Cotrans

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Both the IDL spedas and the python pyspedas contain routines for coordinate transformations in the following systems: GSE, GSM, SM, GEI, GEO, MAG, J2000.

Below, we compare IDL code to python code using some of these cotrans functions.

Main cotrans function.

The main function in both IDL SPEDAS and python pyspedas is called "cotrans". In python it requires either a tplot name or a list of times and a list of data. Here is a comparison of IDL to python code for a simple cotrans operation:

IDL code: SPEDAS

trange = ['2010-02-25/00:00:00', '2010-02-25/23:59:59']
probe = 'a'
name_in = "tha_state_pos"
name_out = "tha_state_pos_new_geo"
thm_load_state, probe=probe, trange=trange
cotrans, name_in, name_out, /gei2geo
get_data, name_in,data=din, limit=l_in, dl=dl_in
get_data, name_out,data=dout, limit=d_l_in, dl=d_dl_in
print, "Input data length: ", n_elements(din.x)
print, "Input data [100-105]:"
transpose(din.y[100:105, *])
print, "Output data length: ", n_elements(dout.x)
print, "Output data [100-105]:"
transpose(dout.y[100:105, *])

IDL results: 

Input data length:         1440
Input data [100-105]:
      -45141.852       13490.809      -6501.9253
      -45287.578       13420.789      -6511.8516
      -45432.707       13350.592      -6521.6914
      -45577.234       13280.219      -6531.4453
      -45721.172       13209.673      -6541.1143
      -45864.516       13138.956      -6550.6982
Output data length:         1440
Output data [100-105]:
       45184.977      -13345.651      -6501.9253
       45271.961      -13473.378      -6511.8516
       45358.098      -13601.920      -6521.6914
       45443.371      -13731.304      -6531.4453
       45527.785      -13861.525      -6541.1143
       45611.340      -13992.556      -6550.6982

Python code: pySPEDAS

import pyspedas
import pytplot
from pyspedas.cotrans.cotrans import cotrans
trange = ['2010-02-25/00:00:00', '2010-02-25/23:59:59']
probe = 'a'
name_in = "tha_pos"
name_out = "tha_pos_new_geo"
pyspedas.themis.state(probe=probe, trange=trange, time_clip=True, varnames=[name_in])
cotrans(name_in=name_in, name_out=name_out, coord_in="gei", coord_out="geo")
din = pytplot.get_data(name_in)
dout = pytplot.get_data(name_out)
print("Input data length: " + str(len(din[0])))
y = din[1]
print("Input data [100-105]:")
print(y[100:106, :])
print("Output data length: " + str(len(dout[0])))
yy = dout[1]
print("Output data [100-105]:")
print(yy[100:106, :])

Python results: 

Input data length: 1440
Input data [100-105]:
[[-45141.85    13490.809   -6501.9253]
 [-45287.58    13420.789   -6511.8516]
 [-45432.707   13350.592   -6521.6914]
 [-45577.234   13280.219   -6531.4453]
 [-45721.17    13209.673   -6541.1143]
 [-45864.516   13138.956   -6550.698 ]]
Output data length: 1440
Output data [100-105]:
[[ 45184.97759641 -13345.65392237  -6501.92529297]
 [ 45271.96223983 -13473.37175482  -6511.8515625 ]
 [ 45358.09480658 -13601.92651913  -6521.69140625]
 [ 45443.36651621 -13731.31250082  -6531.4453125 ]
 [ 45527.78422625 -13861.52509347  -6541.11425781]
 [ 45611.33919795 -13992.55860422  -6550.69824219]]

Basic cotrans functions.

Use the basic cotrans functions to compute the direction of Earth's magnetic axis in GEO, using the IGRF model, and test the results for some other transformation vectors with random data.

IDL code: SPEDAS

; Compile contrans library
cotrans_lib
; Define some data
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22]]
; Define times
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577998800]
t0 = time_string(t)
t1 = time_struct(t0)
print, t0
; Compute direction of Earth's magnetic axis in GEO, using the IGRF model. 
cdipdir_vect,transpose(t1.year[*]),transpose(t1.doy[*]),gd1,gd2,gd3
print, gd1,gd2,gd3
; Compute sun direction in GEI system.
csundir_vect,transpose(t1.year[*]),transpose(t1.doy[*]),transpose(t1.hour[*]),transpose(t1.min[*]),transpose(t1.sec[*]),gst,slong,sra,sdec,obliq
print,gst,slong,sra,sdec,obliq
; Compute GEI to GSE transformation.
tgeigse_vect,transpose(t1.year[*]),transpose(t1.doy[*]),transpose(t1.hour[*]),transpose(t1.min[*]),transpose(t1.sec[*]),transpose(d[0, *]),transpose(d[1, *]),transpose(d[2, *]),xgse,ygse,zgse
print,xgse,ygse,zgse
; Compute GSE to GSM transformation.
tgsegsm_vect,transpose(t1.year[*]),transpose(t1.doy[*]),transpose(t1.hour[*]),transpose(t1.min[*]),transpose(t1.sec[*]),transpose(d[0, *]),transpose(d[1, *]),transpose(d[2, *]),xgsm,ygsm,zgsm
print,xgsm,ygsm,zgsm

IDL results: 


IDL> print, t0
2019-12-23/14:53:20
2019-12-25/21:20:00
2019-12-29/05:53:20
2019-12-29/08:40:00
2020-01-02/21:00:00
IDL> print, gd1,gd2,gd3
    0.0486864    0.0486846    0.0486811    0.0486811    0.0486776
    -0.156116    -0.156111    -0.156101    -0.156101    -0.156091
     0.986538     0.986539     0.986541     0.986541     0.986542
IDL> print,gst,slong,sra,sdec,obliq
      5.50119     0.944179      3.24176      3.97097     0.994296
      4.73823      4.77856      4.83825      4.84031      4.92061
      4.74045      4.78439      4.84933      4.85157      4.93861
    -0.408904    -0.408101    -0.405626    -0.405513    -0.399712
     0.409047     0.409047     0.409047     0.409047     0.409047
IDL> print,xgse,ygse,zgse
    0.0618591      45.9846     -480.516     -112.061      738.670
      245.080      773.652      182.717      321.559      318.591
      270.862     -13.1524     -217.683      867.127     -103.484
IDL> print,xgsm,ygsm,zgsm
      245.000      775.000      121.000      304.650      464.340
     -83.8585      11.7033      545.000     -118.216     -460.356
      257.629     -7.93938     0.929342      872.399     -479.899

Python code: pySPEDAS


from pyspedas.cotrans.cotrans_lib import *
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22]]
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577998800]
a = cdipdir_vect(t)
b = csundir_vect(t)
gse = tgeigse_vect(t, d)
gsm = tgsegsm_vect(t, d)

Python results: 


a
Out[2]: 
(array([0.04868638, 0.04868462, 0.0486811 , 0.0486811 , 0.04867761]),
 array([-0.15611589, -0.15611097, -0.15610113, -0.15610113, -0.15609089]),
 array([0.98653812, 0.98653899, 0.98654072, 0.98654072, 0.98654251]))

b
Out[3]: 
(array([5.50118781, 0.94417896, 3.24175902, 3.9709706 , 0.9942959 ]),
 array([4.73823063, 4.77856341, 4.83825495, 4.84031354, 4.92060693]),
 array([4.74044499, 4.78438591, 4.84932932, 4.85156629, 4.93861416]),
 array([-0.40890358, -0.40810141, -0.40562582, -0.40551314, -0.39971157]),
 array([0.4090472 , 0.40904719, 0.40904716, 0.40904716, 0.40904714]))

gse
Out[4]: 
(array([ 6.17328386e-02,  4.59847513e+01, -4.80515919e+02, -1.12061112e+02, 7.38670168e+02]),
 array([245.07961052, 773.65200071, 182.71689404, 321.55872916, 318.59101371]),
 array([ 270.86155264,  -13.15235508, -217.68322895,  867.12698798, -103.48369801]))

gsm
Out[5]: 
(array([245.  , 775.  , 121.  , 304.65, 464.34]),
 array([ -83.85842685,   11.70325822,  545.00012517, -118.21614302, -460.35592829]),
 array([ 257.6291215 ,   -7.93937951,    0.92928139,  872.39913086, -479.89947926]))

Transform data from MAG to GEO.

This transformation uses many different functions internally: SM -> GSM -> GSE -> GEI -> GEO.

IDL code: SPEDAS

cotrans_lib
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22]]
data_in = transpose(d)
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577998800]
t1 = time_struct(t)
subMAG2GEO, t1, data_in, dout
print, transpose(dout)

IDL results: 

IDL> print, transpose(dout)
     -13.1952     -300.294      207.556
      236.685     -725.359     -136.598
      555.777      48.4522     -20.7720
     -64.8366     -481.680      794.762
     -417.047     -548.897     -427.348

Python code: pySPEDAS

from pyspedas.cotrans.cotrans_lib import submag2geo
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22]]
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577998800]
mag = submag2geo(t, d)
print(mag)

Python results: 

[[ -13.19521536 -300.29393966  207.55586259]
 [ 236.68488882 -725.35935255 -136.59821768]
 [ 555.7768468    48.45227165  -20.77195057]
 [ -64.83660486 -481.68020999  794.76242518]
 [-417.04680107 -548.89736495 -427.34807238]]


Transform data from GEI to J2000.

IDL code: SPEDAS

cotrans_lib
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22], [264.14, 61.55, -56.32]]
data_in = transpose(d)
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577798800, 1577998800]
t1 = time_struct(t)
subGEI2J2000, t1, data_in, dout
print, transpose(dout)

IDL results: 

IDL> print, transpose(dout)
       245.02820      -103.07841       250.53148
       775.01595       6.5942014      -11.479825
       123.39361       544.46259      -1.2287885
       305.37957      -206.64889       855.51530
       461.18337      -563.58286      -357.10918
       264.30012       60.387870      -56.824668

Python code: pySPEDAS

from pyspedas.cotrans.cotrans_lib import subgei2j2000
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22], [264.14, 61.55, -56.32]]
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577798800, 1577998800]
mag = subgei2j2000(t, d)
print(mag)

Python results: 

[[ 245.02820801 -103.07809266  250.53160298]
 [ 775.01595209    6.59521058  -11.47942543]
 [ 123.39317313  544.46268498   -1.22861055]
 [ 305.37948491 -206.64887151  855.51536316]
 [ 461.1836826  -563.58260063 -357.10921253]
 [ 264.30009126   60.38797267  -56.82463388]]


Daisy chain transformations.

Both IDL and python contain the following functions for transformations between coordinate systems:
subGEI2GSE, subGSE2GEI
subGSE2GSM, subGSM2GSE
subGSM2SM, subSM2GSM
subGEI2GEO, subGEO2GEI
subGEO2MAG, subMAG2GEO
subGEI2J2000, subJ20002GEI

These functions can be daisy chained. In pyspedas, this can be done automatically using the function subcotrans(time , data, from, to).

The following example is using: GEI -> GSE -> GSM

IDL code: SPEDAS

cotrans_lib
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22], [264.14, 61.55, -56.32]]
data_in = transpose(d)
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577798800, 1577998800]
t1 = time_struct(t)
subGEI2GSE, t1, data_in, dout
data_in = dout
subGSE2GSM, t1, data_in, dout
print, transpose(dout)

IDL results: 

IDL> print, transpose(dout)
     0.061859131       263.75420       252.71276
       45.984592       762.30346       132.67920
      -480.51590       183.48641      -217.03501
      -112.06107       407.08298       830.41709
       724.92896       341.54693      -125.16594
       21.239977       275.98252      -10.621965

Python code: pySPEDAS

from pyspedas.cotrans.cotrans_lib import subcotrans
d = [[245.0, -102.0, 251.0], [775.0, 10.0, -10], [121.0, 545.0, -1.0], [304.65, -205.3, 856.1], [464.34, -561.55, -356.22], [264.14, 61.55, -56.32]]
t = [1577112800, 1577308800, 1577598800, 1577608800, 1577798800, 1577998800]
mag = subcotrans(t, d, 'gei', 'gsm')
print(mag)

Python results: 

[[ 6.17328386e-02  2.63754240e+02  2.52712677e+02]
 [ 4.59847513e+01  7.62303493e+02  1.32679267e+02]
 [-4.80515919e+02  1.83486338e+02 -2.17035056e+02]
 [-1.12061112e+02  4.07083036e+02  8.30417143e+02]
 [ 7.24928845e+02  3.41547042e+02 -1.25165948e+02]
 [ 2.12400389e+01  2.75982462e+02 -1.06219558e+01]]
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