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GModelSpatialRadialGauss Class Reference

Radial Gaussian model class. More...

#include <GModelSpatialRadialGauss.hpp>

Inheritance diagram for GModelSpatialRadialGauss:
GModelSpatialRadial GModelSpatial GBase

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 GModelSpatialRadialGaussoperator= (const GModelSpatialRadialGauss &model)
 Assignment operator. More...
 
virtual void clear (void)
 Clear radial Gauss model. More...
 
virtual GModelSpatialRadialGaussclone (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 GModelSpatialRadialoperator= (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 GSkyDirdir (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 GModelSpatialoperator= (const GModelSpatial &model)
 Assignment operator. More...
 
virtual GModelParoperator[] (const int &index)
 Returns model parameter. More...
 
virtual const GModelParoperator[] (const int &index) const
 Returns model parameter (const version) More...
 
virtual GModelParoperator[] (const std::string &name)
 Returns model parameter. More...
 
virtual const GModelParoperator[] (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 integrated in circular sky region. More...
 
std::string type (void) const
 Return model type. More...
 
void type (const std::string &type)
 Set model type. More...
 
GModelParat (const int &index)
 Returns model parameter. More...
 
const GModelParat (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 GSkyRegionregion (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]dummyDummy flag.
[in]typeModel 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]dirSky position of Gaussian.
[in]sigmaWidth of Gaussian (in degrees).
[in]coordsysCoordinate system (either "CEL" or "GAL")
Exceptions
GException::invalid_argumentInvalid 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]xmlXML 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]modelRadial 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
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]dirSky direction.
[in]marginMargin 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]modelGaussian 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]thetaAngular distance from Gaussian centre (radians).
[in]energyPhoton energy (not used).
[in]timePhoton arrival time (not used).
[in]gradientsCompute 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().

GSkyDir GModelSpatialRadialGauss::mc ( const GEnergy energy,
const GTime time,
GRan ran 
) const
virtual

Returns MC sky direction.

Parameters
[in]energyPhoton energy.
[in]timePhoton arrival time.
[in,out]ranRandom 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]modelRadial 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]chatterChattiness.
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]xmlXML 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
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]sigmaGaussian 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]gradientsGradient 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]xmlXML 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().

Member Data Documentation

double GModelSpatialRadialGauss::m_g_sigma_norm
mutableprotected

sigma(rad)^-1 sigma_scale deg2rad

Definition at line 107 of file GModelSpatialRadialGauss.hpp.

Referenced by copy_members(), eval(), init_members(), and update().

double GModelSpatialRadialGauss::m_g_theta_norm
mutableprotected

sigma(rad)^-2 deg2rad

Definition at line 106 of file GModelSpatialRadialGauss.hpp.

Referenced by copy_members(), eval(), init_members(), and update().

double GModelSpatialRadialGauss::m_inv_sigma2_rad
mutableprotected

sigma(rad)^-2

Definition at line 104 of file GModelSpatialRadialGauss.hpp.

Referenced by copy_members(), eval(), init_members(), and update().

double GModelSpatialRadialGauss::m_last_sigma
mutableprotected

Last Gaussian sigma.

Definition at line 103 of file GModelSpatialRadialGauss.hpp.

Referenced by copy_members(), init_members(), and update().

GModelPar GModelSpatialRadialGauss::m_sigma
protected

Gaussian width (deg)

Definition at line 100 of file GModelSpatialRadialGauss.hpp.

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

double GModelSpatialRadialGauss::m_value_norm
mutableprotected

(2pi sigma(rad))^-2

Definition at line 105 of file GModelSpatialRadialGauss.hpp.

Referenced by copy_members(), eval(), init_members(), and update().


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