Kernel for elliptical model zenith angle integration of IRF. More...

#include <GCTAResponse_helpers.hpp>

Inheritance diagram for cta_irf_elliptical_kern_rho:

Public Member Functions
	cta_irf_elliptical_kern_rho (const GCTAResponseIrf rsp, const GModelSpatialElliptical model, const double &semimajor, const double &semiminor, const double &posangle, const double &zenith, const double &azimuth, const GEnergy &srcEng, const GTime &srcTime, const GEnergy &obsEng, const double &rho_obs, const double &posangle_obs, const double &rho_pnt, const double &omega_pnt, const double &delta_max, const int &iter)

double	eval (const double &rho)
	Kernel for elliptical model integration over model's zenith angle. More...

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

	GFunction (const GFunction &function)
	Copy constructor. More...

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

GFunction &	operator= (const GFunction &function)
	Assignment operator. More...

Public Attributes
const GCTAResponseIrf *	m_rsp
	CTA response. More...

const GModelSpatialElliptical *	m_model
	Elliptical model. More...

double	m_semimajor
	Ellipse boundary semimajor axis. More...

double	m_semiminor
	Ellipse boundary semiminor axis. More...

double	m_posangle
	Ellipse boundary position angle. More...

double	m_zenith
	Zenith angle. More...

double	m_azimuth
	Azimuth angle. More...

GEnergy	m_srcEng
	True photon energy. More...

GTime	m_srcTime
	True photon time. More...

GEnergy	m_obsEng
	Measured event energy. More...

double	m_rho_obs
	Distance of model centre from measured photon. More...

double	m_cos_rho_obs
	Cosine of m_rho_obs. More...

double	m_sin_rho_obs
	Sine of m_rho_obs. More...

double	m_posangle_obs
	Photon position angle measured from model centre. More...

double	m_rho_pnt
	Distance of model centre from pointing. More...

double	m_cos_rho_pnt
	Cosine of m_rho_pnt. More...

double	m_sin_rho_pnt
	Sine of m_rho_pnt. More...

double	m_omega_pnt
	Azimuth of pointing in model system. More...

double	m_delta_max
	Maximum PSF radius. More...

double	m_cos_delta_max
	Cosine of maximum PSF radius. More...

int	m_iter
	Integration iterations. More...

Additional Inherited Members
Protected Member Functions inherited from GFunction
void	init_members (void)
	Initialise class members. More...

void	copy_members (const GFunction &function)
	Copy class members. More...

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

Detailed Description

Kernel for elliptical model zenith angle integration of IRF.

Kernel for elliptical model zenith angle integration.

This class implements the integration kernel \(K(\rho)\) for the integration

\[ \int_{\rho_{\rm min}}^{\rho_{\rm max}} K(\rho | E, t) d\rho \]

of elliptical spatial models. The eval() method computes

\[ K(\rho | E, t) = \sin \rho \times \int_{\omega_{\rm min}}^{\omega_{\rm max}} S_{\rm p}(\rho, \omega | E, t) \, IRF(\rho, \omega) d\omega \]

where

\(S_{\rm p}(\rho, \omega | E, t)\) is the elliptical model,
\(IRF(\rho, \omega)\) is the IRF
\(\rho\) is the distance from the model centre, and
\(\omega\) is the azimuth angle is the position angle with respect to the connecting line between the model centre and the observed photon arrival direction.

This class implements the integration kernel \(K(\rho)\) for the integration

\[ \int_{\rho_{\rm min}}^{\rho_{\rm max}} K(\rho | E, t) d\rho \]

of elliptical spatial models. The eval() method computes

\[ K(\rho | E, t) = \sin \rho \times \int_{\omega} S_{\rm p}(\rho, \omega | E, t) \, PSF(\rho, \omega) d\omega \]

where \(S_{\rm p}(\rho, \omega | E, t)\) is the elliptical model, \(PSF(\rho, \omega)\) is the point spread function, \(\rho\) is the distance from the model centre, and \(\omega\) is the position angle with respect to the connecting line between the model centre and the observed photon arrival direction.

Definition at line 457 of file GCTAResponse_helpers.hpp.

Constructor & Destructor Documentation

cta_irf_elliptical_kern_rho::cta_irf_elliptical_kern_rho	(	const GCTAResponseIrf *	rsp,
		const GModelSpatialElliptical *	model,
		const double &	semimajor,
		const double &	semiminor,
		const double &	posangle,
		const double &	zenith,
		const double &	azimuth,
		const GEnergy &	srcEng,
		const GTime &	srcTime,
		const GEnergy &	obsEng,
		const double &	rho_obs,
		const double &	posangle_obs,
		const double &	rho_pnt,
		const double &	omega_pnt,
		const double &	delta_max,
		const int &	iter
	)

inline

Definition at line 459 of file GCTAResponse_helpers.hpp.

Member Function Documentation

double cta_irf_elliptical_kern_rho::eval ( const double & rho )

virtual

Kernel for elliptical model integration over model's zenith angle.

Parameters

[in] rho Radial distance from model centre [radians].

Returns: Radial IRF integration kernel.

Computes

\[ K(\rho | E, t) = \sin \rho \times \int_{\omega_{\rm min}}^{\omega_{\rm max}} S_{\rm p}(\rho, \omega | E, t) \, IRF(\rho, \omega) d\omega \]

where \(\omega\) is the azimuth angle with respect to the model centre, counted counterclockwise from the vector connecting the model centre to the observed photon direction, and \(\rho\) is the radial distance from the model centre. \(S_{\rm p}(\rho, \omega | E, t)\) is the elliptical source model for a given true photon energy and photon arrival time, \(IRF(\rho, \omega)\) is the instrument response function.

The method performs the required coordinate transformations from the model system, spanned by \((\rho, \omega)\), to the system needed for IRF computations. Furthermore, the method limits the integration range to area where the ellipse intersects the IRF.

Implements GFunction.

Definition at line 710 of file GCTAResponse_helpers.cpp.

References gammalib::acos(), cos(), GIntegral::fixed_iter(), g_ellipse_kludge_radius, gammalib::is_infinite(), gammalib::is_notanumber(), gammalib::limit_omega(), m_azimuth, m_cos_delta_max, m_cos_rho_obs, m_cos_rho_pnt, m_delta_max, m_iter, m_model, m_obsEng, m_omega_pnt, m_posangle, m_posangle_obs, m_rho_obs, m_rsp, m_semimajor, m_semiminor, m_sin_rho_obs, m_sin_rho_pnt, m_srcEng, m_srcTime, m_zenith, max(), min(), gammalib::pi, gammalib::roi_arclength(), GIntegral::romberg(), sin(), and sqrt().

Member Data Documentation

double cta_irf_elliptical_kern_rho::m_azimuth

Azimuth angle.

Definition at line 504 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_cos_delta_max

Cosine of maximum PSF radius.

Definition at line 517 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_cos_rho_obs

Cosine of m_rho_obs.

Definition at line 509 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_cos_rho_pnt

Cosine of m_rho_pnt.

Definition at line 513 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_delta_max

Maximum PSF radius.

Definition at line 516 of file GCTAResponse_helpers.hpp.

Referenced by eval().

int cta_irf_elliptical_kern_rho::m_iter

Integration iterations.

Definition at line 518 of file GCTAResponse_helpers.hpp.

Referenced by eval().

const GModelSpatialElliptical* cta_irf_elliptical_kern_rho::m_model

Elliptical model.

Definition at line 499 of file GCTAResponse_helpers.hpp.

Referenced by eval().

GEnergy cta_irf_elliptical_kern_rho::m_obsEng

Measured event energy.

Definition at line 507 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_omega_pnt

Azimuth of pointing in model system.

Definition at line 515 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_posangle

Ellipse boundary position angle.

Definition at line 502 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_posangle_obs

Photon position angle measured from model centre.

Definition at line 511 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_rho_obs

Distance of model centre from measured photon.

Definition at line 508 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_rho_pnt

Distance of model centre from pointing.

Definition at line 512 of file GCTAResponse_helpers.hpp.

const GCTAResponseIrf* cta_irf_elliptical_kern_rho::m_rsp

CTA response.

Definition at line 498 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_semimajor

Ellipse boundary semimajor axis.

Definition at line 500 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_semiminor

Ellipse boundary semiminor axis.

Definition at line 501 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_sin_rho_obs

Sine of m_rho_obs.

Definition at line 510 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_sin_rho_pnt

Sine of m_rho_pnt.

Definition at line 514 of file GCTAResponse_helpers.hpp.

Referenced by eval().

GEnergy cta_irf_elliptical_kern_rho::m_srcEng

True photon energy.

Definition at line 505 of file GCTAResponse_helpers.hpp.

Referenced by eval().

GTime cta_irf_elliptical_kern_rho::m_srcTime

True photon time.

Definition at line 506 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_irf_elliptical_kern_rho::m_zenith

Zenith angle.

Definition at line 503 of file GCTAResponse_helpers.hpp.

Referenced by eval().

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

inst/cta/src/GCTAResponse_helpers.hpp
inst/cta/src/GCTAResponse_helpers.cpp

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation