CTA On/Off observation class. More...

#include <GCTAOnOffObservation.hpp>

Inheritance diagram for GCTAOnOffObservation:

Public Member Functions
	GCTAOnOffObservation (void)
	Void constructor. More...

	GCTAOnOffObservation (const bool &dummy, const std::string &instrument)
	Instrument constructor. More...

	GCTAOnOffObservation (const GObservations &obs)
	CTA On/Off observation stacking constructor. More...

	GCTAOnOffObservation (const GPha &pha_on, const GPha &pha_off, const GArf &arf, const GRmf &rmf)
	CTA observation constructor. More...

	GCTAOnOffObservation (const GCTAObservation &obs, const GModels &models, const std::string &srcname, const GEbounds &etrue, const GEbounds &ereco, const GSkyRegions &on, const GSkyRegions &off, const bool &use_model_bkg=true)
	CTA observation constructor (same On and Off observation) More...

	GCTAOnOffObservation (const GCTAObservation &obs_on, const GCTAObservation &obs_off, const GModels &models, const std::string &srcname, const GEbounds &etrue, const GEbounds &ereco, const GSkyRegions &on, const GSkyRegions &off, const bool &use_model_bkg=true)
	CTA observation constructor (different On and Off observations) More...

	GCTAOnOffObservation (const GCTAOnOffObservation &obs)
	Copy constructor. More...

virtual	~GCTAOnOffObservation (void)
	Destructor. More...

GCTAOnOffObservation &	operator= (const GCTAOnOffObservation &obs)
	Assignment operator. More...

virtual void	clear (void)
	Clear instance. More...

virtual GCTAOnOffObservation *	clone (void) const
	Clone instance. More...

virtual std::string	classname (void) const
	Return class name. More...

virtual void	response (const GResponse &rsp)
	Set response function. More...

virtual const GCTAResponse *	response (void) const
	Return pointer to CTA response function. More...

virtual std::string	instrument (void) const
	Return instrument. More...

virtual double	ontime (void) const
	Return ontime. More...

virtual double	livetime (void) const
	Return livetime. More...

virtual double	deadc (const GTime &time=GTime()) const
	Return deadtime correction factor. More...

virtual void	read (const GXmlElement &xml)
	Read On/Off observation from an XML element. More...

virtual void	write (GXmlElement &xml) const
	write observation to an xml element More...

virtual std::string	print (const GChatter &chatter=NORMAL) const
	Print On/Off observation information. More...

virtual double	likelihood (const GModels &models, GVector gradient, GMatrixSparse curvature, double *npred) const
	Evaluate log-likelihood function for On/Off analysis. More...

virtual int	nobserved (void) const
	Return number of observed events. More...

void	instrument (const std::string &instrument)
	Set instrument. More...

bool	has_response (void) const
	Signal if observation contains response information. More...

const GPha &	on_spec (void) const
	Return On spectrum. More...

const GPha &	off_spec (void) const
	Return Off spectrum. More...

const GArf &	arf (void) const
	Return Auxiliary Response File. More...

const GRmf &	rmf (void) const
	Return Redistribution Matrix File. More...

GPha	model_gamma (const GModels &models) const

GPha	model_background (const GModels &models) const

Public Member Functions inherited from GObservation
	GObservation (void)
	Void constructor. More...

	GObservation (const GObservation &obs)
	Copy constructor. More...

virtual	~GObservation (void)
	Destructor. More...

virtual GObservation &	operator= (const GObservation &obs)
	Assignment operator. More...

virtual GEvents *	events (void)
	Return events. More...

virtual const GEvents *	events (void) const
	Return events (const version) More...

virtual void	events (const GEvents &events)
	Set event container. More...

virtual double	model (const GModels &models, const GEvent &event, GVector *gradients=NULL) const
	Return model value and (optionally) gradients. More...

virtual GVector	model (const GModels &models, GMatrixSparse *gradients=NULL) const
	Return vector of model values and (optionally) gradients. More...

virtual double	npred (const GModels &models, GVector *gradients=NULL) const
	Return total number (and optionally gradients) of predicted counts for all models. More...

virtual double	npred (const GModel &model) const
	Return total number of predicted counts for one model. More...

virtual double	model_grad (const GModel &model, const GModelPar &par, const GEvent &event) const
	Returns parameter gradient of model for a given event. More...

virtual GVector	model_grad (const GModel &model, const GModelPar &par) const
	Returns parameter gradients of model for all events. More...

virtual double	npred_grad (const GModel &model, const GModelPar &par) const
	Returns parameter gradient of Npred. More...

virtual void	remove_response_cache (const std::string &name)
	Response cache removal hook. More...

virtual const double &	grad_step_size (void) const
	Return gradient step size. More...

bool	has_events (void) const
	Signal if observation has events. More...

bool	has_gradient (const GModel &model, const GModelPar &par) const
	Check whether a model parameter has an analytical gradient. More...

void	name (const std::string &name)
	Set observation name. More...

void	id (const std::string &id)
	Set observation identifier. More...

void	statistic (const std::string &statistic)
	Set optimizer statistic. More...

const std::string &	name (void) const
	Return observation name. More...

const std::string &	id (void) const
	Return observation identifier. More...

const std::string &	statistic (void) const
	Return optimizer statistic. More...

void	computed_gradient (const GModel &model, const GModelPar &par) const
	Signals that an analytical gradient was computed for a model parameter. More...

Public Member Functions inherited from GBase
virtual	~GBase (void)
	Destructor. More...

Protected Member Functions
void	init_members (void)
	Initialise class members. More...

void	copy_members (const GCTAOnOffObservation &obs)
	Copy class members. More...

void	free_members (void)
	Delete class members. More...

void	set_exposure (void)
	Set ontime, livetime and deadtime correction factor. More...

void	check_consistency (const std::string &method) const
	Check consistency of data members. More...

GArf	arf_stacked (const GArf &arf, const GEnergy &emin, const GEnergy &emax) const
	Return ARF for stacking. More...

GRmf	rmf_stacked (const GRmf &rmf, const GEnergy &emin, const GEnergy &emax) const
	Return RMF for stacking. More...

void	set (const GCTAObservation &obs_on, const GCTAObservation &obs_off, const GModels &models, const std::string &srcname, const GSkyRegions &on, const GSkyRegions &off, const bool &use_model_bkg)
	Set On/Off observation from a CTA observation. More...

void	compute_arf (const GCTAObservation &obs, const GModelSpatial &spatial, const GSkyRegions &on)
	Compute ARF of On/Off observation. More...

void	compute_arf_cut (const GCTAObservation &obs, const GModelSpatial &spatial, const GSkyRegions &on)
	Compute ARF of On/Off observation for a IRF with radius cut. More...

void	compute_bgd (const GCTAObservation &obs, const GSkyRegions &off, const GModels &models, const bool &use_model_bkg)
	Compute background rate in Off regions. More...

void	compute_alpha (const GCTAObservation &obs_on, const GCTAObservation &obs_off, const GSkyRegions &on, const GSkyRegions &off, const GModels &models, const bool &use_model_bkg)
	Compute vector of alpha parameters. More...

void	compute_rmf (const GCTAObservation &obs, const GSkyRegions &on)
	Compute RMF of On/Off observation. More...

void	apply_ebounds (const GCTAObservation &obs)
	Apply CTA observation energy boundaries to On/Off observation. More...

double	arf_rad_max (const GCTAObservation &obs, const GSkyRegions &on) const
	Check if effective area IRF has a radius cut. More...

double	N_gamma (const GModels &models, const int &ibin, GVector *grad) const

double	N_bgd (const GModels &models, const int &ibin, GVector *grad) const

virtual double	likelihood_cstat (const GModels &models, GVector gradient, GMatrixSparse curvature, double *npred) const
	Evaluate log-likelihood function for On/Off analysis in the case of Poisson signal with modeled Poisson background. More...

virtual double	likelihood_wstat (const GModels &models, GVector gradient, GMatrixSparse curvature, double *npred) const
	Evaluate log-likelihood function for On/Off analysis in the case of Poisson signal with measured Poisson background. More...

virtual double	wstat_value (const double &non, const double &noff, const double &alpha, const double &ngam, double &nonpred, double &nbgd, double &dlogLdsky, double &d2logLdsky2) const
	Evaluate log-likelihood value in energy bin for On/Off analysis by profiling over the number of background counts. More...

Protected Member Functions inherited from GObservation
void	init_members (void)
	Initialise class members. More...

void	copy_members (const GObservation &obs)
	Copy class members. More...

void	free_members (void)
	Delete class members. More...

virtual double	likelihood_poisson_unbinned (const GModels &models, GVector gradients, GMatrixSparse curvature, double *npred) const
	Evaluate log-likelihood function for Poisson statistic and unbinned analysis (version with working arrays) More...

virtual double	likelihood_poisson_binned (const GModels &models, GVector gradients, GMatrixSparse curvature, double *npred) const
	Evaluate log-likelihood function for Poisson statistic and binned analysis (version with working arrays) More...

virtual double	likelihood_gaussian_binned (const GModels &models, GVector gradients, GMatrixSparse curvature, double *npred) const
	Evaluate log-likelihood function for Gaussian statistic and binned analysis (version with working arrays) More...

virtual bool	use_event_for_likelihood (const int &index) const
	Check whether bin should be used for likelihood analysis. More...

virtual double	npred_spec (const GModel &model, const GTime &obsTime) const
	Integrates spatially integrated Npred kernel spectrally. More...

Protected Attributes
std::string	m_instrument
	Instrument name. More...

GCTAResponse *	m_response
	Pointer to IRFs. More...

double	m_ontime
	Ontime of On observation (seconds) More...

double	m_livetime
	Livetime of On observation (seconds) More...

double	m_deadc
	Deadtime correction (livetime/ontime) More...

GPha	m_on_spec
	On counts spectrum. More...

GPha	m_off_spec
	Off counts spectrum. More...

GArf	m_arf
	Auxiliary Response Function vector. More...

GRmf	m_rmf
	Redistribution matrix. More...

Protected Attributes inherited from GObservation
std::string	m_name
	Observation name. More...

std::string	m_id
	Observation identifier. More...

std::string	m_statistic
	Optimizer statistic. More...

GEvents *	m_events
	Pointer to event container. More...

double	m_grad_step_size
	Gradient step size. More...

std::vector< std::string >	m_pars_with_gradients

Detailed Description

CTA On/Off observation class.

This class defines a CTA On/Off observation. An On/Off observation is defined by two spectra, one for an On region including the source of interest, and one for an Off region including only background. The response of an On/Off observation is given by the Auxiliary Response File (ARF) and the Redistribution Matrix File (RMF).

The class uses GPha objects to store the On and Off spectra, and GArf and GRmf objects to store the response information. On and Off regions are defined via GSkyRegionMap objects which are essentially finely-pixellized skymaps that allow handling arbitrarily complex shapes

Definition at line 67 of file GCTAOnOffObservation.hpp.

Constructor & Destructor Documentation

GCTAOnOffObservation::GCTAOnOffObservation ( void )

Void constructor.

Constructs empty On/Off observation.

Definition at line 127 of file GCTAOnOffObservation.cpp.

References init_members().

Referenced by clone().

GCTAOnOffObservation::GCTAOnOffObservation	(	const bool &	dummy,
		const std::string &	instrument
	)

Instrument constructor.

Parameters

[in]	dummy	Dummy flag.
[in]	instrument	Instrument name.

Constructs an empty CTA On/Off observation for a given instrument.

This method is specifically used allocation of global class instances for observation registry. By specifying explicit instrument names it is possible to use the "CTA" module are for other Imaging Air Cherenkov Telescopes. So far, the following instrument codes are supported: "CTAOnOff", "HESSOnOff", "VERITASOnOff", "MAGICOnOff", "ASTRIOnOff".

Definition at line 151 of file GCTAOnOffObservation.cpp.

References init_members(), instrument(), and m_instrument.

GCTAOnOffObservation::GCTAOnOffObservation ( const GObservations & obs )

CTA On/Off observation stacking constructor.

Parameters

[in] obs Observation container.

GException::invalid_value Incompatible On/Off observation definition.

Constructs On/Off observation by stacking all On/Off observation in the observation container into a single On/Off observation.

The constructor uses the following formulae:

\[ N^{\rm on}(E_{\rm reco}) = \sum_i N^{\rm on}_i(E_{\rm reco}) \]

\[ N^{\rm off}(E_{\rm reco}) = \sum_i N^{\rm off}_i(E_{\rm reco}) \]

\[ \alpha(E_{\rm reco}) = \frac{\sum_i \alpha_i(E_{\rm reco}) B_i(E_{\rm reco}) \tau_off_i} {\sum_i B_i(E_{\rm reco}) \tau_off_i} \]

\[ B(E_{\rm reco}) = \frac{\sum_i B_i(E_{\rm reco}) \tau_off_i}{\sum_i \tau_off_i} \]

\[ ARF(E_{\rm true}) = \frac{\sum_i ARF_i(E_{\rm true}) \tau_on_i} {\sum_i \tau_i} \]

\[ RMF(E_{\rm true}, E_{\rm reco}) = \frac{\sum_i RMF_i(E_{\rm true}, E_{\rm reco}) ARF_i(E_{\rm true}) \tau_on_i} {\sum_i ARF_i(E_{\rm true}) \tau_on_i} \]

where \(N^{\rm on}_i(E_{\rm reco})\) is the On spectrum of observation \(i\), \(N^{\rm off}_i(E_{\rm reco})\) is the Off spectrum of observation \(i\), \(\alpha_i(E_{\rm reco})\) is the background scaling of observation \(i\), \(B_i(E_{\rm reco})\) is the background rate for observation \(i\), \(ARF_i(E_{\rm true})\) is the Auxiliary Response File of observation \(i\), \(RMF_i(E_{\rm true}, E_{\rm reco})\) is the Redistribution Matrix File of observation \(i\), and \(\tau_on_i\) is the livetime of On observation \(i\). \(\tau_off_i\) is the livetime of Off observation \(i\).

The method extracts the instrument name from the first On/Off observation in the observation container and only stacks subsequent On/Off observations with the same instrument name.

Definition at line 391 of file GCTAOnOffObservation.cpp.

References arf(), arf_stacked(), GPha::backscal(), check_consistency(), GArf::ebounds(), GPha::ebounds(), GPha::emax_obs(), GRmf::emeasured(), GPha::emin_obs(), GRmf::etrue(), GPha::exposure(), G_CONSTRUCTOR2, init_members(), instrument(), livetime(), m_arf, m_instrument, m_livetime, m_off_spec, m_on_spec, m_ontime, m_rmf, GRmf::nmeasured(), norm(), GRmf::ntrue(), off_spec(), on_spec(), ontime(), rmf(), rmf_stacked(), GPha::size(), and GObservations::size().

GCTAOnOffObservation::GCTAOnOffObservation	(	const GPha &	pha_on,
		const GPha &	pha_off,
		const GArf &	arf,
		const GRmf &	rmf
	)

CTA observation constructor.

Parameters

[in]	pha_on	On spectrum.
[in]	pha_off	Off spectrum.
[in]	arf	Auxiliary Response File.
[in]	rmf	Redistribution Matrix File.

Constructs On/Off observation from On and Off spectra, an Auxiliary Response File and a Redistribution Matrix File.

Definition at line 196 of file GCTAOnOffObservation.cpp.

References arf(), check_consistency(), G_CONSTRUCTOR1, init_members(), m_arf, m_off_spec, m_on_spec, m_rmf, rmf(), and set_exposure().

GCTAOnOffObservation::GCTAOnOffObservation	(	const GCTAObservation &	obs,
		const GModels &	models,
		const std::string &	srcname,
		const GEbounds &	etrue,
		const GEbounds &	ereco,
		const GSkyRegions &	on,
		const GSkyRegions &	off,
		const bool &	use_model_bkg = `true`
	)

CTA observation constructor (same On and Off observation)

Parameters

[in]	obs	CTA observation.
[in]	models	Models including source and background model.
[in]	srcname	Name of source in models.
[in]	etrue	True energy boundaries.
[in]	ereco	Reconstructed energy boundaries.
[in]	on	On regions.
[in]	off	Off regions.
[in]	use_model_bkg	Use model background.

Constructs On/Off observation from one osbervation by filling the On and Off spectra and computing the Auxiliary Response File (ARF) and Redistribution Matrix File (RMF).

The method requires the specification of the true and reconstructed energy boundaries, as well as the definition of On and Off regions.

The use_model_bkg flag controls whether a background model should be used for the computations or not. This impacts the computations of the BACKSCAL column in the On spectrum and the BACKRESP column in the Off spectrum. See the compute_alpha() and compute_bgd() methods for more information on the applied formulae.

Definition at line 246 of file GCTAOnOffObservation.cpp.

References init_members(), m_arf, m_off_spec, m_on_spec, m_rmf, and set().

GCTAOnOffObservation::GCTAOnOffObservation	(	const GCTAObservation &	obs_on,
		const GCTAObservation &	obs_off,
		const GModels &	models,
		const std::string &	srcname,
		const GEbounds &	etrue,
		const GEbounds &	ereco,
		const GSkyRegions &	on,
		const GSkyRegions &	off,
		const bool &	use_model_bkg = `true`
	)

CTA observation constructor (different On and Off observations)

Parameters

[in]	obs_on	On CTA observation.
[in]	obs_off	Off CTA observation.
[in]	models	Models including source and background models.
[in]	srcname	Name of source in models.
[in]	etrue	True energy boundaries.
[in]	ereco	Reconstructed energy boundaries.
[in]	on	On regions.
[in]	off	Off regions.
[in]	use_model_bkg	Use model background.

Constructs On/Off observation from two osbervations by filling the On and Off spectra and computing the Auxiliary Response File (ARF) and Redistribution Matrix File (RMF).

The method requires the specification of the true and reconstructed energy boundaries, as well as the definition of On and Off regions.

The use_model_bkg flag controls whether a background model should be used for the computations or not. This impacts the computations of the BACKSCAL column in the On spectrum and the BACKRESP column in the Off spectrum. See the compute_alpha() and compute_bgd() methods for more information on the applied formulae.

Definition at line 301 of file GCTAOnOffObservation.cpp.

References init_members(), m_arf, m_off_spec, m_on_spec, m_rmf, and set().

GCTAOnOffObservation::GCTAOnOffObservation ( const GCTAOnOffObservation & obs )

Copy constructor.

Parameters

[in] obs On/Off observation.

Definition at line 171 of file GCTAOnOffObservation.cpp.

References copy_members(), and init_members().

GCTAOnOffObservation::~GCTAOnOffObservation ( void )

virtual

Destructor.

Definition at line 628 of file GCTAOnOffObservation.cpp.

References free_members().

Member Function Documentation

void GCTAOnOffObservation::apply_ebounds ( const GCTAObservation & obs )

protected

Apply CTA observation energy boundaries to On/Off observation.

Parameters

[in] obs CTA observation.

Applies CTA energy boundaries to all histograms used for the On/Off analysis in.

For the PHA On and Off spectra, all bins are set to zero that do not fully overlap with the CTA observation energy boundaries. Specifically, partially overlapping bins are excluded. Some margin is applied that effectively reduces the width of the PHA energy bin, which should cope with any rounding errors.

For the background response, stored in the Off spectrum, all bins are set to zero that do not fully overlap with the CTA observation energy boundaries.

For the RMF, all reconstructued energy bins are set to zero that do not fully overlap with the CTA observation energy boundaries. True energy bins remain unchanged to properly account for energy migration.

Definition at line 2243 of file GCTAOnOffObservation.cpp.

References GEbounds::contains(), GCTAObservation::ebounds(), GEbounds::emax(), GRmf::emeasured(), GEbounds::emin(), GRmf::etrue(), m_off_spec, m_on_spec, m_rmf, and GEbounds::size().

Referenced by set().

const GArf & GCTAOnOffObservation::arf ( void ) const

inline

Return Auxiliary Response File.

Returns: Auxiliary Response File.

Definition at line 325 of file GCTAOnOffObservation.hpp.

References m_arf.

Referenced by arf_stacked(), GCTAOnOffObservation(), N_gamma(), and read().

double GCTAOnOffObservation::arf_rad_max	(	const GCTAObservation &	obs,
		const GSkyRegions &	on
	)		const

protected

Check if effective area IRF has a radius cut.

Parameters

[in]	obs	CTA observation.
[in]	on	On regions.

Returns: Radius cut value in degrees (zero for no radius cut).

Exceptions

GException::invalid_argument IRF has a radius cut that is incompatible with the On regions

Checks if the effective area IRF has a radius cut. If a radius cut is found the cut value is checked against the radii of the On regions. If the On regions are not circular, or if they have a radius that differs from the IRF cut value, an exception is thrown.

Definition at line 2293 of file GCTAOnOffObservation.cpp.

References abs(), GCTAResponseIrf::aeff(), G_ARF_RADIUS_CUT, GCTAAeff2D::rad_max(), GSkyRegionCircle::radius(), GCTAObservation::response(), GSkyRegions::size(), and gammalib::str().

Referenced by set().

GArf GCTAOnOffObservation::arf_stacked	(	const GArf &	arf,
		const GEnergy &	emin,
		const GEnergy &	emax
	)		const

protected

Return ARF for stacking.

Parameters

[in]	arf	Auxiliary Response File.
[in]	emin	Minimum observation energy.
[in]	emax	Maximum observation energy.

Returns: Auxiliary Response File for stacking.

Returns an Auxiliary Response File for stacking that has all elements with true energies outside the interval [emin, emax] clipped to zero. This prevents spill over from one observation into another.

Definition at line 1233 of file GCTAOnOffObservation.cpp.

References arf(), GArf::ebounds(), GEbounds::emax(), GEbounds::emin(), and GEbounds::size().

Referenced by GCTAOnOffObservation().

void GCTAOnOffObservation::check_consistency ( const std::string & method ) const

protected

Check consistency of data members.

Parameters

[in] method Calling method.

Exceptions

GException::invalid_value Inconsistency found.

Checks the consistency of data members and throw exceptions in case that inconsistencies are found.

Definition at line 1194 of file GCTAOnOffObservation.cpp.

References GArf::ebounds(), GPha::ebounds(), GRmf::emeasured(), GRmf::etrue(), m_arf, m_off_spec, m_on_spec, and m_rmf.

Referenced by GCTAOnOffObservation(), and read().

std::string GCTAOnOffObservation::classname ( void ) const

inlinevirtual

Return class name.

Returns: String containing the class name ("GCTAOnOffObservation").

Implements GObservation.

Definition at line 208 of file GCTAOnOffObservation.hpp.

void GCTAOnOffObservation::clear ( void )

virtual

Clear instance.

Clears the On/Off observation. All class members will be set to the initial state. Any information that was present in the object before will be lost.

Implements GObservation.

Definition at line 689 of file GCTAOnOffObservation.cpp.

References free_members(), and init_members().

Referenced by read().

GCTAOnOffObservation * GCTAOnOffObservation::clone ( void ) const

virtual

Clone instance.

Returns: Pointer to deep copy of On/Off observation.

Returns a pointer to a deep copy of an On/Off observation.

Implements GObservation.

Definition at line 709 of file GCTAOnOffObservation.cpp.

References GCTAOnOffObservation().

void GCTAOnOffObservation::compute_alpha	(	const GCTAObservation &	obs_on,
		const GCTAObservation &	obs_off,
		const GSkyRegions &	on,
		const GSkyRegions &	off,
		const GModels &	models,
		const bool &	use_model_bkg
	)

protected

Compute vector of alpha parameters.

Parameters

[in]	obs_on	On CTA observation.
[in]	obs_off	Off CTA observation.
[in]	on	On regions.
[in]	off	Off regions.
[in]	models	Models including background model.
[in]	use_model_bkg	Use model background.

Exceptions

GException::invalid_argument Observation does not contain relevant response or background information

Compute the \(\alpha\) parameters for all reconstructed energy bins. The \(\alpha\) parameter gives the ratio between the On and Off region background acceptance multiplied by the On and Off region solid angles.

If use_model_bkg is true, the IRF background template will be used for the computation, and \(\alpha(E_{\rm reco})\) is given by

\[ \alpha(E_{\rm reco}) = \frac{\sum_{\rm on} \sum_p {\tt BKG}_{{\rm on},p}(E_{\rm reco}) \times \Omega_{{\rm on},p}} {\sum_{\rm off} \sum_p {\tt BKG}_{{\rm off},p}(E_{\rm reco}) \times \Omega_{{\rm off},p}} \]

where the nominator sums over the On regions, indicated by the index \({\rm on}\), and the denominator sums over the Off regions, indicated by the index \({\rm off}\). Each On or Off region is defined by a region sky map of type GSkyRegionMap, and the pixels of these maps are index by \(p\). \({\tt BKG}_{{\rm on/off},p}(E_{\rm reco})\) is the background rate as provided by the IRF background template in units of \({\rm events} \, {\rm MeV}^{-1} \, {\rm s}^{-1} \, {\rm sr}^{-1}\) for a reconstructed energy \(E_{\rm reco}\) and a pixel index \(p\) in the On or Off region \({\rm on/off}\). \(\Omega_{{\rm on/off},p}\) is the solid angle in units of \({\rm sr}\) of the pixel index \(p\) in the On or Off region \({\rm on/off}\).

If use_model_bkg is false, the background acceptance is assumed constant and hence cancels out, which makes the \(\alpha\) parameter independent of reconstructed energy \(E_{\rm reco}\). The \(\alpha\) parameter is then given by

\[ \alpha = \frac{\sum_{\rm on} \sum_p \Omega_{{\rm on},p}} {\sum_{\rm off} \sum_p \Omega_{{\rm off},p}} \]

Todo:: Compute alpha by integrating the background rate over the energy bins and not at the bin centre.

Definition at line 1922 of file GCTAOnOffObservation.cpp.

References GPha::backscal(), GEbounds::elogmean(), GRmf::emeasured(), GModels::eval(), GCTAPointing::instdir(), GCTAObservation::livetime(), m_on_spec, m_rmf, GSkyRegionMap::map(), GSkyRegionMap::nonzero_indices(), GCTAObservation::pointing(), GSkyRegions::size(), and GEbounds::size().

Referenced by set().

void GCTAOnOffObservation::compute_arf	(	const GCTAObservation &	obs,
		const GModelSpatial &	spatial,
		const GSkyRegions &	on
	)

protected

Compute ARF of On/Off observation.

Parameters

[in]	obs	CTA observation.
[in]	spatial	Spatial source model.
[in]	on	On regions.

Exceptions

GException::invalid_argument No CTA response found in CTA observation.

Computes the ARF for an On/Off observation by integration over the IRF for the specified spatial source model over the on regions.

All On regions contained in on are expected to be sky region maps, i.e. of type GSkyRegionMap.

Definition at line 1524 of file GCTAOnOffObservation.cpp.

References GCTAResponseIrf::apply_edisp(), gammalib::cta_rsp_irf(), GCTAEventBin::dir(), GArf::ebounds(), GEbounds::elogmean(), G_COMPUTE_ARF, GResponse::irf_spatial(), m_arf, m_deadc, GSkyRegionMap::map(), GSkyRegionMap::nonzero_indices(), GSkyRegions::size(), and GEbounds::size().

Referenced by set().

void GCTAOnOffObservation::compute_arf_cut	(	const GCTAObservation &	obs,
		const GModelSpatial &	spatial,
		const GSkyRegions &	on
	)

protected

Compute ARF of On/Off observation for a IRF with radius cut.

Parameters

[in]	obs	CTA observation.
[in]	spatial	Spatial source model.
[in]	on	On regions.

Exceptions

GException::invalid_argument No CTA response found in CTA observation.

Computes the ARF for an On/Off observation by computing the average effective area over the on regions for the specified spatial source model.

All On regions contained in on are expected to be sky region maps, i.e. of type GSkyRegionMap.

Definition at line 1624 of file GCTAOnOffObservation.cpp.

References GCTAResponseIrf::aeff(), GCTAPointing::azimuth(), gammalib::cta_rsp_irf(), GCTAPointing::dir(), GSkyDir::dist(), GArf::ebounds(), GEbounds::elogmean(), G_COMPUTE_ARF, GEnergy::log10TeV(), m_arf, GSkyRegionMap::map(), GSkyRegionMap::nonzero_indices(), GCTAObservation::pointing(), GSkyDir::posang(), GSkyRegions::size(), GEbounds::size(), sum(), and GCTAPointing::zenith().

Referenced by set().

void GCTAOnOffObservation::compute_bgd	(	const GCTAObservation &	obs,
		const GSkyRegions &	off,
		const GModels &	models,
		const bool &	use_model_bkg
	)

protected

Compute background rate in Off regions.

Parameters

[in]	obs	CTA observation.
[in]	off	Off regions.
[in]	models	Models including background model.
[in]	use_model_bkg	Use model background.

Computes the background rate in units of \({\rm events} \, {\rm MeV}^{-1} \, {\rm s}^{-1}\) in the Off regions and stores the result as additional column with name BACKRESP in the Off spectrum.

All Off regions contained in off are expected to be sky region maps, i.e. of type GSkyRegionMap.

If use_model_bkg is true, the IRF background template will be used for the computation, and BACKRESP will be computed using

\[ {\tt BACKRESP}(E_{\rm reco}) = \sum_{\rm off} \sum_p {\tt BKG}_{{\rm off},p}(E_{\rm reco}) \times \Omega_{{\rm off},p} \]

where \({\rm off}\) is the index of the Off region and \(p\) is the pixel in the Off region (note that each Off region is transformed into a region map and \(p\) indicates the pixels of this map). \({\tt BKG}_{{\rm off},p}(E_{\rm reco})\) is the background rate as provided by the IRF background template in units of \({\rm events} \, {\rm MeV}^{-1} \, {\rm s}^{-1} \, {\rm sr}^{-1}\) for a reconstructed energy \(E_{\rm reco}\) and a pixel index \(p\) in the Off region \({\rm off}\). \(\Omega_{{\rm off},p}\) is the solid angle in units of \({\rm sr}\) of the pixel index \(p\) in the Off region \({\rm off}\).

If use_model_bkg is false, BACKRESP will be computed using

\[ {\tt BACKRESP}(E_{\rm reco}) = \sum_{\rm off} \sum_p \Omega_{{\rm off},p} \]

which actually assumes that the background rate is constant over the field of view.

Todo:: Integrate background rate over energy bin instead of computing the rate at the energy bin centre.

Definition at line 1755 of file GCTAOnOffObservation.cpp.

References GPha::append(), GPha::ebounds(), GEbounds::elogmean(), GModels::eval(), GCTAPointing::instdir(), m_off_spec, GSkyRegionMap::map(), GSkyRegionMap::nonzero_indices(), GCTAObservation::pointing(), GSkyRegions::size(), and GEbounds::size().

Referenced by set().

void GCTAOnOffObservation::compute_rmf	(	const GCTAObservation &	obs,
		const GSkyRegions &	on
	)

protected

Compute RMF of On/Off observation.

Parameters

[in]	obs	CTA observation.
[in]	on	On regions.

Exceptions

GException::invalid_argument Observation does not contain IRF response

Compute the energy redistribution matrix for an On/Off observation. The method requires that the RMF energy axes have been defined before.

Definition at line 2123 of file GCTAOnOffObservation.cpp.

References GCTAResponseIrf::aeff(), GCTAPointing::azimuth(), gammalib::cta_rsp_irf(), GCTAPointing::dir(), GSkyDir::dist(), GCTAResponseIrf::edisp(), GEbounds::elogmean(), GEbounds::emax(), GRmf::emeasured(), GEbounds::emin(), GRmf::etrue(), G_COMPUTE_RMF, GEnergy::log10TeV(), m_rmf, GSkyRegionMap::map(), GSkyRegionMap::nonzero_indices(), GCTAObservation::pointing(), GSkyDir::posang(), GCTAEdisp::prob_erecobin(), GSkyRegions::size(), GEbounds::size(), and GCTAPointing::zenith().

Referenced by set().

void GCTAOnOffObservation::copy_members ( const GCTAOnOffObservation & obs )

protected

Copy class members.

Parameters

[in] obs CTA On/Off observation.

Definition at line 1137 of file GCTAOnOffObservation.cpp.

References GCTAResponse::clone(), m_arf, m_deadc, m_instrument, m_livetime, m_off_spec, m_on_spec, m_ontime, m_response, and m_rmf.

Referenced by GCTAOnOffObservation(), and operator=().

double GCTAOnOffObservation::deadc ( const GTime & time = GTime() ) const

inlinevirtual

Return deadtime correction factor.

Parameters

[in] time Time.

Returns: Deadtime correction factor.

Returns the deadtime correction factor. Optionally, this method takes a time argument that takes provision for returning the deadtime correction factor as function of time.

The deadtime correction factor is defined as the livetime divided by the ontime.

Implements GObservation.

Definition at line 264 of file GCTAOnOffObservation.hpp.

References m_deadc.

void GCTAOnOffObservation::free_members ( void )

protected

Delete class members.

Definition at line 1161 of file GCTAOnOffObservation.cpp.

Referenced by clear(), operator=(), and ~GCTAOnOffObservation().

bool GCTAOnOffObservation::has_response ( void ) const

inline

Signal if observation contains response information.

Returns: True if observation contains response information.

Definition at line 276 of file GCTAOnOffObservation.hpp.

References m_response.

void GCTAOnOffObservation::init_members ( void )

protected

Initialise class members.

Definition at line 1114 of file GCTAOnOffObservation.cpp.

References GRmf::clear(), GArf::clear(), GPha::clear(), m_arf, m_deadc, m_instrument, m_livetime, m_off_spec, m_on_spec, m_ontime, m_response, and m_rmf.

Referenced by clear(), GCTAOnOffObservation(), and operator=().

std::string GCTAOnOffObservation::instrument ( void ) const

inlinevirtual

Return instrument.

Returns: Instrument.

Implements GObservation.

Definition at line 220 of file GCTAOnOffObservation.hpp.

References m_instrument.

Referenced by GCTAOnOffObservation(), instrument(), N_gamma(), print(), and set().

void GCTAOnOffObservation::instrument ( const std::string & instrument )

inline

Set instrument.

Parameters

[in] instrument Instrument.

Definition at line 288 of file GCTAOnOffObservation.hpp.

References instrument(), and m_instrument.

double GCTAOnOffObservation::likelihood	(	const GModels &	models,
		GVector *	gradient,
		GMatrixSparse *	curvature,
		double *	npred
	)		const

virtual

Evaluate log-likelihood function for On/Off analysis.

Parameters

[in]	models	Models.
[in,out]	gradient	Pointer to gradients.
[in,out]	curvature	Pointer to curvature matrix.
[in,out]	npred	Pointer to Npred value.

Returns: Log-likelihood value.

Exceptions

GException::invalid_value Invalid statistic encountered.

Reimplemented from GObservation.

Definition at line 914 of file GCTAOnOffObservation.cpp.

References G_LIKELIHOOD, likelihood_cstat(), likelihood_wstat(), GObservation::statistic(), and gammalib::toupper().

double GCTAOnOffObservation::likelihood_cstat	(	const GModels &	models,
		GVector *	gradient,
		GMatrixSparse *	curvature,
		double *	npred
	)		const

protectedvirtual

Evaluate log-likelihood function for On/Off analysis in the case of Poisson signal with modeled Poisson background.

Parameters

[in]	models	Models.
[in,out]	gradient	Pointer to gradients.
[in,out]	curvature	Pointer to curvature matrix.
[in,out]	npred	Pointer to Npred value.

Returns: Log-likelihood value.

Exceptions

GException::invalid_value There are no model parameters.

Computes the log-likelihood value for the On/Off observation. The method loops over the energy bins to update the function value, its derivatives and the curvature matrix. The number of On counts \(N_{\rm on}\) and Off counts \(N_{\rm off}\) are taken from the On and Off spectra, the expected number of gamma-ray events \(N_{\gamma}\) and background events \(N_{\rm bgd}\) are computed from the spectral models of the relevant components in the model container (spatial and temporal components are ignored so far). See the N_gamma() and N_bgd() methods for details about the model computations.

The log-likelihood is given by

\[ \ln L = \sum_i \ln L_i \]

where the sum is taken over all energy bins \(i\) and

\[ \ln L_i = - N_{\rm on} \ln N_{\rm pred} + N_{\rm pred} - N_{\rm off} \ln N_{\rm bgd} + N_{\rm bgd} \]

with

\[ N_{\rm pred} = N_{\gamma} + \alpha N_{\rm bgd} \]

being the total number of predicted events for an energy bin in the On region, \(N_{\rm on}\) is the total number of observed events for an energy bin in the On region, \(N_{\rm off}\) is the total number of observed events for an energy bin in the Off region, and \(N_{\rm bgd}\) is the predicted number of background events for an energy bin in the Off region.

The log-likelihood gradient with respect to sky model parameters \(p_{\rm sky}\) is given by

\[ \left( \frac{\partial \ln L_i}{\partial p_{\rm sky}} \right) = \left( 1 - \frac{N_{\rm on}}{N_{\rm pred}} \right) \left( \frac{\partial N_{\gamma}}{\partial p_{\rm sky}} \right) \]

and with respect to background model parameters \(p_{\rm bgd}\) is given by

\[ \left( \frac{\partial \ln L_i}{\partial p_{\rm bgd}} \right) = \left( 1 + \alpha - \frac{N_{\rm off}}{N_{\rm bgd}} - \frac{\alpha N_{\rm on}}{N_{\rm pred}} \right) \left( \frac{\partial N_{\rm bgd}}{\partial p_{\rm bgd}} \right) \]

The curvature matrix elements are given by

\[ \left( \frac{\partial^2 \ln L_i}{\partial^2 p_{\rm sky}} \right) = \left( \frac{N_{\rm on}}{N_{\rm pred}^2} \right) \left( \frac{\partial N_{\gamma}}{\partial p_{\rm sky}} \right)^2 \]

\[ \left( \frac{\partial^2 \ln L_i}{\partial p_{\rm sky} \partial p_{\rm bgd}} \right) = \left( \frac{\alpha N_{\rm on}}{N_{\rm pred}^2} \right) \left( \frac{\partial N_{\gamma}}{\partial p_{\rm sky}} \right) \left( \frac{\partial N_{\rm bgd}}{\partial p_{\rm bgd}} \right) \]

\[ \left( \frac{\partial^2 \ln L_i}{\partial p_{\rm bgd} \partial p_{\rm sky}} \right) = \left( \frac{\alpha N_{\rm on}}{N_{\rm pred}^2} \right) \left( \frac{\partial N_{\rm bgd}}{\partial p_{\rm bgd}} \right) \left( \frac{\partial N_{\gamma}}{\partial p_{\rm sky}} \right) \]

\[ \left( \frac{\partial^2 \ln L_i}{\partial^2 p_{\rm bgd}} \right) = \left( \frac{N_{\rm off}}{N_{\rm bgd}^2} + \frac{\alpha^2 N_{\rm on}}{N_{\rm pred}^2} \right) \left( \frac{\partial N_{\rm bgd}}{\partial p_{\rm bgd}} \right)^2 \]

Definition at line 2744 of file GCTAOnOffObservation.cpp.

References GMatrixSparse::add_to_column(), GPha::backscal(), gammalib::is_infinite(), log(), m_off_spec, m_on_spec, minmod, N_bgd(), N_gamma(), GModels::npars(), and GPha::size().

Referenced by likelihood().

double GCTAOnOffObservation::likelihood_wstat	(	const GModels &	models,
		GVector *	gradient,
		GMatrixSparse *	curvature,
		double *	npred
	)		const

protectedvirtual

Evaluate log-likelihood function for On/Off analysis in the case of Poisson signal with measured Poisson background.

Parameters

[in]	models	Models.
[in,out]	gradient	Pointer to gradients.
[in,out]	curvature	Pointer to curvature matrix.
[in,out]	npred	Pointer to Npred value.

Returns: Log-likelihood value.

Computes the log-likelihood value for the On/Off observation. The method loops over the energy bins to update the function value, its derivatives and the curvature matrix.

The number of On counts \(n_{\rm on}\) and Off counts \(n_{\rm off}\) are taken from the On and Off spectra, the expected number of gamma-ray events \(\mu_s\) is computed from the spectral models of the relevant components in the model container (spatial and temporal components are ignored so far). See the N_gamma() method for details about the model computations.

The estimated number of background counts \(\mu_b\) is derived based on the measurement in the Off region by analytical minimization of the Poisson likelihood, i.e., it is treated as a nuisance parameter. See the wstat_value function for the derivation.

Definition at line 2983 of file GCTAOnOffObservation.cpp.

References GMatrixSparse::add_to_column(), GPha::backscal(), gammalib::is_infinite(), m_off_spec, m_on_spec, N_gamma(), GModels::npars(), GPha::size(), and wstat_value().

Referenced by likelihood().

double GCTAOnOffObservation::livetime ( void ) const

inlinevirtual

Return livetime.

Returns: Livetime in seconds.

Implements GObservation.

Definition at line 244 of file GCTAOnOffObservation.hpp.

References m_livetime.

Referenced by GCTAOnOffObservation(), and print().

GPha GCTAOnOffObservation::model_background ( const GModels & models ) const

Definition at line 992 of file GCTAOnOffObservation.cpp.

References GPha::backscal(), GPha::ebounds(), GEbounds::emean(), GPha::fill(), G_MODEL_BACKGROUND, m_off_spec, m_on_spec, N_bgd(), N_gamma(), GModels::npars(), GPha::size(), GObservation::statistic(), gammalib::toupper(), and wstat_value().

GPha GCTAOnOffObservation::model_gamma ( const GModels & models ) const

Definition at line 957 of file GCTAOnOffObservation.cpp.

References GPha::ebounds(), GEbounds::emean(), GPha::fill(), m_on_spec, N_gamma(), GModels::npars(), and GPha::size().

double GCTAOnOffObservation::N_bgd	(	const GModels &	models,
		const int &	ibin,
		GVector *	grad
	)		const

protected

Definition at line 2550 of file GCTAOnOffObservation.cpp.

References gammalib::cta_model_spectral(), GPha::ebounds(), GEbounds::elogmean(), GModelSpectral::eval(), GEbounds::ewidth(), GPha::exposure(), GOptimizerPar::factor_gradient(), GObservation::id(), GOptimizerPar::is_free(), GModel::is_valid(), m_off_spec, m_on_spec, GEnergy::MeV(), norm(), GModels::npars(), GPha::size(), GModel::size(), and GModels::size().

Referenced by likelihood_cstat(), and model_background().

double GCTAOnOffObservation::N_gamma	(	const GModels &	models,
		const int &	ibin,
		GVector *	grad
	)		const

protected

int GCTAOnOffObservation::nobserved ( void ) const

inlinevirtual

Return number of observed events.

Returns: Number of observed events.

Reimplemented from GObservation.

Definition at line 349 of file GCTAOnOffObservation.hpp.

References GPha::counts(), and m_on_spec.

const GPha & GCTAOnOffObservation::off_spec ( void ) const

inline

Return Off spectrum.

Returns: Off spectrum.

Definition at line 313 of file GCTAOnOffObservation.hpp.

References m_off_spec.

Referenced by GCTAOnOffObservation().

const GPha & GCTAOnOffObservation::on_spec ( void ) const

inline

Return On spectrum.

Returns: On spectrum.

Definition at line 301 of file GCTAOnOffObservation.hpp.

References m_on_spec.

Referenced by GCTAOnOffObservation().

double GCTAOnOffObservation::ontime ( void ) const

inlinevirtual

Return ontime.

Returns: Ontime in seconds.

Implements GObservation.

Definition at line 232 of file GCTAOnOffObservation.hpp.

References m_ontime.

Referenced by GCTAOnOffObservation(), and print().

GCTAOnOffObservation & GCTAOnOffObservation::operator= ( const GCTAOnOffObservation & obs )

Assignment operator.

Parameters

[in] obs On/Off observation.

Returns: On/Off observation.

Assigns one On/Off observation to another On/Off observation object.

Definition at line 652 of file GCTAOnOffObservation.cpp.

References copy_members(), free_members(), init_members(), and GObservation::operator=().

std::string GCTAOnOffObservation::print ( const GChatter & chatter = NORMAL ) const

virtual

Print On/Off observation information.

Parameters

[in] chatter Chattiness.

Returns: String containing On/Off observation information.

Implements GObservation.

Definition at line 1070 of file GCTAOnOffObservation.cpp.

References instrument(), livetime(), m_arf, m_deadc, GObservation::m_id, GObservation::m_name, m_off_spec, m_on_spec, m_rmf, ontime(), gammalib::parformat(), GRmf::print(), GArf::print(), GPha::print(), gammalib::reduce(), SILENT, GObservation::statistic(), and gammalib::str().

void GCTAOnOffObservation::read ( const GXmlElement & xml )

virtual

Read On/Off observation from an XML element.

Parameters

[in] xml XML element.

Exceptions

GException::invalid_value Invalid statistic attribute encountered

Reads information for an On/Off observation from an XML element. The expected format of the XML element is

<observation name="..." id="..." instrument="...">
  <parameter name="Pha_on"  file="..."/>
  <parameter name="Pha_off" file="..."/>
  <parameter name="Arf"     file="..."/>
  <parameter name="Rmf"     file="..."/>
</observation>

Optionally, the statistic used for maximum likelihood fitting can be specified:

<observation name="..." id="..." instrument="..." statistic="...">

Implements GObservation.

Definition at line 794 of file GCTAOnOffObservation.cpp.

References arf(), GXmlElement::attribute(), check_consistency(), clear(), G_READ, GRmf::load(), GArf::load(), GPha::load(), m_arf, m_instrument, m_off_spec, m_on_spec, m_rmf, rmf(), set_exposure(), GObservation::statistic(), gammalib::toupper(), gammalib::xml_file_expand(), and gammalib::xml_get_attr().

void GCTAOnOffObservation::response ( const GResponse & rsp )

virtual

Set response function.

Parameters

[in] rsp Response function.

Exceptions

GException::invalid_argument Invalid response class specified.

Sets the response function for the On/Off observation.

Implements GObservation.

Definition at line 725 of file GCTAOnOffObservation.cpp.

References GCTAResponse::clone(), gammalib::cta_rsp(), G_RESPONSE_SET, and m_response.

const GCTAResponse * GCTAOnOffObservation::response ( void ) const

virtual

Return pointer to CTA response function.

Returns: Pointer to CTA response function.

Exceptions

GException::invalid_value No valid response found in CTA observation.

Returns a pointer to the CTA response function. An exception is thrown if the pointer is not valid, hence the user does not need to verify the validity of the pointer.

Implements GObservation.

Definition at line 756 of file GCTAOnOffObservation.cpp.

References G_RESPONSE_GET, and m_response.

const GRmf & GCTAOnOffObservation::rmf ( void ) const

inline

Return Redistribution Matrix File.

Returns: Redistribution Matrix File.

Definition at line 337 of file GCTAOnOffObservation.hpp.

References m_rmf.

Referenced by GCTAOnOffObservation(), N_gamma(), read(), and rmf_stacked().

GRmf GCTAOnOffObservation::rmf_stacked	(	const GRmf &	rmf,
		const GEnergy &	emin,
		const GEnergy &	emax
	)		const

protected

Return RMF for stacking.

Parameters

[in]	rmf	Redistribution Matrix File.
[in]	emin	Minimum observation energy.
[in]	emax	Maximum observation energy.

Returns: Redistribution Matrix File for stacking.

Returns a Redistribution Matrix File for stacking that has all matrix elements with true energies outside the interval [emin, emax] clipped to zero. This prevents spill over from one observation into another.

To correct for the missing events at the edges, the Redistribution Matrix File is renormalized so that for each reconstructed energy the sum over the true energies is the same as before the clipping.

Definition at line 1272 of file GCTAOnOffObservation.cpp.

References GEbounds::emax(), GRmf::emeasured(), GEbounds::emin(), GRmf::etrue(), norm(), rmf(), GEbounds::size(), and sum().

Referenced by GCTAOnOffObservation().

void GCTAOnOffObservation::set	(	const GCTAObservation &	obs_on,
		const GCTAObservation &	obs_off,
		const GModels &	models,
		const std::string &	srcname,
		const GSkyRegions &	on,
		const GSkyRegions &	off,
		const bool &	use_model_bkg
	)

protected

Set On/Off observation from a CTA observation.

Parameters

[in]	obs_on	CTA On observation.
[in]	obs_off	CTA Off observation.
[in]	models	Models including source and background model.
[in]	srcname	Name of soucre in models.
[in]	on	On regions.
[in]	off	Off regions.
[in]	use_model_bkg	Use model background.

Exceptions

GException::invalid_value No CTA event list found in CTA observation.

Sets an On/Off observation from a CTA observation by filling the events that fall in the On and Off regions into the PHA spectra and by computing the corresponding ARF and RMF response functions.

The use_model_bkg flags controls whether the background model should be used for computations or not. This impacts the computations of the BACKSCAL column in the On spectrum and the BACKRESP column in the Off spectrum. See the compute_alpha() and compute_bgd() methods for more information on the applied formulae.

Definition at line 1343 of file GCTAOnOffObservation.cpp.

References GSkyRegions::append(), GFitsHeader::append(), GModels::append(), apply_ebounds(), arf_rad_max(), GCTAResponseIrf::caldb(), GModels::classname(), compute_alpha(), compute_arf(), compute_arf_cut(), compute_bgd(), compute_rmf(), GSkyRegions::contains(), GCTAObservation::deadc(), GCTAEventAtom::dir(), GCTAInstDir::dir(), GCTAObservation::ebounds(), GEbounds::emax(), GPha::emax_obs(), GEbounds::emin(), GPha::emin_obs(), GCTAEventAtom::energy(), GObservation::events(), GPha::exposure(), GPha::fill(), G_SET, GRmf::header(), GArf::header(), GPha::header(), GObservation::id(), GCTAObservation::instrument(), instrument(), GCTAObservation::livetime(), m_arf, m_deadc, m_instrument, m_livetime, m_off_spec, m_on_spec, m_ontime, m_rmf, GObservation::model(), GObservation::name(), GCTAObservation::ontime(), GCTAObservation::response(), GCTAResponseIrf::rspname(), GSkyRegions::size(), GCTAEventList::size(), GModels::size(), GModelSky::spatial(), and gammalib::toupper().

Referenced by GCTAOnOffObservation().

void GCTAOnOffObservation::set_exposure ( void )

protected

Set ontime, livetime and deadtime correction factor.

Definition at line 1171 of file GCTAOnOffObservation.cpp.

References GPha::exposure(), m_deadc, m_livetime, m_on_spec, and m_ontime.

Referenced by GCTAOnOffObservation(), and read().

void GCTAOnOffObservation::write ( GXmlElement & xml ) const

virtual

write observation to an xml element

Parameters

[in] xml XML element.

Writes information for an On/Off observation into an XML element. The expected format of the XML element is

<observation name="..." id="..." instrument="..." statistic="...">
  <parameter name="Pha_on"  file="..."/>
  <parameter name="Pha_off" file="..."/>
  <parameter name="Arf"     file="..."/>
  <parameter name="Rmf"     file="..."/>
</observation>

The actual files described in the XML elements are not written.

Implements GObservation.

Definition at line 871 of file GCTAOnOffObservation.cpp.

References GXmlElement::attribute(), GRmf::filename(), GArf::filename(), GPha::filename(), G_WRITE, m_arf, m_off_spec, m_on_spec, m_rmf, GObservation::statistic(), gammalib::xml_file_reduce(), and gammalib::xml_need_par().

double GCTAOnOffObservation::wstat_value	(	const double &	non,
		const double &	noff,
		const double &	alpha,
		const double &	ngam,
		double &	nonpred,
		double &	nbgd,
		double &	dlogLdsky,
		double &	d2logLdsky2
	)		const

protectedvirtual

Evaluate log-likelihood value in energy bin for On/Off analysis by profiling over the number of background counts.

Parameters

[in]	non	number of On counts
[in]	noff	number of Off counts
[in]	alpha	background scaling rate
[in]	ngam	number of predicted gamma-ray counts
[in,out]	nonpred	number of predicted On counts
[in,out]	nbgd	number of predicted background counts
[in,out]	dlogLdsky	first derivative of log-like w.r.t. sky pars
[in,out]	d2logLdsky2	second derivative of log-like w.r.t. sky pars

Returns: Log-likelihood value.

Computes the log-likelihood value for the On/Off observation in an energy bin by treating the number of background counts as nuisance parameter. The method performs an analytical minimisation of the Poisson likelihood and updates the relevant values. In the general case, the log-likelihood function is computed using

\[ L = \mu_s + (1+\alpha) \mu_b - n_{\rm on} - n_{\rm off} - n_{\rm on} \left( \ln(\mu_s + \alpha \mu_b) - \ln(n_{\rm on}) \right) - n_{\rm off} \left( \ln(\mu_b) - \ln(n_{\rm off}) \right) \]

where

\[ \mu_b = \frac{C+D}{2\alpha(1+\alpha)} \]

are the estimated number of background counts with

\[ C = \alpha (n_{\rm on} + n_{\rm off}) - (1 + \alpha) \mu_s \]

and

\[ D = \sqrt{C^2 + 4 (1 + \alpha) \, \alpha \, n_{\rm off} \, \mu_s} \]

\

The first derivative of the log-likelihood function is given by

\[ \frac{\delta L}{\delta \mu_s} = 1 + (1 + \alpha) \frac{\delta \mu_b}{\delta \mu_s} - \frac{n_{\rm on}}{\mu_s + \alpha \mu_b} \left( 1 + \alpha \frac{\delta \mu_b}{\delta \mu_s} \right) - \frac{n_{\rm off}}{\mu_b} \frac{\delta \mu_b}{\delta \mu_s} \]

with

\[ \frac{\delta \mu_b}{\delta \mu_s} = \frac{n_{\rm off} - C}{D} - \frac{1}{2 \alpha} \]

The second derivative of the log-likelihood function is given by

\[ \frac{\delta^2 L}{\delta \mu_s^2} = \frac{n_{\rm on}}{(\mu_s + \alpha \mu_b)^2} \left( 1 + \alpha \frac{\delta \mu_b}{\delta \mu_s} \right) + \frac{\delta^2 \mu_b}{\delta \mu_s^2} \left( (1 + \alpha) - \frac{\alpha n_{\rm on}}{\mu_s + \alpha \mu_b} - \frac{n_{\rm off}}{\mu_b} \right) + \frac{\delta \mu_b}{\delta \mu_s} \left( \frac{\alpha n_{\rm on}}{(\mu_s + \alpha \mu_b)^2} \left( 1 + \alpha \frac{\delta \mu_b}{\delta \mu_s} \right) + \frac{n_{\rm off}}{\mu_b^2} \frac{\delta \mu_b}{\delta \mu_s} \right) \]

with

\[ \frac{\delta^2 \mu_b}{\delta \mu_s^2} = \frac{-1}{2 \alpha} \left( \frac{1}{D} \frac{\delta C}{\delta \mu_s} + \frac{2 \alpha \, n_{\rm off} - C}{D^2} \frac{\delta D}{\delta \mu_s} \right) \]

where

\[ \frac{\delta C}{\delta \mu_s} = -(1 + \alpha) \]

and

\[ \frac{\delta D}{\delta \mu_s} = \frac{4 (1 + \alpha) \, \alpha \, n_{\rm off} - 2 \, C \, (1 + \alpha)} {2D} \]

In the special case \(n_{\rm on}=n_{\rm off}=0\) the formal background estimate becomes negative, hence we set \(\mu_b=0\) and the log-likelihood function becomes

\[ L = \mu_s \]

the first derivative

\[ \frac{\delta L}{\delta \mu_s} = 1 \]

and the second derivative

\[ \frac{\delta^2 L}{\delta \mu_s^2} = 0 \]

In the special case \(n_{\rm on}=0\) and \(n_{\rm off}>0\) the log-likelihood function becomes

\[ L = \mu_s + n_{\rm off} \ln(1 + \alpha) \]

the background estimate

\[ \mu_b = \frac{n_{\rm off}}{1+\alpha} \]

the first derivative

\[ \frac{\delta L}{\delta \mu_s} = 1 \]

and the second derivative

\[ \frac{\delta^2 L}{\delta \mu_s^2} = 0 \]

In the special case \(n_{\rm on}>0\) and \(n_{\rm off}=0\) the background estimate becomes

\[ \mu_b = \frac{n_{\rm on}}{1+\alpha} - \frac{\mu_s}{\alpha} \]

which is positive for

\[ \mu_s < n_{\rm on} \frac{\alpha}{1+\alpha} \]

For positive \(\mu_b\) the log-likelihood function is given by

\[ L = -\frac{\mu_s}{\alpha} - n_{\rm on} \ln \left(\frac{\alpha}{1 + \alpha} \right) \]

the first derivative

\[ \frac{\delta L}{\delta \mu_s} = -\frac{1}{\alpha} \]

and the second derivative

\[ \frac{\delta^2 L}{\delta \mu_s^2} = 0 \]

For negative \(\mu_b\) we set \(\mu_b=0\) and the log-likelihood function becomes

\[ L = \mu_s - n_{\rm on} - n_{\rm on} \left( \ln(\mu_s) - \ln(n_{\rm on}) \right) \]

the first derivative

\[ \frac{\delta L}{\delta \mu_s} = 1 - \frac{n_{\rm on}}{\mu_s} \]

and the second derivative

\[ \frac{\delta^2 L}{\delta \mu_s^2} = \frac{1}{\mu_s^2} \]

Note that the fit results may be biased and the statistical errors overestimated if for some bins \(n_{\rm on}=0\) and/or \(n_{\rm off}=0\) (i.e. if the special cases are encountered).

Definition at line 3343 of file GCTAOnOffObservation.cpp.

References gammalib::is_infinite(), gammalib::is_notanumber(), log(), and sqrt().

Referenced by likelihood_wstat(), and model_background().