Double precision Romberg integration solver (Template class represents class whose method is to be integrate!). More...

#include <RombIntSolver.h>

Public Member Functions
	RombIntSolver (double(T::fce)(double), T pTemplate)
	Constructor - sets function to be integrated. More...

	RombIntSolver (double(T::fce)(double), T pTemplate, float eps)
	Constructor - sets function to be integrated and integration precision. More...

	~RombIntSolver ()
	Destructor. More...

double	Integrate (double endPointA, double endPointB)
	This method returns a definite integral of function fce calculated in interval (a,b) using so-called Romberg algorithm. More...

Protected Member Functions
double	TrapezRuleInt (int n)
	This method returns a definite integral of function fce in interval (a,b) and is based on classical extended trapezium rule. More...

Private Attributes
double	_a
	Left integration endpoint. More...

double	_b
	Right integration endpoint. More...

float	_eps
	Total integration precision (Caution: Don't overestimate this value!) More...

int	_nStepsMin
	Minimum number of integration steps permitted (Avoid spurious early convergence!) More...

int	_nStepsMax
	Maximum number of integration steps permitted. More...

double(T::*	_fce )(double)
	Relative pointer to an integrated function. More...

T *	_pTemplate
	Pointer to the template class. More...

Detailed Description

template<class T>
class sistrip::RombIntSolver< T >

Double precision Romberg integration solver (Template class represents class whose method is to be integrate!).

The template class doesn't have *.cpp file!

See Also: Integrate

Author: Z. Drasal, Charles University in Prague

Definition at line 31 of file RombIntSolver.h.

Constructor & Destructor Documentation

template<class T>

sistrip::RombIntSolver< T >::RombIntSolver	(	double(T::*)(double)	fce,
		T *	pTemplate
	)

inline

Constructor - sets function to be integrated.

Definition at line 36 of file RombIntSolver.h.

template<class T>

sistrip::RombIntSolver< T >::RombIntSolver	(	double(T::*)(double)	fce,
		T *	pTemplate,
		float	eps
	)

inline

Constructor - sets function to be integrated and integration precision.

Definition at line 41 of file RombIntSolver.h.

template<class T>

sistrip::RombIntSolver< T >::~RombIntSolver ( )

inline

Destructor.

Definition at line 46 of file RombIntSolver.h.

Member Function Documentation

template<class T >

double sistrip::RombIntSolver< T >::Integrate	(	double	endPointA,
		double	endPointB
	)

This method returns a definite integral of function fce calculated in interval (a,b) using so-called Romberg algorithm.

The algorithm exploites a very general idea of Richardson's deffered approach to the limit, where the function is integrated using the trapezium rule first (with h subsequently set to (a-b), (a-b)/2, (a-b)/4) and then the result is extrapolated to the limit. For n=0 (h=(a-b)) it corresponds to m=0; for n=1 (h=(a-b)/2) it corresponds to m=0 and m=1; ..., where m represents the m-th step to the limit (Richardson extrapolation).

Calculation (R(0,0); R(1,0)->R(1,1); R(2,0->R(2,1)->R(2,2)):

R(0,0) = 1/2*(b-a)*(f(a)+f(b)
R(n,0) = 1/2*R(n-1,0) + h*Sum(i=1,2^(n-1)){f(a+(2*i-1)*h)}

R(n,m) ... m-th iteration - achieved precision O(h^(2^(m+1)))
R(n,m) = R(n,m-1) + (R(n,m-1)-R(n-1,m-1))/(4^m-1)

Total relative precision (influenced by maximum number of steps permitted):

epsilon = |R(n,n) - R(n,n-1)|/R(n,n)

For more details see J.Stoer, R.Bulirsch: Introduction to Numerical Analysis, chap. 2 and 3, 3rd ed., and www.nr.com

Definition at line 116 of file RombIntSolver.h.

template<class T >

double sistrip::RombIntSolver< T >::TrapezRuleInt ( int n )

protected

This method returns a definite integral of function fce in interval (a,b) and is based on classical extended trapezium rule.

Calculation (n-th iteration):

Int(a,b){f(x)*dx} = h/2*[f(a)+f(b)] + h*Sum(i=1,n-1){f(a+i*h)} - O(h^2)

I(n) = 1/2*I(n-1) + h*Sum(i=1,2^(n-1)){f(a+(2*i-1)*h)}

Where n=0 corresponds to h=(a-b), n=1 to h=(a-b)/2 and the error of the aproximation can be derived from Euler-MacLaurin summation formula and is following:

-B2*h^2/2!*(f'(b)-f'(a)) - B4*h^4/4!*(f'''(b)-f'''(a)) - ...

For more details see J.Stoer, R.Bulirsch: Introduction to Numerical Analysis, chap. 2 and 3, 3rd ed., and www.nr.com

Definition at line 163 of file RombIntSolver.h.

Member Data Documentation

template<class T>

double sistrip::RombIntSolver< T >::_a

private

Left integration endpoint.

Definition at line 98 of file RombIntSolver.h.

template<class T>

double sistrip::RombIntSolver< T >::_b

private

Right integration endpoint.

Definition at line 99 of file RombIntSolver.h.

template<class T>

float sistrip::RombIntSolver< T >::_eps

private

Total integration precision (Caution: Don't overestimate this value!)

Definition at line 101 of file RombIntSolver.h.

template<class T>

double(T::* sistrip::RombIntSolver< T >::_fce)(double)

private

Relative pointer to an integrated function.

Definition at line 106 of file RombIntSolver.h.

template<class T>

int sistrip::RombIntSolver< T >::_nStepsMax

private

Maximum number of integration steps permitted.

Definition at line 104 of file RombIntSolver.h.

template<class T>

int sistrip::RombIntSolver< T >::_nStepsMin

private

Minimum number of integration steps permitted (Avoid spurious early convergence!)

Definition at line 103 of file RombIntSolver.h.

template<class T>

T* sistrip::RombIntSolver< T >::_pTemplate

private

Pointer to the template class.

Definition at line 108 of file RombIntSolver.h.

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

/afs/desy.de/user/d/dudarboh/analysis/iLCSoft/MarlinReco/SiStripDigi/source/include/RombIntSolver.h

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

template<class T> class sistrip::RombIntSolver< T >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class T>
class sistrip::RombIntSolver< T >