So far you used the same instrument response function for all observations. You always specified the calibration database prod2 and the instrument response function South_0.5h that are shipped with ctools in all examples. When combining multiple observations in a joint analysis you may however need to specify dedicated instrument response functions for the different observations.
To illustrate how you can do this, let’s simulate two observations of the Crab nebula, one done with the northern array and the other with the southern array:
$ ctobssim
RA of pointing (degrees) (0-360) [83.63]
Dec of pointing (degrees) (-90-90) [22.01] 21.51
Radius of FOV (degrees) (0-180) [5.0]
Start time (MET in s) [0.0]
End time (MET in s) [1800.0]
Lower energy limit (TeV) [0.1]
Upper energy limit (TeV) [100.0]
Calibration database [prod2]
Instrument response function [South_0.5h] North_0.5h
Input model XML file [$CTOOLS/share/models/crab.xml]
Output event data file or observation definition XML file [events.fits] north.fits
$ ctobssim
RA of pointing (degrees) (0-360) [83.63]
Dec of pointing (degrees) (-90-90) [21.51] 22.51
Radius of FOV (degrees) (0-180) [5.0]
Start time (MET in s) [0.0]
End time (MET in s) [1800.0]
Lower energy limit (TeV) [0.1]
Upper energy limit (TeV) [100.0]
Calibration database [prod2]
Instrument response function [North_0.5h] South_0.5h
Input model XML file [$CTOOLS/share/models/crab.xml]
Output event data file or observation definition XML file [north.fits] south.fits
You now need to combine the information about these two observations in an observation definition XML file:
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="00001" instrument="CTA">
<parameter name="EventList" file="north.fits"/>
<parameter name="Calibration" database="prod2" response="North_0.5h"/>
</observation>
<observation name="Crab" id="00002" instrument="CTA">
<parameter name="EventList" file="south.fits"/>
<parameter name="Calibration" database="prod2" response="South_0.5h"/>
</observation>
</observation_list>
Each observation now has a Calibration parameter with the attributes database and response. To see which calibration databases and response functions are available on your system you can run the cscaldb script (use the debug=yes option to get the output of the script on the console):
$ cscaldb debug=yes
2016-06-29T20:09:44: +============+
2016-06-29T20:09:44: | Parameters |
2016-06-29T20:09:44: +============+
2016-06-29T20:09:44: chatter ...................: 2
2016-06-29T20:09:44: clobber ...................: yes
2016-06-29T20:09:44: debug .....................: yes
2016-06-29T20:09:44: mode ......................: ql
2016-06-29T20:09:44: logfile ...................: cscaldb.log
2016-06-29T20:09:44:
2016-06-29T20:09:44: +==============+
2016-06-29T20:09:44: | Mission: cta |
2016-06-29T20:09:44: +==============+
2016-06-29T20:09:44: === Response functions in database "prod2" ===
2016-06-29T20:09:44: North_0.5h
2016-06-29T20:09:44: North_50h
2016-06-29T20:09:44: North_5h
2016-06-29T20:09:44: South_0.5h
2016-06-29T20:09:44: South_50h
2016-06-29T20:09:44: South_5h
You will see that ctools ships with one database for the CTA observatory. This is the prod2 database. Within this database there are six response functions: North_0.5h, North_5h, North_50h, South_0.5h, South_5h, and South_50h.
You now jointly fit both observations using ctlike:
$ ctlike chatter=3
Input event list, counts cube or observation definition XML file [events.fits] obs_irf.xml
Input model XML file [$CTOOLS/share/models/crab.xml]
Output model XML file [crab_results.xml]
To see the usage of the individual response functions you may inspect the log file (you need to set chatter=3 to see the details of the observations in the log file). You will notice that each observation now has a specific response function and that the filename of the response information differs for both observations.
2016-06-29T20:10:29: +==============+
2016-06-29T20:10:29: | Observations |
2016-06-29T20:10:29: +==============+
2016-06-29T20:10:29: === GObservations ===
2016-06-29T20:10:29: Number of observations ....: 2
2016-06-29T20:10:29: Number of models ..........: 2
2016-06-29T20:10:29: Number of observed events .: 31270
2016-06-29T20:10:29: Number of predicted events : 0
2016-06-29T20:10:29: === GCTAObservation ===
2016-06-29T20:10:29: Name ......................: Crab
2016-06-29T20:10:29: Identifier ................: 00001
...
2016-06-29T20:10:29: === GCTAResponseIrf ===
2016-06-29T20:10:29: Caldb mission .............: cta
2016-06-29T20:10:29: Caldb instrument ..........: prod2
2016-06-29T20:10:29: Response name .............: North_0.5h
2016-06-29T20:10:29: Energy dispersion .........: Not used
2016-06-29T20:10:29: Save energy range .........: undefined
...
2016-06-29T20:10:29: === GCTAObservation ===
2016-06-29T20:10:29: Name ......................: Crab
2016-06-29T20:10:29: Identifier ................: 00002
...
2016-06-29T20:10:29: === GCTAResponseIrf ===
2016-06-29T20:10:29: Caldb mission .............: cta
2016-06-29T20:10:29: Caldb instrument ..........: prod2
2016-06-29T20:10:29: Response name .............: South_0.5h
2016-06-29T20:10:29: Energy dispersion .........: Not used
2016-06-29T20:10:29: Save energy range .........: undefined
...
2016-06-29T20:10:29: +=================================+
2016-06-29T20:10:29: | Maximum likelihood optimisation |
2016-06-29T20:10:29: +=================================+
2016-06-29T20:10:30: >Iteration 0: -logL=216208.923, Lambda=1.0e-03
2016-06-29T20:10:30: >Iteration 1: -logL=216207.021, Lambda=1.0e-03, delta=1.902, max(|grad|)=4.436064 [Index:7]
2016-06-29T20:10:30: >Iteration 2: -logL=216207.021, Lambda=1.0e-04, delta=0.001, max(|grad|)=0.012146 [Index:7]
...
2016-06-29T20:10:30: +=========================================+
2016-06-29T20:10:30: | Maximum likelihood optimisation results |
2016-06-29T20:10:30: +=========================================+
2016-06-29T20:10:30: === GOptimizerLM ===
2016-06-29T20:10:30: Optimized function value ..: 216207.021
2016-06-29T20:10:30: Absolute precision ........: 0.005
2016-06-29T20:10:30: Acceptable value decrease .: 2
2016-06-29T20:10:30: Optimization status .......: converged
2016-06-29T20:10:30: Number of parameters ......: 10
2016-06-29T20:10:30: Number of free parameters .: 4
2016-06-29T20:10:30: Number of iterations ......: 2
2016-06-29T20:10:30: Lambda ....................: 1e-05
2016-06-29T20:10:30: Maximum log likelihood ....: -216207.021
2016-06-29T20:10:30: Observed events (Nobs) ...: 31270.000
2016-06-29T20:10:30: Predicted events (Npred) ..: 31269.998 (Nobs - Npred = 0.00190254)
2016-06-29T20:10:30: === GModels ===
2016-06-29T20:10:30: Number of models ..........: 2
2016-06-29T20:10:30: Number of parameters ......: 10
2016-06-29T20:10:30: === GModelSky ===
2016-06-29T20:10:30: Name ......................: Crab
2016-06-29T20:10:30: Instruments ...............: all
2016-06-29T20:10:30: Instrument scale factors ..: unity
2016-06-29T20:10:30: Observation identifiers ...: all
2016-06-29T20:10:30: Model type ................: PointSource
2016-06-29T20:10:30: Model components ..........: "PointSource" * "PowerLaw" * "Constant"
2016-06-29T20:10:30: Number of parameters ......: 6
2016-06-29T20:10:30: Number of spatial par's ...: 2
2016-06-29T20:10:30: RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)
2016-06-29T20:10:30: DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)
2016-06-29T20:10:30: Number of spectral par's ..: 3
2016-06-29T20:10:30: Prefactor ................: 5.7247e-16 +/- 8.64521e-18 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)
2016-06-29T20:10:30: Index ....................: -2.46519 +/- 0.013273 [-0,-5] (free,scale=-1,gradient)
2016-06-29T20:10:30: PivotEnergy ..............: 300000 [10000,1e+09] MeV (fixed,scale=1e+06,gradient)
2016-06-29T20:10:30: Number of temporal par's ..: 1
2016-06-29T20:10:30: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
2016-06-29T20:10:30: === GCTAModelIrfBackground ===
2016-06-29T20:10:30: Name ......................: CTABackgroundModel
2016-06-29T20:10:30: Instruments ...............: CTA
2016-06-29T20:10:30: Instrument scale factors ..: unity
2016-06-29T20:10:30: Observation identifiers ...: all
2016-06-29T20:10:30: Model type ................: "PowerLaw" * "Constant"
2016-06-29T20:10:30: Number of parameters ......: 4
2016-06-29T20:10:30: Number of spectral par's ..: 3
2016-06-29T20:10:30: Prefactor ................: 1.01522 +/- 0.0104442 [0.001,1000] ph/cm2/s/MeV (free,scale=1,gradient)
2016-06-29T20:10:30: Index ....................: 0.00802507 +/- 0.00643391 [-5,5] (free,scale=1,gradient)
2016-06-29T20:10:30: PivotEnergy ..............: 1e+06 [10000,1e+09] MeV (fixed,scale=1e+06,gradient)
2016-06-29T20:10:30: Number of temporal par's ..: 1
2016-06-29T20:10:30: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
You can have a more fine grained control over the response function by specifying individual filenames for the various response components. An example for an observation definition XML file is shown below. This is definitely expert mode, to be used with utmost care.
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="00001" instrument="CTA">
<parameter name="EventList" file="north.fits"/>
<parameter name="EffectiveArea" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
<parameter name="PointSpreadFunction" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
<parameter name="EnergyDispersion" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
<parameter name="Background" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
</observation>
<observation name="Crab" id="00002" instrument="CTA">
<parameter name="EventList" file="south.fits"/>
<parameter name="EffectiveArea" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
<parameter name="PointSpreadFunction" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
<parameter name="EnergyDispersion" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
<parameter name="Background" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
</observation>
</observation_list>
Finally, response information may also be provided to combine stacked observations. An example for the syntax of the observation definition XML file is given below:
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="00001" instrument="CTA">
<parameter name="CountsCube" file="cntcube1.fits"/>
<parameter name="ExposureCube" file="expcube1.fits"/>
<parameter name="PsfCube" file="psfcube1.fits"/>
<parameter name="EdispCube" file="edispcube1.fits"/>
<parameter name="BkgCube" file="bkgcube1.fits"/>
</observation>
<observation name="Crab" id="00002" instrument="CTA">
<parameter name="CountsCube" file="cntcube2.fits"/>
<parameter name="ExposureCube" file="expcube2.fits"/>
<parameter name="PsfCube" file="psfcube2.fits"/>
<parameter name="EdispCube" file="edispcube2.fits"/>
<parameter name="BkgCube" file="bkgcube2.fits"/>
</observation>
</observation_list>