#include <GModelSpatialEllipticalGauss.hpp>

Inheritance diagram for GModelSpatialEllipticalGauss:

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

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

	GModelSpatialEllipticalGauss (const GSkyDir &dir, const double &major, const double &minor, const double &posangle, const std::string &coordsys="CEL")
	Elliptical Gaussian constructor. More...

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

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

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

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

virtual void	clear (void)
	Clear elliptical Gaussian model. More...

virtual GModelSpatialEllipticalGauss *	clone (void) const
	Clone elliptical Gaussian model. More...

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

virtual double	eval (const double &theta, const double &posangle, const GEnergy &energy, const GTime &time, const bool &gradients=false) const
	Evaluate function (in units of sr^-1) 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 whether 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 information. More...

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

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

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

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

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

virtual GClassCode	code (void) const
	Return class code. 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 elliptical source for Monte Carlo simulations. More...

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

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

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

double	posangle (void) const
	Return Position Angle of model. More...

void	posangle (const double &posangle)
	Set Position Angle of model. More...

double	semiminor (void) const
	Return semi-minor axis of ellipse. More...

double	semimajor (void) const
	Return semi-major axis of ellipse. More...

void	semiminor (const double &semiminor)
	Set semi-minor axis of ellipse. More...

void	semimajor (const double &semimajor)
	Set semi-major axis of ellipse. 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 GModelSpatialEllipticalGauss &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 GModelSpatialElliptical
void	init_members (void)
	Initialise class members. More...

void	copy_members (const GModelSpatialElliptical &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
double	m_last_minor
	Last semi-minor axis. More...

double	m_last_major
	Last semi-major axis. More...

double	m_last_posangle
	Last position angle. More...

double	m_cospos2
	squared cosine of position angle More...

double	m_sinpos2
	squared sine of position angle More...

double	m_sin2pos
	sine of twice the position angle More...

double	m_minor2
	square of minor axis More...

double	m_major2
	square of major axis More...

double	m_minor_rad
	Minor axis in radians. More...

double	m_major_rad
	Major axis in radians. More...

double	m_norm
	Normalization. More...

double	m_term1
	Help term 1. More...

double	m_term2
	Help term 2. More...

double	m_term3
	Help term 3. More...

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

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

GModelPar	m_posangle
	Position angle from North, counterclockwise (deg) More...

GModelPar	m_semiminor
	Semi-minor axis of ellipse (deg) More...

GModelPar	m_semimajor
	Semi-major axis of ellipse (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

Definition at line 54 of file GModelSpatialEllipticalGauss.hpp.

Constructor & Destructor Documentation

GModelSpatialEllipticalGauss::GModelSpatialEllipticalGauss ( void )

Void constructor.

Definition at line 77 of file GModelSpatialEllipticalGauss.cpp.

References init_members().

Referenced by clone().

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

Model type constructor.

Parameters

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

Constructs empty elliptical Gaussian model by specifying a model type.

Definition at line 96 of file GModelSpatialEllipticalGauss.cpp.

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

GModelSpatialEllipticalGauss::GModelSpatialEllipticalGauss	(	const GSkyDir &	dir,
		const double &	semimajor,
		const double &	semiminor,
		const double &	posangle,
		const std::string &	coordsys = `"CEL"`
	)

Elliptical Gaussian constructor.

Parameters

[in]	dir	Centre of elliptical Gaussian.
[in]	semimajor	Semi-major axis (degrees).
[in]	semiminor	Semi-minor axis (degrees).
[in]	posangle	Position angle of semi-major axis (degrees).
[in]	coordsys	Coordinate system (either "CEL" or "GAL")

Exceptions

GException::invalid_argument Invalid coordsys argument specified.

Construct elliptical Gaussian model from the ellipse centre direction (dir), the semimajor and semiminor axes, and the position angle (posangle). The coordsys parameter specifies whether the sky direction should be interpreted in the celestial or Galactic coordinate system.

Definition at line 129 of file GModelSpatialEllipticalGauss.cpp.

References GModelSpatialElliptical::dir(), G_CONSTRUCTOR, init_members(), GModelSpatialElliptical::m_lat, GModelSpatialElliptical::m_lon, GOptimizerPar::name(), GModelSpatialElliptical::posangle(), GModelSpatialElliptical::semimajor(), and GModelSpatialElliptical::semiminor().

GModelSpatialEllipticalGauss::GModelSpatialEllipticalGauss ( const GXmlElement & xml )

explicit

XML constructor.

Parameters

[in] xml XML element.

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

Definition at line 177 of file GModelSpatialEllipticalGauss.cpp.

References init_members(), and read().

GModelSpatialEllipticalGauss::GModelSpatialEllipticalGauss ( const GModelSpatialEllipticalGauss & model )

Copy constructor.

Parameters

[in] model Elliptical Gaussian model.

Definition at line 196 of file GModelSpatialEllipticalGauss.cpp.

References copy_members(), and init_members().

GModelSpatialEllipticalGauss::~GModelSpatialEllipticalGauss ( void )

virtual

Destructor.

Definition at line 213 of file GModelSpatialEllipticalGauss.cpp.

References free_members().

Member Function Documentation

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

inlinevirtual

Return class name.

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

Implements GModelSpatialElliptical.

Definition at line 127 of file GModelSpatialEllipticalGauss.hpp.

void GModelSpatialEllipticalGauss::clear ( void )

virtual

Clear elliptical Gaussian model.

Implements GModelSpatialElliptical.

Definition at line 268 of file GModelSpatialEllipticalGauss.cpp.

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

GModelSpatialEllipticalGauss * GModelSpatialEllipticalGauss::clone ( void ) const

virtual

Clone elliptical Gaussian model.

Returns: Pointer to deep copy of elliptical Gaussian model.

Implements GModelSpatialElliptical.

Definition at line 290 of file GModelSpatialEllipticalGauss.cpp.

References GModelSpatialEllipticalGauss().

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

virtual

Checks whether 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 elliptical gauss model.

Todo:: Implement correct evaluation of effective ellipse radius.

Implements GModelSpatialElliptical.

Definition at line 491 of file GModelSpatialEllipticalGauss.cpp.

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

void GModelSpatialEllipticalGauss::copy_members ( const GModelSpatialEllipticalGauss & model )

protected

Copy class members.

Parameters

[in] model Elliptical Gaussian model.

Definition at line 684 of file GModelSpatialEllipticalGauss.cpp.

References m_cospos2, m_last_major, m_last_minor, m_last_posangle, m_major2, m_major_rad, m_minor2, m_minor_rad, m_norm, m_sin2pos, m_sinpos2, m_term1, m_term2, m_term3, and GModelSpatial::m_type.

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

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

virtual

Evaluate function (in units of sr^-1)

Parameters

[in]	theta	Angular distance from disk centre (radians).
[in]	posangle	Position angle (counterclockwise from North) (radians).
[in]	energy	Photon energy.
[in]	time	Photon arrival time.
[in]	gradients	Compute gradients?

Returns: Model value.

Evaluates the spatial component for an elliptical Gaussian source model.

The elliptical Gaussian function is defined by \(S_{\rm p}(\theta, \phi | E, t)\), where \(\theta\) is the angular separation between elliptical Gaussian centre and the actual location and \(\phi\) the position angle with respect to the model centre, counted counterclockwise from North.

The function \(S_{\rm p}(\theta, \phi | E, t)\) is given by

\[ S_{\rm p}(\theta, \phi | E, t) = {\tt m\_norm} \times \exp \left( -\frac{\theta^2}{2 r_{\rm eff}^2} \right) \]

where the effective ellipse radius \(r_{\rm eff}\) towards a given position angle is given by

\[ r_{\rm eff} = \frac{ab} {\sqrt{\left( a \sin (\phi - \phi_0) \right)^2} + \sqrt{\left( b \cos (\phi - \phi_0) \right)^2}} \]

and \(a\) is the semi-major axis of the ellipse, \(b\) is the semi-minor axis, and \(\phi_0\) is the position angle of the ellipse, counted counterclockwise from North. \({\tt m\_norm}\) is a normalization constant given by

\[ {\tt m\_norm} = \frac{1}{2 \pi \times a \times b} \]

The method will not compute analytical parameter gradients, even if the gradients argument is set to true. Radial disk parameter gradients need to be computed numerically.

Warning: The above formula for an elliptical Gaussian are accurate for small angles, with semimajor and semiminor axes below a few degrees. This should be fine for most use cases, but you should be aware that the ellipse will get distorted for larger angles.; For numerical reasons the elliptical Gaussian will be truncated for \(\theta\) angles that correspond to 3.0 times the effective ellipse radius.

< small angle

Implements GModelSpatialElliptical.

Definition at line 356 of file GModelSpatialEllipticalGauss.cpp.

References cos(), gammalib::deg2rad, exp(), gammalib::is_infinite(), gammalib::is_notanumber(), m_major2, m_major_rad, m_minor2, m_minor_rad, m_norm, m_term1, m_term2, m_term3, GModelSpatialElliptical::posangle(), sin(), sqrt(), theta_max(), and update().

void GModelSpatialEllipticalGauss::free_members ( void )

protected

Delete class members.

Definition at line 713 of file GModelSpatialEllipticalGauss.cpp.

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

void GModelSpatialEllipticalGauss::init_members ( void )

protected

Initialise class members.

Definition at line 652 of file GModelSpatialEllipticalGauss.cpp.

References m_cospos2, m_last_major, m_last_minor, m_last_posangle, m_major2, m_major_rad, m_minor2, m_minor_rad, m_norm, m_sin2pos, m_sinpos2, m_term1, m_term2, m_term3, and GModelSpatial::m_type.

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

GSkyDir GModelSpatialEllipticalGauss::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 elliptical Gaussian model.

Warning: For numerical reasons the elliptical Gaussian will be truncated for \(\theta\) angles that correspond to 3.0 times the effective ellipse radius.

Implements GModelSpatialElliptical.

Definition at line 437 of file GModelSpatialEllipticalGauss.cpp.

References gammalib::atan2d(), GPhoton::dir(), GModelSpatialElliptical::dir(), GPhoton::energy(), GRan::normal(), GModelSpatialElliptical::posangle(), GSkyDir::rotate_deg(), GModelSpatialElliptical::semimajor(), GModelSpatialElliptical::semiminor(), sqrt(), GPhoton::time(), and update().

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

virtual

Assignment operator.

Parameters

[in] model Elliptical gauss model.

Returns: Elliptical Gaussian model.

Definition at line 235 of file GModelSpatialEllipticalGauss.cpp.

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

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

virtual

Print information.

Parameters

[in] chatter Chattiness.

Returns: String containing model information.

Implements GModelSpatialElliptical.

Definition at line 618 of file GModelSpatialEllipticalGauss.cpp.

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

void GModelSpatialEllipticalGauss::read ( const GXmlElement & xml )

virtual

Read model from XML element.

Parameters

[in] xml XML element.

Reads the elliptical gauss model information from an XML element. The XML element shall have either the format

<spatialModel type="EllipticalGaussian">
  <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="PA"          scale="1.0" value="45.0"    min="-360"  max="360" free="1"/>
  <parameter name="MinorRadius" scale="1.0" value="0.5"     min="0.001" max="10"  free="1"/>
  <parameter name="MajorRadius" scale="1.0" value="2.0"     min="0.001" max="10"  free="1"/>
</spatialModel>

or

<spatialModel type="EllipticalGaussian">
  <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="PA"          scale="1.0" value="45.0"    min="-360"  max="360" free="1"/>
  <parameter name="MinorRadius" scale="1.0" value="0.5"     min="0.001" max="10"  free="1"/>
  <parameter name="MajorRadius" scale="1.0" value="2.0"     min="0.001" max="10"  free="1"/>
</spatialModel>

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

Reimplemented from GModelSpatialElliptical.

Definition at line 553 of file GModelSpatialEllipticalGauss.cpp.

References G_READ, GModelSpatialElliptical::m_semimajor, GModelSpatialElliptical::m_semiminor, GOptimizerPar::name(), GModelSpatialElliptical::read(), GModelPar::read(), gammalib::xml_check_parnum(), and gammalib::xml_get_par().

Referenced by GModelSpatialEllipticalGauss().

void GModelSpatialEllipticalGauss::set_region ( void ) const

protectedvirtual

Set boundary sky region.

Implements GModelSpatialElliptical.

Definition at line 809 of file GModelSpatialEllipticalGauss.cpp.

References GModelSpatialElliptical::dir(), GModelSpatial::m_region, GModelSpatial::region(), GModelSpatialElliptical::semimajor(), and GModelSpatialElliptical::semiminor().

double GModelSpatialEllipticalGauss::theta_max ( void ) const

virtual

Return maximum model radius (in radians)

Returns: Returns maximum model radius.

Returns the maximum of 3.0 semimajor() and 3.0 semiminor() as approximate edge of the Gaussian. This limit is of course arbitrary, but allows to limit the integration region for response computation. The value of 3.0 has been determined by experiment (#1561).

Implements GModelSpatialElliptical.

Definition at line 512 of file GModelSpatialEllipticalGauss.cpp.

References gammalib::deg2rad, GModelSpatialElliptical::semimajor(), and GModelSpatialElliptical::semiminor().

Referenced by contains(), and eval().

void GModelSpatialEllipticalGauss::update ( void ) const

protected

Update precomputation cache.

Computes the normalization

\[ {\tt m\_norm} = \frac{1}{2 \pi \times a \times b} \]

where \(a\) is the semi-major axis and \(b\) is the semi-minor axis of the ellipse.

Warning: The normalization of the elliptical Gaussian is only valid in the small angle approximation.

Definition at line 735 of file GModelSpatialEllipticalGauss.cpp.

References cos(), gammalib::deg2rad, m_cospos2, m_last_major, m_last_minor, m_last_posangle, m_major2, m_major_rad, m_minor2, m_minor_rad, m_norm, m_sin2pos, m_sinpos2, m_term1, m_term2, m_term3, GModelSpatialElliptical::posangle(), GModelSpatialElliptical::semimajor(), GModelSpatialElliptical::semiminor(), sin(), and gammalib::twopi.

Referenced by eval(), and mc().

void GModelSpatialEllipticalGauss::write ( GXmlElement & xml ) const

virtual

Write model into XML element.

Parameters

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

Write the elliptical gauss model information into an XML element. The XML element will have the format

<spatialModel type="EllipticalGaussian">
  <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="PA"          scale="1.0" value="45.0"    min="-360"  max="360" free="1"/>
  <parameter name="MinorRadius" scale="1.0" value="0.5"     min="0.001" max="10"  free="1"/>
  <parameter name="MajorRadius" scale="1.0" value="2.0"     min="0.001" max="10"  free="1"/>
</spatialModel>

Reimplemented from GModelSpatialElliptical.

Definition at line 591 of file GModelSpatialEllipticalGauss.cpp.

References G_WRITE, GModelSpatialElliptical::m_semimajor, GModelSpatialElliptical::m_semiminor, GOptimizerPar::name(), GModelSpatial::type(), GModelSpatialElliptical::write(), GModelPar::write(), gammalib::xml_check_type(), and gammalib::xml_need_par().