TrapezoidIntegral< IntegrationPolicy > Class Template Reference

Integral of a one-dimensional function. More...

#include <trapezoidintegral.hpp>

Inheritance diagram for TrapezoidIntegral< IntegrationPolicy >:

Collaboration diagram for TrapezoidIntegral< IntegrationPolicy >:

Public Member Functions
	TrapezoidIntegral (Real accuracy, Size maxIterations)
Public Member Functions inherited from Integrator
	Integrator (Real absoluteAccuracy, Size maxEvaluations)
virtual	~Integrator ()=default
Real	operator() (const ext::function< Real(Real)> &f, Real a, Real b) const
void	setAbsoluteAccuracy (Real)
void	setMaxEvaluations (Size)
Real	absoluteAccuracy () const
Size	maxEvaluations () const
Real	absoluteError () const
Size	numberOfEvaluations () const
virtual bool	integrationSuccess () const

Protected Member Functions
Real	integrate (const ext::function< Real(Real)> &f, Real a, Real b) const override
Protected Member Functions inherited from Integrator
void	setAbsoluteError (Real error) const
void	setNumberOfEvaluations (Size evaluations) const
void	increaseNumberOfEvaluations (Size increase) const

Detailed Description

template<class IntegrationPolicy>
class QuantLib::TrapezoidIntegral< IntegrationPolicy >

Integral of a one-dimensional function.

Given a target accuracy \( \epsilon \), the integral of a function \( f \) between \( a \) and \( b \) is calculated by means of the trapezoid formula

\[ \int_{a}^{b} f \mathrm{d}x = \frac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + \dots + f(x_{N-1}) + \frac{1}{2} f(x_{N}) \]

where \( x_0 = a \), \( x_N = b \), and \( x_i = a+i \Delta x \) with \( \Delta x = (b-a)/N \). The number \( N \) of intervals is repeatedly increased until the target accuracy is reached.

Tests:

the correctness of the result is tested by checking it against known good values.

Examples

MultidimIntegral.cpp.

Definition at line 52 of file trapezoidintegral.hpp.

Constructor & Destructor Documentation

TrapezoidIntegral()

TrapezoidIntegral	(	Real	accuracy,
		Size	maxIterations
	)

Definition at line 54 of file trapezoidintegral.hpp.

Member Function Documentation

integrate()

Real integrate ( const ext::function< Real(Real)> &  f, Real  a, Real  b  ) const

overrideprotectedvirtual

Implements Integrator.

Definition at line 59 of file trapezoidintegral.hpp.

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