Integration class for set of functions. More...

#include <GIntegrals.hpp>

Inheritance diagram for GIntegrals:

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

	GIntegrals (GFunctions *kernels)
	Vector function kernels constructor. More...

	GIntegrals (const GIntegrals &integral)
	Copy constructor. More...

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

GIntegrals &	operator= (const GIntegrals &integral)
	Assignment operator. More...

void	clear (void)
	Clear integral. More...

GIntegrals *	clone (void) const
	Clone integral. More...

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

void	max_iter (const int &iter)
	Set maximum number of iterations. More...

const int &	max_iter (void) const
	Return maximum number of iterations. More...

void	fixed_iter (const int &iter)
	Set fixed number of iterations. More...

const int &	fixed_iter (void) const
	Return fixed number of iterations. More...

void	eps (const double &eps)
	Set relative precision. More...

const double &	eps (void) const
	Get relative precision. More...

void	silent (const bool &silent)
	Set silence flag. More...

const bool &	silent (void) const
	Get silence flag. More...

const int &	iter (void) const
	Return number of iterations. More...

const int &	calls (void) const
	Get number of function calls. More...

const bool &	is_valid (void) const
	Signal if integration result is valid. More...

const std::string &	message (void) const
	Return integration status message. More...

void	kernels (GFunctions *kernels)
	Set function kernels. More...

const GFunctions *	kernels (void) const
	Get function kernels. More...

GVector	romberg (std::vector< double > bounds, const int &order=5)
	Perform Romberg integration. More...

GVector	romberg (const double &a, const double &b, const int &order=5)
	Perform Romberg integration. More...

GVector	trapzd (const double &a, const double &b, const int &n, const GVector &previous_result)
	Perform Trapezoidal integration for a set of functions. More...

std::string	print (const GChatter &chatter=NORMAL) const
	Print integral information. 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 GIntegrals &integral)
	Copy class members. More...

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

GVector	polint (const double xa, const GVector ya, const int &order, const double &x, GVector *dy)
	Perform Polynomial interpolation. More...

Protected Attributes
GFunctions *	m_kernels
	Pointer to function kernels. More...

double	m_eps
	Requested relative integration precision. More...

int	m_max_iter
	Maximum number of iterations. More...

int	m_fix_iter
	Fixed number of iterations. More...

bool	m_silent
	Suppress integration warnings in console. More...

int	m_iter
	Number of iterations used. More...

int	m_calls
	Number of function calls used. More...

bool	m_isvalid
	Integration result valid (true=yes) More...

bool	m_has_abserr
	Has absolute integration errors. More...

bool	m_has_relerr
	Has relative integration errors. More...

GVector	m_abserr
	Absolute integration errors. More...

GVector	m_relerr
	Absolute integration errors. More...

std::string	m_message
	Status message (if result is invalid) More...

Detailed Description

Integration class for set of functions.

This class allows to perform integration of a set of functions. The integrand is implemented by a derived class of GFunctions.

Definition at line 47 of file GIntegrals.hpp.

Constructor & Destructor Documentation

GIntegrals::GIntegrals ( void )

explicit

Void constructor.

Definition at line 62 of file GIntegrals.cpp.

References init_members().

Referenced by clone().

GIntegrals::GIntegrals ( GFunctions * kernels )

explicit

Vector function kernels constructor.

Parameters

[in] kernels Pointer to function kernels.

The vector function kernels constructor assigns the vector function kernels pointer in constructing the object.

Definition at line 80 of file GIntegrals.cpp.

References init_members(), kernels(), and m_kernels.

GIntegrals::GIntegrals ( const GIntegrals & integrals )

Copy constructor.

Parameters

[in] integrals Integrals.

Definition at line 98 of file GIntegrals.cpp.

References copy_members(), and init_members().

GIntegrals::~GIntegrals ( void )

virtual

Destructor.

Definition at line 114 of file GIntegrals.cpp.

References free_members().

Member Function Documentation

const int & GIntegrals::calls ( void ) const

inline

Get number of function calls.

Returns: Number of function calls.

Definition at line 229 of file GIntegrals.hpp.

References m_calls.

Referenced by print(), and romberg().

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

inlinevirtual

Return class name.

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

Implements GBase.

Definition at line 125 of file GIntegrals.hpp.

void GIntegrals::clear ( void )

virtual

Clear integral.

Implements GBase.

Definition at line 166 of file GIntegrals.cpp.

References free_members(), and init_members().

GIntegrals * GIntegrals::clone ( void ) const

virtual

Clone integral.

Returns: Pointer to deep copy of integrals.

Implements GBase.

Definition at line 184 of file GIntegrals.cpp.

References GIntegrals().

void GIntegrals::copy_members ( const GIntegrals & integral )

protected

Copy class members.

Parameters

[in] integral Integral.

Definition at line 670 of file GIntegrals.cpp.

References m_abserr, m_calls, m_eps, m_fix_iter, m_has_abserr, m_has_relerr, m_isvalid, m_iter, m_kernels, m_max_iter, m_message, m_relerr, and m_silent.

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

void GIntegrals::eps ( const double & eps )

inline

Set relative precision.

Parameters

[in] eps Relative precision.

Definition at line 204 of file GIntegrals.hpp.

References eps(), and m_eps.

const double & GIntegrals::eps ( void ) const

inline

Get relative precision.

Returns: Relative precision.

Definition at line 217 of file GIntegrals.hpp.

References m_eps.

Referenced by eps(), and print().

void GIntegrals::fixed_iter ( const int & iter )

inline

Set fixed number of iterations.

Parameters

[in] iter Fixed number of iterations.

If the fixed number of iterations is set, the integration algorithm will always performed the given number of iterations, irrespectively of the precision that is reached. This feature is relevant for computing numerical derivates from numerically integrated functions.

Definition at line 179 of file GIntegrals.hpp.

References iter(), and m_fix_iter.

Referenced by GResponse::convolve(), cta_psf_radial_kerns_delta::eval(), com_radial_kerns_rho::eval(), com_elliptical_kerns_rho::eval(), GCOMResponse::irf_elliptical(), GCOMResponse::irf_radial(), and GCTAResponseCube::psf_radial().

const int & GIntegrals::fixed_iter ( void ) const

inline

Return fixed number of iterations.

Returns: Fixed number of iterations.

Definition at line 192 of file GIntegrals.hpp.

References m_fix_iter.

Referenced by print().

void GIntegrals::free_members ( void )

protected

Delete class members.

Definition at line 697 of file GIntegrals.cpp.

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

void GIntegrals::init_members ( void )

protected

Initialise class members.

Definition at line 641 of file GIntegrals.cpp.

References GVector::clear(), m_abserr, m_calls, m_eps, m_fix_iter, m_has_abserr, m_has_relerr, m_isvalid, m_iter, m_kernels, m_max_iter, m_message, m_relerr, and m_silent.

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

const bool & GIntegrals::is_valid ( void ) const

inline

Signal if integration result is valid.

Returns: True is integration result is valid.

Definition at line 293 of file GIntegrals.hpp.

References m_isvalid.

Referenced by print().

const int & GIntegrals::iter ( void ) const

inline

Return number of iterations.

Returns: Number of iterations.

Definition at line 137 of file GIntegrals.hpp.

References m_iter.

Referenced by fixed_iter(), max_iter(), and print().

void GIntegrals::kernels ( GFunctions * kernels )

inline

Set function kernels.

Parameters

[in] kernels Function kernels.

Sets the function kernels for which the integral should be determined.

Definition at line 268 of file GIntegrals.hpp.

References kernels(), and m_kernels.

const GFunctions * GIntegrals::kernels ( void ) const

inline

Get function kernels.

Returns: Function kernels.

Definition at line 281 of file GIntegrals.hpp.

References m_kernels.

Referenced by GIntegrals(), and kernels().

void GIntegrals::max_iter ( const int & iter )

inline

Set maximum number of iterations.

Parameters

[in] iter Maximum number of iterations.

Definition at line 149 of file GIntegrals.hpp.

References iter(), and m_max_iter.

const int & GIntegrals::max_iter ( void ) const

inline

Return maximum number of iterations.

Returns: Maximum number of iterations.

Definition at line 162 of file GIntegrals.hpp.

References m_max_iter.

Referenced by print(), and romberg().

const std::string & GIntegrals::message ( void ) const

inline

Return integration status message.

Returns: Integration status message.

Definition at line 305 of file GIntegrals.hpp.

References m_message.

Referenced by print().

GIntegrals & GIntegrals::operator= ( const GIntegrals & integrals )

Assignment operator.

Parameters

[in] integrals Integrals.

Returns: Integrals.

Definition at line 136 of file GIntegrals.cpp.

References copy_members(), free_members(), and init_members().

GVector GIntegrals::polint	(	const double *	xa,
		const GVector *	ya,
		const int &	order,
		const double &	x,
		GVector *	dy
	)

protected

Perform Polynomial interpolation.

Parameters

[in]	xa	Pointer to array of X values.
[in]	ya	Pointer to GVector of Y values.
[in]	order	Number of elements in arrays.
[in]	x	X value for which interpolations should be performed.
[out]	dy	Pointer to vector of error estimates for interpolated values.

Returns: Vector of interpolated values.

Given arrays xa[1,..,n] and ya[1,..,n], and given a value x, this method returns a value y, and an error estimate dy. If P(x) is the polynomial of degree n-1, then the returned value y=P(x).

Definition at line 718 of file GIntegrals.cpp.

References abs(), G_POLINT, m_isvalid, m_message, m_silent, GVector::size(), gammalib::str(), and gammalib::warning().

Referenced by romberg().

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

virtual

Print integral information.

Parameters

[in] chatter Chattiness.

Returns: String containing integral information.

Implements GBase.

Definition at line 572 of file GIntegrals.cpp.

References calls(), eps(), fixed_iter(), is_valid(), iter(), m_abserr, m_fix_iter, m_has_abserr, m_has_relerr, m_relerr, max_iter(), message(), gammalib::parformat(), GVector::print(), SILENT, silent(), and gammalib::str().

Referenced by romberg().

GVector GIntegrals::romberg	(	std::vector< double >	bounds,
		const int &	order = `5`
	)

Perform Romberg integration.

Parameters

[in]	bounds	Integration boundaries.
[in]	order	Integration order (default: 5)

Returns: Vector of integration results.

Returns the integral of the integrand, computed over a number of intervals [a0,a1], [a1,a2], ... that are given as an unordered vector by the bounds argument.

Integration is performed by Romberg's method of order 2*order, where

order=1 is equivalent to the trapezoidal rule,
order=2 is equivalent to Simpson's rule, and
order=3 is equivalent to Boole's rule.

The number of iterations is limited by m_max_iter. m_eps specifies the requested fractional accuracy. By default it is set to 1e-6.

Definition at line 210 of file GIntegrals.cpp.

References calls(), G_ROMBERG1, m_calls, m_kernels, and GFunctions::size().

Referenced by GResponse::convolve(), cta_psf_radial_kerns_delta::eval(), com_radial_kerns_rho::eval(), com_elliptical_kerns_rho::eval(), GCOMResponse::irf_elliptical(), GCOMResponse::irf_radial(), and GCTAResponseCube::psf_radial().

GVector GIntegrals::romberg	(	const double &	a,
		const double &	b,
		const int &	order = `5`
	)

Perform Romberg integration.

Parameters

[in]	a	Left integration boundary.
[in]	b	Right integration boundary.
[in]	order	Integration order (default: 5)

Returns: Vector of integration results.

Exceptions

GException::invalid_value	Function kernels not set.
GException::invalid_argument	Integration order incompatible with number of iterations.

Returns the integral of the integrand from a to b. Integration is performed by Romberg's method of order 2*order, where

order=1 is equivalent to the trapezoidal rule,
order=2 is equivalent to Simpson's rule, and
order=3 is equivalent to Boole's rule.

The number of iterations is limited by m_max_iter. m_eps specifies the requested fractional accuracy. By default it is set to 1e-6.

Definition at line 265 of file GIntegrals.cpp.

References abs(), G_ROMBERG2, gammalib::is_infinite(), gammalib::is_notanumber(), m_abserr, m_calls, m_eps, m_fix_iter, m_has_abserr, m_has_relerr, m_isvalid, m_iter, m_kernels, m_max_iter, m_message, m_relerr, m_silent, max_iter(), polint(), print(), GVector::print(), GFunctions::size(), gammalib::str(), trapzd(), and gammalib::warning().

void GIntegrals::silent ( const bool & silent )

inline

Set silence flag.

Parameters

[in] silent Silence flag.

Definition at line 241 of file GIntegrals.hpp.

References m_silent, and silent().

const bool & GIntegrals::silent ( void ) const

inline

Get silence flag.

Returns: True is class is silent, false otherwise.

Definition at line 254 of file GIntegrals.hpp.

References m_silent.

Referenced by print(), and silent().

GVector GIntegrals::trapzd	(	const double &	a,
		const double &	b,
		const int &	n,
		const GVector &	previous_result
	)

Perform Trapezoidal integration for a set of functions.

Parameters

[in]	a	Left integration boundary.
[in]	b	Right integration boundary.
[in]	n	Number of steps.
[in]	previous_result	Result vector from a previous trapezoidal integration step.

Returns: Vector of integration results.

Exceptions

GException::invalid_value Function kernels not set.

The method performs a trapezoidal integration of a set of functions for the integration interval [a,b].

If n = 1 the integral for each function \(j\) is computed using

\[ \int_a^b f_j(x) \, dx = \frac{1}{2} (b-a) (f_j(a) + f_j(b)) \]

For n > 1 the integral is computed using

\[ \int_a^b f_j(x) \, dx = \frac{1}{2} \left[{\tt previous\_result}_j + \frac{b-a}{2^{n-1}} \sum_{i=0}^{2^{n-1}-1} f_j \left( a + (0.5+i) \frac{b-a}{2^{n-1}} \right) \right] \]

where \({\tt previous\_result}_j\) is the integration result for function \(j\) from a previous call to the method with n = n - 1.

Definition at line 450 of file GIntegrals.cpp.

References GFunctions::eval(), G_TRAPZD, m_calls, m_isvalid, m_kernels, m_message, m_silent, GVector::print(), GVector::size(), gammalib::str(), and gammalib::warning().