1+ import sys
12import numpy as np
3+ from itertools import combinations
24
35from ...config import Config
6+ from ...constants import Constants as c
7+ from .gauss import gaussIOD
8+ from ..propagate import propagateOrbits
49
5- __all__ = ["selectObservations" ]
10+ __all__ = ["selectObservations" ,
11+ "iod" ]
612
7- def selectObservations (observations , method = "first+middle+last" , columnMapping = Config .columnMapping ):
13+ MU = c .G * c .M_SUN
14+
15+
16+ def selectObservations (observations , method = "combinations" , columnMapping = Config .columnMapping ):
817 """
918 Selects which three observations to use for IOD depending on the method.
1019
1120 Methods:
1221 'first+middle+last' : Grab the first, middle and last observations in time.
1322 'thirds' : Grab the middle observation in the first third, second third, and final third.
23+ 'combinations' : Return the observation IDs corresponding to every possible combination of three observations with
24+ non-coinciding observation times.
1425
1526 Parameters
1627 ----------
1728 observations : `~pandas.DataFrame`
1829 Pandas DataFrame containing observations with at least a column of observation IDs and a column
1930 of exposure times.
20- method : {'first+middle+last', 'thirds}, optional
31+ method : {'first+middle+last', 'thirds', 'combinations' }, optional
2132 Which method to use to select observations.
22- [Default = `first+middle+last` ]
33+ [Default = 'combinations' ]
2334 columnMapping : dict, optional
2435 Column name mapping of observations to internally used column names.
2536 [Default = `~thor.Config.columnMapping`]
2637
2738 Returns
2839 -------
29- obs_id : `~numpy.ndarray' (3 or 0)
40+ obs_id : `~numpy.ndarray' (N, 3 or 0)
3041 An array of selected observation IDs. If three unique observations could
31- not be selected than returns an empty array.
42+ not be selected then returns an empty array.
3243 """
44+ obs_ids = observations [columnMapping ["obs_id" ]].values
45+ if len (obs_ids ) < 3 :
46+ return np .array ([])
47+
48+ indexes = np .arange (0 , len (obs_ids ))
49+ times = observations [columnMapping ["exp_mjd" ]].values
50+ selected = np .array ([])
51+
3352 if method == "first+middle+last" :
34- selected = np .percentile (observations [columnMapping ["exp_mjd" ]].values , [0 , 50 , 100 ], interpolation = "nearest" )
53+ selected_times = np .percentile (times ,
54+ [0 , 50 , 100 ],
55+ interpolation = "nearest" )
56+ selected_index = np .intersect1d (times , selected_times , return_indices = True )[1 ]
57+ selected_index = np .array ([selected_index ])
58+
3559 elif method == "thirds" :
36- selected = np .percentile (observations [columnMapping ["exp_mjd" ]].values , [1 / 6 * 100 , 50 , 5 / 6 * 100 ], interpolation = "nearest" )
60+ selected_times = np .percentile (times ,
61+ [1 / 6 * 100 , 50 , 5 / 6 * 100 ],
62+ interpolation = "nearest" )
63+ selected_index = np .intersect1d (times , selected_times , return_indices = True )[1 ]
64+ selected_index = np .array ([selected_index ])
65+
66+ elif method == "combinations" :
67+ # Make all possible combinations of 3 observations
68+ selected_index = np .array ([np .array (index ) for index in combinations (indexes , 3 )])
69+
3770 else :
3871 raise ValueError ("method should be one of {'first+middle+last', 'thirds'}" )
39-
40- if len (np .unique (selected )) != 3 :
41- print ("Could not find three observations that satisfy the criteria." )
72+
73+ # Make sure each returned combination of observation ids have at least 3 unique
74+ # times
75+ keep = []
76+ for i , comb in enumerate (times [selected_index ]):
77+ if len (np .unique (comb )) == 3 :
78+ keep .append (i )
79+ keep = np .array (keep )
80+
81+ # Return an empty array if no observations satisfy the criteria
82+ if len (keep ) == 0 :
4283 return np .array ([])
4384
44- index = np .intersect1d (observations [columnMapping ["exp_mjd" ]].values , selected , return_indices = True )[1 ]
45- return observations [columnMapping ["obs_id" ]].values [index ]
46-
85+ return obs_ids [selected_index [keep , :]]
86+
87+
88+ def iod (observations ,
89+ observation_selection_method = "combinations" ,
90+ iterate = True ,
91+ light_time = True ,
92+ max_iter = 50 ,
93+ tol = 1e-15 ,
94+ propagatorKwargs = {
95+ "observatoryCode" : "I11" ,
96+ "mjdScale" : "UTC" ,
97+ "dynamical_model" : "2" ,
98+ },
99+ mu = MU ,
100+ columnMapping = Config .columnMapping ):
101+
102+ # Extract column names
103+ obs_id_col = columnMapping ["obs_id" ]
104+ ra_col = columnMapping ["RA_deg" ]
105+ dec_col = columnMapping ["Dec_deg" ]
106+ time_col = columnMapping ["exp_mjd" ]
107+ ra_err_col = columnMapping ["RA_sigma_deg" ]
108+ dec_err_col = columnMapping ["Dec_sigma_deg" ]
109+ obs_x_col = columnMapping ["obs_x_au" ]
110+ obs_y_col = columnMapping ["obs_y_au" ]
111+ obs_z_col = columnMapping ["obs_z_au" ]
112+
113+ # Extract observation IDs, sky-plane positions, sky-plane position uncertainties, times of observation,
114+ # and the location of the observer at each time
115+ obs_ids_all = observations [obs_id_col ].values
116+ coords_eq_ang_all = observations [observations [obs_id_col ].isin (obs_ids_all )][[ra_col , dec_col ]].values
117+ coords_eq_ang_err_all = observations [observations [obs_id_col ].isin (obs_ids_all )][[ra_err_col , dec_err_col ]].values
118+ coords_obs_all = observations [observations [obs_id_col ].isin (obs_ids_all )][[obs_x_col , obs_y_col , obs_z_col ]].values
119+ times_all = observations [observations [obs_id_col ].isin (obs_ids_all )][time_col ].values
120+
121+ # Select observation IDs to use for IOD
122+ obs_ids = selectObservations (observations , method = observation_selection_method , columnMapping = columnMapping )
123+
124+ min_chi2 = 1e10
125+ best_orbit = None
126+ best_obs_ids = None
127+
128+ for ids in obs_ids :
129+ # Grab sky-plane positions of the selected observations, the heliocentric ecliptic position of the observer,
130+ # and the times at which the observations occur
131+ coords_eq_ang = observations [observations [obs_id_col ].isin (ids )][[ra_col , dec_col ]].values
132+ coords_obs = observations [observations [obs_id_col ].isin (ids )][[obs_x_col , obs_y_col , obs_z_col ]].values
133+ times = observations [observations [obs_id_col ].isin (ids )][time_col ].values
134+
135+ # Run IOD
136+ orbits_iod = gaussIOD (coords_eq_ang , times , coords_obs , light_time = light_time , iterate = iterate , max_iter = max_iter , tol = tol )
137+ if np .all (np .isnan (orbits_iod )) == True :
138+ continue
139+
140+ # Propagate initial orbit to all observation times
141+ orbits = propagateOrbits (orbits_iod [:, 1 :], orbits_iod [:, 0 ], times_all , ** propagatorKwargs )
142+ orbits = orbits [['orbit_id' , 'mjd' , 'RA_deg' , 'Dec_deg' ,
143+ 'HEclObj_X_au' , 'HEclObj_Y_au' , 'HEclObj_Z_au' ,
144+ 'HEclObj_dX/dt_au_p_day' , 'HEclObj_dY/dt_au_p_day' , 'HEclObj_dZ/dt_au_p_day' ]].values
145+
146+ # For each unique initial orbit calculate residuals and chi-squared
147+ # Find the orbit which yields the lowest chi-squared
148+ orbit_ids = np .unique (orbits [:, 0 ])
149+ for i , orbit_id in enumerate (orbit_ids ):
150+ orbit = orbits [np .where (orbits [:, 0 ] == orbit_id )]
151+
152+ pred_dec = np .radians (orbit [:, 3 ])
153+ residual_ra = (coords_eq_ang_all [:, 0 ] - orbit [:, 2 ]) * np .cos (pred_dec )
154+ residual_dec = (coords_eq_ang_all [:, 1 ] - orbit [:, 3 ])
155+
156+ chi2 = np .sum (residual_ra ** 2 / coords_eq_ang_err_all [:, 0 ]** 2 + residual_dec ** 2 / coords_eq_ang_err_all [:, 1 ]** 2 ) / (2 * len (residual_ra ) - 6 )
157+
158+ if chi2 < min_chi2 :
159+ best_orbit = orbits_iod [i , :]
160+ best_obs_ids = ids
161+ min_chi2 = chi2
162+
163+ return best_orbit , best_obs_ids , min_chi2
164+
165+
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