Radial Profile CTA model class. More...

#include <GCTAModelRadialProfile.hpp>

Inheritance diagram for GCTAModelRadialProfile:

Classes
class	integrand

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

	GCTAModelRadialProfile (const double &width, const double &core, const double &tail)
	Constructor. More...

	GCTAModelRadialProfile (const GXmlElement &xml)
	XML constructor. More...

	GCTAModelRadialProfile (const GCTAModelRadialProfile &model)
	Copy constructor. More...

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

virtual GCTAModelRadialProfile &	operator= (const GCTAModelRadialProfile &model)
	Assignment operator. More...

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

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

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

virtual std::string	type (void) const
	Return model type. More...

virtual double	eval (const double &offset, const bool &gradients=false) const
	Evaluate function. More...

virtual GCTAInstDir	mc (GRan &ran) const
	Returns MC instrument direction. More...

virtual double	mc_max_value (const GCTAObservation &obs) const
	Return maximum function value for Monte Carlo simulations. More...

virtual double	omega (void) const
	Returns integral over radial model (in steradians) More...

virtual void	read (const GXmlElement &xml)
	Read model from XML element. More...

virtual void	write (GXmlElement &xml) const
	Write model into XML element. More...

virtual std::string	print (const GChatter &chatter=NORMAL) const
	Print point source information. More...

double	width (void) const
	Return profile width. More...

double	core (void) const
	Return profile core. More...

double	tail (void) const
	Return profile tail. More...

void	width (const double &width)
	Set profile width. More...

void	core (const double &core)
	Set profile core. More...

void	tail (const double &tail)
	Set profile tail. More...

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

	GCTAModelRadial (const GCTAModelRadial &model)
	Copy constructor. More...

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

virtual GCTAModelRadial &	operator= (const GCTAModelRadial &model)
	Assignment operator. More...

virtual double	eval (const GCTAInstDir &dir, const GEnergy &energy, const GTime &time, const bool &gradients=false) const
	Evaluate function. More...

virtual GCTAInstDir	mc (const GEnergy &energy, const GTime &time, const GCTAObservation &obs, GRan &ran) const
	Returns MC instrument direction. More...

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

	GCTAModelSpatial (const GCTAModelSpatial &model)
	Copy constructor. More...

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

virtual GCTAModelSpatial &	operator= (const GCTAModelSpatial &model)
	Assignment operator. More...

virtual GModelPar &	operator[] (const int &index)
	Returns model parameter. More...

virtual const GModelPar &	operator[] (const int &index) const
	Returns model parameter (const version) More...

virtual GModelPar &	operator[] (const std::string &name)
	Returns reference to model parameter. More...

virtual const GModelPar &	operator[] (const std::string &name) const
	Returns reference to model parameter (const version) More...

int	size (void) const
	Return number of model parameters. More...

virtual double	npred (const GEnergy &energy, const GTime &time, const GObservation &obs) const
	Return integral of spatial model component. 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 GCTAModelRadialProfile &model)
	Copy class members. More...

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

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

void	copy_members (const GCTAModelRadial &model)
	Copy class members. More...

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

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

void	copy_members (const GCTAModelSpatial &model)
	Copy class members. More...

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

Protected Attributes
GModelPar	m_width
	Width parameter. More...

GModelPar	m_core
	Core parameter. More...

GModelPar	m_tail
	Tail parameter. More...

Protected Attributes inherited from GCTAModelSpatial
std::vector< GModelPar * >	m_pars
	Parameter pointers. More...

Detailed Description

Radial Profile CTA model class.

This class implements the radial profile function

\[f(\theta) = (1 + (\theta/c_0)^{c_1})^{-c_2/c_1}\]

where \(\theta\) is the offset angle (in degrees), \(c_0\) is the width of the profile (width), \(c_1\) is the width of the central plateau (core), and \(c_2\) is the size of the tail (tail). Note that all 3 parameters are positive values.

Definition at line 59 of file GCTAModelRadialProfile.hpp.

Constructor & Destructor Documentation

GCTAModelRadialProfile::GCTAModelRadialProfile ( void )

Void constructor.

Definition at line 71 of file GCTAModelRadialProfile.cpp.

References init_members().

Referenced by clone().

GCTAModelRadialProfile::GCTAModelRadialProfile	(	const double &	width,
		const double &	core,
		const double &	tail
	)

explicit

Constructor.

Parameters

[in]	width	Width.
[in]	core	Core size.
[in]	tail	Tail size.

Definition at line 88 of file GCTAModelRadialProfile.cpp.

References core(), init_members(), tail(), and width().

GCTAModelRadialProfile::GCTAModelRadialProfile ( const GXmlElement & xml )

explicit

XML constructor.

Parameters

[in] xml XML element.

Creates instance of a radial Profile model by extracting information from an XML element. See GCTAModelRadialProfile::read() for more information about the expected structure of the XML element.

Definition at line 114 of file GCTAModelRadialProfile.cpp.

References init_members(), and read().

GCTAModelRadialProfile::GCTAModelRadialProfile ( const GCTAModelRadialProfile & model )

Copy constructor.

Parameters

[in] model Radial Profile model.

Definition at line 133 of file GCTAModelRadialProfile.cpp.

References copy_members(), and init_members().

GCTAModelRadialProfile::~GCTAModelRadialProfile ( void )

virtual

Destructor.

Definition at line 150 of file GCTAModelRadialProfile.cpp.

References free_members().

Member Function Documentation

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

inlinevirtual

Return class name.

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

Implements GCTAModelRadial.

Definition at line 126 of file GCTAModelRadialProfile.hpp.

void GCTAModelRadialProfile::clear ( void )

virtual

Clear instance.

Implements GCTAModelRadial.

Definition at line 204 of file GCTAModelRadialProfile.cpp.

References GCTAModelRadial::free_members(), free_members(), GCTAModelRadial::init_members(), and init_members().

GCTAModelRadialProfile * GCTAModelRadialProfile::clone ( void ) const

virtual

Clone instance.

Implements GCTAModelRadial.

Definition at line 222 of file GCTAModelRadialProfile.cpp.

References GCTAModelRadialProfile().

void GCTAModelRadialProfile::copy_members ( const GCTAModelRadialProfile & model )

protected

Copy class members.

Parameters

[in] model Radial Profileian model.

Definition at line 564 of file GCTAModelRadialProfile.cpp.

References m_core, GCTAModelSpatial::m_pars, m_tail, and m_width.

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

double GCTAModelRadialProfile::core ( void ) const

inline

Return profile core.

Returns: Profile core.

Definition at line 162 of file GCTAModelRadialProfile.hpp.

References m_core, and GOptimizerPar::value().

Referenced by eval(), GCTAModelRadialProfile(), read(), and write().

void GCTAModelRadialProfile::core ( const double & core )

inline

Set profile core.

Parameters

[in] core Profile core.

Definition at line 199 of file GCTAModelRadialProfile.hpp.

References m_core, and GOptimizerPar::value().

double GCTAModelRadialProfile::eval	(	const double &	offset,
		const bool &	gradients = `false`
	)		const

virtual

Evaluate function.

Parameters

[in]	offset	Offset angle [degrees].
[in]	gradients	Compute gradients?

Returns: Function value

Evaluates the Profile model for a given offset. The Profile model is defined as

\[f(\theta) = (1 + (\theta/c_0)^{c_1})^{-c_2/c_1}\]

where \(\theta\) is the offset angle (in degrees), \(c_0\) is the width of the profile (width), \(c_1\) is the width of the central plateau (core), and \(c_2\) is the size of the tail (tail).

Note that no analytical partial derivatives are implemented for this function.

Implements GCTAModelRadial.

Definition at line 247 of file GCTAModelRadialProfile.cpp.

References core(), gammalib::is_infinite(), gammalib::is_notanumber(), pow(), tail(), and width().

Referenced by GCTAModelRadialProfile::integrand::eval(), and mc().

void GCTAModelRadialProfile::free_members ( void )

protected

Delete class members.

Definition at line 585 of file GCTAModelRadialProfile.cpp.

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

void GCTAModelRadialProfile::init_members ( void )

protected

Initialise class members.

Definition at line 515 of file GCTAModelRadialProfile.cpp.

References GOptimizerPar::clear(), GOptimizerPar::fix(), GOptimizerPar::free(), GOptimizerPar::gradient(), GOptimizerPar::has_grad(), m_core, GCTAModelSpatial::m_pars, m_tail, m_width, GOptimizerPar::min(), GOptimizerPar::name(), GOptimizerPar::scale(), GOptimizerPar::unit(), and GOptimizerPar::value().

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

GCTAInstDir GCTAModelRadialProfile::mc ( GRan & ran ) const

virtual

Returns MC instrument direction.

Parameters

[in,out] ran Random number generator.

Returns: CTA instrument direction.

Draws an arbitrary CTA instrument position from

\[f(\theta) = \sin(\theta) (1 + (\theta/c_0)^{c_1})^{-c_2/c_1}\]

where \(\theta\) is the offset angle (in degrees), \(c_0\) is the width of the profile (width), \(c_1\) is the width of the central plateau (core), and \(c_2\) is the size of the tail (tail). using the rejection method.

The maximum offset angle that is thrown by this method is fixed to 10 degrees.

Todo:: Method can be optimised by using a random deviate of sin instead of the uniform random deviate which leads to many unnecessary rejections.

Implements GCTAModelRadial.

Definition at line 294 of file GCTAModelRadialProfile.cpp.

References cos(), gammalib::deg2rad, eval(), sin(), and GRan::uniform().

double GCTAModelRadialProfile::mc_max_value ( const GCTAObservation & obs ) const

virtual

Return maximum function value for Monte Carlo simulations.

Parameters

[in] obs CTA Observation (not used).

Returns: Maximum function value for Monte Carlo simulations.

Implements GCTAModelRadial.

Definition at line 361 of file GCTAModelRadialProfile.cpp.

References gammalib::deg2rad, and sin().

double GCTAModelRadialProfile::omega ( void ) const

virtual

Returns integral over radial model (in steradians)

Computes

\[\Omega = 2 \pi \int_0^{\pi} \sin \theta f(\theta) d\theta\]

where

\[f(\theta) = (1 + (\theta/c_0)^{c_1})^{-c_2/c_1}\]

\(\theta\) is the offset angle (in degrees), \(c_0\) is the width of the profile (width), \(c_1\) is the width of the central plateau (core), and \(c_2\) is the size of the tail (tail).

The integration is performed numerically, and the upper integration bound \(\pi\) is fixed to 10 degrees.

Implements GCTAModelRadial.

Definition at line 388 of file GCTAModelRadialProfile.cpp.

References gammalib::deg2rad, GIntegral::romberg(), and gammalib::twopi.

GCTAModelRadialProfile & GCTAModelRadialProfile::operator= ( const GCTAModelRadialProfile & model )

virtual

Assignment operator.

Parameters

[in] model Radial Profile model.

Definition at line 171 of file GCTAModelRadialProfile.cpp.

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

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

virtual

Print point source information.

Parameters

[in] chatter Chattiness.

Returns: String containing point source information.

Implements GCTAModelRadial.

Definition at line 481 of file GCTAModelRadialProfile.cpp.

References GCTAModelSpatial::m_pars, gammalib::parformat(), SILENT, GCTAModelSpatial::size(), and gammalib::str().

void GCTAModelRadialProfile::read ( const GXmlElement & xml )

virtual

Read model from XML element.

Parameters

[in] xml XML element.

Read the Profile radial model information from an XML element in the following format

<radialModel type="...">
  <parameter name="Width"  scale="1.0" value="1.5" min="0.1" max="10.0" free="1"/>
  <parameter name="Core"   scale="1.0" value="3.0" min="1.0" max="10.0" free="1"/>
  <parameter name="Tail"   scale="1.0" value="5.0" min="1.0" max="10.0" free="1"/>
</radialModel>

Implements GCTAModelRadial.

Definition at line 421 of file GCTAModelRadialProfile.cpp.

References core(), G_READ, m_core, m_tail, m_width, GOptimizerPar::name(), GModelPar::read(), tail(), width(), gammalib::xml_check_parnum(), and gammalib::xml_get_par().

Referenced by GCTAModelRadialProfile().

double GCTAModelRadialProfile::tail ( void ) const

inline

Return profile tail.

Returns: Profile tail.

Definition at line 174 of file GCTAModelRadialProfile.hpp.

References m_tail, and GOptimizerPar::value().

Referenced by eval(), GCTAModelRadialProfile(), read(), and write().

void GCTAModelRadialProfile::tail ( const double & tail )

inline

Set profile tail.

Parameters

[in] tail Profile tail.

Definition at line 212 of file GCTAModelRadialProfile.hpp.

References m_tail, and GOptimizerPar::value().

std::string GCTAModelRadialProfile::type ( void ) const

inlinevirtual

Return model type.

Returns: Model type "Profile".

Implements GCTAModelRadial.

Definition at line 138 of file GCTAModelRadialProfile.hpp.

Referenced by write().

double GCTAModelRadialProfile::width ( void ) const

inline

Return profile width.

Returns: Profile width.

Definition at line 150 of file GCTAModelRadialProfile.hpp.

References m_width, and GOptimizerPar::value().

Referenced by eval(), GCTAModelRadialProfile(), read(), and write().

void GCTAModelRadialProfile::width ( const double & width )

inline

Set profile width.

Parameters

[in] width Profile width.

Definition at line 186 of file GCTAModelRadialProfile.hpp.

References m_width, and GOptimizerPar::value().

void GCTAModelRadialProfile::write ( GXmlElement & xml ) const

virtual

Write model into XML element.

Parameters

[in] xml XML element.

Write the radial Profile model information into an XML element in the following format

<radialModel type="...">
  <parameter name="Width"  scale="1.0" value="1.5" min="0.1" max="10.0" free="1"/>
  <parameter name="Core"   scale="1.0" value="3.0" min="1.0" max="10.0" free="1"/>
  <parameter name="Tail"   scale="1.0" value="5.0" min="1.0" max="10.0" free="1"/>
</radialModel>

Implements GCTAModelRadial.

Definition at line 455 of file GCTAModelRadialProfile.cpp.

References core(), G_WRITE, m_core, m_tail, m_width, GOptimizerPar::name(), tail(), type(), width(), GModelPar::write(), gammalib::xml_check_type(), and gammalib::xml_need_par().