Class for integration of functions with one independent parameter. More...

#include "utl/Integrator.h"

Inheritance diagram for utl::Integrator< Functor >:

Public Member Functions
double	GetIntegral (const double a, const double b) const
	call this method when you do not care about the specific implementation More...

double	GetRombergIntegral (const double a, const double b, const int order=5, const int maxIterations=20) const
	Romberg integration Setting order to 2 is equivalent to the Simpson's method. More...

double	GetSimpsonIntegral (const double a, const double b, const int minLevel=4, const int maxLevel=20) const
	Simpson improvement build on top of the trapezoidal integration. More...

double	GetTrapezoidalIntegral (const double a, const double b, const int minLevel=4, const int maxLevel=20) const
	basic trapezoidal integration More...

	Integrator (Functor &functor, const double accuracy=1e-5)

void	SetAccuracy (const double accuracy)
	final accuracy goal of the integration More...

Private Member Functions
	for (int i=0;i< n;++i)

double	GetTrapezoidalAverage (const double previousApproximation, const double a, const double delta, const int level) const
	Calculates succsessive approximations to the function average. More...

Private Attributes
double	const
	average of a function represented with equidistant boxes More...

double	fAccuracy

Functor &	fFunctor

return sum	n

Detailed Description

template<class Functor>
class utl::Integrator< Functor >

Class for integration of functions with one independent parameter.

Author: Darko Veberic

Date: 15 Mar 2007

Example of usage:

// define function through the functor class
class SinFunctor {
public:
  SinFunctor(const double frequency, const double amplitude)
    : fFrequency(frequency), fAmplitude(amplitude) { }
  double operator()(const double x) const
  { return fAmplitude * sin(fFrequency * x); }
private:
  const double fFrequency;
  const double fAmplitude;
};
...
// one time integration
SinFunctor sinf(3.1415, 2);
const double intSin =  MakeIntegrator(sinf).GetIntegral(0, 1);
...
// repeated use of the integrator
double result = 0;
SinFunctor sinf(3.1415, 10);
const utl::Integrator<SinFunctor> integrator(sinf);
for (double d = 0; d < 100; d += 3)
  result += integrator.GetIntegral(d, d+3);
...
// use lambda to hide parameters
const double frequency = 3.1415;
const double amplitude = 10;
auto sinf = [&frequency, &amplitude](const double x) { return amplitude * sin(frequency * x); }
const double res = MakeIntegrator(sinf).GetIntegral(1, 2);

Simple functions that do not need initialization or additional parameters can be used directly (without the functor):

double MyLog(const double x) { return std::log(x); }
const double res = MakeIntegrator(MyLog).GetIntegral(1, 2);

Note that some built-in function do not have a static binding (like log(), exp() etc) and have to be wrapped in functor or function.

Definition at line 72 of file Integrator.h.

Constructor & Destructor Documentation

template<class Functor>

utl::Integrator< Functor >::Integrator	(	Functor &	functor,
		const double	accuracy = `1e-5`
	)

inline

Definition at line 75 of file Integrator.h.

Member Function Documentation

template<class Functor>

utl::Integrator< Functor >::for ( )

inlineprivate

Definition at line 219 of file Integrator.h.

template<class Functor>

double utl::Integrator< Functor >::GetIntegral	(	const double	a,
		const double	b
	)		const

inline

call this method when you do not care about the specific implementation

Definition at line 82 of file Integrator.h.

template<class Functor>

double utl::Integrator< Functor >::GetRombergIntegral	(	const double	a,
		const double	b,
		const int	order = `5`,
		const int	maxIterations = `20`
	)		const

inline

Romberg integration Setting order to 2 is equivalent to the Simpson's method.

Definition at line 89 of file Integrator.h.

Referenced by utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetIntegral(), IntegratorTest::testSpeed(), atm::Arbeletche2021CherenkovAngularModel::UnnormalizedIntegralRight(), and atm::Arbeletche2021CherenkovAngularModel::UnnormalizedIntegralSineRight().

template<class Functor>

double utl::Integrator< Functor >::GetSimpsonIntegral	(	const double	a,
		const double	b,
		const int	minLevel = `4`,
		const int	maxLevel = `20`
	)		const

inline

Simpson improvement build on top of the trapezoidal integration.

Definition at line 124 of file Integrator.h.

Referenced by IntegratorTest::testSpeed().

template<class Functor>

double utl::Integrator< Functor >::GetTrapezoidalAverage	(	const double	previousApproximation,
		const double	a,
		const double	delta,
		const int	level
	)		const

inlineprivate

Calculates succsessive approximations to the function average.

Parameters

previousApproximation,:	result of the level-1 call
a,:	start of the integration interval
delta,:	width of the integration interval (b - a)
level,:	should be greater or equal to 1 (see point scheme below)

The evaluation points are generated according to the following scheme:

                   interval
level  a                               b    n
  0    x                               x    2  <-- done by GetBoxAverage()
  1    |               x               |    1
  2    |       x               x       |    2
  3    |   x       x       x       x   |    4
  4    | x   x   x   x   x   x   x   x |    8
  5    |x x x x x x x x x x x x x x x x|   16
x = function evaluation

Definition at line 203 of file Integrator.h.

Referenced by utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetRombergIntegral(), utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetSimpsonIntegral(), and utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetTrapezoidalIntegral().

template<class Functor>

double utl::Integrator< Functor >::GetTrapezoidalIntegral	(	const double	a,
		const double	b,
		const int	minLevel = `4`,
		const int	maxLevel = `20`
	)		const

inline

basic trapezoidal integration

Definition at line 155 of file Integrator.h.

Referenced by IntegratorTest::testSpeed().

template<class Functor>

void utl::Integrator< Functor >::SetAccuracy ( const double accuracy )

inline

final accuracy goal of the integration

Definition at line 79 of file Integrator.h.

Member Data Documentation

template<class Functor>

double utl::Integrator< Functor >::const

private

Initial value:

{

double sum = 0

average of a function represented with equidistant boxes

Definition at line 217 of file Integrator.h.

template<class Functor>

double utl::Integrator< Functor >::fAccuracy

private

Definition at line 227 of file Integrator.h.

Referenced by utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetRombergIntegral(), utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetSimpsonIntegral(), utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetTrapezoidalIntegral(), and utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::SetAccuracy().

template<class Functor>

Functor& utl::Integrator< Functor >::fFunctor

private

Definition at line 226 of file Integrator.h.

Referenced by utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::for().

template<class Functor>

return sum utl::Integrator< Functor >::n

private

Definition at line 223 of file Integrator.h.

Referenced by utl::Integrator< utl::MuonArrivalTime::TimePDFArg >::GetTrapezoidalAverage().

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

Integrator.h

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<class Functor> class utl::Integrator< Functor >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Functor>
class utl::Integrator< Functor >