Gaussian spectral model class. More...

#include <GModelSpectralGauss.hpp>

Inheritance diagram for GModelSpectralGauss:

Classes
class	eflux_kernel

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

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

	GModelSpectralGauss (const double &norm, const GEnergy &mean, const GEnergy &sigma)
	Constructor. More...

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

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

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

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

virtual GModelSpectralGauss *	clone (void) const
	Clone Gaussian spectral model. 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 GEnergy &srcEng, const GTime &srcTime=GTime(), const bool &gradients=false) const
	Evaluate model value. More...

virtual double	flux (const GEnergy &emin, const GEnergy &emax) const
	Returns model photon flux between emin, emax More...

virtual double	eflux (const GEnergy &emin, const GEnergy &emax) const
	Returns model energy flux between emin, emax More...

virtual GEnergy	mc (const GEnergy &emin, const GEnergy &emax, const GTime &time, GRan &ran) const
	Returns MC energy between [emin, emax]. 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 spectral model information. More...

double	norm (void) const
	Return normalization. More...

void	norm (const double &norm)
	Set normalization. More...

GEnergy	mean (void) const
	Return mean energy. More...

void	mean (const GEnergy &mean)
	Set mean energy. More...

GEnergy	sigma (void) const
	Return energy width. More...

void	sigma (const GEnergy &sigma)
	Set energy width. More...

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

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

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

virtual GModelSpectral &	operator= (const GModelSpectral &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...

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...

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

void	autoscale (void)
	Autoscale parameters. 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 GModelSpectralGauss &model)
	Copy class members. More...

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

void	update_eval_cache (const GEnergy &energy) const

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

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

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

Protected Attributes
GModelPar	m_norm
	Normalization factor. More...

GModelPar	m_mean
	Gaussian mean energy. More...

GModelPar	m_sigma
	Gaussian energy width. More...

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

Detailed Description

Gaussian spectral model class.

This class implements a Gaussian spectrum. The model is defined by

\[ S_{\rm E}(E | t) = \frac{\tt m\_norm}{\sqrt{2 \pi} m\_sigma^2} \exp \left(\frac{-(E - m\_mean)^2}{2 m_\sigma^2} \right) \]

where

\({\tt m\_norm}\) is the normalization,
\({\tt m\_mean}\) is the mean energy,
\({\tt m\_sigma}\) is the energy width.

Definition at line 61 of file GModelSpectralGauss.hpp.

Constructor & Destructor Documentation

GModelSpectralGauss::GModelSpectralGauss ( void )

Void constructor.

Definition at line 69 of file GModelSpectralGauss.cpp.

References init_members().

Referenced by clone().

GModelSpectralGauss::GModelSpectralGauss ( const GXmlElement & xml )

explicit

XML constructor.

Parameters

[in] xml XML element.

Constructs constant spectral 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 88 of file GModelSpectralGauss.cpp.

References init_members(), and read().

GModelSpectralGauss::GModelSpectralGauss	(	const double &	norm,
		const GEnergy &	mean,
		const GEnergy &	sigma
	)

Constructor.

Parameters

[in]	norm	Total flux under Gaussian (in ph/cm2/s).
[in]	mean	Mean energy.
[in]	sigma	Energy width.

Definition at line 109 of file GModelSpectralGauss.cpp.

References GModelSpectral::autoscale(), init_members(), m_mean, m_norm, m_sigma, GEnergy::MeV(), and GOptimizerPar::value().

GModelSpectralGauss::GModelSpectralGauss ( const GModelSpectralGauss & model )

Copy constructor.

Parameters

[in] model Spectral Gaussian model.

Definition at line 135 of file GModelSpectralGauss.cpp.

References copy_members(), and init_members().

GModelSpectralGauss::~GModelSpectralGauss ( void )

virtual

Destructor.

Definition at line 152 of file GModelSpectralGauss.cpp.

References free_members().

Member Function Documentation

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

inlinevirtual

Return class name.

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

Implements GModelSpectral.

Definition at line 140 of file GModelSpectralGauss.hpp.

void GModelSpectralGauss::clear ( void )

virtual

Clear Gaussian spectral model.

Implements GModelSpectral.

Definition at line 207 of file GModelSpectralGauss.cpp.

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

GModelSpectralGauss * GModelSpectralGauss::clone ( void ) const

virtual

Clone Gaussian spectral model.

Returns: Pointer to deep copy of Gaussian spectral model.

Implements GModelSpectral.

Definition at line 227 of file GModelSpectralGauss.cpp.

References GModelSpectralGauss().

void GModelSpectralGauss::copy_members ( const GModelSpectralGauss & model )

protected

Copy class members.

Parameters

[in] model Spectral constant model.

Definition at line 640 of file GModelSpectralGauss.cpp.

References m_mean, m_norm, GModelSpectral::m_pars, and m_sigma.

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

double GModelSpectralGauss::eflux	(	const GEnergy &	emin,
		const GEnergy &	emax
	)		const

virtual

Returns model energy flux between emin, emax

Parameters

[in]	emin	Minimum photon energy.
[in]	emax	Maximum photon energy.

Returns: Energy flux (erg/cm2/s).

Computes

\[ \int_{\tt emin}^{\tt emax} S_{\rm E}(E | t) E \, dE \]

where

[emin, emax] is an energy interval, and
\(S_{\rm E}(E | t)\) is the spectral model (ph/cm2/s/MeV). The integration is done analytically.

Implements GModelSpectral.

Definition at line 397 of file GModelSpectralGauss.cpp.

References m_mean, m_norm, m_sigma, GEnergy::MeV(), gammalib::MeV2erg, and GOptimizerPar::value().

double GModelSpectralGauss::eval	(	const GEnergy &	srcEng,
		const GTime &	srcTime = `GTime()`,
		const bool &	gradients = `false`
	)		const

virtual

Evaluate model value.

Parameters

[in]	srcEng	True photon energy.
[in]	srcTime	True photon arrival time.
[in]	gradients	Compute gradients?

Returns: Model value (ph/cm2/s/MeV).

Evaluates

\[ S_{\rm E}(E | t) = \frac{m\_norm}{\sqrt{2\pi}m\_sigma} \exp(\frac{-(E-m\_mean)^2}{2 m\_sigma^2}) \]

where

\({\tt m\_norm}\) is the normalization,
\({\tt m\_mean}\) is the mean energy, and
\({\tt m\_sigma}\) is the energy width.

If the gradients flag is true the method will also compute the partial derivatives of the model with respect to the parameters using

\[ \frac{\delta S_{\rm E}(E | t)}{\delta {\tt m\_norm}} = \frac{S_{\rm E}(E | t)}{{\tt m\_norm}} \]

\[ \frac{\delta S_{\rm E}(E | t)}{\delta {\tt m\_mean}} = S_{\rm E}(E | t) \frac{E-m\_mean}{m\_sigma^2} \]

\[ \frac{\delta S_{\rm E}(E | t)}{\delta {\tt m\_sigma}} = \frac{S_{\rm E}(E | t)}{{\tt m\_sigma}} \left( \frac{(E-m\_mean)^2}{m\_sigma^2} - 1 \right) \]

Implements GModelSpectral.

Definition at line 273 of file GModelSpectralGauss.cpp.

References exp(), GOptimizerPar::factor_gradient(), gammalib::inv_sqrt2pi, GOptimizerPar::is_free(), gammalib::is_infinite(), gammalib::is_notanumber(), m_mean, m_norm, m_sigma, mean(), GEnergy::MeV(), norm(), GOptimizerPar::scale(), sigma(), and GOptimizerPar::value().

double GModelSpectralGauss::flux	(	const GEnergy &	emin,
		const GEnergy &	emax
	)		const

virtual

Returns model photon flux between emin, emax

Parameters

[in]	emin	Minimum photon energy.
[in]	emax	Maximum photon energy.

Returns: Photon flux (ph/cm2/s).

Computes

\[ \int_{\tt emin}^{\tt emax} S_{\rm E}(E | t) dE \]

where

[emin, emax] is an energy interval, and
\(S_{\rm E}(E | t)\) is the spectral model (ph/cm2/s/MeV). The integration is done analytically.

Implements GModelSpectral.

Definition at line 351 of file GModelSpectralGauss.cpp.

References gammalib::gauss_integral(), m_mean, m_norm, m_sigma, mean(), GEnergy::MeV(), norm(), sigma(), and GOptimizerPar::value().

void GModelSpectralGauss::free_members ( void )

protected

Delete class members.

Definition at line 661 of file GModelSpectralGauss.cpp.

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

void GModelSpectralGauss::init_members ( void )

protected

Initialise class members.

Definition at line 589 of file GModelSpectralGauss.cpp.

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

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

GEnergy GModelSpectralGauss::mc	(	const GEnergy &	emin,
		const GEnergy &	emax,
		const GTime &	time,
		GRan &	ran
	)		const

virtual

Returns MC energy between [emin, emax].

Parameters

[in]	emin	Minimum photon energy.
[in]	emax	Maximum photon energy.
[in]	time	True photon arrival time.
[in,out]	ran	Random number generator.

Returns: Energy.

Exceptions

GException::erange_invalid Energy range is invalid (emin < emax required).

Returns Monte Carlo energy by randomly drawing from a constant between the minimum and maximum photon energy.

Method Used: Box-Muller transform, outlined here: http://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform

Code from: http://www.design.caltech.edu/erik/Misc/Gaussian.html

Implements GModelSpectral.

Definition at line 448 of file GModelSpectralGauss.cpp.

References gammalib::check_energy_interval(), G_MC, m_mean, m_sigma, GEnergy::MeV(), GRan::normal(), and GOptimizerPar::value().

GEnergy GModelSpectralGauss::mean ( void ) const

inline

Return mean energy.

Returns: Mean energy.

Definition at line 190 of file GModelSpectralGauss.hpp.

References m_mean, GEnergy::MeV(), and GOptimizerPar::value().

Referenced by GResponse::ebounds_model(), eval(), flux(), read(), and write().

void GModelSpectralGauss::mean ( const GEnergy & mean )

inline

Set mean energy.

Parameters

[in] mean Mean energy.

Definition at line 204 of file GModelSpectralGauss.hpp.

References m_mean, GEnergy::MeV(), and GOptimizerPar::value().

double GModelSpectralGauss::norm ( void ) const

inline

Return normalization.

Returns: Normalization (ph/cm2/s).

Definition at line 166 of file GModelSpectralGauss.hpp.

References m_norm, and GOptimizerPar::value().

Referenced by eval(), flux(), read(), and write().

void GModelSpectralGauss::norm ( const double & norm )

inline

Set normalization.

Parameters

[in] norm Normalization (ph/cm2/s).

Definition at line 178 of file GModelSpectralGauss.hpp.

References m_norm, and GOptimizerPar::value().

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

virtual

Assignment operator.

Parameters

[in] model Gauss spectral model.

Returns: Gauss spectral model.

Definition at line 174 of file GModelSpectralGauss.cpp.

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

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

virtual

Print spectral model information.

Parameters

[in] chatter Chattiness (defaults to NORMAL).

Returns: String containing spectral model information.

Implements GModelSpectral.

Definition at line 555 of file GModelSpectralGauss.cpp.

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

void GModelSpectralGauss::read ( const GXmlElement & xml )

virtual

Read model from XML element.

Parameters

[in] xml XML element containing Gaussian model information.

Read the spectral Gaussian information from an XML element. The format of the XML elements is:

<spectrum type="Gaussian">
  <parameter name="Normalization" scale=".." value=".." min=".." max=".." free=".."/>
  <parameter name="Mean"          scale=".." value=".." min=".." max=".." free=".."/>
  <parameter name="Sigma"         scale=".." value=".." min=".." max=".." free=".."/>
</spectrum>

Implements GModelSpectral.

Definition at line 495 of file GModelSpectralGauss.cpp.

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

Referenced by GModelSpectralGauss().

GEnergy GModelSpectralGauss::sigma ( void ) const

inline

Return energy width.

Returns: Energy width

Definition at line 216 of file GModelSpectralGauss.hpp.

References m_sigma, GEnergy::MeV(), and GOptimizerPar::value().

Referenced by GResponse::ebounds_model(), eval(), flux(), read(), and write().

void GModelSpectralGauss::sigma ( const GEnergy & sigma )

inline

Set energy width.

Parameters

[in] sigma Energy width.

Definition at line 230 of file GModelSpectralGauss.hpp.

References m_sigma, GEnergy::MeV(), and GOptimizerPar::value().

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

inlinevirtual

Return model type.

Returns: "ConstantValue".

Returns the type of the Gaussian spectral model.

Implements GModelSpectral.

Definition at line 154 of file GModelSpectralGauss.hpp.

Referenced by write().

void GModelSpectralGauss::update_eval_cache ( const GEnergy & energy ) const

protected

void GModelSpectralGauss::write ( GXmlElement & xml ) const

virtual

Write model into XML element.

Parameters

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

Writes the spectral information into an XML element. The format of the XML element is

<spectrum type="Gaussian">
  <parameter name="Normalization" scale=".." value=".." min=".." max=".." free=".."/>
  <parameter name="Mean"          scale=".." value=".." min=".." max=".." free=".."/>
  <parameter name="Sigma"         scale=".." value=".." min=".." max=".." free=".."/>
</spectrum>

Implements GModelSpectral.

Definition at line 529 of file GModelSpectralGauss.cpp.

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