Generalized radial Gaussian model class. More...

#include <GModelSpatialRadialGeneralGauss.hpp>

Inheritance diagram for GModelSpatialRadialGeneralGauss:

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

	GModelSpatialRadialGeneralGauss (const GSkyDir &dir, const double &radius, const double &ridx, const std::string &coordsys="CEL")
	Constructor. More...

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

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

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

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

virtual void	clear (void)
	Clear radial Gauss model. More...

virtual GModelSpatialRadialGeneralGauss *	clone (void) const
	Clone radial Gauss model. More...

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

virtual double	eval (const double &theta, const GEnergy &energy, const GTime &time, const bool &gradients=false) const
	Evaluate Generalised Gaussian source model. More...

virtual GSkyDir	mc (const GEnergy &energy, const GTime &time, GRan &ran) const
	Returns MC sky direction. More...

virtual bool	contains (const GSkyDir &dir, const double &margin=0.0) const
	Checks where model contains specified sky direction. More...

virtual double	theta_max (void) const
	Return maximum model radius (in radians) 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 generalised radial Gaussian source information. More...

double	radius (void) const
	Return radius. More...

void	radius (const double &radius)
	Set radius. More...

double	ridx (void) const
	Return ridx. More...

void	ridx (const double &ridx)
	Set reciprocal index. More...

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

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

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

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

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

virtual GClassCode	code (void) const
	Return class code. More...

virtual bool	is_energy_dependent (void) const
	Signals whether radial model is energy dependent. More...

virtual bool	is_time_dependent (void) const
	Signals whether radial model is time dependent. More...

virtual double	eval (const GPhoton &photon, const bool &gradients=false) const
	Return model value. More...

virtual double	mc_norm (const GSkyDir &dir, const double &radius) const
	Return normalization of radial source for Monte Carlo simulations. More...

std::string	coordsys (void) const
	Return coordinate system. More...

const GSkyDir &	dir (void) const
	Return position of radial spatial model. More...

void	dir (const GSkyDir &dir)
	Set position of radial spatial model. More...

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

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

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

virtual GModelSpatial &	operator= (const GModelSpatial &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 model parameter. More...

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

virtual double	flux (const GSkyRegion &region, const GEnergy &srcEng=GEnergy(), const GTime &srcTime=GTime()) const
	Returns model flux within sky region. More...

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

void	type (const std::string &type)
	Set model type. More...

GModelPar &	at (const int &index)
	Returns model parameter. More...

const GModelPar &	at (const int &index) const
	Returns model parameter (const version) More...

bool	has_par (const std::string &name) const
	Checks if parameter name exists. More...

bool	has_free_pars (void) const
	Checks if the spatial model has free parameters. More...

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

void	autoscale (void)
	Autoscale parameters. More...

const GSkyRegion *	region (void) const
	Return boundary sky region. 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 GModelSpatialRadialGeneralGauss &model)
	Copy class members. More...

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

void	update (void) const
	Update precomputation cache. More...

virtual void	set_region (void) const
	Set boundary sky region. More...

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

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

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

bool	is_celestial (void) const
	Check if model holds celestial coordinates. More...

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

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

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

Protected Attributes
GModelPar	m_radius
	Gaussian width (deg) More...

GModelPar	m_ridx
	Reciprocal of exponent of the radial profile. More...

double	m_last_radius
	Last radius. More...

double	m_inv_radius_rad
	radius(rad)^-1 More...

double	m_last_ridx
	Last reciprocal radial index. More...

double	m_inv_ridx
	Spatial profile index. More...

double	m_value_norm
	1/(2pi radius(rad)^2 ridx Gamma(ridx)) More...

Protected Attributes inherited from GModelSpatialRadial
GModelPar	m_lon
	Right Ascension or Galactic longitude (deg) More...

GModelPar	m_lat
	Declination or Galactic latitude (deg) More...

GSkyDir	m_dir
	Sky direction representing parameters. More...

double	m_last_lon
	Last longitude. More...

double	m_last_lat
	Last latitude. More...

Protected Attributes inherited from GModelSpatial
std::string	m_type
	Spatial model type. More...

GSkyRegionCircle	m_region
	Bounding circle. More...

std::vector< GModelPar * >	m_pars
	Parameter pointers. More...

Detailed Description

Generalized radial Gaussian model class.

This class implements the spatial component of the factorised source model for a generalised radial Gaussian source.

Definition at line 54 of file GModelSpatialRadialGeneralGauss.hpp.

Constructor & Destructor Documentation

GModelSpatialRadialGeneralGauss::GModelSpatialRadialGeneralGauss ( void )

Void constructor.

Constructs empty radial Gaussian model.

Definition at line 71 of file GModelSpatialRadialGeneralGauss.cpp.

References init_members().

Referenced by clone().

GModelSpatialRadialGeneralGauss::GModelSpatialRadialGeneralGauss	(	const GSkyDir &	dir,
		const double &	radius,
		const double &	ridx,
		const std::string &	coordsys = `"CEL"`
	)

Constructor.

Parameters

[in]	dir	Sky position of Gaussian.
[in]	radius	Width of generalised Gaussian (deg).
[in]	ridx	Reciprocal of exponential index of radial profile.
[in]	coordsys	Coordinate system (either "CEL" or "GAL")

Exceptions

GException::invalid_argument Invalid coordsys argument specified.

Constructs a generalised Gaussian spatial model using a sky direction (dir), a Gaussian width parameter radius in degrees and a reciprocal of the exponential index ridx. The coordsys parameter specifies whether the sky direction should be interpreted in the celestial or Galactic coordinate system.

Definition at line 99 of file GModelSpatialRadialGeneralGauss.cpp.

References GModelSpatialRadial::dir(), init_members(), GModelSpatialRadial::m_lat, GModelSpatialRadial::m_lon, GOptimizerPar::name(), radius(), and ridx().

GModelSpatialRadialGeneralGauss::GModelSpatialRadialGeneralGauss ( const GXmlElement & xml )

explicit

XML constructor.

Parameters

[in] xml XML element.

Constructs a generalised Gaussian spatial model by extracting information from an XML element. See the method read() for more information about the expected structure of the XML element.

Definition at line 137 of file GModelSpatialRadialGeneralGauss.cpp.

References init_members(), and read().

GModelSpatialRadialGeneralGauss::GModelSpatialRadialGeneralGauss ( const GModelSpatialRadialGeneralGauss & model )

Copy constructor.

Parameters

[in] model Generalised radial Gaussian model.

Definition at line 156 of file GModelSpatialRadialGeneralGauss.cpp.

References copy_members(), and init_members().

GModelSpatialRadialGeneralGauss::~GModelSpatialRadialGeneralGauss ( void )

virtual

Destructor.

Definition at line 173 of file GModelSpatialRadialGeneralGauss.cpp.

References free_members().

Member Function Documentation

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

inlinevirtual

Return class name.

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

Implements GModelSpatialRadial.

Definition at line 121 of file GModelSpatialRadialGeneralGauss.hpp.

void GModelSpatialRadialGeneralGauss::clear ( void )

virtual

Clear radial Gauss model.

Implements GModelSpatialRadial.

Definition at line 228 of file GModelSpatialRadialGeneralGauss.cpp.

References free_members(), GModelSpatialRadial::free_members(), GModelSpatial::free_members(), init_members(), GModelSpatialRadial::init_members(), and GModelSpatial::init_members().

GModelSpatialRadialGeneralGauss * GModelSpatialRadialGeneralGauss::clone ( void ) const

virtual

Clone radial Gauss model.

Implements GModelSpatialRadial.

Definition at line 248 of file GModelSpatialRadialGeneralGauss.cpp.

References GModelSpatialRadialGeneralGauss().

bool GModelSpatialRadialGeneralGauss::contains	(	const GSkyDir &	dir,
		const double &	margin = `0.0`
	)		const

virtual

Checks where model contains specified sky direction.

Parameters

[in]	dir	Sky direction.
[in]	margin	Margin to be added to sky direction (deg)

Returns: True if the model contains the sky direction.

Signals whether a sky direction is contained in the radial gauss model.

Implements GModelSpatialRadial.

Definition at line 386 of file GModelSpatialRadialGeneralGauss.cpp.

References gammalib::deg2rad, GModelSpatialRadial::dir(), GSkyDir::dist(), and theta_max().

void GModelSpatialRadialGeneralGauss::copy_members ( const GModelSpatialRadialGeneralGauss & model )

protected

Copy class members.

Parameters

[in] model Generalised radial Gaussian spatial model.

We do not have to push back the members on the parameter stack as this should have been done by init_members() that was called before. Otherwise we would have sigma twice on the stack.

Definition at line 588 of file GModelSpatialRadialGeneralGauss.cpp.

References m_inv_radius_rad, m_inv_ridx, m_last_radius, m_last_ridx, m_radius, m_ridx, GModelSpatial::m_type, and m_value_norm.

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

double GModelSpatialRadialGeneralGauss::eval	(	const double &	theta,
		const GEnergy &	energy,
		const GTime &	time,
		const bool &	gradients = `false`
	)		const

virtual

Evaluate Generalised Gaussian source model.

Parameters

[in]	theta	Angular distance from source centre (radians).
[in]	energy	Photon energy (not used).
[in]	time	Photon arrival time (not used).
[in]	gradients	Compute gradients?

Returns: Model value ( \({\rm sr}^{-1}\)).

Evaluates the spatial component for a Generalised Gaussian source model using

\[ M_{\rm S}({\bf p} | E, t) = M_{\rm S}(\theta) = \frac{1}{2 \pi r^2 \eta \Gamma(\eta)} \exp \left(-(\frac{\theta}{r})^1/\eta \right) \]

where

\(\theta\) is the angular separation from the centre of the model, and
\(r\) is the Generalised Gaussian radius.
\(\eta\) is the reciprocal of the radial profile exponent.

If gradients is true the method will also compute parameter gradients

Note that the model normalisation is only correct in the small angle approximation and for \(\eta\) order unity or smaller.

Implements GModelSpatialRadial.

Definition at line 284 of file GModelSpatialRadialGeneralGauss.cpp.

References exp(), G_EVAL, gammalib::is_infinite(), gammalib::is_notanumber(), m_inv_radius_rad, m_inv_ridx, GModelSpatial::m_pars, m_value_norm, pow(), GEnergy::print(), GTime::print(), gammalib::str(), update(), and gammalib::warning().

Referenced by mc().

void GModelSpatialRadialGeneralGauss::free_members ( void )

protected

Delete class members.

Definition at line 610 of file GModelSpatialRadialGeneralGauss.cpp.

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

void GModelSpatialRadialGeneralGauss::init_members ( void )

protected

Initialise class members.

Note that the minimum Gaussian width is set to 1 arcsec and w set the minimum reciprocal index to 1.e-15

Definition at line 536 of file GModelSpatialRadialGeneralGauss.cpp.

References GOptimizerPar::clear(), GOptimizerPar::free(), GOptimizerPar::gradient(), GOptimizerPar::has_grad(), m_inv_radius_rad, m_inv_ridx, m_last_radius, m_last_ridx, GModelSpatial::m_pars, m_radius, m_ridx, GModelSpatial::m_type, m_value_norm, GOptimizerPar::min(), GOptimizerPar::name(), GOptimizerPar::scale(), GOptimizerPar::unit(), and GOptimizerPar::value().

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

GSkyDir GModelSpatialRadialGeneralGauss::mc	(	const GEnergy &	energy,
		const GTime &	time,
		GRan &	ran
	)		const

virtual

Returns MC sky direction.

Parameters

[in]	energy	Photon energy.
[in]	time	Photon arrival time.
[in,out]	ran	Random number generator.

Returns: Sky direction.

Draws an arbitrary sky direction from the 2D Generalised Gaussian distribution as function of the photon energy and arrival time.

Todo:: This method is only valid in the small angle approximation.

Implements GModelSpatialRadial.

Definition at line 328 of file GModelSpatialRadialGeneralGauss.cpp.

References GModelSpatialRadial::dir(), eval(), G_MC, m_value_norm, gammalib::rad2deg, GSkyDir::rotate_deg(), sin(), theta_max(), GRan::uniform(), and update().

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

virtual

Assignment operator.

Parameters

[in] model Generalised radial Gaussian model.

Returns: Radial Generalised radial Gaussian model.

Definition at line 195 of file GModelSpatialRadialGeneralGauss.cpp.

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

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

virtual

Print generalised radial Gaussian source information.

Parameters

[in] chatter Chattiness.

Returns: String containing model information.

Implements GModelSpatialRadial.

Definition at line 499 of file GModelSpatialRadialGeneralGauss.cpp.

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

double GModelSpatialRadialGeneralGauss::radius ( void ) const

inline

Return radius.

Returns: Radius (deg).

Returns the radius in degrees.

Definition at line 135 of file GModelSpatialRadialGeneralGauss.hpp.

References m_radius, and GOptimizerPar::value().

Referenced by GModelSpatialRadialGeneralGauss(), read(), theta_max(), update(), and write().

void GModelSpatialRadialGeneralGauss::radius ( const double & radius )

inline

Set radius.

Parameters

[in] radius (deg).

Sets the radius in degrees.

Definition at line 148 of file GModelSpatialRadialGeneralGauss.hpp.

References m_radius, and GOptimizerPar::value().

void GModelSpatialRadialGeneralGauss::read ( const GXmlElement & xml )

virtual

Read model from XML element.

Parameters

[in] xml XML element.

Reads the generalised radial Gaussian model information from an XML element. The XML element shall have either the format

<spatialModel type="RadialGeneralGaussian">
  <parameter name="RA"      scale="1.0" value="83.6331" min="-360" max="360" free="1"/>
  <parameter name="DEC"     scale="1.0" value="22.0145" min="-90"  max="90"  free="1"/>
  <parameter name="Radius"  scale="1.0" value="0.45"    min="0.01" max="10"  free="1"/>
  <parameter name="R_Index" scale="1.0" value="0.5"     min="0.01" max="10"  free="1"/>
</spatialModel>

or

<spatialModel type="RadialGeneralGaussian">
  <parameter name="GLON"    scale="1.0" value="83.6331" min="-360" max="360" free="1"/>
  <parameter name="GLAT"    scale="1.0" value="22.0145" min="-90"  max="90"  free="1"/>
  <parameter name="Radius"  scale="1.0" value="0.45"    min="0.01" max="10"  free="1"/>
  <parameter name="R_Index" scale="1.0" value="0.5"     min="0.01" max="10"  free="1"/>
</spatialModel>

Todo:: Implement a test of the radius and radius boundary. The sigma and sigma minimum should be >0.

Reimplemented from GModelSpatialRadial.

Definition at line 438 of file GModelSpatialRadialGeneralGauss.cpp.

References G_READ, m_radius, m_ridx, GOptimizerPar::name(), radius(), GModelSpatialRadial::read(), GModelPar::read(), ridx(), gammalib::xml_check_parnum(), and gammalib::xml_get_par().

Referenced by GModelSpatialRadialGeneralGauss().

double GModelSpatialRadialGeneralGauss::ridx ( void ) const

inline

Return ridx.

Returns: Reciprocal of the radial profile index.

Returns the reciprocal of the radial profile index.

Definition at line 162 of file GModelSpatialRadialGeneralGauss.hpp.

References m_ridx, and GOptimizerPar::value().

Referenced by GModelSpatialRadialGeneralGauss(), read(), update(), and write().

void GModelSpatialRadialGeneralGauss::ridx ( const double & ridx )

inline

Set reciprocal index.

Parameters

[in] ridx Reciprocal of the radial profile index.

Sets the reciprocal index of the radial profile.

Definition at line 175 of file GModelSpatialRadialGeneralGauss.hpp.

References m_ridx, and GOptimizerPar::value().

void GModelSpatialRadialGeneralGauss::set_region ( void ) const

protectedvirtual

Set boundary sky region.

Implements GModelSpatialRadial.

Definition at line 653 of file GModelSpatialRadialGeneralGauss.cpp.

References GModelSpatialRadial::dir(), m_radius, GModelSpatial::m_region, GModelSpatial::region(), and GOptimizerPar::value().

double GModelSpatialRadialGeneralGauss::theta_max ( void ) const

virtual

Return maximum model radius (in radians)

Returns \(5 \sigma\) as approximate edge of the Gaussian. This limit is of course arbitrary, but allows to limit the integration region for response computation.

Implements GModelSpatialRadial.

Definition at line 404 of file GModelSpatialRadialGeneralGauss.cpp.

References gammalib::deg2rad, and radius().

Referenced by contains(), and mc().

void GModelSpatialRadialGeneralGauss::update ( void ) const

protected

Update precomputation cache.

Definition at line 620 of file GModelSpatialRadialGeneralGauss.cpp.

References gammalib::deg2rad, exp(), gammalib::gammln(), m_inv_radius_rad, m_inv_ridx, m_last_radius, m_last_ridx, m_value_norm, radius(), ridx(), and gammalib::twopi.

Referenced by eval(), and mc().

void GModelSpatialRadialGeneralGauss::write ( GXmlElement & xml ) const

virtual

Write model into XML element.

Parameters

[in] xml XML element into which model information is written.

Writes the radial disk model information into an XML element. The XML element will have the format

<spatialModel type="RadialGeneralGaussian">
  <parameter name="RA"      scale="1.0" value="83.6331" min="-360" max="360" free="1"/>
  <parameter name="DEC"     scale="1.0" value="22.0145" min="-90"  max="90"  free="1"/>
  <parameter name="Sigma"   scale="1.0" value="0.45"    min="0.01" max="10"  free="1"/>
  <parameter name="R_Index" scale="1.0" value="0.5"     min="0.01" max="10"  free="1"/>
</spatialModel>

Reimplemented from GModelSpatialRadial.

Definition at line 475 of file GModelSpatialRadialGeneralGauss.cpp.

References G_WRITE, m_radius, m_ridx, GOptimizerPar::name(), radius(), ridx(), GModelSpatialRadial::write(), GModelPar::write(), and gammalib::xml_need_par().