themis/state/cotrans/sse2sel.pro)
procedure: ssl2dsl
Purpose: despins (spins) THEMIS data
SSL<-->DSL;
interpolates the spinphase, spin period
updates coord_sys atribute of output tplot variable.
inputs
name_thx_xxx_in ... data in the input coordinate system (t-plot variable name)
keywords:
/NAME_INPUT : Always required; this argument is the name of a tplot
variable to use as the input data.
/NAME_OUTPUT: Always required; this argument is the name of a tplot
variable to receive the output.
TRANSFORMATIONS
/DSL2SSL inverse transformation
/IGNORE_DLIMITS if the specified from coord is different from the
coord system labeled in the dlimits structure of the tplot variable
setting this keyword prevents an error
/INTERPOLATE_STATE : if specified, interpolate the spin phase
from the 1-minute samples in the state CDF. Otherwise,
use the spinmodel routines by default.
/NAME_THX_SPINPER : required if /INTERPOLATE_STATE is specified;
this is the name of a tplot variable containing the 1-minute
spinper samples from the state CDF.
/NAME_THX_SPINPHASE : required if /INTERPOLATE_STATE is specified;
this is the name of a tplot variable containing the 1-minute
spinphase samples from the state CDF.
/SPINMODEL_PTR : required if /INTERPOLATE_STATE is NOT specified;
this argument is a pointer to the appropriate spin model data structure.
Example:
ssl2dsl,name_input='tha_fgl_ssl',$
name_output='tha_fgl_dsl',$
/INTERPOLATE_STATE,$
name_thx_spinper='tha_state_spinper',$
name_thx_spinphase='tha_state_spinphase'
ssl2dsl,name_input='tha_fgl_dsl',$
/INTERPOLATE_STATE,$
name_thx_spinper='tha_state_spinper',$
name_thx_spinphase='tha_state_spinphase',$
name_output='tha_fgl_ssl',$
/DSL2SSL
ssl2dsl,name_input='tha_fgl_dsl',$
spinmodel_ptr=spinmodel_get_ptr('a'),$
name_output='tha_fgl_ssl'
Notes: under construction!!
Written by Hannes Schwarzl
$LastChangedBy: jwl $
$LastChangedDate: 2012-06-04 10:26:03 -0700 (Mon, 04 Jun 2012) $
$LastChangedRevision: 10493 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/projects/themis/state/cotrans/ssl2dsl.pro $
(See projects/themis/state/cotrans/ssl2dsl.pro)
Procedure: thm_cotrans
Purpose: Transform between various THEMIS and geophysical coordinate systems
keywords:
probe = Probe name. The default is 'all', i.e., transform data for all
available probes.
This can be an array of strings, e.g., ['a', 'b'] or a
single string delimited by spaces, e.g., 'a b'
datatype = The type of data to be transformed, can take any of the values
allowed for datatype for the various thm_load routines. You
can use wildcards like ? and [lh].
'all' is not accepted. You can use '*', but you may get unexpected
results if you are using suffixes.
in_coord = 'spg', 'ssl', 'dsl', 'gse', 'gsm','sm', 'gei','geo', 'sse', 'sel' or
'mag' coordinate system of input.
This keyword is optional if the dlimits.data_att.coord_sys attribute
is present for the tplot variable, and if present, it must match
the value of that attribute. See cotrans_set_coord,
cotrans_get_coord
out_coord = 'spg', 'ssl', 'dsl', 'gse', 'gsm', 'sm', 'gei','geo', 'sse','sel', or 'mag'
coordinate system of output. This keyword is optional if
out_suffix is specified and last 3 characters of suffix specify
the output coordinate system.
in_suffix = optional suffix needed to generate the input data quantity name:
'th'+probe+'_'datatype+in_suffix
out_suffix = optional suffix to add to output data quantity name. If
in_suffix is present, then in_suffix will be replaced by out_suffix
in the output data quantity name.
valid_names:return valid coordinate system names in named varibles supplied to
in_coord and/or out_coord keywords.
support_suffix: if support_data is loaded with a suffix you can
specify it here
slp_suffix: if slp_sun_pos, slp_lun_pos, slp_lunn_att variables have
this suffix, you can specify it here
out_vars: return a list of the names of any transformed variables
ignore_dlimits: set this keyword to true so that an error will not
be produced if the internal label of the coordinate system clashed
with the user provided coordinate system.
interpolate_state: use interpolation on 1-minute state CDF spinper/spinphase
samples for despinning instead of spin model
no_update_labels: Set this keyword if you want the routine to not update the labels automatically
Optional Positional Parameters:
in_name Name(s) of input tplot variable(s) (or glob patern)
(space-separated list or array of strings.). If the in_name
parameter is provided, the probe and datatype
keywords will be ignored. However, if the input name
is not of format 'th[a-e]_*', use the probe keyword to indicate
which probe's state data should be used for each input variable.
out_name Name(s) of output tplot variable(s). glob patterns not accepted.
Number of output names must match number of input names (after glob
expansion of input names). (single string, or array of strings.)
Examples:
thm_load_state, /get_support
thm_cotrans, probe='a', datatype='fgl', out_suffix='_gsm'
; or equivalently
thm_cotrans, 'tha_fgl', 'tha_fgl_gsm', out_coord='gsm'
; to transform all th?_fg?_dsl to th?_fg?_gsm
thm_cotrans, 'th?_fg?', in_suffix='_dsl', out_suffix='_gsm'
; for arbitrary input variables, specify in_coord and probe:
thm_cotrans,'mydslvar1 mydslvar2 mydslvar3', $
in_coord='dsl', probe='b c d', out_suff='_gse'
$LastChangedBy: jimm $
$LastChangedDate: 2019-02-13 16:05:02 -0800 (Wed, 13 Feb 2019) $
$LastChangedRevision: 26625 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/projects/themis/state/cotrans/thm_cotrans.pro $
(See projects/themis/state/cotrans/thm_cotrans.pro)
NAME:
thm_cotrans_matrix
PURPOSE:
brute force method of creating rotation matrix for a
THEMIS coordinate transform.
CALLING SEQUENCE:
rotmat = thm_cotrans_matrix(in_name, $
in_coord=in_coord, $
out_coord=out_coord, $
interpolate_state=interpolate_state, $
use_spinaxis_correction=use_spinaxis_correction, $
use_spinphase_correction=use_spinphase_correction, $
use_eclipse_corrections=use_eclipse_corrections)
INPUT:
in_name = a THEMIS tplot variable,
OUTPUT:
rotmat = a 3x3 transformation matrix for each time given by the
input variable
KEYWORDS:
Standard thm_cotrans keywords:
probe = 'a', 'b', 'c', 'd', 'e', If not set, then we will try to
get it from the variable name
in_coord = 'spg', 'ssl', 'dsl', 'gse', 'gsm','sm', 'gei','geo', 'sse', 'sel' or
'mag' coordinate system of input.
This keyword is optional if the dlimits.data_att.coord_sys attribute
is present for the tplot variable, and if present, it must match
the value of that attribute. See cotrans_set_coord,
cotrans_get_coord
out_coord = 'spg', 'ssl', 'dsl', 'gse', 'gsm', 'sm', 'gei','geo', 'sse','sel', or 'mag'
coordinate system of output. This keyword is optional if
out_suffix is specified and last 3 characters of suffix specify
the output coordinate system.
interpolate_state: use interpolation on 1-minute state CDF spinper/spinphase
samples for despinning instead of spin model
use_spinaxis_correction: uses spinaxis correction as in THM_COTRANS
use_spinphase_correction: uses spinphase correction as in THM_COTRANS
use_eclipse_correction: uses eclipse correction as in THM_COTRANS
support_suffix: if support_data is loaded with a suffix you can
specify it here
slp_suffix: if slp_sun_pos, slp_lun_pos, slp_lunn_att variables have
this suffix, you can specify it here
EXAMPLE:
For converting DSL to GSE coordinates, using ptens variable
rotmat = thm_cotrans_matrix('tha_peif_ptens', out_coord = 'GSE')
Any input can be used, only the time variable is important, but if
the variable has no coordinate system defined (e.g., density) then
the in_coord keyword should be set.
HISTORY:
2019-01-16, jmm, jimm@ssl.berkeley.edu
$LastChangedBy: jimm $
$LastChangedDate: 2019-02-13 11:37:26 -0800 (Wed, 13 Feb 2019) $
$LastChangedRevision: 26620 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/projects/themis/state/cotrans/thm_cotrans_matrix.pro $
(See projects/themis/state/cotrans/thm_cotrans_matrix.pro)
NAME:
thm_cotrans_tensor
PURPOSE:
wrapper for coordinate transforms to prssure and momentum
flux tensors
CALLING SEQUENCE:
in_coord is optional if dlimits includes a data_att.coord_sys element.
pro thm_cotrans_tensor, in_name, out_name, $
in_coord=in_coord, out_coord=out_coord, verbose=verbose, $
in_suffix=in_suf, out_suffix=out_suf, $
support_suffix=support_suffix,ignore_dlimits=ignore_dlimits,$
interpolate_state=interpolate_state,out_vars=out_vars,$
use_spinaxis_correction=use_spinaxis_correction, $
use_spinphase_correction=use_spinphase_correction, $
use_eclipse_corrections=use_eclipse_corrections,$
slp_suffix=slp_suffix,no_update_labels=no_update_labels
INPUT:
in_name Name(s) of input tplot variable(s) (or glob patern)
(space-separated list or array of strings.). Non-tensor
variables can be mixed in, these will be passed to
thm_cotrans directly.
out_name Name(s) of output tplot variable(s). glob patterns not accepted.
Number of output names must match number of input names (after glob
expansion of input names). (single string, or array of strings.)
KEYWORDS:
in_coord = 'spg', 'ssl', 'dsl', 'gse', 'gsm','sm', 'gei','geo', 'sse', 'sel' or
'mag' coordinate system of input.
This keyword is optional if the dlimits.data_att.coord_sys attribute
is present for the tplot variable, and if present, it must match
the value of that attribute. See cotrans_set_coord,
cotrans_get_coord
out_coord = 'spg', 'ssl', 'dsl', 'gse', 'gsm', 'sm', 'gei','geo', 'sse','sel', or 'mag'
coordinate system of output. This keyword is optional if
out_suffix is specified and last 3 characters of suffix specify
the output coordinate system.
in_suffix = optional suffix needed to generate the input data quantity name:
'th'+probe+'_'datatype+in_suffix
out_suffix = optional suffix to add to output data quantity name. If
in_suffix is present, then in_suffix will be replaced by out_suffix
in the output data quantity name.
valid_names:return valid coordinate system names in named varibles supplied to
in_coord and/or out_coord keywords.
support_suffix: if support_data is loaded with a suffix you can
specify it here
out_vars: return a list of the names of any transformed variables
ignore_dlimits: set this keyword to true so that an error will not
be produced if the internal label of the coordinate system clashed
with the user provided coordinate system.
interpolate_state: use interpolation on 1-minute state CDF spinper/spinphase
samples for despinning instead of spin model
use_spinaxis_correction: use spinaxis correction
use_spinphase_correction: use spinphase correction
use_eclipse_corrections: use eclipse corrections
no_update_labels: Set this keyword if you want the routine to not
update the labels automatically
reuse_rotation_matrix: If set, use the same rotation atrix for all
inputs, if the time arrays are the same
delete_rotation_matrix: If set, delete the rotation matirx variable
$LastChangedBy: jimm $
$LastChangedDate: 2019-02-19 11:14:39 -0800 (Tue, 19 Feb 2019) $
$LastChangedRevision: 26642 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_6_1/projects/themis/state/cotrans/thm_cotrans_tensor.pro $
(See projects/themis/state/cotrans/thm_cotrans_tensor.pro)
Procedure: thm_fac_matrix_make
Purpose: generates a field aligned coordinate transformation matrix
from an input B vector array(and sometimes a position vector array)
then stores it in a tplot variable.
This code has been modified from fac_matrix_make to handle input data that are
in DSL coordinates.
Arguments:
mag_var_name=the name of the tplot variable storing the magnetic field
vectors to be used in transformation matrix generation
pos_var_name(optional)=the name of the tplot variable storing the position
vectors to be used in transformation matrix generation
newname(optional)=the name of the tplot variable in which to store
the output
error(optional) = named variable that holds the error state of the
computation 1 = success 0 = failure
other_dim(optional) = the second axis for the field aligned
coordinate system.
probe=probe(optional) = string indicating the THEMIS probe for systems that use the DSL system.
If this keyword is not specified and probe name is required, thm_fac_matrix_make will infer the probe
from the 3rd letter of the magnetic field variable. (eg. 'tha_fgs_gsm') If the tplot variable doesn't have
a probe label in the name, this can lead to very irregular behavior, so it is recommended that you
always specify probe.
/DEGAP: Set to call TDEGAP to remove any gaps from the data. See TDEGAP for
for other options that can be invoked using the _extra keyword.
E.g. thm_fac_matrix_make, 'tha_fgs', other_dim='xgse', /degap, dt=3
************For all transformations Z = B************
Warning about coordinate systems:
B field tplot variable must be in gse,gsm, or dsl coordinates,
depending on what transformation has been selected.
Position tplot variable must be in gei coordinates. Gei is the default coordinate
system of thm_load_state.
Warning: The resulting transformation matrices will only correctly
transform data from the coordinate system of the input variable to
the field aligned coordinate system. So if mag_var_name is in dsl
coordinates then you should only use the output matrices to transform
other data in dsl coordinates.
valid second coord(other_dim) options:
'Xgse', (DEFAULT) translates from gse or gsm into FAC
Definition(works on GSE, or GSM):
X Axis = on plane defined by Xgse - Z
Second coordinate definition: Y = Z x X_gse
Third coordinate, X completes orthogonal RHS
(right hand system) triad: XYZ
Note: X_gse is a unit vector pointing in direction from
earth to the sun
'Rgeo',translate from geo into FAC using radial position vector
Rgeo is radial position vector, positive radialy outwards.
Second coordinate definition: Y = Z x Rgeo (eastward)
Third coordinate, X completes orthogonal RHS XYZ.
'mRgeo',translate into FAC using radial position vector
mRgeo is radial position vector, positive radially inwards.
Second coordinate definition: Y = Z x mRgeo (westward)
Third coordinate, X completes orthogonal RHS XYZ.
'Phigeo', translate into FAC using azimuthal position vector
Phigeo is the azimuthal geo position vector, positive Eastward
First coordinate definition: X = Phigeo x Z (positive outwards)
Second coordinate, Y ~ Phigeo (eastward) completes orthogonal RHS XYZ
'mPhigeo', translate into FAC using azimuthal position vector
mPhigeo is minus the azimuthal geo position vector; positive Westward
First coordinate definition: X = mPhigeo x Z (positive inwards)
Second coordinate, Y ~ mPhigeo (Westward) completes orthogonal RHS XYZ
'Phism', translate into FAC using azimuthal Solar Magnetospheric vector.
Phism is "phi" vector of satellite position in SM coordinates.
Y Axis = on plane defined by Phism-Z, normal to Z
Second coordinate definition: X = Phism x Z
Third completes orthogonal RHS XYZ
'mPhism', translate into FAC using azimuthal Solar Magnetospheric vector.
mPhism is minus "phi" vector of satellite position in SM coordinates.
Y Axis = on plane defined by Phism-Z, normal to Z
Second coordinate definition: X = mPhism x Z
Third completes orthogonal RHS XYZ
'Ygsm', translate into FAC using cartesian Ygsm position as other dimension.
Y Axis on plane defined by Ygsm and Z
First coordinate definition: X = Ygsm x Z
Third completes orthogonal RHS XYZ
'Zdsl', translates from dsl into FAC
Definition:
X Axis = on plane defined by Zdsl - Z
Second coordinate definition: X = Z x Zdsl
Third coordinate, Y completes orthogonal RHS
(right hand system) triad: XYZ
Example:
fac_matrix_make,'tha_fgs',other_dim='Xgse',pos_var_name='tha_pos',out_var_name='tha_fgs_fac_mat',probe='a'
(See projects/themis/state/cotrans/thm_fac_matrix_make.pro)
NAME:
THM_GSM2LMN_WRAP
PURPOSE:
Wrapper transforms THEMIS-generated vector field from GSM to LMN (boundary-normal)
coordinate system for magnetopause with help of routine gsm2lmn.pro.
It gets the necessary solar wind data with help of routine
get_sw_data.pro and passes all necessary keywords to it.
In distinction of GSM2LMN_WRAP, it finds space-time coordinates using
reference to a THEMIS probe.
CATEGORY:
Coordinate Transformation
CALLING SEQUENCE:
thm_gsm2lmn_wrap,data_in,data_out,probe,SWkeywords
INPUTS:
data_in: structure {x:time, y:data}
probe: string specify which spacecraft caught data_in.
KEYWORDS: Solarwind_load.pro keywords (Any combination of keywords defining
output of solarwind_load.pro)
PARAMETERS: none
OUTPUTS:
data_out: structure {x:time, y:transformed_data}
DEPENDENCIES: gsm2lmn.pro, solarwind_load.pro. Intermediate-level part of LMN
transform package.
MODIFICATION HISTORY:
Written by: Liu Jiang 09/21/2007
Modified for new background routines by: Vladimir Kondratovich 2007/12/28
Modified for error handling and changed () to [] for arrays
by: Lynn B. Wilson III 2012/10/26
(See projects/themis/state/cotrans/thm_gsm2lmn_wrap.pro)