Radial Gaussian CTA model class. More...

#include <GCTAModelRadialGauss.hpp>

Inheritance diagram for GCTAModelRadialGauss:

Classes
class	integrand

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

	GCTAModelRadialGauss (const double &sigma)
	Constructor. More...

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

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

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

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

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

virtual GCTAModelRadialGauss *	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	sigma (void) const
	Return Gaussian width parameter. More...

void	sigma (const double &sigma)
	Set Gaussian width parameter. 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 GCTAModelRadialGauss &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_sigma
	Width parameter (degrees^2) More...

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

Detailed Description

Radial Gaussian CTA model class.

This class implements the radial function

\[f(\theta) = \exp \left(-\frac{1}{2} \left( \frac{\theta^2}{\sigma} \right)^2 \right)\]

where \(\theta\) is the offset angle (in degrees), and \(\sigma\) is the width parameter (in degrees \(^2\)).

This function represents a Gaussian in \(\theta^2\).

Definition at line 58 of file GCTAModelRadialGauss.hpp.

Constructor & Destructor Documentation

GCTAModelRadialGauss::GCTAModelRadialGauss ( void )

Void constructor.

Definition at line 71 of file GCTAModelRadialGauss.cpp.

References init_members().

Referenced by clone().

GCTAModelRadialGauss::GCTAModelRadialGauss ( const double & sigma )

explicit

Constructor.

Parameters

[in] sigma Gaussian width (degrees \(^2\)).

Definition at line 86 of file GCTAModelRadialGauss.cpp.

References init_members(), and sigma().

GCTAModelRadialGauss::GCTAModelRadialGauss ( const GXmlElement & xml )

explicit

XML constructor.

Parameters

[in] xml XML element.

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

Definition at line 108 of file GCTAModelRadialGauss.cpp.

References init_members(), and read().

GCTAModelRadialGauss::GCTAModelRadialGauss ( const GCTAModelRadialGauss & model )

Copy constructor.

Parameters

[in] model Radial Gaussian model.

Definition at line 126 of file GCTAModelRadialGauss.cpp.

References copy_members(), and init_members().

GCTAModelRadialGauss::~GCTAModelRadialGauss ( void )

virtual

Destructor.

Definition at line 143 of file GCTAModelRadialGauss.cpp.

References free_members().

Member Function Documentation

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

inlinevirtual

Return class name.

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

Implements GCTAModelRadial.

Definition at line 121 of file GCTAModelRadialGauss.hpp.

void GCTAModelRadialGauss::clear ( void )

virtual

Clear instance.

Implements GCTAModelRadial.

Definition at line 197 of file GCTAModelRadialGauss.cpp.

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

GCTAModelRadialGauss * GCTAModelRadialGauss::clone ( void ) const

virtual

Clone instance.

Implements GCTAModelRadial.

Definition at line 215 of file GCTAModelRadialGauss.cpp.

References GCTAModelRadialGauss().

void GCTAModelRadialGauss::copy_members ( const GCTAModelRadialGauss & model )

protected

Copy class members.

Parameters

[in] model Radial Gaussian model.

Definition at line 526 of file GCTAModelRadialGauss.cpp.

References GCTAModelSpatial::m_pars, and m_sigma.

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

double GCTAModelRadialGauss::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 Gaussian model for a given offset. The Gaussian model is defined as

\[f(\theta) = \exp \left(-\frac{1}{2} \left( \frac{\theta^2}{\sigma} \right)^2 \right)\]

where \(\theta\) is the offset angle (in degrees), and \(\sigma\) is the Gaussian width (in degrees \(^2\)).

If the gradients flag is true the method will also compute the partial derivatives of the parameters. The partial derivative of the Gaussian width is given by

\[\frac{df}{d\sigma_v} = f(\theta) \frac{\theta^4}{\sigma^3} \sigma_s\]

where \(\sigma_v\) is the value part, \(\sigma_s\) is the scaling part, and \(\sigma = \sigma_v \sigma_s\).

Note that this method implements a function which is unity for \(\theta=0\).

Implements GCTAModelRadial.

Definition at line 248 of file GCTAModelRadialGauss.cpp.

References exp(), GOptimizerPar::factor_gradient(), gammalib::is_infinite(), gammalib::is_notanumber(), m_sigma, GOptimizerPar::scale(), and sigma().

void GCTAModelRadialGauss::free_members ( void )

protected

Delete class members.

Definition at line 543 of file GCTAModelRadialGauss.cpp.

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

void GCTAModelRadialGauss::init_members ( void )

protected

Initialise class members.

Definition at line 499 of file GCTAModelRadialGauss.cpp.

References GOptimizerPar::clear(), GOptimizerPar::free(), GOptimizerPar::gradient(), GOptimizerPar::has_grad(), GCTAModelSpatial::m_pars, m_sigma, GOptimizerPar::min(), GOptimizerPar::name(), GOptimizerPar::scale(), GOptimizerPar::unit(), and GOptimizerPar::value().

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

GCTAInstDir GCTAModelRadialGauss::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

\[f(\theta) = \sin(\theta) \exp \left(-\frac{1}{2}\frac{\theta^4}{\sigma^2} \right)\]

where \(\theta\) is the offset angle (in degrees), and \(\sigma\) is the Gaussian width (in degrees \(^2\)), using the rejection method.

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 301 of file GCTAModelRadialGauss.cpp.

References cos(), gammalib::deg2rad, exp(), sigma(), sin(), sqrt(), and GRan::uniform().

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

virtual

Return maximum function value for Monte Carlo simulations.

Parameters

[in] obs CTA Observation.

Returns: Maximum function value for Monte Carlo simulations.

Implements GCTAModelRadial.

Definition at line 355 of file GCTAModelRadialGauss.cpp.

double GCTAModelRadialGauss::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

\[f(\theta) = \exp \left(-\frac{1}{2} \left( \frac{\theta^2}{\sigma} \right)^2 \right)\]

\(\theta\) is the offset angle (in degrees), and \(\sigma\) is the Gaussian width (in degrees \(^2\)).

The integration is performed numerically, and the upper integration bound \(\pi\) is set to \(\sqrt(10 \sigma)\) to reduce inaccuracies in the numerical integration.

Implements GCTAModelRadial.

Definition at line 379 of file GCTAModelRadialGauss.cpp.

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

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

virtual

Assignment operator.

Parameters

[in] model Radial Gaussian model.

Definition at line 164 of file GCTAModelRadialGauss.cpp.

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

std::string GCTAModelRadialGauss::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 465 of file GCTAModelRadialGauss.cpp.

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

void GCTAModelRadialGauss::read ( const GXmlElement & xml )

virtual

Read model from XML element.

Parameters

[in] xml XML element.

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

<radialModel type="...">
  <parameter name="Sigma"  scale="1.0" value="3.0" min="0.01" max="10.0" free="1"/>
</radialModel>

Implements GCTAModelRadial.

Definition at line 415 of file GCTAModelRadialGauss.cpp.

References G_READ, m_sigma, GOptimizerPar::name(), GModelPar::read(), sigma(), gammalib::xml_check_parnum(), and gammalib::xml_get_par().

Referenced by GCTAModelRadialGauss().

double GCTAModelRadialGauss::sigma ( void ) const

inline

Return Gaussian width parameter.

Returns: Gaussian width parameter.

Definition at line 145 of file GCTAModelRadialGauss.hpp.

References m_sigma, and GOptimizerPar::value().

Referenced by eval(), GCTAModelRadialGauss(), mc(), omega(), read(), and write().

void GCTAModelRadialGauss::sigma ( const double & sigma )

inline

Set Gaussian width parameter.

Parameters

[in] sigma Gaussian width parameter.

Definition at line 157 of file GCTAModelRadialGauss.hpp.

References m_sigma, and GOptimizerPar::value().

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

inlinevirtual

Return model type.

Returns: Model type "Gaussian".

Implements GCTAModelRadial.

Definition at line 133 of file GCTAModelRadialGauss.hpp.

Referenced by write().

void GCTAModelRadialGauss::write ( GXmlElement & xml ) const

virtual

Write model into XML element.

Parameters

[in] xml XML element.

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

<radialModel type="...">
  <parameter name="Sigma"  scale="1.0" value="3.0" min="0.01" max="10.0" free="1"/>
</radialModel>

Implements GCTAModelRadial.

Definition at line 443 of file GCTAModelRadialGauss.cpp.

References G_WRITE, m_sigma, GOptimizerPar::name(), sigma(), type(), GModelPar::write(), gammalib::xml_check_type(), and gammalib::xml_need_par().

Member Data Documentation

GModelPar GCTAModelRadialGauss::m_sigma

protected

Width parameter (degrees^2)

Definition at line 111 of file GCTAModelRadialGauss.hpp.

Referenced by copy_members(), eval(), init_members(), read(), sigma(), and write().

The documentation for this class was generated from the following files:

inst/cta/include/GCTAModelRadialGauss.hpp
inst/cta/src/GCTAModelRadialGauss.cpp

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation