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

#include <GCTAResponse_helpers.hpp>

Inheritance diagram for cta_nroi_elliptical_kern_rho:

Public Member Functions
	cta_nroi_elliptical_kern_rho (const GCTAResponseIrf rsp, const GCTAObservation obs, const GModelSpatialElliptical model, const GMatrix rot, const double &semimajor, const double &semiminor, const double &posangle, const GEnergy &srcEng, const GTime &srcTime, const GEnergy &obsEng, const GTime &obsTime, const double &rho_roi, const double &posangle_roi, const double &radius_roi, const int &iter)

double	eval (const double &rho)
	Kernel for zenith angle Nroi integration of elliptical model. 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...

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

const GCTAObservation *	m_obs
	CTA observation. More...

const GModelSpatialElliptical *	m_model
	Elliptical model. More...

const GMatrix *	m_rot
	Rotation matrix. 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...

GEnergy	m_srcEng
	True photon energy. More...

GTime	m_srcTime
	True photon arrival time. More...

GEnergy	m_obsEng
	Observed photon energy. More...

GTime	m_obsTime
	Observed photon arrival time. More...

double	m_rho_roi
	Distance between model and ROI centre. More...

double	m_cos_rho_roi
	Cosine of m_rho_roi. More...

double	m_sin_rho_roi
	Sine of m_rho_roi. More...

double	m_posangle_roi
	Position angle of ROI. More...

double	m_radius_roi
	ROI+PSF radius. More...

double	m_cos_radius_roi
	Cosine of m_radius_roi. 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 zenith angle Nroi integration of elliptical model.

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 elliptical models. The eval() method computes

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

where

\(S_{\rm p}(\rho,\omega | E, t)\) is the elliptical model,
\(N_{\rm pred}(\rho,\omega)\) is the data space integral of the Instrument Response Function for a point spread function over the Region Of Interest,
\(\rho\) 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.

Definition at line 621 of file GCTAResponse_helpers.hpp.

Constructor & Destructor Documentation

cta_nroi_elliptical_kern_rho::cta_nroi_elliptical_kern_rho	(	const GCTAResponseIrf *	rsp,
		const GCTAObservation *	obs,
		const GModelSpatialElliptical *	model,
		const GMatrix *	rot,
		const double &	semimajor,
		const double &	semiminor,
		const double &	posangle,
		const GEnergy &	srcEng,
		const GTime &	srcTime,
		const GEnergy &	obsEng,
		const GTime &	obsTime,
		const double &	rho_roi,
		const double &	posangle_roi,
		const double &	radius_roi,
		const int &	iter
	)

inline

Definition at line 623 of file GCTAResponse_helpers.hpp.

Member Function Documentation

double cta_nroi_elliptical_kern_rho::eval ( const double & rho )

virtual

Kernel for zenith angle Nroi integration of elliptical model.

Parameters

[in] rho Elliptical model offset angle (radians).

Computes

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

where \(\omega\) is the azimuth angle with respect to the model centre, counted counterclockwise from the vector connecting the model centre to the ROI centre, 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, \(N_{\rm pred}(\rho,\omega)\) is the data space integral over the response function.

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

Implements GFunction.

Definition at line 1018 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_cos_radius_roi, m_cos_rho_roi, m_iter, m_model, m_obs, m_obsEng, m_obsTime, m_posangle, m_posangle_roi, m_radius_roi, m_rho_roi, m_rot, m_rsp, m_semimajor, m_semiminor, m_sin_rho_roi, m_srcEng, m_srcTime, max(), min(), gammalib::pi, gammalib::roi_arclength(), GIntegral::romberg(), sin(), and sqrt().

Member Data Documentation

double cta_nroi_elliptical_kern_rho::m_cos_radius_roi

protected

Cosine of m_radius_roi.

Definition at line 674 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_cos_rho_roi

protected

Cosine of m_rho_roi.

Definition at line 670 of file GCTAResponse_helpers.hpp.

Referenced by eval().

int cta_nroi_elliptical_kern_rho::m_iter

protected

Integration iterations.

Definition at line 675 of file GCTAResponse_helpers.hpp.

Referenced by eval().

const GModelSpatialElliptical* cta_nroi_elliptical_kern_rho::m_model

protected

Elliptical model.

Definition at line 660 of file GCTAResponse_helpers.hpp.

Referenced by eval().

const GCTAObservation* cta_nroi_elliptical_kern_rho::m_obs

protected

CTA observation.

Definition at line 659 of file GCTAResponse_helpers.hpp.

Referenced by eval().

GEnergy cta_nroi_elliptical_kern_rho::m_obsEng

protected

Observed photon energy.

Definition at line 667 of file GCTAResponse_helpers.hpp.

Referenced by eval().

GTime cta_nroi_elliptical_kern_rho::m_obsTime

protected

Observed photon arrival time.

Definition at line 668 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_posangle

protected

Ellipse boundary position angle.

Definition at line 664 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_posangle_roi

protected

Position angle of ROI.

Definition at line 672 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_radius_roi

protected

ROI+PSF radius.

Definition at line 673 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_rho_roi

protected

Distance between model and ROI centre.

Definition at line 669 of file GCTAResponse_helpers.hpp.

Referenced by eval().

const GMatrix* cta_nroi_elliptical_kern_rho::m_rot

protected

Rotation matrix.

Definition at line 661 of file GCTAResponse_helpers.hpp.

Referenced by eval().

const GCTAResponseIrf* cta_nroi_elliptical_kern_rho::m_rsp

protected

CTA response.

Definition at line 658 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_semimajor

protected

Ellipse boundary semimajor axis.

Definition at line 662 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_semiminor

protected

Ellipse boundary semiminor axis.

Definition at line 663 of file GCTAResponse_helpers.hpp.

Referenced by eval().

double cta_nroi_elliptical_kern_rho::m_sin_rho_roi

protected

Sine of m_rho_roi.

Definition at line 671 of file GCTAResponse_helpers.hpp.

Referenced by eval().

GEnergy cta_nroi_elliptical_kern_rho::m_srcEng

protected

True photon energy.

Definition at line 665 of file GCTAResponse_helpers.hpp.

Referenced by eval().

GTime cta_nroi_elliptical_kern_rho::m_srcTime

protected

True photon arrival time.

Definition at line 666 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

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation