Contents

This notebook covers the basics of creating an event list object and carrying out various operations such as simulating time and energies, joining, storing and retrieving event lists.

Setup

Import some useful libraries.

import numpy as np

from matplotlib import pyplot as plt
%matplotlib inline

Import some relevant stingray classes.

from stingray import EventList, Lightcurve

Creating EventList from Photon Arrival Times

Given photon arrival times, an eventlist object can be created. Times are assumed to be seconds from a reference MJD, that can optionally be specified with the mjdref keyword and attribute.

times = [0.5, 1.1, 2.2, 3.7]
mjdref=58000.

Create event list object by passing arrival times as argument.

ev = EventList(times, mjdref=mjdref)
ev.time

array([0.5, 1.1, 2.2, 3.7])

One can add all sorts of data to the EventList object, it is very flexible. In general, we suggest to stick with easily interpretable attributes, like energy or pi.

ev.energy = [0., 3., 4., 20.]

is the same as

energy = [0., 3., 4., 20.]
ev = EventList(times, energy=energy, mjdref=mjdref)

It is always recommended to specify the good time intervals (GTIs) of the event list, as the time intervals where the instrument was fully operational. If not specified, GTIs are defined automatically as the first and the last event time.

gti = [[0, 4]]
ev = EventList(times, gti=gti, energy=energy, mjdref=mjdref)

Roundtrip to Astropy-compatible formats

EventList has the following methods that allow an easy roundtrip to Astropy objects: to_astropy_table, to_astropy_timeseries, from_astropy_table, from_astropy_timeseries

This allows a better interoperability with the Astropy ecosystem.

In this roundtrip, a Table or Timeseries object is created, having as columns time and all other attributes of the same size (e.g. pi, energy), and the rest of the attributes (e.g. gti, mjdref) in the table’s metadata.

table = ev.to_astropy_table()
table

Table length=4

energy	time
float64	float64
0.0	0.5
3.0	1.1
4.0	2.2
20.0	3.7

When converting to Timeseries, times are transformed into astropy.time.TimeDelta objects.

timeseries = ev.to_astropy_timeseries()
timeseries

TimeSeries length=4

time	energy
object	float64
5.787037037037037e-06	0.0
1.2731481481481482e-05	3.0
2.5462962962962965e-05	4.0
4.282407407407408e-05	20.0

table.meta

OrderedDict([('dt', 0),
             ('gti', array([[0, 4]])),
             ('mjdref', 58000.0),
             ('ncounts', 4),
             ('notes', '')])

Of course, these objects can be converted back to event lists. The user should be careful in defining the proper column names and metadata so that the final object is a valid EventList

table_ev = EventList.from_astropy_table(table)
table_ts = EventList.from_astropy_timeseries(timeseries)

table_ev.time, table_ts.time

(array([0.5, 1.1, 2.2, 3.7]), array([0.5, 1.1, 2.2, 3.7]))

Loading and writing EventList objects

We made it possible to save and load data in a number of different formats.

The general syntax is

ev = EventList.read(filename, format)

ev.write(filename, format)

There are three main blocks of formats that might be useful:

1. (read-only) HEASoft-compatible formats -> read event data from HEASOFT-supported missions

2. pickle: reading and saving EventLists from/to Python pickle objects

3. Any format compatible with astropy.table.Table objects.

Loading an EventList from an X-ray observation in HEASoft-compatible format

Loading event data from HEASoft-supported missions in FITS format is easy. It’s sufficient to use the read method with hea or, equivalently, ogip, as format.

Beware: please use hea or ogip, not fits! It would make the roundrip to Astropy tables more complicated, as Astropy supports a generic FITS writer which is not necessarily compatible with HEASoft.

ev = EventList.read('events.fits', 'ogip')

Times are saved to the time attribute, GTIs to the gti attribute, MJDREF to the mjdref attribute, etc.

ev.time[:10]

array([80000000.23635569, 80000001.47479323, 80000001.78458866,
       80000002.78943624, 80000003.42859936, 80000004.07943003,
       80000006.09310323, 80000007.18041813, 80000008.17602143,
       80000008.20403489], dtype=float128)

ev.mjdref

55197.00076601852

ev.gti

array([[80000000., 80001025.]], dtype=float128)

Roundtrip to pickle objects

It is possible to save and load eventlist objects using pickle.

ev.write("events.p", "pickle")
ev2 = EventList.read("events.p", "pickle")

np.allclose(ev2.time, ev.time), np.allclose(ev2.gti, ev.gti)

(True, True)

Roundtrip to Astropy-compatible formats

If the read and write methods receive a format which is not hea, ogip, or pickle, the event list is transformed into an Astropy Table object with the methods described above, and the readers and writers from the Table class are used instead. This allows to extend the save/load operations to a large number of formats, including hdf5 and enhanced CSV (ascii.ecsv).

Note that columns coming from the EVENTS (or equivalent) fits extension, those having the same length as time, when converting to astropy tables they become columns of the table. All the others, including gti, are treated as metadata.

Care should be used in selecting formats that preserve metadata. For example, simple CSV format loses all metadata, including MJDREF, GTIs etc.

ev.write("events.hdf5", "hdf5")
ev3 = EventList.read("events.hdf5", "hdf5")
ev3.time[:10]

array([80000000.23635569, 80000001.47479323, 80000001.78458866,
       80000002.78943624, 80000003.42859936, 80000004.07943003,
       80000006.09310323, 80000007.18041813, 80000008.17602143,
       80000008.20403489], dtype=float128)

# Try the round trip again to verify that everything works

ev.write("events.ecsv", "ascii.ecsv")
ev4 = EventList.read("events.ecsv", "ascii.ecsv")
!cat events.ecsv
ev4.time[:10]

# %ECSV 1.0
# ---
# datatype:
# - {name: energy, datatype: float32}
# - {name: pi, datatype: float32}
# - {name: time, datatype: float128}
# meta: !!omap
# - {dt: 0}
# - gti: !numpy.ndarray
#     buffer: !!binary |
#       QUFBQUFBQ0FscGdaUURHRnBuOEFBQUFBQUFBZ0FKZVlHVUF4aGFaL0FBQT0=
#     dtype: float128
#     order: C
#     shape: !!python/tuple [1, 2]
# - {header: 'XTENSION= ''BINTABLE''           / binary table extension                         BITPIX  =                    8 / array
#     data type                                NAXIS   =                    2 / number of array dimensions                     NAXIS1  =                   12
#     / length of dimension 1                          NAXIS2  =                 1000 / length of dimension 2                          PCOUNT  =                    0
#     / number of group parameters                     GCOUNT  =                    1 / number of groups                               TFIELDS
#     =                    2 / number of table fields                         TTYPE1  = ''TIME    ''                                                            TFORM1  =
#     ''1D      ''                                                            TTYPE2  = ''PI      ''                                                            TFORM2  =
#     ''1J      ''                                                            EXTNAME = ''EVENTS  ''           / extension name                                 OBSERVER=
#     ''Edwige Bubble''                                                       TELESCOP= ''NuSTAR  ''           / Telescope (mission) name                       INSTRUME=
#     ''FPMA    ''           / Instrument name                                OBS_ID  = ''00000000001''        / Observation ID                                 TARG_ID
#     =                    0 / Target ID                                      OBJECT  = ''Fake X-1''           / Name of observed object                        RA_OBJ  =                  0.0
#     / [deg] R.A. Object                              DEC_OBJ =                  0.0 / [deg] Dec Object                               RA_NOM  =                  0.0
#     / Right Ascension used for barycenter correctionsDEC_NOM =                  0.0 / Declination used for barycenter corrections    RA_PNT  =                  0.0
#     / [deg] RA pointing                              DEC_PNT =                  0.0 / [deg] Dec pointing                             PA_PNT  =                  0.0
#     / [deg] Position angle (roll)                    EQUINOX =               2000.0 / Equinox of celestial coord system              RADECSYS=
#     ''FK5     ''           / Coordinate Reference System                    TASSIGN = ''SATELLITE''          / Time assigned by onboard
#     clock                 TIMESYS = ''TDB     ''           / All times in this file are TDB                 MJDREFI =                55197
#     / TDB time reference; Modified Julian Day (int)  MJDREFF =        0.00076601852 / TDB time reference; Modified Julian Day (frac)
#     TIMEREF = ''SOLARSYSTEM''        / Times are pathlength-corrected to barycenter   CLOCKAPP=                    F / TRUE if timestamps
#     corrected by gnd sware      TIMEUNIT= ''s       ''           / unit for time keywords                         TSTART  =           80000000.0
#     / Elapsed seconds since MJDREF at start of file  TSTOP   =           80001025.0 / Elapsed seconds since MJDREF at end of file    LIVETIME=               1025.0
#     / On-source time                                 TIMEZERO=                  0.0 / Time Zero                                      COMMENT
#     FITS (Flexible Image Transport System) format is defined in ''Astronomy aCOMMENT nd Astrophysics'', volume 376, page 359; bibcode:
#     2001A&A...376..359H    COMMENT MJDREFI+MJDREFF = epoch of Jan 1, 2010, in TT time system.              HISTORY File modified by
#     user ''meo'' with fv  on 2015-08-17T14:10:02             HISTORY File modified by user ''meo'' with fv  on 2015-08-17T14:48:52             END                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             '}
# - {instr: fpma}
# - {mission: nustar}
# - {mjdref: 55197.00076601852}
# - {ncounts: 1000}
# - {notes: ''}
# - {timeref: solarsystem}
# - {timesys: tdb}
# schema: astropy-2.0
energy pi time
8.56 174.0 80000000.23635569215
33.039997 786.0 80000001.47479322553
7.9999995 160.0 80000001.78458866477
27.84 656.0 80000002.789436236024
8.84 181.0 80000003.428599357605
13.92 308.0 80000004.079430028796
37.839996 906.0 80000006.09310323
40.559998 974.0 80000007.180418133736
5.8799996 107.0 80000008.176021426916
41.239998 991.0 80000008.204034894705
33.64 801.0 80000009.69214613736
8.72 178.0 80000010.36281684041
17.32 393.0 80000010.78324916959
6.56 124.0 80000011.8733625412
21.28 492.0 80000013.92633379996
10.24 216.0 80000014.204483643174
10.68 227.0 80000014.26073910296
26.68 627.0 80000015.256171390414
3.96 59.0 80000018.08373501897
13.96 309.0 80000018.83911728859
28.32 668.0 80000019.98157013953
38.319996 918.0 80000020.76013682783
17.76 404.0 80000021.14855520427
12.64 276.0 80000022.02460347116
29.76 704.0 80000023.50157275796
24.08 562.0 80000023.61806283891
10.400001 220.0 80000024.97833034396
41.519997 998.0 80000025.95996727049
4.24 66.0 80000026.16019311547
23.32 543.0 80000027.089139238
41.399998 995.0 80000028.596908301115
19.72 453.0 80000031.065731182694
36.559998 874.0 80000031.10555113852
38.399998 920.0 80000032.516511276364
24.28 567.0 80000032.808356150985
29.48 697.0 80000033.18797942996
36.76 879.0 80000033.85146795213
10.6 225.0 80000034.861510172486
20.0 460.0 80000038.22435864806
3.3600001 44.0 80000038.39090189338
15.08 337.0 80000042.41919325292
22.48 522.0 80000043.69195660949
4.24 66.0 80000045.52997684479
21.88 507.0 80000052.78282105923
39.6 950.0 80000052.919592529535
3.24 41.0 80000054.28180256486
14.32 318.0 80000056.48970986903
7.4399996 146.0 80000057.49698485434
7.9599996 159.0 80000058.55781446397
21.36 494.0 80000059.284333616495
35.159996 839.0 80000060.359298199415
21.64 501.0 80000063.666031733155
36.44 871.0 80000064.78927731514
35.319996 843.0 80000067.341705307364
26.08 612.0 80000068.267971634865
12.12 263.0 80000070.24889309704
11.400001 245.0 80000072.99266758561
35.839996 856.0 80000073.4422865361
6.68 127.0 80000073.81521306932
28.4 670.0 80000074.7710172981
22.08 512.0 80000076.15446573496
29.64 701.0 80000076.61943152547
34.319996 818.0 80000078.37191092968
9.04 186.0 80000079.364117503166
42.399998 1020.0 80000080.12182110548
14.08 312.0 80000080.4114151746
12.64 276.0 80000083.704568862915
26.16 614.0 80000084.38392549753
21.12 488.0 80000084.49645087123
7.7599998 154.0 80000084.73323458433
5.64 101.0 80000085.518022567034
4.2799997 67.0 80000086.06328216195
39.039997 936.0 80000087.00356020033
14.88 332.0 80000087.108956605196
11.24 241.0 80000087.3983823657
42.199997 1015.0 80000088.44739763439
28.16 664.0 80000088.72279639542
2.48 22.0 80000089.15565529466
42.28 1017.0 80000090.20357654989
5.32 93.0 80000090.7642698288
14.28 317.0 80000090.80305439234
40.319996 968.0 80000091.500082850456
18.44 421.0 80000092.158643990755
32.239998 766.0 80000092.89413803816
4.4 70.0 80000094.805209457874
38.879997 932.0 80000095.04941494763
32.199997 765.0 80000096.56686630845
30.4 720.0 80000096.91533789039
35.719997 853.0 80000098.67825654149
29.32 693.0 80000098.92884159088
17.199999 390.0 80000099.199268594384
37.92 908.0 80000100.14995288849
1.96 9.0 80000100.935947969556
13.12 288.0 80000102.76762147248
30.6 725.0 80000103.05724072456
34.239998 816.0 80000104.193173110485
8.88 182.0 80000107.33343601227
29.6 700.0 80000107.40127386153
8.24 166.0 80000107.56737007201
39.76 954.0 80000109.40503971279
41.399998 995.0 80000109.51361806691
32.399998 770.0 80000111.27798360586
20.2 465.0 80000112.93057106435
22.36 519.0 80000113.545409321785
41.559998 999.0 80000113.71510283649
36.64 876.0 80000115.363516911864
5.12 88.0 80000116.62624913454
24.32 568.0 80000117.5390470773
11.4800005 247.0 80000118.313546299934
10.0 210.0 80000118.64352825284
13.36 294.0 80000119.64161340892
4.48 72.0 80000119.70217871666
5.68 102.0 80000119.87085522711
25.76 604.0 80000120.67677563429
1.9200001 8.0 80000121.80093438923
2.92 33.0 80000122.09129279852
5.12 88.0 80000122.545517489314
33.32 793.0 80000122.93073017895
13.76 304.0 80000123.276563555
37.159996 889.0 80000125.506356075406
30.56 724.0 80000125.6568851918
37.079998 887.0 80000127.336458325386
6.4399996 121.0 80000127.45361994207
11.96 259.0 80000128.36573840678
14.08 312.0 80000129.43040788174
14.36 319.0 80000130.30537183583
34.239998 816.0 80000131.993975520134
29.92 708.0 80000132.51598034799
21.8 505.0 80000132.877141192555
10.84 231.0 80000134.958766937256
15.72 353.0 80000136.26415735483
9.32 193.0 80000136.271308645606
38.44 921.0 80000136.491618439555
34.559998 824.0 80000136.59682570398
29.64 701.0 80000136.81391918659
13.6 300.0 80000137.111403808
15.0 335.0 80000137.99286413193
8.2 165.0 80000140.02283409238
31.0 735.0 80000141.585879951715
18.12 413.0 80000141.88128243387
27.64 651.0 80000142.301297202706
29.44 696.0 80000144.258596763015
4.32 68.0 80000146.35952179134
9.92 208.0 80000146.431891173124
26.6 625.0 80000146.93531550467
32.719997 778.0 80000147.86272408068
4.4 70.0 80000148.20213320851
14.04 311.0 80000148.998638793826
10.76 229.0 80000150.13331639767
8.12 163.0 80000150.40001221001
31.96 759.0 80000150.51030369103
41.6 1000.0 80000158.27798460424
2.96 34.0 80000158.565826013684
19.76 454.0 80000160.18738743663
14.440001 321.0 80000162.67192919552
11.72 253.0 80000163.52692268789
37.44 896.0 80000164.03886182606
32.84 781.0 80000164.495729878545
17.24 391.0 80000165.17495532334
3.44 46.0 80000166.38718263805
25.76 604.0 80000168.38902553916
25.44 596.0 80000169.68685694039
23.56 549.0 80000169.713349059224
19.08 437.0 80000170.805011570454
41.039997 986.0 80000172.42077590525
2.16 14.0 80000172.43760578334
2.16 14.0 80000174.10814335942
37.28 892.0 80000174.15144339204
30.76 729.0 80000174.80246704817
28.24 666.0 80000174.83830589056
23.52 548.0 80000176.110384613276
33.399998 795.0 80000176.43801294267
7.08 137.0 80000177.71353569627
39.12 938.0 80000178.329968214035
9.44 196.0 80000180.91684667766
6.56 124.0 80000181.358734831214
24.96 584.0 80000182.17984089255
14.08 312.0 80000182.2385392189
29.92 708.0 80000183.21093174815
8.52 173.0 80000183.68284714222
23.92 558.0 80000184.32184153795
33.96 809.0 80000187.16848820448
13.0 285.0 80000188.89809964597
2.56 24.0 80000189.59268042445
8.52 173.0 80000190.39239893854
29.6 700.0 80000190.987773641944
8.04 161.0 80000191.39765946567
9.84 206.0 80000191.63218219578
37.399998 895.0 80000191.7998701334
37.48 897.0 80000194.591946706176
2.44 21.0 80000195.17524069548

33.039997 786.0 80000195.60482543707
15.4 345.0 80000197.01553657651
20.56 474.0 80000198.18857589364
12.8 280.0 80000199.30817961693
20.16 464.0 80000200.066078454256
1.6800001 2.0 80000201.68090777099
12.04 261.0 80000202.814891934395
18.32 418.0 80000203.25650832057
40.359997 969.0 80000203.48255087435
34.28 817.0 80000204.7061804533
34.64 826.0 80000207.248482748866
30.4 720.0 80000208.40996426344
28.76 679.0 80000208.54558329284
3.6 50.0 80000212.2733836025
39.399998 945.0 80000213.37501113117
23.64 551.0 80000214.05003093183
10.24 216.0 80000214.76189556718
15.440001 346.0 80000214.94751133025
33.839996 806.0 80000215.30322690308
2.88 32.0 80000215.606552898884
17.56 399.0 80000216.67295819521
17.199999 390.0 80000216.721879810095
22.0 510.0 80000217.02722400427
7.3199997 143.0 80000218.21801964939
6.3199997 118.0 80000223.690936505795
40.519997 973.0 80000224.71057784557
10.6 225.0 80000224.88408643007
31.08 737.0 80000225.81306296587
21.0 485.0 80000228.288003221154
15.64 351.0 80000229.47965101898
34.719997 828.0 80000229.982017084956
25.88 607.0 80000230.13939705491
16.52 373.0 80000230.207446575165
1.8 5.0 80000233.628895014524
33.0 785.0 80000233.858214601874
36.879997 882.0 80000235.58721217513
1.76 4.0 80000236.03008031845
42.239998 1016.0 80000239.206377997994
31.119999 738.0 80000240.66440632939
34.159996 814.0 80000241.05537928641
13.56 299.0 80000242.91226673126
18.92 433.0 80000243.34091578424
22.44 521.0 80000246.23444570601
40.8 980.0 80000246.39591316879
21.28 492.0 80000248.63243843615
24.28 567.0 80000249.259784281254
9.56 199.0 80000249.85402186215
5.04 86.0 80000250.17666938901
3.0 35.0 80000251.49163559079
25.44 596.0 80000251.50295473635
24.4 570.0 80000252.06601053476
30.56 724.0 80000252.272911697626
38.12 913.0 80000252.985514968634
38.8 930.0 80000253.836741268635
30.76 729.0 80000255.06581965089
41.719997 1003.0 80000255.60727831721
41.64 1001.0 80000256.902037888765
19.8 455.0 80000258.60432396829
42.359997 1019.0 80000260.50080451369
25.6 600.0 80000260.75552198291
11.56 249.0 80000260.88460493088
33.839996 806.0 80000261.36898006499
37.48 897.0 80000262.92271217704
18.2 415.0 80000262.99845524132
23.36 544.0 80000263.33590015769
40.96 984.0 80000264.96524555981
9.28 192.0 80000265.84508921206
10.84 231.0 80000266.91673760116
4.44 71.0 80000268.235334053636
22.76 529.0 80000271.489329367876
23.96 559.0 80000271.64101035893
35.879997 857.0 80000271.98798702657
11.16 239.0 80000273.71523039043
36.199997 865.0 80000275.30799421668
32.76 779.0 80000275.81958813965
27.32 643.0 80000276.46777294576
27.0 635.0 80000277.24329108
11.360001 244.0 80000277.80254943669
3.08 37.0 80000278.42643971741
18.68 427.0 80000278.52543953061
5.8399997 106.0 80000278.78952820599
25.24 591.0 80000279.13904826343
11.400001 245.0 80000279.32166413963
6.72 128.0 80000279.47431126237
34.6 825.0 80000281.05502511561
14.2 315.0 80000281.66787202656
18.08 412.0 80000281.735276550055
14.16 314.0 80000283.60641156137
12.4800005 272.0 80000284.68940325081
22.72 528.0 80000284.771769434214
7.2 140.0 80000285.59601339698
37.519997 898.0 80000287.934347867966
37.559998 899.0 80000288.457227408886
25.36 594.0 80000288.84559759498
37.039997 886.0 80000289.283936053514
32.48 772.0 80000289.74665103853
21.36 494.0 80000290.772457659245
1.64 1.0 80000290.879882499576
19.32 443.0 80000291.225027650595
21.84 506.0 80000291.23198154569
2.8 30.0 80000293.356203347445
31.92 758.0 80000296.29710520804
32.52 773.0 80000297.10793355107
37.159996 889.0 80000298.52665117383
12.64 276.0 80000298.93143287301
7.4399996 146.0 80000299.927507817745
17.199999 390.0 80000300.818491622806
2.52 23.0 80000302.07161732018
2.56 24.0 80000302.72473844886
36.319996 868.0 80000305.32900521159
4.52 73.0 80000305.93047915399
3.24 41.0 80000306.89711469412
16.64 376.0 80000309.568026304245
4.4 70.0 80000310.67230030894
18.36 419.0 80000311.17736788094
8.24 166.0 80000311.37703952193
20.12 463.0 80000313.92710117996
36.76 879.0 80000316.52630840242
3.6399999 51.0 80000316.576121881604
2.56 24.0 80000316.61531569064
4.68 77.0 80000316.991498693824
30.92 733.0 80000318.496204048395
4.44 71.0 80000318.759574487805
25.72 603.0 80000318.99812464416
24.16 564.0 80000323.19316992164
39.64 951.0 80000323.76615965366
2.6799998 27.0 80000324.23196092248
30.8 730.0 80000325.30946139991
13.68 302.0 80000325.49627235532
40.64 976.0 80000325.76096495986
9.04 186.0 80000326.018922537565
23.56 549.0 80000328.51117782295
32.12 763.0 80000330.33366891742
21.16 489.0 80000331.37347571552
38.8 930.0 80000332.161390304565
6.2 115.0 80000332.54631538689
37.319996 893.0 80000333.515790537
2.6799998 27.0 80000335.46171656251
27.8 655.0 80000336.63410934806
38.92 933.0 80000339.03143580258
5.7599998 104.0 80000339.16872346401
18.32 418.0 80000340.030776798725
5.8399997 106.0 80000340.41478018463
17.48 397.0 80000340.533760264516
33.32 793.0 80000341.72407652438
11.360001 244.0 80000344.206543818116
24.88 582.0 80000344.78012427688
32.96 784.0 80000345.00482337177
2.52 23.0 80000345.26880034804
13.2 290.0 80000345.654379203916
34.359997 819.0 80000345.975308820605
42.359997 1019.0 80000346.41354955733
7.8799996 157.0 80000346.86677853763
39.6 950.0 80000347.32460169494
9.32 193.0 80000347.35750260949
16.0 360.0 80000349.31582227349
37.879997 907.0 80000351.124539494514
19.44 446.0 80000352.37143753469
36.76 879.0 80000353.196565657854
2.24 16.0 80000354.17744512856
30.88 732.0 80000355.20202793181
39.8 955.0 80000355.60426925123
40.12 963.0 80000355.82318587601
16.4 370.0 80000356.5162641108
10.360001 219.0 80000357.642409190536
4.12 63.0 80000359.16175606847
7.68 152.0 80000359.8546615839
4.12 63.0 80000362.5537327677
20.8 480.0 80000362.92154058814
17.199999 390.0 80000363.773983463645
39.999996 960.0 80000365.48620200157
36.319996 868.0 80000368.489620789886
19.6 450.0 80000369.631684705615
41.679996 1002.0 80000370.6534255296
39.159996 939.0 80000371.82940942049
34.399998 820.0 80000373.43823419511
29.28 692.0 80000373.8585408777
39.039997 936.0 80000374.209455892444
34.44 821.0 80000374.64683301747
2.96 34.0 80000375.620239943266
32.36 769.0 80000378.87894229591
35.999996 860.0 80000378.97707155347
14.28 317.0 80000379.42757484317
37.839996 906.0 80000379.917373120785
8.92 183.0 80000381.10625052452
37.239998 891.0 80000382.077453806996
31.039999 736.0 80000382.17598539591
34.079998 812.0 80000382.22633959353
25.84 606.0 80000382.22792515159
27.6 650.0 80000382.55412106216
2.8 30.0 80000383.94620233774
37.12 888.0 80000384.37110866606
28.16 664.0 80000387.30780394375
20.44 471.0 80000387.87746040523
25.119999 588.0 80000388.37795352936
2.6799998 27.0 80000389.268874913454
37.199997 890.0 80000392.62231977284
28.16 664.0 80000393.17818275094
11.52 248.0 80000393.43643279374
2.6 25.0 80000395.12563699484
15.6 350.0 80000395.77989049256
6.48 122.0 80000396.31284117699
32.039997 761.0 80000399.1847140342
37.92 908.0 80000399.54459910095
16.84 381.0 80000400.72491231561
20.64 476.0 80000403.17735889554
8.88 182.0 80000403.54358610511
20.72 478.0 80000404.22769507766
5.4 95.0 80000404.47602318227
42.479996 1022.0 80000404.67004515231
16.64 376.0 80000408.95574080944
7.16 139.0 80000410.03962627053
16.72 378.0 80000410.75551979244
8.52 173.0 80000412.09823872149
31.8 755.0 80000412.219870209694
1.9200001 8.0 80000412.81054663658
21.96 509.0 80000414.8682410419
24.44 571.0 80000415.37962676585
27.92 658.0 80000416.70795631409
24.56 574.0 80000417.1444568038
37.039997 886.0 80000418.38563929498
1.96 9.0 80000420.47344271839
8.88 182.0 80000420.53409618139
26.48 622.0 80000420.80564555526
41.719997 1003.0 80000420.863403081894
5.96 109.0 80000420.942480519414
35.8 855.0 80000422.02582614124
8.44 171.0 80000422.79813404381
12.76 279.0 80000424.42955330014
7.8399997 156.0 80000424.81564453244
7.4799995 147.0 80000425.28199738264
40.319996 968.0 80000425.867245197296
33.719997 803.0 80000426.62731541693
40.12 963.0 80000427.133511930704
14.52 323.0 80000427.36044855416
7.0 135.0 80000428.54412809014
15.56 349.0 80000428.88726851344
30.6 725.0 80000429.38063727319
19.6 450.0 80000432.95051422715
3.08 37.0 80000434.64868846536
2.4 20.0 80000435.51728320122
39.76 954.0 80000436.24377171695
23.64 551.0 80000437.577606111765
9.48 197.0 80000438.05216662586
34.039997 811.0 80000438.70308248699
2.3600001 19.0 80000442.052734196186
27.36 644.0 80000442.764658123255
14.4800005 322.0 80000443.238895997405
12.76 279.0 80000445.098355308175
14.6 325.0 80000446.023702159524
32.879997 782.0 80000446.16962249577
10.92 233.0 80000448.83636845648
7.7999997 155.0 80000450.061449572444
9.12 188.0 80000450.52947856486
32.079998 762.0 80000450.55909974873
28.32 668.0 80000451.879113674164
22.28 517.0 80000452.064453706145
10.08 212.0 80000452.13652163744
26.32 618.0 80000452.9472001791
35.399998 845.0 80000453.03071194887
9.48 197.0 80000454.07206726074
3.32 43.0 80000456.48143340647
34.399998 820.0 80000458.18602730334
11.56 249.0 80000459.0324331224
4.2799997 67.0 80000459.4572635144
32.36 769.0 80000459.920432657
41.239998 991.0 80000464.06256014109
10.76 229.0 80000464.33307418227
34.079998 812.0 80000466.34134361148
26.84 631.0 80000467.24169912934
16.119999 363.0 80000467.884447038174
40.319996 968.0 80000468.7550342083
10.72 228.0 80000469.84887549281
22.52 523.0 80000469.8745007813
39.92 958.0 80000472.20344258845
27.4 645.0 80000472.30986727774
31.84 756.0 80000473.21885484457
15.440001 346.0 80000473.694500654936
17.24 391.0 80000476.0327218622
32.84 781.0 80000476.96122226119
39.28 942.0 80000480.92292739451
35.319996 843.0 80000481.06054444611
4.4 70.0 80000481.37218731642
24.36 569.0 80000481.933602169156
26.16 614.0 80000481.98567260802
40.879997 982.0 80000482.9210729748
40.479996 972.0 80000483.857440814376
4.64 76.0 80000484.32165810466
39.8 955.0 80000484.80663745105
29.16 689.0 80000486.771085351706
11.84 256.0 80000487.217004179955
14.16 314.0 80000487.990593642
28.92 683.0 80000491.276099190116
37.999996 910.0 80000491.747016862035
6.4399996 121.0 80000493.35879443586
25.2 590.0 80000494.31928488612
12.16 264.0 80000495.14925374091
14.6 325.0 80000495.4605127275
20.64 476.0 80000496.37845928967
5.16 89.0 80000496.85824956
19.88 457.0 80000497.20662690699
35.92 858.0 80000502.43506611884
25.8 605.0 80000502.71769653261
17.119999 388.0 80000502.80815401673
36.159996 864.0 80000504.42526854575
21.4 495.0 80000505.48890078068
12.4800005 272.0 80000506.024649724364
21.92 508.0 80000506.17142087221
4.56 74.0 80000508.07841642201
4.72 78.0 80000508.71263246238
31.56 749.0 80000509.140583753586
28.119999 663.0 80000509.95569059253
27.28 642.0 80000510.86728909612
12.04 261.0 80000512.479585409164
30.199999 715.0 80000516.56570722163
33.36 794.0 80000516.99862577021
5.16 89.0 80000517.344923987985
11.12 238.0 80000519.38823206723
11.32 243.0 80000519.57560668886
5.0 85.0 80000519.58020955324
33.239998 791.0 80000520.51779472828
6.3999996 120.0 80000520.546872377396
9.72 203.0 80000521.153368234634
30.64 726.0 80000521.42145887017
21.96 509.0 80000521.63308496773
12.6 275.0 80000523.057834371924
8.36 169.0 80000525.05073848367
10.56 224.0 80000527.819232299924
29.24 691.0 80000531.12523216009
24.6 575.0 80000532.10568276048
40.8 980.0 80000533.20108996332
17.0 385.0 80000534.29738210142
23.48 547.0 80000534.340845018625
18.28 417.0 80000534.83431440592
2.08 12.0 80000534.87653042376
41.92 1008.0 80000534.895185917616
8.52 173.0 80000535.94042633474
19.84 456.0 80000537.48509004712
10.400001 220.0 80000538.26394830644
23.92 558.0 80000540.002261936665
37.719997 903.0 80000540.1134250015
13.84 306.0 80000546.718622386456
4.32 68.0 80000546.84028501809
18.56 424.0 80000547.30754908919
3.08 37.0 80000549.5327937603
27.88 657.0 80000550.56298401952
29.0 685.0 80000550.60222132504
35.159996 839.0 80000552.734096348286
38.519997 923.0 80000553.922179594636
5.52 98.0 80000555.44246518612
18.56 424.0 80000558.82404534519
39.319996 943.0 80000558.947059229016
32.399998 770.0 80000559.282619684935
33.0 785.0 80000560.58969677985
29.72 703.0 80000560.70387540758
10.24 216.0 80000561.323437169194
17.88 407.0 80000562.679025664926
27.44 646.0 80000563.71705073118
14.4800005 322.0 80000563.95132599771
25.24 591.0 80000564.861919119954
23.24 541.0 80000565.76752875745
37.92 908.0 80000565.78528097272
24.92 583.0 80000566.29958720505
31.88 757.0 80000567.06900238991
42.359997 1019.0 80000569.15245625377
11.68 252.0 80000570.583770141006
11.56 249.0 80000571.260604158044
22.48 522.0 80000572.77767854929
24.64 576.0 80000574.140301436186
28.119999 663.0 80000574.51526069641
3.28 42.0 80000577.082364201546
35.559998 849.0 80000578.60487310588
5.72 103.0 80000579.25371134281
3.4 45.0 80000579.63681046665
6.3199997 118.0 80000581.21821717918
6.3199997 118.0 80000582.04014620185
22.12 513.0 80000583.46193483472
9.5199995 198.0 80000586.03360375762
3.48 47.0 80000589.798507750034
31.72 753.0 80000591.46542161703
2.88 32.0 80000591.97941620648
10.8 230.0 80000593.13316428661
15.84 356.0 80000594.042805209756
15.56 349.0 80000594.91821274161
37.159996 889.0 80000595.397889867425
28.16 664.0 80000595.763835296035
6.8399997 131.0 80000596.830532982945
37.559998 899.0 80000598.901824980974
31.16 739.0 80000599.64194495976
28.88 682.0 80000600.793473765254
31.56 749.0 80000602.10744164884
7.8399997 156.0 80000602.55246156454
17.24 391.0 80000603.4955958724
7.12 138.0 80000606.650620505214
2.16 14.0 80000608.090855017304
37.879997 907.0 80000609.993093535304
4.7999997 80.0 80000610.186307400465
15.56 349.0 80000611.37006236613
30.48 722.0 80000611.83906060457
19.96 459.0 80000611.8572294265
34.64 826.0 80000611.95349282026
41.839996 1006.0 80000613.84575891495
23.2 540.0 80000617.17802332342
17.56 399.0 80000617.24794691801
34.559998 824.0 80000617.35718101263
28.16 664.0 80000617.732587218285
20.64 476.0 80000618.9578525275
28.84 681.0 80000619.30346444249
39.239998 941.0 80000621.2265856415
18.16 414.0 80000621.38765838742
7.9999995 160.0 80000621.735619053245
33.079998 787.0 80000623.792137786746
37.64 901.0 80000623.85770910978
2.6 25.0 80000626.21549396217
31.039999 736.0 80000627.16449086368
33.12 788.0 80000628.88948699832
39.319996 943.0 80000630.68285809457
11.32 243.0 80000630.789920687675
30.48 722.0 80000632.821838498116
27.199999 640.0 80000632.881889894605
24.84 581.0 80000634.78217072785
20.28 467.0 80000635.002951964736
33.679996 802.0 80000635.41563603282
36.199997 865.0 80000635.88681785762
8.56 174.0 80000637.371477141976
35.519997 848.0 80000642.38429802656
30.4 720.0 80000643.78843893111
25.44 596.0 80000644.600917607546
11.68 252.0 80000644.882760211825
10.28 217.0 80000645.594902947545
9.2 190.0 80000645.93502403796
16.439999 371.0 80000646.383003011346
2.6399999 26.0 80000646.53795617819
34.64 826.0 80000647.63100332022
22.84 531.0 80000648.47574129701
5.12 88.0 80000649.00771085918
42.079998 1012.0 80000649.114930674434
24.92 583.0 80000650.1061706841
22.88 532.0 80000655.68533721566
24.68 577.0 80000657.16480255127
26.68 627.0 80000657.258827999234
19.8 455.0 80000657.33367057145
35.64 851.0 80000658.74945259094
2.08 12.0 80000660.18671748042
17.439999 396.0 80000660.63745248318
33.999996 810.0 80000661.82945792377
6.48 122.0 80000661.90170559287
17.16 389.0 80000662.26141363382
33.32 793.0 80000662.64840815961
41.64 1001.0 80000663.12676268816
14.56 324.0 80000663.227578774095
24.44 571.0 80000664.475006356835
3.3600001 44.0 80000664.552283763885
17.24 391.0 80000665.17621576786
27.4 645.0 80000666.08528217673
39.079998 937.0 80000670.71755500138
7.72 153.0 80000671.198174357414
6.8799996 132.0 80000673.345912232995
34.199997 815.0 80000674.87888632715
35.28 842.0 80000676.18293096125
11.64 251.0 80000676.64919489622
40.359997 969.0 80000676.80372226238
31.44 746.0 80000678.275382354856
11.8 255.0 80000680.48982979357

26.24 616.0 80000684.38221885264
2.8 30.0 80000685.43452076614
22.0 510.0 80000686.74407067895
31.199999 740.0 80000686.81872756779
30.84 731.0 80000688.30932036042
42.319996 1018.0 80000688.81981065869
20.16 464.0 80000691.197261437774
16.4 370.0 80000692.15807239711
27.92 658.0 80000693.03427194059
10.360001 219.0 80000694.3066085726
36.8 880.0 80000694.962600558996
40.44 971.0 80000697.02309130132
38.48 922.0 80000698.11148573458
21.56 499.0 80000698.516439035535
40.28 967.0 80000699.06620439887
42.44 1021.0 80000701.39014860988
27.76 654.0 80000701.87561401725
11.8 255.0 80000702.62369687855
27.88 657.0 80000702.988359063864
39.159996 939.0 80000705.296378955245
23.96 559.0 80000705.433091163635
11.440001 246.0 80000705.599841311574
2.8400002 31.0 80000709.3684746474
12.2 265.0 80000709.77955941856
3.7199998 53.0 80000709.794584959745
11.2 240.0 80000709.846471622586
27.0 635.0 80000711.9785169363
19.4 445.0 80000712.899810910225
1.9200001 8.0 80000713.0795609951
21.96 509.0 80000713.76596863568
36.48 872.0 80000716.780457377434
22.039999 511.0 80000717.29924210906
17.32 393.0 80000720.5562723279
12.68 277.0 80000720.58715964854
41.239998 991.0 80000722.03180555999
29.32 693.0 80000722.03699606657
7.9599996 159.0 80000722.478862181306
29.96 709.0 80000723.87889204919
5.52 98.0 80000724.7961999625
37.44 896.0 80000726.34677195549
40.28 967.0 80000727.47035036981
26.84 631.0 80000728.90236452222
41.92 1008.0 80000729.3514444083
26.16 614.0 80000730.33039654791
4.2 65.0 80000730.81428743899
4.4 70.0 80000731.42920610309
16.359999 369.0 80000732.61377693713
14.04 311.0 80000733.754086226225
17.08 387.0 80000733.79874679446
3.52 48.0 80000733.991308033466
38.28 917.0 80000734.417156770825
1.96 9.0 80000738.45621095598
11.08 237.0 80000739.78259626031
39.319996 943.0 80000739.904296547174
29.36 694.0 80000742.26487219334
20.8 480.0 80000742.58448088169
18.0 410.0 80000743.84713715315
7.0 135.0 80000745.445721656084
33.32 793.0 80000745.704266637564
4.96 84.0 80000746.49740232527
2.88 32.0 80000748.3739194572
40.76 979.0 80000749.18420062959
39.559998 949.0 80000749.238480210304
40.8 980.0 80000749.36030867696
15.36 344.0 80000751.06558699906
35.64 851.0 80000751.55830208957
39.479996 947.0 80000752.70824530721
9.12 188.0 80000752.72337460518
20.64 476.0 80000752.881983697414
29.52 698.0 80000753.15865902603
35.28 842.0 80000753.76198838651
27.92 658.0 80000754.23456764221
18.08 412.0 80000754.3275937736
35.76 854.0 80000755.37613813579
26.56 624.0 80000756.66476659477
6.7599998 129.0 80000758.372802481055
23.48 547.0 80000759.07206888497
29.16 689.0 80000759.892510056496
36.48 872.0 80000761.603752076626
17.16 389.0 80000762.42036630213
11.0 235.0 80000765.06811144948
31.76 754.0 80000765.382397055626
35.44 846.0 80000765.4667224288
41.28 992.0 80000765.93857854605
37.039997 886.0 80000767.26963350177
25.72 603.0 80000767.7786257714
20.28 467.0 80000770.32975102961
7.3999996 145.0 80000771.69804634154
3.32 43.0 80000773.945546999574
37.399998 895.0 80000774.221253693104
10.92 233.0 80000775.89942243695
24.6 575.0 80000777.312041819096
12.4800005 272.0 80000777.77507701516
31.72 753.0 80000777.79259891808
12.360001 269.0 80000779.33480271697
22.64 526.0 80000779.554390221834
36.999996 885.0 80000780.81437155604
29.28 692.0 80000780.933462917805
35.159996 839.0 80000781.15924490988
24.64 576.0 80000781.26206161082
25.119999 588.0 80000781.72611118853
4.7599998 79.0 80000782.172751545906
20.28 467.0 80000783.125701248646
38.64 926.0 80000785.342386975884
4.92 83.0 80000785.36341136694
34.6 825.0 80000785.92007930577
20.56 474.0 80000786.1086602211
17.279999 392.0 80000786.253573834896
33.6 800.0 80000787.553292140365
32.32 768.0 80000787.658161982894
4.68 77.0 80000790.072870031
24.64 576.0 80000792.274298503995
9.44 196.0 80000792.443054273725
17.52 398.0 80000792.46565423906
14.4800005 322.0 80000792.808876529336
33.879997 807.0 80000795.87703709304
32.719997 778.0 80000795.91278010607
5.44 96.0 80000797.14426906407
11.04 236.0 80000797.26987493038
34.719997 828.0 80000798.51847578585
2.2 15.0 80000799.48481544852
31.72 753.0 80000799.881970733404
31.039999 736.0 80000803.51909430325
18.52 423.0 80000803.731096595526
32.16 764.0 80000803.883781552315
40.92 983.0 80000805.29773187637
18.0 410.0 80000805.306009307504
17.32 393.0 80000807.21232941747
11.88 257.0 80000808.28512185812
21.36 494.0 80000808.454649567604
2.48 22.0 80000808.523783952
41.76 1004.0 80000809.73774009943
39.92 958.0 80000810.001270249486
13.12 288.0 80000810.86777666211
41.319996 993.0 80000811.438306853175
6.16 114.0 80000812.21489995718
28.199999 665.0 80000815.07969661057
29.56 699.0 80000815.974775359035
19.44 446.0 80000816.16485761106
3.32 43.0 80000816.704811513424
33.679996 802.0 80000816.80518731475
6.68 127.0 80000816.81600318849
3.1599998 39.0 80000819.00975045562
19.32 443.0 80000819.48453132808
34.079998 812.0 80000821.329228281975
8.8 180.0 80000821.52698163688
36.319996 868.0 80000822.00912617147
34.199997 815.0 80000824.46000294387
10.52 223.0 80000824.66023361683
11.28 242.0 80000825.05113039911
25.0 585.0 80000827.12451052666
3.96 59.0 80000827.4073446542
24.68 577.0 80000828.5048404783
38.159996 914.0 80000828.622610628605
31.88 757.0 80000828.63124883175
24.0 560.0 80000829.2215629518
20.6 475.0 80000829.66059269011
5.32 93.0 80000830.33870181441
13.76 304.0 80000831.20006233454
11.88 257.0 80000831.21613633633
15.16 339.0 80000832.059845909476
21.84 506.0 80000832.423598602414
13.6 300.0 80000833.69929590821
34.999996 835.0 80000834.46965831518
41.159996 989.0 80000836.12533031404
8.12 163.0 80000836.71061439812
28.4 670.0 80000836.78514607251
19.56 449.0 80000837.03853216767
12.88 282.0 80000839.699784219265
5.2799997 92.0 80000841.037233412266
31.76 754.0 80000843.41804847121
35.48 847.0 80000844.98050430417
31.199999 740.0 80000845.57550364733
28.76 679.0 80000850.37028862536
24.039999 561.0 80000850.423752725124
41.839996 1006.0 80000851.28334981203
36.76 879.0 80000851.615449771285
17.4 395.0 80000851.654990166426
38.999996 935.0 80000851.67317868769
12.32 268.0 80000852.59776712954
11.2 240.0 80000854.87065626681
7.4399996 146.0 80000855.74864292145
14.76 329.0 80000855.829678565264
7.2799997 142.0 80000856.83493223786
21.36 494.0 80000858.589912459254
26.28 617.0 80000859.1553748399
37.44 896.0 80000859.18091611564
5.56 99.0 80000859.44560496509
21.44 496.0 80000859.509354412556
25.28 592.0 80000860.59416265786
24.96 584.0 80000861.303189352155
19.4 445.0 80000861.96652762592
10.92 233.0 80000863.23499922454
20.24 466.0 80000864.197188302875
7.04 136.0 80000865.590956673026
42.319996 1018.0 80000865.72700405121
33.6 800.0 80000866.084478631616
31.8 755.0 80000866.50517678261
32.8 780.0 80000866.850857138634
41.239998 991.0 80000867.7263391763
22.0 510.0 80000868.06848114729
14.4800005 322.0 80000869.2763479501
34.44 821.0 80000870.65760450065
19.72 453.0 80000871.05340576172
23.28 542.0 80000873.14886234701
38.239998 916.0 80000874.297571882606
36.039997 861.0 80000874.73376466334
22.28 517.0 80000879.41517931223
33.999996 810.0 80000881.185400635004
15.6 350.0 80000882.22257082164
21.56 499.0 80000884.97935457528
27.84 656.0 80000885.29664757848
11.72 253.0 80000886.4507638216
37.8 905.0 80000888.94126729667
23.28 542.0 80000889.59991361201
33.079998 787.0 80000890.74508482218
32.719997 778.0 80000893.32567283511
13.32 293.0 80000893.43082770705
35.48 847.0 80000893.56059738994
4.68 77.0 80000894.35489681363
39.64 951.0 80000897.77023650706
23.039999 536.0 80000899.03790041804
14.4 320.0 80000899.37754881382
18.4 420.0 80000900.8128515929
10.84 231.0 80000901.414481043816
20.32 468.0 80000901.48123975098
42.359997 1019.0 80000901.93236474693
25.2 590.0 80000901.972453475
23.64 551.0 80000902.81782488525
38.399998 920.0 80000903.59163464606
30.199999 715.0 80000903.92151616514
13.4800005 297.0 80000904.27971172333
11.76 254.0 80000904.998699590564
16.76 379.0 80000905.63441582024
13.2 290.0 80000905.648124307394
2.04 11.0 80000906.234885290265
12.64 276.0 80000907.07798694074
9.16 189.0 80000908.87027671933
25.52 598.0 80000909.368400886655
4.56 74.0 80000909.811767444015
27.24 641.0 80000910.33445057273
17.199999 390.0 80000910.60975474119
2.16 14.0 80000911.29370170832
34.519997 823.0 80000913.69095006585
12.2 265.0 80000914.1802495867
26.88 632.0 80000914.66017211974
28.199999 665.0 80000916.50571863353
42.399998 1020.0 80000916.718121901155
37.44 896.0 80000919.645673155785
27.6 650.0 80000920.63476088643
18.88 432.0 80000922.45012420416
8.48 172.0 80000925.23763982952
12.28 267.0 80000926.283655911684
28.32 668.0 80000926.6409278512
30.96 734.0 80000928.05741724372
32.079998 762.0 80000933.627166330814
39.44 946.0 80000933.76277536154
30.24 716.0 80000934.16055440903
6.7599998 129.0 80000935.81169986725
24.48 572.0 80000936.16736589372
14.6 325.0 80000936.44196587801
25.68 602.0 80000936.549025550485
11.4800005 247.0 80000938.685712620616
6.2 115.0 80000939.08911083639
36.239998 866.0 80000940.29467050731
27.28 642.0 80000941.77238176763
4.2799997 67.0 80000942.128024578094
12.92 283.0 80000942.38229085505
20.96 484.0 80000944.63000917435
9.64 201.0 80000945.404179006815
14.32 318.0 80000945.718157589436
8.32 168.0 80000945.91892364621
42.28 1017.0 80000948.791864678264
29.32 693.0 80000948.85667587817
2.32 18.0 80000949.93122699857
2.6399999 26.0 80000950.1588781476
8.44 171.0 80000950.502268999815
39.8 955.0 80000951.22832208872
21.08 487.0 80000951.838016077876
20.32 468.0 80000952.52954874933
33.96 809.0 80000952.626723498106
21.68 502.0 80000956.18126910925
33.079998 787.0 80000956.38345962763
23.76 554.0 80000957.466738790274
8.32 168.0 80000959.38979135454
14.28 317.0 80000960.34404800832
29.92 708.0 80000962.452562466264
11.64 251.0 80000964.24332383275
25.6 600.0 80000966.99032564461
28.36 669.0 80000967.36089865863
15.4 345.0 80000968.338882282376
25.48 597.0 80000968.875151097775
16.72 378.0 80000969.143758147955
14.76 329.0 80000971.409240707755
19.6 450.0 80000974.77004908025
28.76 679.0 80000974.80595380068
38.359997 919.0 80000975.64050154388
40.6 975.0 80000975.95903091133
4.2 65.0 80000980.43536031246
3.1599998 39.0 80000980.572394132614
41.679996 1002.0 80000981.61112074554
17.439999 396.0 80000981.74807231128
40.239998 966.0 80000983.25735516846
36.359997 869.0 80000985.01507012546
18.12 413.0 80000985.20637777448
38.28 917.0 80000986.77888666093
40.479996 972.0 80000988.17710210383
29.72 703.0 80000988.92275629938
16.96 384.0 80000990.097374781966
30.8 730.0 80000990.79127365351
21.72 503.0 80000991.06344228983
42.28 1017.0 80000991.80377283692
28.24 666.0 80000993.049590453506
7.04 136.0 80000994.441833391786
36.28 867.0 80000994.527631640434
24.4 570.0 80000995.25695282221
21.76 504.0 80000995.29652753472
11.52 248.0 80000995.99297225475
41.319996 993.0 80000996.40901064873
35.239998 841.0 80000996.557712092996
10.52 223.0 80000997.22821688652
33.96 809.0 80000997.405183792114
11.96 259.0 80000997.93263950944
15.440001 346.0 80000998.813208565116
30.92 733.0 80000999.3882278502
3.96 59.0 80000999.59336720407
18.36 419.0 80001000.09518702328
32.039997 761.0 80001001.49414373934
28.48 672.0 80001002.54425382614
39.8 955.0 80001003.1178855896
18.72 428.0 80001003.56476637721
7.52 148.0 80001005.884933292866
9.68 202.0 80001007.618157073855
3.6799998 52.0 80001009.596397176385
13.56 299.0 80001015.068401411176
40.519997 973.0 80001015.44013249874
24.0 560.0 80001017.39824913442
34.12 813.0 80001017.49642172456
25.88 607.0 80001017.91779854894
7.3199997 143.0 80001017.95813263953
12.84 281.0 80001018.01935687661
6.56 124.0 80001023.587887212634
30.64 726.0 80001023.69297429919

array([80000000.23635569, 80000001.47479323, 80000001.78458866,
       80000002.78943624, 80000003.42859936, 80000004.07943003,
       80000006.09310323, 80000007.18041813, 80000008.17602143,
       80000008.20403489], dtype=float128)

Transforming a Lightcurve into an EventList.

Event lists can be obtained from light curves, where the standard followed is as follows: as many events are created as the counts in the lightcurve at the time specified by time bins.

To demonstrate this, let us define a light curve.

times = np.arange(3)
counts = np.floor(np.random.rand(3)*5)
lc = Lightcurve(times, counts, skip_checks=True, dt=1.)

lc.time, lc.counts

(array([0, 1, 2]), array([1., 4., 3.]))

Now, eventlist can be loaded by calling static from_lc() method.

ev = EventList.from_lc(lc)
ev.time

array([0, 1, 1, 1, 1, 2, 2, 2])

Simulating EventList from Lightcurve

An arguably better way is having proper random events, reproducing the initial light curve within the errors. Stingray does this by using the inverse CDF method, using the light curve as a binned probability distribution. Please note that in this case we will have to create the EventList object before (in technical terms, simulate_times is not a static method.). See simulation tutorial for more details.

ev = EventList()
ev.simulate_times(lc)
ev.time

array([0.60459939, 0.8644437 , 1.47100837, 1.54281243, 1.80725171,
       2.47032653])

Creating a light curve from an EventList object

After simulating event list, the original light curve can be recovered. Let’s demonstrate by creating a light curve.

dt = 1.
times = np.arange(50)
counts = np.floor(np.random.rand(50)*50000)
lc = Lightcurve(times, counts, skip_checks=True, dt=1.)

Simulate an event list.

ev = EventList()
ev = ev.from_lc(lc)

ev.gti

array([[-0.5, 49.5]])

Recover original light curve curve using to_lc() method. Here, dt defines time resolution, tstart the starting time, and tseg the total time duration.

lc_new = ev.to_lc(dt=1)

Let us verify that this has worked properly, by comparing the input and output light curves

plt.plot(lc.time, lc.counts,'r-', lc_new.counts, 'g-', drawstyle="steps-mid")
plt.xlabel('Times')
plt.ylabel('Counts')

Text(0, 0.5, 'Counts')

… and their difference

plt.plot(lc.time, lc.counts - lc_new.counts, 'g-', drawstyle="steps-mid")
plt.xlabel('Times')
plt.ylabel('Counts')

Text(0, 0.5, 'Counts')

As can be seen from the figure above, the recovered light curve is aligned with the original light curve.

Simulating Energies

In order to simulate photon energies, a spectral distribution needs to be passed. The spectrum input is a two-dimensional array, with the energies in keV in the first dimension and the number of counts in the second. The count array will be normalized before the simulation: the raw counts do not matter, but only the ratio of the counts in each bin to the total. Again, the energies are simulated using an inverse CDF method.

spectrum = [[1, 2, 3, 4, 5, 6],[1000, 2040, 1000, 3000, 4020, 2070]]

ev = EventList(time=np.sort(np.random.uniform(0, 1000, 12)))
ev.simulate_energies(spectrum)

ev.energy

array([4.84164641, 3.62741142, 3.68169619, 4.70867585, 4.92065534,
       4.93644725, 2.26749277, 5.45959615, 3.01137686, 4.86366818,
       0.63048041, 6.26300006])

Joining EventLists

Two event lists can also be joined together. If the GTI do not overlap, the event times and GTIs are appended. Otherwise, the GTIs are crossed (i.e., only the overlapping parts are saved) and the events merged together.

ev1 = EventList(time=[1,2,3], gti=[[0.5, 3.5]])
ev2 = EventList(time=[4,5], gti=[[3.5, 5.5]])
ev = ev1.join(ev2)
ev.time, ev.gti

(array([1, 2, 3, 4, 5]), array([[0.5, 5.5]]))

ev1 = EventList(time=[1,2,3], gti=[[0.5, 3.5]])
ev2 = EventList(time=[1.2, 3.3, 5.6], gti=[[0.6, 7.8]])
ev = ev1.join(ev2)
ev.time, ev.gti

(array([1. , 1.2, 2. , 3. , 3.3, 5.6]), array([[0.6, 3.5]]))