Radial Gaussian model class. More...

#include <GModelSpatialRadialGauss.hpp>

Inheritance diagram for GModelSpatialRadialGauss:

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

	GModelSpatialRadialGauss (const bool &dummy, const std::string &type)
	Model type constructor. More...

	GModelSpatialRadialGauss (const GSkyDir &dir, const double &sigma, const std::string &coordsys="CEL")
	Constructor. More...

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

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

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

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

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

virtual GModelSpatialRadialGauss *	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 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 Gaussian source information. More...

double	sigma (void) const
	Return Gaussian sigma. More...

void	sigma (const double &sigma)
	Set Gaussian sigma. 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 GModelSpatialRadialGauss &model)
	Copy class members. More...

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

void	update (const bool &gradients) 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_sigma
	Gaussian width (deg) More...

double	m_last_sigma
	Last Gaussian sigma. More...

double	m_inv_sigma2_rad
	sigma(rad)^-2 More...

double	m_value_norm
	(2pi sigma(rad))^-2 More...

double	m_g_theta_norm
	sigma(rad)^-2 deg2rad More...

double	m_g_sigma_norm
	sigma(rad)^-1 sigma_scale deg2rad 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

Radial Gaussian model class.

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

Definition at line 53 of file GModelSpatialRadialGauss.hpp.

Constructor & Destructor Documentation

GModelSpatialRadialGauss::GModelSpatialRadialGauss ( void )

Void constructor.

Constructs empty radial Gaussian model.

Definition at line 73 of file GModelSpatialRadialGauss.cpp.

References init_members().

Referenced by clone().

GModelSpatialRadialGauss::GModelSpatialRadialGauss	(	const bool &	dummy,
		const std::string &	type
	)

Model type constructor.

Parameters

[in]	dummy	Dummy flag.
[in]	type	Model type.

Constructs empty radial Gaussian model by specifying a model type.

Definition at line 91 of file GModelSpatialRadialGauss.cpp.

References init_members(), GModelSpatial::m_type, and GModelSpatial::type().

GModelSpatialRadialGauss::GModelSpatialRadialGauss	(	const GSkyDir &	dir,
		const double &	sigma,
		const std::string &	coordsys = `"CEL"`
	)

Constructor.

Parameters

[in]	dir	Sky position of Gaussian.
[in]	sigma	Width of Gaussian (in degrees).
[in]	coordsys	Coordinate system (either "CEL" or "GAL")

Exceptions

GException::invalid_argument Invalid coordsys argument specified.

Constructs a Gaussian spatial model using a sky direction (dir) and a Gaussian width parameter sigma in degrees. The coordsys parameter specifies whether the sky direction should be interpreted in the celestial or Galactic coordinate system.

Definition at line 121 of file GModelSpatialRadialGauss.cpp.

References GModelSpatialRadial::dir(), G_CONSTRUCTOR, init_members(), GModelSpatialRadial::m_lat, GModelSpatialRadial::m_lon, GOptimizerPar::name(), and sigma().

GModelSpatialRadialGauss::GModelSpatialRadialGauss ( const GXmlElement & xml )

explicit

XML constructor.

Parameters

[in] xml XML element.

Constructs a 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 165 of file GModelSpatialRadialGauss.cpp.

References init_members(), and read().

GModelSpatialRadialGauss::GModelSpatialRadialGauss ( const GModelSpatialRadialGauss & model )

Copy constructor.

Parameters

[in] model Radial Gaussian model.

Definition at line 184 of file GModelSpatialRadialGauss.cpp.

References copy_members(), and init_members().

GModelSpatialRadialGauss::~GModelSpatialRadialGauss ( void )

virtual

Destructor.

Definition at line 201 of file GModelSpatialRadialGauss.cpp.

References free_members().

Member Function Documentation

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

inlinevirtual

Return class name.

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

Implements GModelSpatialRadial.

Definition at line 117 of file GModelSpatialRadialGauss.hpp.

void GModelSpatialRadialGauss::clear ( void )

virtual

Clear radial Gauss model.

Implements GModelSpatialRadial.

Definition at line 256 of file GModelSpatialRadialGauss.cpp.

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

GModelSpatialRadialGauss * GModelSpatialRadialGauss::clone ( void ) const

virtual

Clone radial Gauss model.

Implements GModelSpatialRadial.

Definition at line 276 of file GModelSpatialRadialGauss.cpp.

References GModelSpatialRadialGauss().

bool GModelSpatialRadialGauss::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 (degrees)

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 451 of file GModelSpatialRadialGauss.cpp.

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

void GModelSpatialRadialGauss::copy_members ( const GModelSpatialRadialGauss & model )

protected

Copy class members.

Parameters

[in] model 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 637 of file GModelSpatialRadialGauss.cpp.

References m_g_sigma_norm, m_g_theta_norm, m_inv_sigma2_rad, m_last_sigma, m_sigma, GModelSpatial::m_type, and m_value_norm.

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

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

virtual

Evaluate Gaussian source model.

Parameters

[in]	theta	Angular distance from Gaussian 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 Gaussian source model using

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

where

\(\theta\) is the angular separation from the centre of the model, and
\(\sigma\) is the Gaussian width.

If gradients is true the method will also compute analytical parameter gradients

\[ \frac{\partial M_{\rm S}}{\partial \alpha_0} = \frac{\partial M_{\rm S}}{\partial \theta} \frac{\partial \theta}{\partial \alpha_0} \]

\[ \frac{\partial M_{\rm S}}{\partial \beta_0} = \frac{\partial M_{\rm S}}{\partial \theta} \frac{\partial \theta}{\partial \beta_0} \]

with

\[ \frac{\partial M_{\rm S}}{\partial \theta} = -\frac{\theta}{\sigma^2} M_{\rm S}(\theta) \]

and

\[ \frac{\partial M_{\rm S}}{\partial \sigma} = \left( \frac{\theta^2}{\sigma^3} - \frac{2}{\sigma} \right) M_{\rm S}(\theta) \]

where

\(\alpha_0\) is the Right Ascension of the model centre, and
\(\beta_0\) is the Declination of the model centre.

The computation of the analytical gradients with respect to the model centre relies on the computation of the partial derivatives \(\frac{\partial \theta}{\partial \alpha_0}\) and \(\frac{\partial \theta}{\partial \beta_0}\) which are assumed to be stored in m_lon.factor_gradient() and m_lat.factor_gradient() when the method is entered. No check is performed whether these values are actually available and valid.

Note that the model normalisation is only correct in the small angle approximation.

Implements GModelSpatialRadial.

Definition at line 349 of file GModelSpatialRadialGauss.cpp.

References exp(), GOptimizerPar::factor_gradient(), G_EVAL, GOptimizerPar::is_free(), gammalib::is_infinite(), gammalib::is_notanumber(), m_g_sigma_norm, m_g_theta_norm, m_inv_sigma2_rad, GModelSpatialRadial::m_lat, GModelSpatialRadial::m_lon, GModelSpatial::m_pars, m_sigma, m_value_norm, GEnergy::print(), GTime::print(), GOptimizerPar::scale(), gammalib::str(), update(), and gammalib::warning().

void GModelSpatialRadialGauss::free_members ( void )

protected

Delete class members.

Definition at line 658 of file GModelSpatialRadialGauss.cpp.

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

void GModelSpatialRadialGauss::init_members ( void )

protected

Initialise class members.

Note that the minimum Gaussian width is set to 1 arcsec.

Definition at line 593 of file GModelSpatialRadialGauss.cpp.

References GOptimizerPar::clear(), GOptimizerPar::free(), GOptimizerPar::gradient(), GOptimizerPar::has_grad(), m_g_sigma_norm, m_g_theta_norm, m_inv_sigma2_rad, m_last_sigma, GModelSpatialRadial::m_lat, GModelSpatialRadial::m_lon, GModelSpatial::m_pars, m_sigma, GModelSpatial::m_type, m_value_norm, GOptimizerPar::min(), GOptimizerPar::name(), GOptimizerPar::scale(), GOptimizerPar::unit(), and GOptimizerPar::value().

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

GSkyDir GModelSpatialRadialGauss::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 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 425 of file GModelSpatialRadialGauss.cpp.

References GRan::chisq2(), GModelSpatialRadial::dir(), GSkyDir::rotate_deg(), sigma(), and GRan::uniform().

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

virtual

Assignment operator.

Parameters

[in] model Radial Gaussian model.

Returns: Radial Gaussian model.

Definition at line 223 of file GModelSpatialRadialGauss.cpp.

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

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

virtual

Print Gaussian source information.

Parameters

[in] chatter Chattiness.

Returns: String containing model information.

Implements GModelSpatialRadial.

Definition at line 557 of file GModelSpatialRadialGauss.cpp.

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

void GModelSpatialRadialGauss::read ( const GXmlElement & xml )

virtual

Read model from XML element.

Parameters

[in] xml XML element.

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

<spatialModel type="RadialGaussian">
  <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"/>
</spatialModel>

or

<spatialModel type="RadialGaussian">
  <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="Sigma" scale="1.0" value="0.45"    min="0.01" max="10"  free="1"/>
</spatialModel>

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

Reimplemented from GModelSpatialRadial.

Definition at line 501 of file GModelSpatialRadialGauss.cpp.

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

Referenced by GModelSpatialRadialGauss().

void GModelSpatialRadialGauss::set_region ( void ) const

protectedvirtual

Set boundary sky region.

Implements GModelSpatialRadial.

Definition at line 706 of file GModelSpatialRadialGauss.cpp.

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

double GModelSpatialRadialGauss::sigma ( void ) const

inline

Return Gaussian sigma.

Returns: Gaussian sigma (degrees).

Returns the Gaussian sigma in degrees.

Definition at line 131 of file GModelSpatialRadialGauss.hpp.

References m_sigma, and GOptimizerPar::value().

Referenced by GModelSpatialRadialGauss(), mc(), read(), theta_max(), update(), and write().

void GModelSpatialRadialGauss::sigma ( const double & sigma )

inline

Set Gaussian sigma.

Parameters

[in] sigma Gaussian sigma (degrees).

Sets the Gaussian sigma in degrees.

Definition at line 145 of file GModelSpatialRadialGauss.hpp.

References m_sigma, and GOptimizerPar::value().

double GModelSpatialRadialGauss::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 469 of file GModelSpatialRadialGauss.cpp.

References gammalib::deg2rad, and sigma().

Referenced by contains().

void GModelSpatialRadialGauss::update ( const bool & gradients ) const

protected

Update precomputation cache.

Parameters

[in] gradients Gradient computation requested?

Definition at line 670 of file GModelSpatialRadialGauss.cpp.

References gammalib::deg2rad, m_g_sigma_norm, m_g_theta_norm, m_inv_sigma2_rad, m_last_sigma, m_sigma, m_value_norm, GOptimizerPar::scale(), sigma(), and gammalib::twopi.

Referenced by eval().

void GModelSpatialRadialGauss::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="RadialGaussian">
  <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"/>
</spatialModel>

Reimplemented from GModelSpatialRadial.

Definition at line 535 of file GModelSpatialRadialGauss.cpp.

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